# Colorado Curriculum

Students of FutureSchool in Colorado receive an excellent supplement to their education, and homeschoolers alike. Parents are able to set up their children’s lesson plans, manage their accounts from their own portal. There is another portal for student use, it is here that students are able to enter lessons parents set for them, set their avatar, look up terminology, play games (both fun and educational), or even talk to a online tutor. When each child begins, they can start with an assessment for grade-level so see where in that subject they are. Many students enjoy taking the assessment!

**Students Come a Long Way With FutureSchool**

FutureSchool Colorado curriculum online math course begins each grade level with self-assessments. Kindergarten courses are great, starting off just right with teaching numbers 1-5 to begin with, then moving up to 6-9. After reviewing 1-9, students move on to learning number 10. This program is wonderful; students are not rushed through their learning with online classes. Through use of FutureSchool online math courses, students move all the way through to Pre-Calculus. Parents of these students will be extremely proud of how far they come with this education supplement, and students enjoy every minute of getting there!

FutureSchool has extraordinary online English courses, with many students utilizing it to learn English as a second language. There are several parents that use this program as a tutor for their education they receive in their classroom, and many use it to add to their homeschooling program. The curriculum is the same to that, which is used for the Colorado School District. Some components students learn while taking online classes include reading comprehension, spelling skills, punctuation, writing skills, parts of speech, and usage of words in the correct way along with their structure.

Find out more about home schooling in America. FutureSchool brings the importance of Math and English right to students by use of fun, effective online classes!

## Mathematics

- Kindergarten Mathematics
- Grade 1 Mathematics
- Grade 2 Mathematics
- Grade 3 Mathematics
- Grade 4 Mathematics
- Grade 5 Mathematics
- Grade 6 Mathematics
- Grade 7 Mathematics
- Grade 8 Mathematics
- Grade 9 Mathematics
- Grade 10 Mathematics
- Grade 11 - ACT Pre-Algebra and Elementary Algebra Entrance Exam Mathematics
- Grade 11 - ACT Intermediate Algebra and Coordinate Geometry Entrance Exam Mathematics
- Grade 11 - ACT Plane Geometry and Trigonometry Entrance Exam Mathematics
- Grades 11 - 12: Algebra I Mathematics
- Grades 11 - 12: Algebra II Mathematics
- Grades 11 - 12: Geometry Mathematics
- Grades 11 - 12: Probability - Statistics Mathematics
- Grades 11 - 12: Pre-Calculus Mathematics

### Kindergarten Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Kindergarten | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The Numbers 1 to 5 | |

Objective: To match words and numbers from 1 to 5 | |||

3 | Basic mathematics part 1 | The Numbers 6 to 9 | |

Objective: To write and match the numeral and word for the numbers 6 to 9 | |||

4 | Basic mathematics part 1 | Ordinal numbers 1-9 | |

Objective: To match ordinal words and numbers with groups of 1-9 objects | |||

5 | Basic mathematics part 1 | Zero and the Counting Numbers 1 to 9 | |

Objective: To identify ‘0’, to establish numerical order (1-10) and to match spelling | |||

6 | Basic mathematics part 1 | The Number 10 | |

Objective: To identify 10 things and to match groups (1-10) of things to their number | |||

7 | Basic mathematics part 1 | The Numbers 11 to 20 | |

Objective: To write the numeral and word for the numbers 11 to 20 and to count up to 20 | |||

8 | Basic mathematics part 1 | Using Place Value to Order Numbers up to 20 | |

Objective: To use place value to understand the value of numbers up to 20 | |||

9 | Basic mathematics part 1 | Simple addition up to the number 10 | |

Objective: To construct addition sentences (sum to 10) using + and = | |||

10 | Basic mathematics part 1 | Simple addition up to the number 20 | |

Objective: To add numbers 1 to 10 to a sum <20 using horizontal and vertical formats | |||

11 | Basic mathematics part 1 | Subtraction up to the number 10 | |

Objective: To subtract numbers 0 to 10 using pictures and numerals | |||

12 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

13 | Basic mathematics part 1 | Subtraction up to the number 20 | |

Objective: To accurately subtract numbers 1-20 using horizontal and vertical formats | |||

14 | Time | Duration | |

Objective: To choose the difference between a short time and a long time | |||

15 | Exam | Exam – Kindergarten | |

Objective: Exam |

### Grade 1 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 1 | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The Numbers 1 to 5 | |

Objective: To match words and numbers from 1 to 5 | |||

3 | Basic mathematics part 1 | The Numbers 6 to 9 | |

Objective: To write and match the numeral and word for the numbers 6 to 9 | |||

4 | Basic mathematics part 1 | Ordinal numbers 1-9 | |

Objective: To match ordinal words and numbers with groups of 1-9 objects | |||

5 | Basic mathematics part 1 | Zero and the Counting Numbers 1 to 9 | |

Objective: To identify ‘0’, to establish numerical order (1-10) and to match spelling | |||

6 | Basic mathematics part 1 | The Number 10 | |

Objective: To identify 10 things and to match groups (1-10) of things to their number | |||

7 | Basic mathematics part 1 | The Numbers 11 to 20 | |

Objective: To write the numeral and word for the numbers 11 to 20 and to count up to 20 | |||

8 | Basic mathematics part 1 | The numbers 20 to 99 | |

Objective: To recognise, name and add multiples of ten | |||

9 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

10 | Basic mathematics part 1 | Using Place Value to Order Numbers up to 20 | |

Objective: To use place value to understand the value of numbers up to 20 | |||

11 | Basic mathematics part 1 | Simple addition up to the number 10 | |

Objective: To construct addition sentences (sum to 10) using + and = | |||

12 | Basic mathematics part 1 | Simple addition up to the number 20 | |

Objective: To add numbers 1 to 10 to a sum <20 using horizontal and vertical formats | |||

13 | Basic mathematics part 1 | Subtraction up to the number 10 | |

Objective: To subtract numbers 0 to 10 using pictures and numerals | |||

14 | Basic mathematics part 1 | Subtraction: by comparison | |

Objective: To establish concept of more and to use subtraction to work out how many more | |||

15 | Basic mathematics part 1 | Subtraction up to the number 20 | |

Objective: To accurately subtract numbers 1-20 using horizontal and vertical formats | |||

16 | Time | Days of the Week | |

Objective: To name and recognise the days of the week in order | |||

17 | Time | Duration | |

Objective: To choose the difference between a short time and a long time | |||

18 | Time | Months and Seasons of the year | |

Objective: To name and order the months of the year, the number of days in each month and name the seasons in order | |||

19 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

20 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

21 | Exam | Exam – Grade 1 | |

Objective: Exam |

### Grade 2 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 2 | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The numbers 20 to 99 | |

Objective: To recognise, name and add multiples of ten | |||

3 | Basic mathematics part 1 | The number 100 | |

Objective: To count by 1, 2, 5 and 10s to 100 and recognise that 10 x 10 = 100 | |||

4 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

5 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

6 | Basic mathematics part 1 | Subtraction up to the number 20 | |

Objective: To accurately subtract numbers 1-20 using horizontal and vertical formats | |||

7 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

8 | Basic mathematics part 1 | Multiplication using equal groups | |

Objective: To identify multiplication as a number of groups of objects | |||

9 | Basic mathematics part 1 | Multiplication using repeated addition | |

Objective: To perform repeated addition in preparation for multiplication | |||

10 | Basic mathematics part 1 | The Multiplication Sign | |

Objective: To use the ‘x’ sign for repeated addition and perform 1-digit multiplication | |||

11 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

12 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

13 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

14 | Time | Days of the Week | |

Objective: To name and recognise the days of the week in order | |||

15 | Time | Duration | |

Objective: To choose the difference between a short time and a long time | |||

16 | Time | Months and Seasons of the year | |

Objective: To name and order the months of the year, the number of days in each month and name the seasons in order | |||

17 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

18 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

19 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

20 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

21 | Exam | Exam – Grade 2 | |

Objective: Exam |

### Grade 3 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 3 | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The number 100 | |

Objective: To count by 1, 2, 5 and 10s to 100 and recognise that 10 x 10 = 100 | |||

3 | Basic mathematics part 1 | The numbers 100 to 999 | |

Objective: To use pictures and numerals for numbers 100 to 999 and count by 10s and 100s | |||

4 | Basic mathematics part 1 | Addition up to the number 99 | |

Objective: To add two 2-digit numbers to 99 | |||

5 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

6 | Basic mathematics part 1 | Subtraction up to the number 99 | |

Objective: To subtract multiples of 10 and subtract 2-digit numbers without trading | |||

7 | Basic mathematics part 1 | Subtraction with trading | |

Objective: To subtract 1 and 2-digit numbers with trading | |||

8 | Basic mathematics part 1 | Multiplication using equal groups | |

Objective: To identify multiplication as a number of groups of objects | |||

9 | Basic mathematics part 1 | Multiplication using repeated addition | |

Objective: To perform repeated addition in preparation for multiplication | |||

10 | Basic mathematics part 1 | The Multiplication Sign | |

Objective: To use the ‘x’ sign for repeated addition and perform 1-digit multiplication | |||

11 | Basic mathematics part 1 | Multiples of 10 up to 100 | |

Objective: To match numerals and word names for multiples of 10 and add multiples of 10 | |||

12 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

13 | Long multiplication | Multiplying 2-digit numbers by multiples of 10 | |

Objective: To multiply 2-digit numbers by multiples of 10 using long multiplication | |||

14 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

15 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

16 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

17 | Basic mathematics part 2 | Division with and without a remainder | |

Objective: To divide by 1-digit divisor with/without remainder and form division problems | |||

18 | Basic mathematics part 2 | Dividing two and three-digit numbers by a single-digit number | |

Objective: To divide 3-digit by 1-digit numbers and solve word problems | |||

19 | Time | Days of the Week | |

Objective: To name and recognise the days of the week in order | |||

20 | Time | Months and Seasons of the year | |

Objective: To name and order the months of the year, the number of days in each month and name the seasons in order | |||

21 | Time | O’clock and half past using digital time | |

Objective: To use the terms ‘o’clock’ and ‘half past’ on a digital clock | |||

22 | Time | O’clock and half past on the analogue clock | |

Objective: To read and use the terms o’clock and half past on an analogue clock | |||

23 | Time | Analogue – Telling time – minutes in the hour | |

Objective: To recognise the coordinated movements of the hands on an analogue clock | |||

24 | Time | Quarter past and quarter to | |

Objective: To associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes | |||

25 | Time | Units of time | |

Objective: To convert units of time by reading simple timetables, timelines and calendars | |||

26 | Time | am and pm time | |

Objective: To distinguish between am and pm time and to use the correct notation for am and pm time | |||

27 | Time | Telling the time – minutes past the hour | |

Objective: To read analogue time to the minute past the hour | |||

28 | Time | Telling the time – minutes to the hour | |

Objective: To read analogue clocks in minutes to the hour | |||

29 | Time | Relating analogue and digital time | |

Objective: To read analogue and digital clocks to the minute | |||

30 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

31 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

32 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

33 | Space | Position | |

Objective: To use positional terms such as behind, next to and above, accurately | |||

34 | Measurement – Advanced area | Comparing and Ordering Areas | |

Objective: To estimate size order and count or estimate area as the number of cm squares | |||

35 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

36 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

37 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

38 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

39 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

40 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

41 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

42 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

43 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

44 | Exam | Exam – Grade 3 | |

Objective: Exam |

### Grade 4 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 4 | |

Objective: Assessment | |||

2 | Basic mathematics part 1 | The numbers 100 to 999 | |

Objective: To use pictures and numerals for numbers 100 to 999 and count by 10s and 100s | |||

3 | Basic mathematics part 2 | The numbers 1000 to 9999 | |

Objective: To write words and numbers to 9999 and count by 1, 10, 100 and 1000 to 9999 | |||

4 | Basic mathematics part 2 | The Numbers 10 000 to 99 999 | |

Objective: To determine the place value of digits in, order of and name of 5-digit numbers | |||

5 | Basic mathematics part 2 | Addition up to the number 999 | |

Objective: To add up to three 2 and 3-digit numbers with and without trading | |||

6 | Basic mathematics part 1 | Subtraction up to the number 99 | |

Objective: To subtract multiples of 10 and subtract 2-digit numbers without trading | |||

7 | Basic mathematics part 1 | Subtraction with trading | |

Objective: To subtract 1 and 2-digit numbers with trading | |||

8 | Basic mathematics part 1 | Subtraction with Word Problems | |

Objective: To construct suitable subtraction sums in order to solve word problems and puzzles | |||

9 | Basic mathematics part 2 | Subtraction up to the number 999 | |

Objective: To subtract 3-digit numbers with and without trading and find missing digits | |||

10 | Basic mathematics part 1 | Multiplication with important facts | |

Objective: To practice multiplication facts to 10 x 10 | |||

11 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

12 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

13 | Long multiplication | Multiplying 2-digit numbers by multiples of 10 | |

Objective: To multiply 2-digit numbers by multiples of 10 using long multiplication | |||

14 | Long multiplication | Multiplying 2-digit numbers by 2-digit numbers | |

Objective: To multiply 2-digit numbers by 2-digit numbers using long multiplication | |||

15 | Long multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |

Objective: To multiply 4-digit numbers by multiples of 100 using long multiplication | |||

16 | Basic mathematics part 1 | Strategies for division | |

Objective: To perform division by arranging objects into groups | |||

17 | Basic mathematics part 2 | Solve and record division using known facts and sharing | |

Objective: To divide 100 by its factors and divide 2-digit multiples by factors 1 to 5 | |||

18 | Basic mathematics part 2 | Division with and without a remainder | |

Objective: To divide by 1-digit divisor with/without remainder and form division problems | |||

19 | Basic mathematics part 2 | Dividing two and three-digit numbers by a single-digit number | |

Objective: To divide 3-digit by 1-digit numbers and solve word problems | |||

20 | Long division | Repeated subtraction with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction | |||

21 | Long division | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction of 10x the divisor | |||

22 | Time | Days of the Week | |

Objective: To name and recognise the days of the week in order | |||

23 | Time | Units of time | |

Objective: To convert units of time by reading simple timetables, timelines and calendars | |||

24 | Time | Analogue – Telling time – minutes in the hour | |

Objective: To recognise the coordinated movements of the hands on an analogue clock | |||

25 | Time | am and pm time | |

Objective: To distinguish between am and pm time and to use the correct notation for am and pm time | |||

26 | Time | O’clock and half past using digital time | |

Objective: To use the terms ‘o’clock’ and ‘half past’ on a digital clock | |||

27 | Time | O’clock and half past on the analogue clock | |

Objective: To read and use the terms o’clock and half past on an analogue clock | |||

28 | Time | Quarter past and quarter to | |

Objective: To associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes | |||

29 | Time | Telling the time – minutes past the hour | |

Objective: To read analogue time to the minute past the hour | |||

30 | Time | Telling the time – minutes to the hour | |

Objective: To read analogue clocks in minutes to the hour | |||

31 | Time | Relating analogue and digital time | |

Objective: To read analogue and digital clocks to the minute | |||

32 | Measurement – Length | Compare length by using informal units of measurement | |

Objective: To choose the most appropriate body part as a unit for measuring common objects | |||

33 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

34 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

35 | Measurement – Advanced area | Comparing and Ordering Areas | |

Objective: To estimate size order and count or estimate area as the number of cm squares | |||

36 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

37 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

38 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

39 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

40 | Measurement – Mass | Introducing the concept of mass | |

Objective: To distinguish between light and heavy objects | |||

41 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

42 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

43 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

44 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

45 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

46 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

47 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

48 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

49 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

50 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

51 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: To compare and order decimals to two decimal places | |||

52 | Decimals | Decimals with whole numbers 10th and 100th | |

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

53 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

54 | Space | Using the prefix to determine polygons | |

Objective: To continue sequences of shapes and recognise prefixes and name polygons | |||

55 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

56 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

57 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

58 | Space | Position | |

Objective: To use positional terms such as behind, next to and above, accurately | |||

59 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

60 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

61 | Exam | Exam – Grade 4 | |

Objective: Exam |

### Grade 5 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 5 | |

Objective: Assessment | |||

2 | Basic mathematics part 2 | The numbers 1000 to 9999 | |

Objective: To write words and numbers to 9999 and count by 1, 10, 100 and 1000 to 9999 | |||

3 | Basic mathematics part 2 | The Numbers 10 000 to 99 999 | |

Objective: To determine the place value of digits in, order of and name of 5-digit numbers | |||

4 | Basic mathematics part 2 | Seven digit numbers | |

Objective: To determine the place value of digits in, and the name of numbers to 1 000 000 | |||

5 | Basic mathematics part 2 | Addition up to the number 999 | |

Objective: To add up to three 2 and 3-digit numbers with and without trading | |||

6 | Basic mathematics part 2 | Addition to 9999 and beyond | |

Objective: To add up to five 3, 4 or 5-digit numbers from 0 to 99 999 | |||

7 | Basic mathematics part 2 | Subtraction up to the number 999 | |

Objective: To subtract 3-digit numbers with and without trading and find missing digits | |||

8 | Basic mathematics part 2 | Subtraction involving four-digit numbers and beyond | |

Objective: To subtract 4 or 5-digit numbers from 5-digit numbers using the Renaming Method | |||

9 | Long multiplication | Multiplying 2-digit numbers by multiples of 10 | |

Objective: To multiply 2-digit numbers by multiples of 10 using long multiplication | |||

10 | Long multiplication | Multiplying 3 and 4-digit numbers by multiples of 100 | |

Objective: To multiply 4-digit numbers by multiples of 100 using long multiplication | |||

11 | Long multiplication | Multiplying 2-digit numbers by 2-digit numbers | |

Objective: To multiply 2-digit numbers by 2-digit numbers using long multiplication | |||

12 | Basic mathematics part 2 | Multiplication by 2 and 3 Digits | |

Objective: To multiply 3 or 4-digit numbers by 2 or 3-digit numbers | |||

13 | Long multiplication | Multiplying 3-digit numbers by 4-digit numbers | |

Objective: To multiply 4-digit numbers by 3-digit numbers using long multiplication | |||

14 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

15 | Long division | Repeated subtraction with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction | |||

16 | Long division | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction of 10x the divisor | |||

17 | Long division | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction of multiples of the divisor | |||

18 | Long division | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction with remainder | |||

19 | Long division | Repeated subtraction by multiples of 10 with divisors less than 20 with remainders | |

Objective: To divide 3-digit numbers by repeated subtraction of 10x divisor, with remainder | |||

20 | Long division | Using divide, multiple and subtraction in the bring down method | |

Objective: To use the divide, subtract, multiply, bring down long division method | |||

21 | Basic mathematics part 2 | Dividing two and three-digit numbers by a single-digit number | |

Objective: To divide 3-digit by 1-digit numbers and solve word problems | |||

22 | Basic mathematics part 2 | Divide whole numbers by a 2-digit divisor | |

Objective: To divide up to 4-digit by 1 or 2-digit numbers with remainders as reduced fractions | |||

23 | Time | Units of time | |

Objective: To convert units of time by reading simple timetables, timelines and calendars | |||

24 | Time | Analogue – Telling time – minutes in the hour | |

Objective: To recognise the coordinated movements of the hands on an analogue clock | |||

25 | Time | am and pm time | |

Objective: To distinguish between am and pm time and to use the correct notation for am and pm time | |||

26 | Time | Quarter past and quarter to | |

Objective: To associate the numerals 3, 6 and 9 with 15, 30 and 45 minutes | |||

27 | Time | Telling the time – minutes past the hour | |

Objective: To read analogue time to the minute past the hour | |||

28 | Time | Telling the time – minutes to the hour | |

Objective: To read analogue clocks in minutes to the hour | |||

29 | Time | Relating analogue and digital time | |

Objective: To read analogue and digital clocks to the minute | |||

30 | Time | O’clock and half past using digital time | |

Objective: To use the terms ‘o’clock’ and ‘half past’ on a digital clock | |||

31 | Time | O’clock and half past on the analogue clock | |

Objective: To read and use the terms o’clock and half past on an analogue clock | |||

32 | Time | 24-hour time | |

Objective: To tell the time accurately using 24-hour time and change the time from am and pm time to 24-hour time | |||

33 | Time | Time Zones | |

Objective: To recognise and compare different time zones within Australia | |||

34 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

35 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

36 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

37 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

38 | Measurement – Advanced area | Comparing and Ordering Areas | |

Objective: To estimate size order and count or estimate area as the number of cm squares | |||

39 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

40 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

41 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

42 | Measurement – Volume | Introduction to Volume: using the cubic centimetre as a standard unit | |

Objective: To count volume using 1 cm cubes | |||

43 | Measurement – Volume | Constructing Models | |

Objective: To develop volume of prisms as layers of a number of 1 cm cubes | |||

44 | Measurement – Volume | Using the Cubic Centimetre to Measure Volume | |

Objective: To use the 1 cm cube as the unit for volume | |||

45 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

46 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

47 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

48 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

49 | Measurement – Capacity | Converting between volume and capacity using kiloliters and liters | |

Objective: To know the formal units of measurement for volume and capacity for bigger objects | |||

50 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

51 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

52 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

53 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

54 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

55 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe part of a whole | |

Objective: To name and use the fractions 1/2, 1/4 and 1/8 in describing parts of a whole | |||

56 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

57 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

58 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

59 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

60 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

61 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

62 | Fractions | Reducing fractions to lowest equivalent form | |

Objective: To reduce a fraction to its lowest form | |||

63 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

64 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

65 | Fractions | Adding and subtracting fractions with the same denominator | |

Objective: To add and subtract fractions with the same denominator | |||

66 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

67 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

68 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

69 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: To compare and order decimals to two decimal places | |||

70 | Decimals | Decimals with whole numbers 10th and 100th | |

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

71 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

72 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

73 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

74 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

75 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

76 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

77 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

78 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

79 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

80 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

81 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

82 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

83 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

84 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

85 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

86 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

87 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

88 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

89 | Space | Using the prefix to determine polygons | |

Objective: To continue sequences of shapes and recognise prefixes and name polygons | |||

90 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

91 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

92 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

93 | Space | Use grids to enlarge/reduce 2-D shapes | |

Objective: To recognise shapes that tessellate and specify position on a grid | |||

94 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

95 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

96 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

97 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

98 | Space | Position | |

Objective: To use positional terms such as behind, next to and above, accurately | |||

99 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

100 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

101 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

102 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

103 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

104 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

105 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

106 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

107 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

108 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

109 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

110 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

111 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

112 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

113 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

114 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

115 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

116 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

117 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

118 | Exam | Exam – Grade 5 | |

Objective: Exam |

### Grade 6 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 6 | |

Objective: Assessment | |||

2 | Basic mathematics part 2 | The Numbers 10 000 to 99 999 | |

Objective: To determine the place value of digits in, order of and name of 5-digit numbers | |||

3 | Basic mathematics part 2 | Seven digit numbers | |

Objective: To determine the place value of digits in, and the name of numbers to 1 000 000 | |||

4 | Basic mathematics part 2 | Addition to 9999 and beyond | |

Objective: To add up to five 3, 4 or 5-digit numbers from 0 to 99 999 | |||

5 | Basic mathematics part 2 | Subtraction involving four-digit numbers and beyond | |

Objective: To subtract 4 or 5-digit numbers from 5-digit numbers using the Renaming Method | |||

6 | Basic mathematics part 2 | Multiplication using extended algorithms | |

Objective: To multiply 3-digit by 1-digit numbers and solve multiplication word problems | |||

7 | Long multiplication | Multiplying 3-digit numbers by 4-digit numbers | |

Objective: To multiply 4-digit numbers by 3-digit numbers using long multiplication | |||

8 | Basic mathematics part 2 | Divide whole numbers by a 2-digit divisor | |

Objective: To divide up to 4-digit by 1 or 2-digit numbers with remainders as reduced fractions | |||

9 | Long division | Repeated subtraction with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction | |||

10 | Long division | Repeated subtraction by multiples of 10 with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction of 10x the divisor | |||

11 | Long division | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction of multiples of the divisor | |||

12 | Long division | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction with remainder | |||

13 | Long division | Repeated subtraction by multiples of 10 with divisors less than 20 with remainders | |

Objective: To divide 3-digit numbers by repeated subtraction of 10x divisor, with remainder | |||

14 | Long division | Repeated subtraction with divisors greater than 50 with dividends of 000’s and some remainders | |

Objective: To divide 4-digit numbers using 10 and 100x divisor, Divisor > 50 | |||

15 | Long division | Using divide, multiple and subtraction in the bring down method | |

Objective: To use the divide, subtract, multiply, bring down long division method | |||

16 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

17 | Time | 24-hour time | |

Objective: To tell the time accurately using 24-hour time and change the time from am and pm time to 24-hour time | |||

18 | Time | Time Zones | |

Objective: To recognise and compare different time zones within Australia | |||

19 | Measurement – Length | Using the metre as a formal unit to measure perimeter | |

Objective: To calculate the perimeter of shapes whose measurements are given in metres | |||

20 | Measurement – Length | Using the formal unit of the centimetre to measure length and perimeter | |

Objective: To use a ruler to find lengths and perimeters in centimetres | |||

21 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

22 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

23 | Measurement – Area | Introduction to the square centimetre | |

Objective: To determine the area of a shape by counting the number of square centimetres | |||

24 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

25 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

26 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

27 | Measurement – Area | Larger Areas: Square Metre, Hectare, Square Kilometre | |

Objective: To calculate areas in square centimetres, square metres, square kilometres and hectares and convert one to another | |||

28 | Measurement – Volume | Introduction to Volume: using the cubic centimetre as a standard unit | |

Objective: To count volume using 1 cm cubes | |||

29 | Measurement – Volume | Constructing Models | |

Objective: To develop volume of prisms as layers of a number of 1 cm cubes | |||

30 | Measurement – Volume | Using the Cubic Centimetre to Measure Volume | |

Objective: To use the 1 cm cube as the unit for volume | |||

31 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

32 | Measurement – Volume | Using the Cubic Metre to Measure Volume | |

Objective: To calculate the volume of rectangular prisms in cubic metres | |||

33 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

34 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

35 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

36 | Measurement – Capacity | Using the cubic cm and displacement to measure volume and capacity | |

Objective: To find volume and capacity using displacement | |||

37 | Measurement – Capacity | Using the Cubic cm as a Standard Unit of measurement for Volume and Capacity | |

Objective: To understand a cubic centimetre and how it can be used to find the volume and capacity of a three-dimensional shape | |||

38 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

39 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

40 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

41 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

42 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

43 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

44 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

45 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

46 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

47 | Fractions | Reducing fractions to lowest equivalent form | |

Objective: To reduce a fraction to its lowest form | |||

48 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

49 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

50 | Fractions | Adding and subtracting fractions with the same denominator | |

Objective: To add and subtract fractions with the same denominator | |||

51 | Fractions | Adding and subtracting fractions with different denominators | |

Objective: To add fractions with different denominators and the answer is less than 1 | |||

52 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

53 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

54 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

55 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

56 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

57 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

58 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

59 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

60 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

61 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

62 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: To compare and order decimals to two decimal places | |||

63 | Decimals | Decimals with whole numbers 10th and 100th | |

Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals | |||

64 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

65 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

66 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

67 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

68 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

69 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

70 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

71 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

72 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

73 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

74 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

75 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

76 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

77 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

78 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

79 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

80 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

81 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

82 | Space | Using the prefix to determine polygons | |

Objective: To continue sequences of shapes and recognise prefixes and name polygons | |||

83 | Space | Spatial properties of quadrilaterals | |

Objective: To recall and recognise properties of different quadrilaterals | |||

84 | Space | Measure and classify angles | |

Objective: To classify and measure angles and calculate angles in a triangle | |||

85 | Space | Recognise and name triangles | |

Objective: To recall properties of different triangles | |||

86 | Space | Use grids to enlarge/reduce 2-D shapes | |

Objective: To recognise shapes that tessellate and specify position on a grid | |||

87 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

88 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

89 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

90 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

91 | Space | Position | |

Objective: To use positional terms such as behind, next to and above, accurately | |||

92 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

93 | Space | Main and intermediate compass points | |

Objective: To specify direction using the eight points of a compass | |||

94 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

95 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

96 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

97 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

98 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

99 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

100 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

101 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

102 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

103 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

104 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

105 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

106 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

107 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

108 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

109 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

110 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

111 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

112 | Exam | Exam – Grade 6 | |

Objective: Exam |

### Grade 7 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 7 | |

Objective: Assessment | |||

2 | Space | Use grids to enlarge/reduce 2-D shapes | |

Objective: To recognise shapes that tessellate and specify position on a grid | |||

3 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

4 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

5 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

6 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

7 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

8 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

9 | Graphs – Basic | Picture Graphs | |

Objective: To construct, read and interpret picture graphs | |||

10 | Graphs – Basic | Column Graphs | |

Objective: To read and interpret column graphs | |||

11 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

12 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

13 | Long multiplication | Multiplying 3-digit numbers by 4-digit numbers | |

Objective: To multiply 4-digit numbers by 3-digit numbers using long multiplication | |||

14 | Basic mathematics part 2 | Divide whole numbers by a 2-digit divisor | |

Objective: To divide up to 4-digit by 1 or 2-digit numbers with remainders as reduced fractions | |||

15 | Long division | Repeated subtraction with divisors less than 20 with no remainders | |

Objective: To divide 2-digit numbers by repeated subtraction | |||

16 | Long division | Repeated subtraction by multiples of 2, 3 and 4 with divisors greater than 20 with no remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction of multiples of the divisor | |||

17 | Long division | Repeated subtraction by multiples of 1,2 and 3 with divisors less than 20 with remainders | |

Objective: To divide 2 or 3-digit numbers by repeated subtraction with remainder | |||

18 | Long division | Repeated subtraction with divisors greater then 20 with remainders as fractions | |

Objective: To divide by repeated subtraction, with remainder expressed as a fraction D>20 | |||

19 | Long division | Repeated subtraction with divisors less than 55 with dividends of 3 and 4-digits with some remainders | |

Objective: To divide 4-digit numbers using 10 and 100x divisor, Divisor < 55 | |||

20 | Long division | Using divide, multiple and subtraction in the bring down method | |

Objective: To use the divide, subtract, multiply, bring down long division method | |||

21 | Basic mathematics part 2 | Multiples and factors of whole numbers | |

Objective: To identify the factors, multiples and squares of numbers | |||

22 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

23 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

24 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

25 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

26 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

27 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

28 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

29 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

30 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

31 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

32 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

33 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

34 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

35 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

36 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

37 | Fractions | Adding and subtracting fractions with the same denominator | |

Objective: To add and subtract fractions with the same denominator | |||

38 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

39 | Fractions | Comparing and ordering fractions greater than 1 | |

Objective: To use diagrams, number lines and equivalent fractions to compare and order fractions greater than 1 | |||

40 | Fractions | Adding and subtracting fractions with different denominators | |

Objective: To add fractions with different denominators and the answer is less than 1 | |||

41 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

42 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

43 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

44 | Fractions | Reducing fractions to lowest equivalent form | |

Objective: To reduce a fraction to its lowest form | |||

45 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

46 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

47 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

48 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

49 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

50 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

51 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

52 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height | |||

53 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

54 | Measurement – Area | Larger Areas: Square Metre, Hectare, Square Kilometre | |

Objective: To calculate areas in square centimetres, square metres, square kilometres and hectares and convert one to another | |||

55 | Measurement – Capacity | The relationship between the common units of capacity: the litre and the millilitre | |

Objective: To convert L to mL and vice versa using 1000 mL = 1 L | |||

56 | Measurement – Capacity | Converting between volume and capacity using kiloliters and liters | |

Objective: To know the formal units of measurement for volume and capacity for bigger objects | |||

57 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

58 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

59 | Measurement – Volume | Using the Cubic Metre to Measure Volume | |

Objective: To calculate the volume of rectangular prisms in cubic metres | |||

60 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

61 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

62 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

63 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

64 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

65 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

66 | Problem solving | Sign Words | |

Objective: To recognise words and phrases that correspond to + – x and / | |||

67 | Problem solving | Problem Solving Strategies | |

Objective: To review problem solving words and an effective problem solving approach | |||

68 | Problem solving | Word Problems with Numbers | |

Objective: To solve number word problems using + – x and / | |||

69 | Problem solving | Word Problems with Money | |

Objective: To solve money word problems using + – x and / | |||

70 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

71 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

72 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

73 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

74 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

75 | Geometry part 1 | Measuring Angles | |

Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex | |||

76 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

77 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

78 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

79 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

80 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

81 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

82 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

83 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

84 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

85 | Probability | Simple events | |

Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S) | |||

86 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

87 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

88 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

89 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

90 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

91 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

92 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

93 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

94 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

95 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

96 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

97 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

98 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

99 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

100 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

101 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

102 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

103 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

104 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

105 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

106 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

107 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

108 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

109 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

110 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

111 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

112 | Exam | Exam – Grade 7 | |

Objective: Exam |

### Grade 8 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 8 | |

Objective: Assessment | |||

2 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

3 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

4 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

5 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

6 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

7 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

8 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

9 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

10 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

11 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

12 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

13 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

14 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

15 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

16 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

17 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

18 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

19 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

20 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

21 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

22 | Probability | Simple events | |

23 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

24 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

25 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

26 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

27 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

28 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

29 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

30 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

31 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

32 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

33 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

34 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

35 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

36 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

37 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

38 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

39 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

40 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

41 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

42 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

43 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

44 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

45 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

46 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

47 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

48 | Space | Mapping | |

Objective: To locate places and describe navigation on a map and use a row/column grid | |||

49 | Space | Informal coordinate system | |

Objective: To specify location using a map coordinate system – origin top left | |||

50 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

51 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

52 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

53 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

54 | Measurement – Mass | The Kilogram | |

Objective: To recognise which of two (or more) objects has the greater mass | |||

55 | Measurement – Mass | The Gram | |

Objective: To calculate net mass in grams and solve shopping problems involving mass | |||

56 | Measurement – Mass | The Tonne | |

Objective: To convert kg to tonnes and solve problems involving heavy masses | |||

57 | Problem solving | Word Problems with Length | |

Objective: To solve length word problems using + – x and / | |||

58 | Problem solving | Word Problems with Mass | |

Objective: To solve mass word problems using + – x and / | |||

59 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

60 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

61 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

62 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

63 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

64 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

65 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

66 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

67 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

68 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

69 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

70 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

71 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

72 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

73 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

74 | Geometry part 1 | Adjacent Angles | |

Objective: To recognise and calculate the size of adjacent angles | |||

75 | Geometry part 1 | Complementary and Supplementary Angles | |

Objective: To recognise and calculate the size of complementary and supplementary angles | |||

76 | Geometry part 1 | Vertically Opposite Angles | |

Objective: To determine values of pronumerals in vertically opposite angles | |||

77 | Geometry part 1 | Angles at a Point | |

Objective: To use angles at a point to calculate unknown angles | |||

78 | Geometry part 1 | Parallel Lines | |

Objective: To identify angle pairs and calculate angles formed by a transversal and parallel lines | |||

79 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

80 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

81 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

82 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

83 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

84 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

85 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

86 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

87 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

88 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

89 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

90 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

91 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

92 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

93 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

94 | Exam | Exam – Grade 8 | |

Objective: Exam |

### Grade 9 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 9 | |

Objective: Assessment | |||

2 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

3 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

4 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

5 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

6 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

7 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

8 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

9 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

10 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

11 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

12 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

13 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

14 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

15 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

16 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

17 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

18 | Graphs – Basic | Line Graphs | |

Objective: To read and interpret line graphs | |||

19 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

20 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

21 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

22 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

23 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

24 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

25 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

26 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

27 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

28 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

29 | Probability | Simple events | |

30 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

31 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

32 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

33 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

34 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

35 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

36 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

37 | Measurement – Length | Read and calculate distances on a map using the formal unit kilometre | |

Objective: To read distances (km) from a map and calculate total distances between locations | |||

38 | Measurement – Length | Compare and convert formal units of measurement | |

Objective: To change cm to mm and then convert mm, cm, m and km from one to another | |||

39 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

40 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

41 | Measurement – Capacity | Converting between volume and capacity using milliliters and liters | |

Objective: To solve capacity problems involving mixed dimensional units | |||

42 | Measurement – Capacity | Estimate, measure and compare the capacity of containers | |

Objective: To understand estimation and a way to go about it | |||

43 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

44 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

45 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

46 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

47 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

48 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

49 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

50 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

51 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

52 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

53 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

54 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

55 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

56 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

57 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

58 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

59 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

60 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

61 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

62 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

63 | Time | Average speed | |

Objective: To understand what is meant by the speed and average speed of an object and read the instantaneous speed of a vehicle on a speedometer | |||

64 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

65 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

66 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

67 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

68 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

69 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

70 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

71 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

72 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

73 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | |

Objective: To identify images produced by a given sequence of transformations | |||

74 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

75 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

76 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

77 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

78 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

79 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

80 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

81 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

82 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

83 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

84 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

85 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

86 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

87 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

88 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

89 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

90 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

91 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

92 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

93 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

94 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

95 | Exam | Exam – Grade 9 | |

Objective: Exam |

### Grade 10 Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 10 | |

Objective: Assessment | |||

2 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

3 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

4 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

5 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

6 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

7 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

8 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

9 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

10 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

11 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

12 | Standard/Scientific notation | Significant Figures | |

Objective: To write a number to a specified number of significant figures | |||

13 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

14 | Graphs – Basic | Pie and Bar Graphs | |

Objective: To read and interpret pie and bar graphs | |||

15 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

16 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

17 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

18 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

19 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

20 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

21 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

22 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

Objective: To identify class centres, get frequency counts and determine mean, mode and median values | |||

23 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

24 | Statistics part 2 | Measures of Spread | |

Objective: To determine a range and use it in decision making | |||

25 | Statistics part 2 | Standard deviation applications | |

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator | |||

26 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

27 | Statistics part 2 | The Normal Distribution | |

Objective: To use the standard deviation of a normal distribution to find a percentage of scores within ranges | |||

28 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

29 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

30 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

31 | Probability | Simple events | |

32 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

33 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

34 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

35 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

36 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

37 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

38 | Space | Recognise and name prisms according to spatial properties | |

Objective: To name prisms according to the shape of the base | |||

39 | Space | Recognise and name pyramids according to spatial properties | |

Objective: To name pyramids according to the shape of the base | |||

40 | Space | Recognise nets for prisms, pyramids, cubes and cones | |

Objective: To match a net with a solid and determine whether a given net forms a solid | |||

41 | Space | Viewing 3-D Shapes | |

Objective: To recognise what a solid looks like when viewed from a given direction | |||

42 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

43 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

44 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

45 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

46 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

47 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

48 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

49 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

50 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

51 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

52 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

53 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

54 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

55 | Problem solving | Word Problems with Area | |

Objective: To solve area word problems using + – x and / | |||

56 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

57 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

58 | Problem solving | Word Problems with Volume/Capacity | |

Objective: To solve volume and capacity word problems using + – x and / | |||

59 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

60 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

61 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

62 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

63 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

64 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

65 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

66 | Uniform motion | The Speed Formula | |

Objective: To calculate speed, distance or time using speed = distance/time | |||

67 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

68 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

69 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

70 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

71 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

72 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

73 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

74 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

75 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

76 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | |

Objective: To identify images produced by a given sequence of transformations | |||

77 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

78 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

79 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

80 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

81 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

82 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

83 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

84 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

85 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

86 | Algebra – Basic | Inequalities | |

Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign | |||

87 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

88 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

89 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

90 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

91 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

92 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

93 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

94 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

95 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

96 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

97 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

98 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

99 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

100 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

101 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

102 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

103 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

104 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

105 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

106 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

107 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

108 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

109 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

110 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

111 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

112 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

113 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

114 | Co-ordinate geometry part 1 | The Distance Formula | |

Objective: To use the distance formula to calculate the lengths of lines and distances | |||

115 | Co-ordinate geometry part 1 | The Mid-Point Formula | |

Objective: To determine the mid-point of an interval using the mid-point formula | |||

116 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

117 | Co-ordinate geometry part 1 | The Gradient Formula | |

Objective: To use the gradient formula to find the gradient of straight lines | |||

118 | Co-ordinate geometry part 1 | The Straight Line | |

Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b | |||

119 | Co-ordinate geometry part 1 | Lines Through the Origin | |

Objective: To state the equation of lines passing through the origin and to graph y = mx | |||

120 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | |

Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area | |||

121 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | |

Objective: To change equation to slope intercept form and graph it and to find equation given graph | |||

122 | Co-ordinate geometry part 1 | Point Slope Form of a Line | |

Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) | |||

123 | Exam | Exam – Grade 10 | |

Objective: Exam |

### Grade 11 - ACT Pre-Algebra and Elementary Algebra Entrance Exam Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 11 – ACT Pre-Algebra & Elementary Algebra Entrance Exam | |

Objective: Assessment | |||

2 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

3 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

4 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

5 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

6 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

7 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

8 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

9 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

10 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

11 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

12 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

13 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

14 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

15 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

16 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

17 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

18 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

19 | Surds/Radicals | Some rules for the operations with surds | |

Objective: To learn rules for the division and multiplication of surds | |||

20 | Surds/Radicals | Simplifying Surds | |

Objective: To simplify numerical expressions and solve equations involving surds | |||

21 | Surds/Radicals | Creating entire surds | |

Objective: To write numbers as entire surds and compare numbers by writing as entire surds | |||

22 | Surds/Radicals | Adding and subtracting like surds | |

Objective: To add and subtract surds and simplify expressions by collecting like surds | |||

23 | Surds/Radicals | Expanding surds | |

Objective: To expand and simplify binomial expressions involving surds | |||

24 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

25 | Probability | Simple events | |

26 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

27 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

28 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

29 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

30 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

31 | Statistics part 1 | The Range | |

Objective: To determine the range of data in either raw form or in a frequency distribution table | |||

32 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

33 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

34 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

35 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

36 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

37 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

38 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

39 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

40 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

41 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

42 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

43 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

44 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

45 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

46 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

47 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

48 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

49 | Algebra – Basic | Inequalities | |

50 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

51 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

52 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

53 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

54 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

55 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

56 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

57 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

58 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

59 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

60 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

61 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

62 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

63 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

64 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

65 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. | |||

66 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 2 | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

67 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

68 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 4 | |

Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

69 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

70 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

71 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

72 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

73 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

74 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

75 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

76 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

77 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

78 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

79 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

80 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

81 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

82 | Exam | Exam – Grade 11 – ACT Pre-Algebra & Elementary Algebra Entrance Exam | |

Objective: Exam |

### Grade 11 - ACT Intermediate Algebra and Coordinate Geometry Entrance Exam Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 11 – ACT Intermediate Algebra & Coordinate Geometry Entrance Exam | |

Objective: Assessment | |||

2 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

3 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

4 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

5 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

6 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

7 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

8 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

9 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

10 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

11 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

12 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

13 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

14 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

15 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

16 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. | |||

17 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 2 | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

18 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

19 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 4 | |

Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

20 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

21 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

22 | Algebra – Products and factors | Simplifying algebraic fractions | |

Objective: To simplify algebraic fractions by factorisation and cancellation | |||

23 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

24 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

25 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

26 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

27 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

28 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

29 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

30 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

31 | Series and sequences part 1 | General Sequences | |

Objective: To use the general form of the n’th term of a sequence to find the first 3 terms | |||

32 | Series and sequences part 1 | Finding Tn Given Sn | |

Objective: To find the value of the n’th term in a sequence given the sum of the first n terms | |||

33 | Series and sequences part 1 | The Arithmetic Progression | |

Objective: To find the common difference of a given arithmetic progression | |||

34 | Series and sequences part 1 | Finding the position of a term in an A.P. | |

Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term | |||

35 | Series and sequences part 1 | Given two terms of A.P. find the sequence | |

Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms | |||

36 | Series and sequences part 1 | Arithmetic Means | |

Objective: To find the arithmetic mean of two values | |||

37 | Series and sequences part 1 | The sum to n terms of an A.P. | |

Objective: To find the sum of n terms of an arithmetic progression given the first three terms | |||

38 | Series and sequences part 1 | The Geometric Progression | |

Objective: To find the common ratio of a given geometric progression | |||

39 | Series and sequences part 1 | Finding the position of a term in a G.P. | |

Objective: To find the place of a term in a given geometric progression | |||

40 | Series and sequences part 1 | Given two terms of G.P. find the sequence | |

Objective: To find the first term given two terms of a geometric progression | |||

41 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

42 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

43 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

44 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

45 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

46 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

47 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

48 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

49 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

50 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

51 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

52 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

53 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

54 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

55 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

56 | Co-ordinate geometry part 1 | The Distance Formula | |

Objective: To use the distance formula to calculate the lengths of lines and distances | |||

57 | Co-ordinate geometry part 1 | The Mid-Point Formula | |

Objective: To determine the mid-point of an interval using the mid-point formula | |||

58 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

59 | Co-ordinate geometry part 1 | The Gradient Formula | |

Objective: To use the gradient formula to find the gradient of straight lines | |||

60 | Co-ordinate geometry part 1 | The Straight Line | |

Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b | |||

61 | Co-ordinate geometry part 1 | Lines Through the Origin | |

Objective: To state the equation of lines passing through the origin and to graph y = mx | |||

62 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | |

Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area | |||

63 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | |

Objective: To change equation to slope intercept form and graph it and to find equation given graph | |||

64 | Co-ordinate geometry part 1 | Point Slope Form of a Line | |

Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) | |||

65 | Co-ordinate geometry part 2 | Two Point Formula: equation of a line which joins a pair of points | |

Objective: To find the equation of the line which joins a pair of points | |||

66 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | |

Objective: To find the equation of a line given the x-axis and y-axis intercepts | |||

67 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

68 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

69 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

70 | Co-ordinate geometry part 2 | Perpendicular Distance | |

Objective: To calculate the perpendicular distance from a point to a line and between lines | |||

71 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

72 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

73 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

74 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

75 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

76 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

77 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

78 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

79 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

80 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

81 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

82 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

83 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

84 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

85 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

86 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

87 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

88 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

89 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

90 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

91 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

92 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

93 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

94 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

95 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

96 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

97 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

98 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

99 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

100 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

101 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

102 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

103 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

104 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

105 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

106 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

107 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

108 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

109 | Exam | Exam – Grade 11 – ACT Intermediate Algebra & Coordinate Geometry Entrance Exam | |

Objective: Exam |

### Grade 11 - ACT Plane Geometry and Trigonometry Entrance Exam Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grade 11 – ACT Plane Geometry & Trigonometry Entrance Exam | |

Objective: Assessment | |||

2 | Geometry part 1 | Adjacent Angles | |

Objective: To recognise and calculate the size of adjacent angles | |||

3 | Geometry part 1 | Complementary and Supplementary Angles | |

Objective: To recognise and calculate the size of complementary and supplementary angles | |||

4 | Geometry part 1 | Vertically Opposite Angles | |

Objective: To determine values of pronumerals in vertically opposite angles | |||

5 | Geometry part 1 | Angles at a Point | |

Objective: To use angles at a point to calculate unknown angles | |||

6 | Geometry part 1 | Parallel Lines | |

Objective: To identify angle pairs and calculate angles formed by a transversal and parallel lines | |||

7 | Geometry part 1 | Additional questions involving parallel lines | |

Objective: To determine angle magnitude for angles formed by parallel lines and transversals | |||

8 | Geometry part 1 | Angle Sum of a Triangle | |

Objective: To use the angle sum for a triangle to calculate unknown angles | |||

9 | Geometry part 1 | Exterior angle theorem | |

Objective: To use the external angle of a triangle theorem to calculate unknown angles | |||

10 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

11 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

12 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

13 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

14 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

15 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

16 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

17 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

18 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

19 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

20 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

21 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

22 | Co-ordinate geometry part 2 | Transformations: Reflections | |

Objective: To identify reflections and to use isometric properties of reflections | |||

23 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

24 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

25 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

26 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | |

Objective: To identify images produced by a given sequence of transformations | |||

27 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

28 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

29 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

30 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

31 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

32 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

33 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

34 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

35 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

36 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

37 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

38 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

39 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

40 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

41 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

42 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

43 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

44 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

45 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

46 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

47 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

48 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

49 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

50 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

51 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

52 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

53 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

54 | Trigonometry part 2 | Solving Trigonometric Equations – Type I | |

Objective: To Solve trigonometric equations for angles from 0 to 360 degrees. | |||

55 | Trigonometry part 2 | Solving Trigonometric Equations – Type II | |

Objective: To solve trigonometric equations for angles from 0 to 360 degrees. | |||

56 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

57 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

58 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

59 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

60 | Measurement – Advanced volume | Composite Solids | |

Objective: To calculate the volume of composite figures using appropriate formulae | |||

61 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

62 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

63 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

64 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

65 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

66 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

67 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

68 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

69 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

70 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

71 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

72 | Exam | Exam – Grade 11 – ACT Plane Geometry & Trigonometry Entrance Exam | |

Objective: Exam |

### Grades 11 - 12: Algebra I Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grades 11 – 12: Algebra I | |

Objective: Assessment | |||

2 | Fractions | Using fractions 1/2, 1/4, 1/8 to describe parts of a group or collection | |

Objective: To use the fractions 1/2, 1/4 and 1/8 to describe equal parts of a collection of objects | |||

3 | Fractions | Comparing and ordering fractions | |

Objective: To compare and order fractions with the same and different numbers of equal parts | |||

4 | Fractions | Mixed numerals | |

Objective: To name and recognise mixed numerals | |||

5 | Fractions | Improper fractions | |

Objective: To use diagrams and number lines to recognise and represent mixed numerals and improper fractions | |||

6 | Fractions | Fractions 1/5, 1/10, 1/100 | |

Objective: To compare and represent fractions with the denominator 5, 10, 100 | |||

7 | Fractions | Finding equivalent fractions | |

Objective: To reduce a fraction to its lowest form | |||

8 | Fractions | Multiplying and dividing to obtain equivalent fractions. | |

Objective: To find equivalent fractions using multiplication or division. | |||

9 | Fractions | Reducing fractions to lowest equivalent form | |

Objective: To reduce a fraction to its lowest form | |||

10 | Fractions | Comparing and ordering fractions greater than 1 | |

11 | Fractions | Subtracting fractions from whole numbers | |

Objective: To use a diagram and mental strategies to subtract fractions from whole numbers | |||

12 | Fractions | Adding and subtracting fractions with the same denominator | |

Objective: To add and subtract fractions with the same denominator | |||

13 | Fractions | Adding and subtracting fractions with different denominators | |

Objective: To add fractions with different denominators and the answer is less than 1 | |||

14 | Fractions | Multiplying fractions by whole numbers | |

Objective: To multiply common fractions by whole numbers | |||

15 | Fractions | Fractions of whole numbers | |

Objective: To find fractions of whole numbers | |||

16 | Fractions | Multiplying fractions | |

Objective: To multiply fractions and reduce the answer to its lowest form | |||

17 | Fractions | Multiplying mixed numbers | |

Objective: To multiply mixed numbers and reduce the answer to its lowest form | |||

18 | Fractions | Finding reciprocals of fractions and mixed numbers | |

Objective: To find the reciprocals of fractions and mixed numbers | |||

19 | Fractions | Dividing fractions | |

Objective: To divide fractions by other fractions | |||

20 | Fractions | Dividing mixed numbers | |

Objective: To divide mixed numbers | |||

21 | Fractions | BODMAS | |

Objective: To calculate answers for fraction and mixed number questions using BODMAS | |||

22 | Percentages | Calculating Percentages and Fractions of Quantities | |

Objective: To find percentages and fractions of quantities and solve problems with percentages | |||

23 | Decimals | Intro to Decimals | |

Objective: To relate the equivalent fraction to a decimal | |||

24 | Decimals | Comparing and ordering decimals to two decimal places | |

Objective: To compare and order decimals to two decimal places | |||

25 | Decimals | Decimals with whole numbers 10th and 100th | |

26 | Decimals | Adding decimals to two decimal places | |

Objective: To add decimals with the same number of decimal places (to two decimal Places) | |||

27 | Decimals | Subtracting decimals to two decimal places | |

Objective: To subtract decimals with the same number of decimal places (to two decimal places) | |||

28 | Decimals | Using decimals – shopping problems | |

Objective: To read and interpret problems involving money | |||

29 | Decimals | Using decimals to record length | |

Objective: To interpret the everyday use of fractions and decimals | |||

30 | Decimals | Rounding Decimals | |

Objective: To round a number with one or two decimal places to the nearest whole number | |||

31 | Decimals | Decimals to three decimal places | |

Objective: To express a number on a thousand as a decimal in thousandths | |||

32 | Decimals | Adding decimals with a different number of decimal places | |

Objective: To add decimal numbers with a different number of decimal places | |||

33 | Decimals | Subtracting decimals with a different number of places | |

Objective: To subtract decimals with a different number of decimal places | |||

34 | Decimals | Multiplying decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are multiplied by 10, 100 and 1000 | |||

35 | Decimals | Multiplying decimals by single-digit numbers | |

Objective: To multiply decimals by single-digit numbers | |||

36 | Decimals | Multiplication of decimals by decimals to two decimal places | |

Objective: To multiply decimals to two digits | |||

37 | Decimals | Dividing decimals by 10, 100 and 1000 | |

Objective: To recognise the pattern formed when decimals are divided by 10, 100 and 1000 | |||

38 | Decimals | Dividing decimals by whole numbers | |

Objective: To divide decimals by whole numbers | |||

39 | Decimals | Dividing numbers by decimals | |

Objective: To divide a whole number by a decimal fraction | |||

40 | Percentages | Understanding percentages | |

Objective: To recognise the percentage symbol and relate a common percentage to a fraction | |||

41 | Percentages | Changing fractions and decimals to percentages tenths and hundredths | |

Objective: To represent fractions and decimals as percentages | |||

42 | Percentages | Changing percentages to fractions and decimals | |

Objective: To change percentages to fractions and decimals | |||

43 | Percentages | One Quantity as a Percentage of Another | |

Objective: To determine what one quantity is as a percentage of another | |||

44 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

45 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

46 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

47 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

48 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

49 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

50 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

51 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

52 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

53 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

54 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

55 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

56 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

57 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

58 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

59 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

60 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

61 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

62 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

63 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

64 | Algebra – Basic | Inequalities | |

65 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

66 | Algebra – Basic | Simplifying algebraic fractions using the Index Laws | |

Objective: To use the index laws for division to simplify algebraic fractions | |||

67 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

68 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

69 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

70 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

71 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

72 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

73 | Indices/Exponents | Adding indices when multiplying terms with the same base | |

Objective: To add indices when multiplying powers that have the same base | |||

74 | Indices/Exponents | Subtracting indices when dividing terms with the same base | |

Objective: To subtract indices when dividing powers of the same base | |||

75 | Indices/Exponents | Multiplying indices when raising a power to a power | |

Objective: To multiply indices when raising a power to a power | |||

76 | Indices/Exponents | Multiplying indices when raising to more than one term | |

Objective: To raise power products to a power | |||

77 | Indices/Exponents | Terms raised to the power of zero | |

Objective: To evaluate expressions where quantities are raised to the power 0 | |||

78 | Indices/Exponents | Negative Indices | |

Objective: To evaluate or simplify expressions containing negative indices | |||

79 | Indices/Exponents | Fractional Indices | |

Objective: To evaluate or simplify expressions containing fractional indices | |||

80 | Indices/Exponents | Complex fractions as indices | |

Objective: To evaluate or simplify expressions containing complex fractional indices and radicals | |||

81 | Standard/Scientific notation | Scientific notation with larger numbers | |

Objective: To write large numbers in standard or scientific notation | |||

82 | Standard/Scientific notation | Scientific notation with small numbers | |

Objective: To write small numbers in standard or scientific notation | |||

83 | Standard/Scientific notation | Changing scientific notation to numerals | |

Objective: To interpret scientific notation by writing in base 10 numerals | |||

84 | Standard/Scientific notation | Significant Figures | |

Objective: To write a number to a specified number of significant figures | |||

85 | Number sets | Number Sets and Their Members | |

Objective: To distinguish between number sets and identify elements and subsets of number sets | |||

86 | Number sets | Addition and Multiplication Properties for Real Numbers | |

Objective: To identify and name addition and multiplication properties for real numbers | |||

87 | Number sets | Transformations That Produce Equivalent Equations | |

Objective: To name properties of equality used to create equivalent equations and solve equations | |||

88 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

89 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

90 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

91 | Simultaneous equations | Applications of simultaneous equations | |

Objective: To solve problems using simultaneous equations | |||

92 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

93 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

94 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

95 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

96 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

97 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

98 | Surds/Radicals | Some rules for the operations with surds | |

Objective: To learn rules for the division and multiplication of surds | |||

99 | Surds/Radicals | Simplifying Surds | |

Objective: To simplify numerical expressions and solve equations involving surds | |||

100 | Surds/Radicals | Creating entire surds | |

Objective: To write numbers as entire surds and compare numbers by writing as entire surds | |||

101 | Surds/Radicals | Adding and subtracting like surds | |

Objective: To add and subtract surds and simplify expressions by collecting like surds | |||

102 | Surds/Radicals | Expanding surds | |

Objective: To expand and simplify binomial expressions involving surds | |||

103 | Surds/Radicals | Binomial expansions | |

Objective: To expand and simplify the squares of binomial sums and differences involving surds | |||

104 | Surds/Radicals | Conjugate binomials with surds | |

Objective: To expand and simplify products of conjugate binomial expressions | |||

105 | Surds/Radicals | Rationalising the denominator | |

Objective: To rationalise the denominator of a fraction where the denominator is a monomial surd | |||

106 | Surds/Radicals | Rationalising binomial denominators | |

Objective: To rationalise the denominator of a fraction when the denominator is a binomial with surds | |||

107 | Graphs part 1 | The Circle: to find radii of circles | |

Objective: To find radii of circles, centre (0, 0) using x^2 + y^2 = a^2 and write equations of circles | |||

108 | Graphs part 1 | The semicircle: to select the equation given the semicircle and vice versa | |

Objective: To select the equation given a semicircle and vice versa | |||

109 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

110 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

111 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

112 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

113 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

114 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

115 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

116 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

117 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

118 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

119 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

120 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

121 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

122 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

123 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

124 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

125 | Algebra – Products and factors | Common factor and the difference of two squares | |

Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares. | |||

126 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

Objective: On completion of the lesson the student will understand the factorization of quadratic trinomial equations with all terms positive. | |||

127 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 2 | |

Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. | |||

128 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

Objective: On completion of the lesson the student will have an increased knowledge on factorizing quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. | |||

129 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 4 | |

Objective: On completion of the lesson the student will understand how to factorize all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. | |||

130 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

131 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

132 | Algebra – Products and factors | Sum and Difference of Two Cubes | |

Objective: To factorise the sum and difference of two cubes | |||

133 | Algebra – Products and factors | Simplifying algebraic fractions | |

Objective: To simplify algebraic fractions by factorisation and cancellation | |||

134 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

135 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

136 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

137 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

138 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

139 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

140 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

141 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

142 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

143 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

144 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

145 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

146 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

147 | Co-ordinate geometry part 1 | The Distance Formula | |

Objective: To use the distance formula to calculate the lengths of lines and distances | |||

148 | Co-ordinate geometry part 1 | The Mid-Point Formula | |

Objective: To determine the mid-point of an interval using the mid-point formula | |||

149 | Co-ordinate geometry part 1 | The Gradient | |

Objective: To find the gradient of a line given its angle of inclination or given rise and run | |||

150 | Co-ordinate geometry part 1 | The Gradient Formula | |

Objective: To use the gradient formula to find the gradient of straight lines | |||

151 | Co-ordinate geometry part 1 | The Straight Line | |

Objective: To state the equation of lines parallel to the axes and to graph equations x = a and y = b | |||

152 | Co-ordinate geometry part 1 | Lines Through the Origin | |

Objective: To state the equation of lines passing through the origin and to graph y = mx | |||

153 | Co-ordinate geometry part 1 | General Form of a Line and the x and y Intercepts | |

Objective: To write linear equations in general form, to find the x and y intercepts and to calculate area | |||

154 | Co-ordinate geometry part 1 | Slope Intercept Form of a Line | |

Objective: To change equation to slope intercept form and graph it and to find equation given graph | |||

155 | Co-ordinate geometry part 1 | Point Slope Form of a Line | |

Objective: To find the equation of a line given its slope and a point on the line (y-y1) = m(x-x1) | |||

156 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

157 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

158 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

159 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

160 | Statistics part 2 | Measures of Spread: the interquartile range | |

Objective: To find the upper and lower quartiles and the interquartile range | |||

161 | Co-ordinate geometry part 2 | Two Point Formula: equation of a line which joins a pair of points | |

Objective: To find the equation of the line which joins a pair of points | |||

162 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | |

Objective: To find the equation of a line given the x-axis and y-axis intercepts | |||

163 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

164 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

165 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

166 | Exam | Exam – Grades 11 – 12: Algebra I | |

Objective: Exam |

### Grades 11 - 12: Algebra II Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grades 11 – 12: Algebra II | |

Objective: Assessment | |||

2 | Algebra – Basic | Algebraic Expressions | |

Objective: To simplify numerical expressions and simplify and expand algebraic expressions | |||

3 | Algebra – Basic | Substitution into Algebraic Expressions | |

Objective: To evaluate simple algebraic expressions using whole numbers, fractions and decimals | |||

4 | Algebra – Basic | Directed Numbers: Addition and Subtraction | |

Objective: To add/subtract numbers using a number line – first number and answer can be negative | |||

5 | Algebra – Basic | Directed Numbers: Multiplication and Division | |

Objective: To multiply and divide directed numbers and evaluate powers of directed numbers | |||

6 | Algebra – Basic | Simplifying Algebraic Expressions: Adding Like Terms | |

Objective: To simplify numeric and algebraic addition expressions by collecting like terms | |||

7 | Algebra – Basic | Simplifying Algebraic Expressions: Subtracting Like Terms | |

Objective: To simplify algebraic subtractions by collecting like terms | |||

8 | Algebra – Basic | Simplifying Algebraic Expressions: Combining Addition and Subtraction | |

Objective: To simplify expressions containing addition and subtraction and two unlike terms | |||

9 | Algebra – Basic | Simplifying Algebraic Expressions: Multiplication | |

Objective: To simplify algebraic products using (but not stating) the commutative law | |||

10 | Algebra – Basic | Simplifying Algebraic Expressions: Division | |

Objective: To divide algebraic terms where the divisor is a factor of the dividend | |||

11 | Algebra – Basic | Expanding Algebraic Expressions: multiplication | |

Objective: To remove grouping symbols from an expression where the multiplier is monomial | |||

12 | Algebra – Basic | Expanding Algebraic Expressions: Negative multiplier | |

Objective: To expand parentheses when there is a negative multiplier | |||

13 | Algebra – Basic | Expanding and simplifying algebraic expressions | |

Objective: To expand and simplify algebraic expressions involving grouping symbols | |||

14 | Algebra – Basic | Solving Equations containing Addition and Subtraction | |

Objective: To solve one-step equations involving addition or subtraction | |||

15 | Algebra – Basic | Solving Equations containing Multiplication and Division | |

Objective: To solve one-step equations involving multiplication or division | |||

16 | Algebra – Basic | Solving Two-Step Equations | |

Objective: To solve two-step equations without division in the initial problem | |||

17 | Algebra – Basic | Solving Equations Containing Binomial Expressions | |

Objective: To solve equations with binomial expressions on each side | |||

18 | Algebra – Basic | Equations involving Grouping Symbols | |

Objective: To solve equations containing grouping symbols on each side | |||

19 | Algebra – Basic | Equations involving fractions | |

Objective: To solve fraction equations with the unknown in either the numerator or denominator | |||

20 | Algebra – Basic | Equations Resulting from Substitution into Formulae | |

Objective: To solve equations created by substituting values into formulae | |||

21 | Algebra – Basic | Changing the Subject of the Formula | |

Objective: To change the subject of algebraic formulae using equation-solving techniques | |||

22 | Algebra – Basic | Inequalities | |

23 | Algebra – Basic | Simplifying easy algebraic fractions | |

Objective: To simplify simple algebraic fractions using cancellation of common factors | |||

24 | Algebra – Basic | Simplifying algebraic fractions using the Index Laws | |

Objective: To use the index laws for division to simplify algebraic fractions | |||

25 | Algebra – Basic | Algebraic fractions resulting in negative Indices | |

Objective: To simplify algebraic fractions using negative indices (as required) in the answer | |||

26 | Algebra – Basic | Factorisation of algebraic fractions including binomials | |

Objective: To simplify algebraic fractions requiring the factorisation of binomial expressions | |||

27 | Algebra – Basic | Cancelling binomial factors in algebraic fractions | |

Objective: To simplify algebraic fractions with binomials in both the numerator and denominator | |||

28 | Absolute value | Evaluating Absolute Value Expressions | |

Objective: To evaluate numeric and algebraic expressions involving absolute value | |||

29 | Absolute value | Solving Absolute Value Equations | |

Objective: To solve equations involving absolute values | |||

30 | Absolute value | Solving and Graphing Inequalities | |

Objective: To graph the solution set of absolute value inequalities | |||

31 | Simultaneous equations | Simultaneous Equations | |

Objective: To solve simultaneous equations by substitution | |||

32 | Simultaneous equations | Elimination method | |

Objective: To solve simultaneous equations by elimination | |||

33 | Simultaneous equations | Elimination method part 2 | |

Objective: To solve more difficult simultaneous equations by elimination | |||

34 | Simultaneous equations | Applications of simultaneous equations | |

Objective: To solve problems using simultaneous equations | |||

35 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

36 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

37 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

38 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

39 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

40 | Surds/Radicals | Introducing surds | |

Objective: To recognise and simplify numerical expressions involving surds | |||

41 | Surds/Radicals | Some rules for the operations with surds | |

Objective: To learn rules for the division and multiplication of surds | |||

42 | Surds/Radicals | Simplifying Surds | |

Objective: To simplify numerical expressions and solve equations involving surds | |||

43 | Surds/Radicals | Creating entire surds | |

Objective: To write numbers as entire surds and compare numbers by writing as entire surds | |||

44 | Surds/Radicals | Adding and subtracting like surds | |

Objective: To add and subtract surds and simplify expressions by collecting like surds | |||

45 | Surds/Radicals | Expanding surds | |

Objective: To expand and simplify binomial expressions involving surds | |||

46 | Surds/Radicals | Binomial expansions | |

Objective: To expand and simplify the squares of binomial sums and differences involving surds | |||

47 | Surds/Radicals | Conjugate binomials with surds | |

Objective: To expand and simplify products of conjugate binomial expressions | |||

48 | Surds/Radicals | Rationalising the denominator | |

Objective: To rationalise the denominator of a fraction where the denominator is a monomial surd | |||

49 | Surds/Radicals | Rationalising binomial denominators | |

Objective: To rationalise the denominator of a fraction when the denominator is a binomial with surds | |||

50 | Graphs part 1 | The Circle: to find radii of circles | |

Objective: To find radii of circles, centre (0, 0) using x^2 + y^2 = a^2 and write equations of circles | |||

51 | Graphs part 1 | The semicircle: to select the equation given the semicircle and vice versa | |

Objective: To select the equation given a semicircle and vice versa | |||

52 | Graphs part 1 | The parabola: to describe properties of a parabola from its equation | |

Objective: To describe properties of a parabola from its equation and sketch the parabola | |||

53 | Graphs part 1 | Quadratic Polynomials of the form y = ax^2 + bx + c | |

Objective: To describe and sketch parabolas of the form y = x^2 + bx + c | |||

54 | Graphs part 1 | Graphing perfect squares: y=(a-x) squared | |

Objective: To describe and sketch parabolas of the form y = (x – a)^2 | |||

55 | Graphs part 1 | Graphing irrational roots | |

Objective: To determine the vertex (using -b/2a), and other derived properties, to sketch a parabola | |||

56 | Graphs part 1 | Solving Simultaneous Equations graphically | |

Objective: To solve simultaneous equations graphically | |||

57 | Algebra – Products and factors | Binomial Products | |

Objective: To expand and simplify monic binomial products of the form (x + a)(x +/- b) | |||

58 | Algebra – Products and factors | Binomial products with negative multiplier | |

Objective: To expand and simplify monic binomial products of the form (x – a)(x +/- b) | |||

59 | Algebra – Products and factors | Binomial Products (nonmonic) | |

Objective: To expand and simplify nonmonic binomial products | |||

60 | Algebra – Products and factors | Squaring a Binomial (monic) | |

Objective: To expand the square of a binomial by multiplication and by inspection | |||

61 | Algebra – Products and factors | Squaring a Binomial (nonmonic) | |

Objective: To expand the square of a nonmonic binomial by inspection | |||

62 | Algebra – Products and factors | Expansions Leading to the Difference of Two Squares | |

Objective: To expand the product of conjugate binomials leading to differences of squares | |||

63 | Algebra – Products and factors | Products in Simplification of Algebraic Expressions | |

Objective: To simplify algebraic expressions containing binomial products | |||

64 | Algebra – Products and factors | Larger Expansions | |

Objective: To expand and simplify the product of a binomial and a trinomial | |||

65 | Algebra – Products and factors | Highest Common Factor | |

Objective: To factorise an expression by identifying and extracting the highest common factor | |||

66 | Algebra – Products and factors | Factors by Grouping | |

Objective: To factorise a four-term expression by grouping | |||

67 | Algebra – Products and factors | Difference of Two Squares | |

Objective: To factorise differences of two squares | |||

68 | Algebra – Products and factors | Common factor and the difference of two squares | |

69 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 1 | |

70 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 2 | |

71 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 3 | |

72 | Algebra – Products and factors | Quadratic Trinomials (monic): Case 4 | |

73 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials | |

Objective: To factorise nonmonic quadratic trinomials using the ‘X’ method | |||

74 | Algebra – Products and factors | Factorisation of nonmonic quadratic trinomials: Moon method | |

Objective: To factorise nonmonic quadratic trinomials using the ‘Moon’ method | |||

75 | Algebra – Products and factors | Sum and Difference of Two Cubes | |

Objective: To factorise the sum and difference of two cubes | |||

76 | Algebra – Products and factors | Simplifying algebraic fractions | |

Objective: To simplify algebraic fractions by factorisation and cancellation | |||

77 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

78 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

79 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

80 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

81 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) | |

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

82 | Algebra – Quadratic equations | Introduction to Quadratic Equations | |

Objective: To find the solutions of quadratic equations presented as a product of factors | |||

83 | Algebra – Quadratic equations | Solving Quadratic Equations with Factorisation | |

Objective: To solve quadratic equations requiring factorisation | |||

84 | Algebra – Quadratic equations | Solving Quadratic Equations | |

Objective: To solve quadratic equations that need to be changed into the form ax^2 + bx + c = 0 | |||

85 | Algebra – Quadratic equations | Completing the square | |

Objective: To complete an incomplete square | |||

86 | Algebra – Quadratic equations | Solving Quadratic Equations by Completing the Square | |

Objective: To solve quadratic equations by completing the square | |||

87 | Algebra – Quadratic equations | The Quadratic Formula | |

Objective: To find the roots of a quadratic equation by using the quadratic formula | |||

88 | Algebra – Quadratic equations | Problem solving with quadratic equations | |

Objective: To solve problems which require finding the roots of a quadratic equation | |||

89 | Algebra – Quadratic equations | Solving Simultaneous Quadratic Equations Graphically | |

Objective: To determine points of intersection of quadratic and linear equations | |||

90 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

91 | Probability | Simple events | |

92 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

93 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

94 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

95 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

96 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

97 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

98 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

99 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

100 | Probability | Unordered selections – combinations | |

Objective: To use the nCr formula to solve problems where unordered selections occur | |||

101 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

102 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

103 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

104 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

105 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

106 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

107 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

108 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

109 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

110 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

111 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

112 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

113 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

114 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

115 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

116 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

117 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

118 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

119 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

120 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

121 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

122 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

123 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

124 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

125 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

126 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

127 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

128 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

129 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

130 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

131 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

132 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

133 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

134 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

135 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

136 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

137 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

138 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

139 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

140 | Logarithms | Powers of 2 | |

Objective: To convert between logarithm statements and indice statements | |||

141 | Logarithms | Equations of type log x to the base 3 = 4 | |

Objective: To find the value of x in a statement of type log x to the base 3 = 4 | |||

142 | Logarithms | Equations of type log 32 to the base x = 5 | |

Objective: To solve Logrithmic Equation where the variable is the base x = 5 | |||

143 | Logarithms | Laws of Logarithms | |

Objective: To review the logarithm laws | |||

144 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | |

Objective: To expand expressions using the logarithm laws | |||

145 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | |

Objective: To simplify expressions using the logarithm laws | |||

146 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | |

Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws | |||

147 | Logarithms | Equations Involving Logarithms | |

Objective: To solve equations involving logarithms using the logarithm laws | |||

148 | Logarithms | Using Logarithms to Solve Equations | |

Objective: To use logarithms to solve exponential equations | |||

149 | Logarithms | Change of Base Formula | |

Objective: To evaluate log expressions using logarithms | |||

150 | Logarithms | The Graph of the Logarithmic Curve | |

Objective: To learn the properties of the logarithmic curve | |||

151 | Logarithms | The Graph of the Logarithmic Curve | |

Objective: To solve problems involving logarithmic curves | |||

152 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

153 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

154 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

155 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

156 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

157 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

158 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

159 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

160 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

161 | Polynomials | Introduction to polynomials | |

Objective: To define polynomials by degree, leading term, leading coefficient, constant term and monic | |||

162 | Polynomials | The Sum, Difference and Product of Two Polynomials | |

Objective: To add, subtract and multiply polynomials | |||

163 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

164 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

165 | Polynomials | More on Remainder Theorem | |

Objective: To determine polynomial coefficients given a divisor and remainder | |||

166 | Polynomials | The factor theorem | |

Objective: To use the factor theorem to show that (x-a) is a factor of P(x) | |||

167 | Polynomials | More on the factor theorem | |

Objective: To use the factor theorem to find algebraic variables in polynomials | |||

168 | Polynomials | Complete factorisations using the factor theorem | |

Objective: To use the factor theorem to derive factors of a polynomial | |||

169 | Polynomials | Polynomial equations | |

Objective: To practise solving polynomial equations | |||

170 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

171 | Polynomials | The Sum and Product of the Roots of Quadratic Equations. | |

Objective: Sum and product of roots of quadratic equations. | |||

172 | Polynomials | The Sum and Product of the Roots of Cubic and Quartic Equations. | |

Objective: Sum and product of toots of cubic and quartic equations. | |||

173 | Polynomials | Methods of Approximating Roots. | |

Objective: Methods of approximating roots. | |||

174 | Polynomials | Newton’s Method of Approximation. | |

Objective: Newton’s method of approximation. | |||

175 | Series and sequences part 1 | General Sequences | |

Objective: To use the general form of the n’th term of a sequence to find the first 3 terms | |||

176 | Series and sequences part 1 | Finding Tn Given Sn | |

Objective: To find the value of the n’th term in a sequence given the sum of the first n terms | |||

177 | Series and sequences part 1 | The Arithmetic Progression | |

Objective: To find the common difference of a given arithmetic progression | |||

178 | Series and sequences part 1 | Finding the position of a term in an A.P. | |

Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term | |||

179 | Series and sequences part 1 | Given two terms of A.P. find the sequence | |

Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms | |||

180 | Series and sequences part 1 | Arithmetic Means | |

Objective: To find the arithmetic mean of two values | |||

181 | Series and sequences part 1 | The sum to n terms of an A.P. | |

Objective: To find the sum of n terms of an arithmetic progression given the first three terms | |||

182 | Series and sequences part 1 | The Geometric Progression | |

Objective: To find the common ratio of a given geometric progression | |||

183 | Series and sequences part 1 | Finding the position of a term in a G.P. | |

Objective: To find the place of a term in a given geometric progression | |||

184 | Series and sequences part 1 | Given two terms of G.P. find the sequence | |

Objective: To find the first term given two terms of a geometric progression | |||

185 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

186 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

187 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

188 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

189 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

190 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

191 | Series and sequences part 2 | Superannuation | |

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time | |||

192 | Series and sequences part 2 | Time Payments | |

Objective: To calculate the payments required to pay off a loan | |||

193 | Exam | Exam – Grades 11 – 12: Algebra II | |

Objective: Exam |

### Grades 11 - 12: Geometry Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grades 11 – 12: Geometry | |

Objective: Assessment | |||

2 | Measurement – Area | Introducing the Rules for Finding the Area of a Rectangle and a Parallelogram | |

3 | Measurement – Area | Finding the Area of a Triangle and Other Composite Shapes | |

Objective: To calculate the area of triangles and measure and calculate composite shape area | |||

4 | Measurement – Volume | Introducing the Formula for Volume | |

Objective: To calculate the volume of rectangular prisms using V=l x b x h | |||

5 | Measurement – Volume | Solving Problems about Volume Part 1 | |

Objective: To solve volume problems using same and mixed units of length | |||

6 | Measurement – Volume | Solving Problems about Volume Part 2 | |

Objective: To solve volume problems involving larger objects | |||

7 | Measurement – Advanced area | Area of a Trapezium | |

Objective: To calculate the area of trapezia using A=(h/2)(a+b) | |||

8 | Measurement – Advanced area | Area of a Rhombus | |

Objective: To calculate the area of a rhombus using diagonal products | |||

9 | Measurement – Advanced area | Area of a Circle | |

Objective: To calculate the area of circles and sectors and to solve circle problems | |||

10 | Measurement – Advanced area | Area of Regular Polygons and Composite Figures | |

Objective: To calculate area of composite figures and solve problems using correct formulae | |||

11 | Measurement – Advanced volume | Finding the volume of prisms | |

Objective: To calculate the volume of prisms using V=Ah and solve volume problems | |||

12 | Measurement – Advanced volume | Volume of a Cylinder and Sphere | |

Objective: To solve problems and calculate volumes of cylinders and spheres and parts of each | |||

13 | Measurement – Advanced volume | Volume of Pyramids and Cones | |

Objective: To calculate the volumes of pyramids and cones | |||

14 | Measurement – Advanced volume | Composite Solids | |

Objective: To calculate the volume of composite figures using appropriate formulae | |||

15 | Surface area | Surface Area of a Cube/Rectangular Prism | |

Objective: To calculate the surface area of cubes and rectangular prisms | |||

16 | Surface area | Surface Area of a Triangular/Trapezoidal Prism | |

Objective: To calculate the surface area of triangular and trapezoidal prisms | |||

17 | Surface area | Surface Area of a Cylinder and Sphere | |

Objective: To calculate the surface area of cylinders and spheres | |||

18 | Surface area | Surface Area of Pyramids | |

Objective: To calculate the surface area of pyramids | |||

19 | Surface area | Surface Area of Composite Solids | |

Objective: To calculate the surface area of composite solids | |||

20 | Surface area | Surface area of composite solids | |

Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. | |||

21 | Geometry part 1 | Measuring Angles | |

Objective: To use a protractor to measure angles and identify angles as acute, obtuse or reflex | |||

22 | Geometry part 1 | Adjacent Angles | |

Objective: To recognise and calculate the size of adjacent angles | |||

23 | Geometry part 1 | Complementary and Supplementary Angles | |

Objective: To recognise and calculate the size of complementary and supplementary angles | |||

24 | Geometry part 1 | Vertically Opposite Angles | |

Objective: To determine values of pronumerals in vertically opposite angles | |||

25 | Geometry part 1 | Angles at a Point | |

Objective: To use angles at a point to calculate unknown angles | |||

26 | Geometry part 1 | Parallel Lines | |

Objective: To identify angle pairs and calculate angles formed by a transversal and parallel lines | |||

27 | Geometry part 1 | Additional questions involving parallel lines | |

Objective: To determine angle magnitude for angles formed by parallel lines and transversals | |||

28 | Geometry part 1 | Angle Sum of a Triangle | |

Objective: To use the angle sum for a triangle to calculate unknown angles | |||

29 | Geometry part 1 | Exterior angle theorem | |

Objective: To use the external angle of a triangle theorem to calculate unknown angles | |||

30 | Geometry part 1 | Special triangles | |

Objective: To use the properties of equilateral and isosceles triangles to calculate angle size | |||

31 | Geometry part 1 | Quadrilaterals | |

Objective: To use the angle sum of a quadrilateral to calculate unknown angles | |||

32 | Geometry part 1 | Geometric Constructions | |

Objective: To bisect a line, bisect an angle and construct a perpendicular using a compass and ruler | |||

33 | Geometry part 3 | Points, Lines and Planes | |

Objective: To identify collinear points and coplanar lines and points in 2 and 3 dimensions | |||

34 | Geometry part 3 | Angles | |

Objective: To label and classify angles and calculate pronumeral values within angles | |||

35 | Geometry part 3 | Angle Bisector Construction and its Properties | |

Objective: To geometrically bisect angles and calculate angle size given bisection | |||

36 | Geometry part 3 | Circumcenter and Incenter | |

Objective: To use properties of triangles, circles, circumcentres and incentres | |||

37 | Geometry part 3 | Orthocentre and Centroids | |

Objective: To use properties of triangles, circles orthocentres and centroids | |||

38 | Geometry part 3 | Midsegments | |

Objective: To determine midsegments, their length, slope and other properties | |||

39 | Quadrilaterals | Quadrilaterals 1 | |

Objective: To recognise, name and describe the properties of quadrilaterals | |||

40 | Quadrilaterals | Properties of Parallelograms – Opposite Angles Equal | |

Objective: To prove and use ‘Opposite angles of a parallelogram are congruent’ | |||

41 | Quadrilaterals | Properties of Parallelograms – Diagonals, Sides and Angles | |

Objective: To prove parallelogram properties and calculate unknown angles and lengths | |||

42 | Quadrilaterals | The Parallelogram Umbrella | |

Objective: To prove properties of specific parallelograms and find angles and lengths | |||

43 | Quadrilaterals | Properties of Trapezoids | |

Objective: To prove properties of trapezoids and find unknown lengths and angles | |||

44 | Quadrilaterals | Quadrilaterals 6 | |

Objective: To establish the properties of quadrilaterals in the number plane | |||

45 | Locus | Constructions and Loci 1: Transformations | |

Objective: To identify and use the locus of a point with simple constraints | |||

46 | Locus | Constructions and Loci 2 | |

Objective: To identify and use the locus of a point with multiple constraints | |||

47 | Geometry part 2 | More difficult exercises involving parallel lines | |

Objective: To determine the angles of geometric figures using known properties and theorems | |||

48 | Geometry part 2 | Further difficult exercises involving formal reasoning | |

Objective: To determine formally angles of geometric figures using known properties and theorems | |||

49 | Geometry part 2 | Angles of regular polygons | |

Objective: To calculate the internal and external angles of a polygon | |||

50 | Geometry part 2 | Congruent triangles: Tests 1 and 2 | |

Objective: To recognise congruent triangles and matching sides and angles using SSS and SAS | |||

51 | Geometry part 2 | Congruent triangles: Tests 3 and 4 | |

Objective: To recognise congruent triangles and matching sides and angles using AAS and RHS | |||

52 | Geometry part 2 | Proofs and Congruent Triangles | |

Objective: To use congruency in formal proofs in order to determine unknown angles and sides | |||

53 | Geometry part 2 | Similar Triangles | |

Objective: To use similarity tests for triangles and determine unknown sides and angles in triangles | |||

54 | Geometry part 2 | Using Similar Triangles to Calculate Lengths | |

Objective: To determine unknown sides and angles of similar triangles | |||

55 | Geometry part 2 | Examples involving overlapping triangles | |

Objective: To determine the lengths of unknown sides in overlapping or adjacent similar triangles | |||

56 | Geometry part 3 | The Triangle Inequality Theorem | |

Objective: To use the triangle inequality theorem to determine constructability of triangles | |||

57 | Pythagoras | Pythagoras’ Theorem: Finding the Hypotenuse | |

Objective: To calculate the length of a hypotenuse using Pythagoras’ Theorem | |||

58 | Pythagoras | Using Pythagorean Triples to Identify Right Triangles | |

Objective: To identify right triangles by using Pythagorean Triples or Pythagoras’ Theorem | |||

59 | Pythagoras | Calculating the Hypotenuse of a right-angled Triangle | |

Objective: To calculate the length of a hypotenuse where lengths are given as surds or decimals | |||

60 | Pythagoras | Calculating a Leg of a right-angled Triangle | |

Objective: To calculate the length of sides other than the hypotenuse using Pythagoras’ Theorem | |||

61 | Pythagoras | Proofs of Pythagoras’ Theorem | |

Objective: To examine and complete proofs of Pythagoras’ Theorem | |||

62 | Logic | Inductive and Deductive Reasoning | |

Objective: To identify and use inductive and deductive reasoning | |||

63 | Logic | Disproof of Counter Example | |

Objective: To identify a statement as a counter example to disprove a statement | |||

64 | Logic | Proof by Disproof of a Contradictory Statement | |

Objective: To prove that a statement is true by proving that the contradictory statement is false | |||

65 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

66 | Trigonometry part 1 | Trigonometric Ratios | |

Objective: To name the sides of a right-angled triangle and to determine the trig ratios of an angle | |||

67 | Trigonometry part 1 | Using the Calculator | |

Objective: To determine trigonometric ratios using a calculator | |||

68 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 1 Sin] | |

Objective: To use the sine ratio to calculate the opposite side of a right-angled triangle | |||

69 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 2 Cosine] | |

Objective: To use the cosine ratio to calculate the adjacent side of a right-angle triangle | |||

70 | Trigonometry part 1 | Using the Trigonometric Ratios to find unknown length [Case 3 Tangent Ratio] | |

Objective: To use the tangent ratio to calculate the opposite side of a right-angled triangle | |||

71 | Trigonometry part 1 | Unknown in the Denominator [Case 4] | |

Objective: To use trigonometry to find sides of a right-angled triangle and the Unknown in denominator | |||

72 | Trigonometry part 1 | Bearings: The Compass | |

Objective: To change from true bearings to compass bearings and vice versa | |||

73 | Trigonometry part 1 | Angles of Elevation and Depression | |

Objective: To identify and distinguish between angles of depression and elevation | |||

74 | Trigonometry part 1 | Trigonometric Ratios in Practical Situations | |

Objective: To solve problems involving bearings and angles of elevation and depression | |||

75 | Trigonometry part 1 | Using the Calculator to Find an Angle Given a Trigonometric Ratio | |

Objective: To find angles in right-angled triangles given trigonometric ratios | |||

76 | Trigonometry part 1 | Using the Trigonometric Ratios to Find an Angle in a Right-Angled Triangle | |

Objective: To use trigonometric ratios to determine angles in right-angled triangles and in problems | |||

77 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

78 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

79 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

80 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

81 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

82 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

83 | Geometry transformations | Geometry Transformations without Matrices: Translation | |

Objective: To find the image of a point or object after a translation | |||

84 | Geometry transformations | Geometry Transformations without Matrices: Rotation | |

Objective: To determine rotation angle and to perform prescribed rotations | |||

85 | Geometry transformations | Geometry Transformations without Matrices: Dilation or Enlargement | |

Objective: To describe dilations and to calculate lengths and scale factors of dilated figures | |||

86 | Geometry transformations | Geometry Transformations without Matrices: Mixed and Combined Transformations | |

Objective: To identify images produced by a given sequence of transformations | |||

87 | Circle geometry part 1 | Theorem – Equal arcs subtend equal angles at the centre | |

Objective: To know that equal arcs on circles of equal radii subtend equal angles at the centre | |||

88 | Circle geometry part 1 | Theorem – The perpendicular from the centre to a chord bisects the chord | |

Objective: To know that the perpendicular from the centre of a circle to a chord bisects the chord and to know that the line from the centre of a circle to the mid-point of a chord is perpendicular to the chord | |||

89 | Circle geometry part 1 | Theorem – Equal chords in a circle are equidistant from the centre | |

Objective: To know that equal chords in equal circles are equidistant from the centres | |||

90 | Circle geometry part 1 | Theorem – The angle at the centre is double the angle at the circumference | |

Objective: To know that the angle at the centre of a circle is double the angle at the circumference standing on the same arc | |||

91 | Circle geometry part 1 | Theorem: Angles in the same segment of a circle are equal | |

Objective: To know that angles in the same segment of a circle are equal | |||

92 | Circle geometry part 1 | Theorem: The angle of a semi-circle is a right angle | |

Objective: To know that the angle of a semi-circle is a right angle | |||

93 | Circle geometry part 1 | Theorem: The opposite angles of a cyclic quadrilateral are supplementary | |

Objective: To know that the opposite angles of a cyclic quadrilateral are supplementary | |||

94 | Circle geometry part 1 | Theorem – Exterior angle of cyclic quadrilateral equals interior opposite angles | |

Objective: To know that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle | |||

95 | Circle geometry part 1 | Theorem – At the point of contact a tangent is perpendicular to the radius | |

Objective: To know that the tangent to a circle is perpendicular to the radius drawn to it | |||

96 | Circle geometry part 1 | Theorem: Tangents to a circle from an external point are equal | |

Objective: To know that the tangents to a circle from an external point are equal | |||

97 | Circle geometry part 1 | Theorem – Angle between a tangent and chord equals angle in alternate segment | |

Objective: To know that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment | |||

98 | Exam | Exam – Grades 11 – 12: Geometry | |

Objective: Exam |

### Grades 11 - 12: Probability - Statistics Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grades 11 – 12: Probability – Statistics | |

Objective: Assessment | |||

2 | Probability | Simple events | |

3 | Probability | Rolling a pair of dice | |

Objective: To find the probability of selected events when two dice are rolled | |||

4 | Probability | Experimental probability | |

Objective: To find the experimental probabilities of an experimental trial | |||

5 | Probability | Experimental probability | |

Objective: To use tree diagrams to determine sample spaces and compound probabilities | |||

6 | Probability | Tree diagrams: depending on previous outcomes | |

Objective: To use tree diagrams where the probability is dependent on previous outcomes | |||

7 | Probability | The Complementary Result | |

Objective: To calculate the probability of complementary events using P(E) = 1 – P(not E) | |||

8 | Probability | P[A or B] When A and B are NOT mutually exclusive | |

Objective: To calculate the probability of non exclusive events using P(A or B) = P(A)+P(B) | |||

9 | Probability | The Binomial Theorem and Binomial Coefficients | |

Objective: To calculate binomial coefficients and expand binomial powers. | |||

10 | Probability | Binomial probabilities using the Binomial Theorem | |

Objective: To calculate the binomial probability of a given number of successful trials | |||

11 | Statistics part 2 | Calculating mean, mode and median from grouped data | |

Objective: To identify class centres, get frequency counts and determine mean, mode and median values | |||

12 | Statistics part 1 | The Mode | |

Objective: To find the mode from raw data and from a frequency distribution table | |||

13 | Statistics part 1 | The Mean | |

Objective: To calculate means from raw data and from a frequency table using an fx column | |||

14 | Statistics part 1 | The Median | |

Objective: To determine the median of a set of raw scores | |||

15 | Statistics part 1 | Calculating the Mean from a Frequency Distribution | |

Objective: To determine averages (mean, median and mode) from cumulative frequency polygons | |||

16 | Statistics part 2 | Using the Calculator for Statistics | |

Objective: To find a mean, using a data set or a frequency distribution table and calculator. | |||

17 | Statistics part 2 | Standard deviation applications | |

Objective: To find a standard deviation, using a data set or a frequency distribution table and calculator | |||

18 | Statistics part 2 | Applications of Standard Deviation | |

Objective: To use standard deviation as a measure of deviation from a mean | |||

19 | Statistics part 1 | Frequency distribution table | |

Objective: To construct a frequency distribution table for raw data and to interpret the table | |||

20 | Statistics part 1 | Frequency histograms and polygons | |

Objective: To construct and interpret frequency histograms and polygons | |||

21 | Statistics part 1 | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: To derive statistics from data represented as stem & leaf or box & whisker plots | |||

22 | Statistics part 1 | The Scatter plot | |

Objective: To make a valid interpretation of data presented as a scatter plot | |||

23 | Exam | Exam – Grades 11 – 12: Probability – Statistics | |

Objective: Exam |

### Grades 11 - 12: Pre-Calculus Mathematics

# | TOPIC | TITLE | |
---|---|---|---|

1 | Self Assessment | Self Assessment – Grades 11 – 12: Pre-Calculus | |

Objective: Assessment | |||

2 | Graphs part 2 | Graphing complex polynomials: quadratics with no real roots | |

Objective: To graph quadratics that have no real roots, hence don’t cut the x-axis | |||

3 | Graphs part 2 | General equation of a circle: determine and graph the equation | |

Objective: To determine and graph the equation of a circle with radius a and centre (h,k) | |||

4 | Graphs part 2 | Graphing cubic curves | |

Objective: To graph cubic curves whose equation is of the form y = (x – a)^3 + b or y = (a – x)^3 + b | |||

5 | Trigonometry part 1 | Trigonometric Ratios of 30, 45 and 60 Degrees: Exact Ratios | |

Objective: To determine the exact values of sin, cos and tan of 30, 45 and 60 degrees | |||

6 | Graphs part 2 | Absolute Value Equations | |

Objective: To graph equations involving absolute values | |||

7 | Graphs part 2 | The Rectangular Hyperbola | |

Objective: To graph rectangular hyperbolae whose equations are of the form xy = a and y = a/x | |||

8 | Graphs part 2 | The Exponential Function | |

Objective: To graph exponential curves whose exponents are either positive or negative | |||

9 | Graphs part 2 | Logarithmic Functions | |

Objective: To graph and describe log curves whose equations are of the form y = log (ax + b) | |||

10 | Function | Functions and Relations: domain and range | |

Objective: To identify and represent functions and relations | |||

11 | Function | Function Notation | |

Objective: To write and evaluate functions using function notation | |||

12 | Function | Selecting Appropriate Domain and Range | |

Objective: To determine appropriate domains for functions | |||

13 | Function | Domain and Range from Graphical Representations | |

Objective: To determine the range of a function from its graphical representation | |||

14 | Function | Evaluating and Graphing Piecewise Functions | |

Objective: To evaluate and graph piecewise functions | |||

15 | Function | Combining Functions | |

Objective: To determine the resultant function after functions have been combined by plus, minus, times and divide | |||

16 | Function | Simplifying Composite Functions | |

Objective: To simplify, evaluate and determine the domain of composite functions | |||

17 | Function | Inverse Functions | |

Objective: To find the inverse of a function and determine whether this inverse is itself a function | |||

18 | Function | Graphing Rational Functions Part 1 | |

Objective: To determine asymptotes and graph rational functions using intercepts and asymptotes | |||

19 | Function | Graphing Rational Functions Part 2 | |

Objective: To determine asymptotes and graph rational functions | |||

20 | Function | Parametric Equations | |

Objective: To interchange parametric and Cartesian equations and to identify graphs | |||

21 | Function | Polynomial Addition: in Combining and Simplifying Functions | |

Objective: To evaluate, simplify and graph rational functions | |||

22 | Function | Parametric Functions | |

Objective: To change Cartesian and parametric equations and to graph parametric functions | |||

23 | Polynomials | Polynomials and Long Division | |

Objective: To perform long division of polynomials, finding quotient and remainder | |||

24 | Polynomials | The Remainder Theorem | |

Objective: To determine a remainder when a first polynomial is divided by a second | |||

25 | Polynomials | More on Remainder Theorem | |

Objective: To determine polynomial coefficients given a divisor and remainder | |||

26 | Polynomials | The factor theorem | |

Objective: To use the factor theorem to show that (x-a) is a factor of P(x) | |||

27 | Polynomials | More on the factor theorem | |

Objective: To use the factor theorem to find algebraic variables in polynomials | |||

28 | Polynomials | Complete factorisations using the factor theorem | |

Objective: To use the factor theorem to derive factors of a polynomial | |||

29 | Polynomials | Polynomial equations | |

Objective: To practise solving polynomial equations | |||

30 | Polynomials | Graphs of polynomials | |

Objective: To derive graphs of polynomials by factorising | |||

31 | Logarithms | Powers of 2 | |

Objective: To convert between logarithm statements and indice statements | |||

32 | Logarithms | Equations of type log x to the base 3 = 4 | |

Objective: To find the value of x in a statement of type log x to the base 3 = 4 | |||

33 | Logarithms | Equations of type log 32 to the base x = 5 | |

Objective: To solve Logrithmic Equation where the variable is the base x = 5 | |||

34 | Logarithms | Laws of Logarithms | |

Objective: To review the logarithm laws | |||

35 | Logarithms | Using the Log Laws to Expand Logarithmic Expressions | |

Objective: To expand expressions using the logarithm laws | |||

36 | Logarithms | Using the Log Laws to Simplify Expressions Involving Logarithms | |

Objective: To simplify expressions using the logarithm laws | |||

37 | Logarithms | Using the Log Laws to Find the Logarithms of Numbers | |

Objective: To find the logarithm of a number, with an unknown base, using the logarithm laws | |||

38 | Logarithms | Equations Involving Logarithms | |

Objective: To solve equations involving logarithms using the logarithm laws | |||

39 | Logarithms | Using Logarithms to Solve Equations | |

Objective: To use logarithms to solve exponential equations | |||

40 | Logarithms | Change of Base Formula | |

Objective: To evaluate log expressions using logarithms | |||

41 | Logarithms | The Graph of the Logarithmic Curve | |

Objective: To learn the properties of the logarithmic curve | |||

42 | Logarithms | The Graph of the Logarithmic Curve | |

Objective: To solve problems involving logarithmic curves | |||

43 | Complex numbers | Complex Numbers: Adding and Subtracting | |

Objective: To recognise and manipulate simple complex numbers and expressions | |||

44 | Complex numbers | Complex Numbers: Multiplying and Dividing | |

Objective: To perform multiplication and division of complex numbers | |||

45 | Complex numbers | Adding and Subtracting Complex Numbers using Vectors | |

Objective: To perform complex number operations graphically using vectors | |||

46 | Trigonometry part 1 | The Cosine Rule to find an unknown side [Case 1 SAS] | |

Objective: To complete the cosine rule to find a subject side for given triangles | |||

47 | Trigonometry part 1 | The Sine Rule to find an unknown side: Case 1 | |

Objective: To complete the cosine rule to find a subject angle for given triangles | |||

48 | Trigonometry part 1 | The Sine Rule: Finding a Side | |

Objective: To find an unknown side of a triangle using the sine rule | |||

49 | Trigonometry part 1 | The Sine Rule: Finding an Angle | |

Objective: To find an unknown angle of a triangle using the sine rule | |||

50 | Trigonometry part 1 | The Sine Area Formula for a Triangle | |

Objective: To use the sine formula for the area of a triangle to calculate area | |||

51 | Trigonometry part 2 | Reciprocal Ratios | |

Objective: To find the trigonometric ratios for a given right-angled triangle | |||

52 | Trigonometry part 2 | Complementary Angle Results | |

Objective: To use complementary angle ratios to find an unknown angle given a trigonometric equality | |||

53 | Trigonometry part 2 | Trigonometric Identities | |

Objective: To simplify expressions using trigonometric equalities | |||

54 | Trigonometry part 2 | Angles of Any Magnitude | |

Objective: To assign angles to quadrants and to find trigonometric values for angles | |||

55 | Trigonometry part 2 | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: To find trigonometric ratios of 0, 90, 180, 270 and 360 degrees | |||

56 | Trigonometry part 2 | Graphing the Trigonometric Ratios I: Sine Curve | |

Objective: To recognise the sine curve and explore shifts of phase and amplitude | |||

57 | Trigonometry part 2 | Graphing the Trigonometric Ratios II: Cosine Curve | |

Objective: To recognise the cosine curve and explore shifts of phase and amplitude | |||

58 | Trigonometry part 2 | Graphing the Trigonometric Ratios III: Tangent Curve | |

Objective: To recognise the tangent curve and explore shifts of phase and amplitude | |||

59 | Trigonometry part 2 | Graphing the Trigonometric Ratios IV: Reciprocal Ratios | |

Objective: To graph the primary trigonometric functions and their inverses | |||

60 | Trigonometry part 2 | Trigonometric Sum and Difference Identities | |

Objective: To evaluate trig functions of angles using sum and difference identities | |||

61 | Trigonometry part 2 | Double Angle Identities | |

Objective: To use double angle identities to evaluate trig. functions and solve trig equations | |||

62 | Trigonometry part 2 | Half-angle Identities | |

Objective: To evaluate trig. functions of angles using half-angle identities | |||

63 | Trigonometry part 2 | t Formulas | |

Objective: To write t-formulae for trig. functions. To solve equations using t-formulae | |||

64 | Complex numbers | The Absolute Value of a Complex Number | |

Objective: To find the absolute value of a complex number | |||

65 | Complex numbers | Trigonometric Form of a Complex Number | |

Objective: To find the trigonometric form of a complex number | |||

66 | Complex numbers | Multiplication and Division of Complex Numbers in Trigonometric Form | |

Objective: To multiply and divide complex numbers using DeMoivre’s Theorem | |||

67 | Complex numbers | DeMoivre’s theorem | |

Objective: To find powers of complex numbers using DeMoivre’s theorem | |||

68 | Complex numbers | The nth Root of Real and Complex Numbers | |

Objective: To find the roots of a complex function using DeMoivre’s theorem | |||

69 | Complex numbers | Fundamental Theorem of Algebra | |

Objective: To find the nth zeros of a polynomial function both real and complex | |||

70 | Matrices | Matrices: basic concepts | |

Objective: To write and state the order of a matrix and to identify square matrices | |||

71 | Matrices | Addition and Subtraction of Matrices | |

Objective: To add and subtract matrices | |||

72 | Matrices | Scalar matrix: multiplication | |

Objective: To multiply a matrix by a scalar | |||

73 | Matrices | Multiplication of one matrix by another matrix | |

Objective: To perform matrix multiplication and to recognise that AB is not equal to BA | |||

74 | Matrices | Translation in the number plane | |

Objective: To use matrix addition to translate points | |||

75 | Matrices | Translation by matrix multiplication | |

Objective: To transform points and objects by matrix multiplication | |||

76 | Matrices | Special Transformations: Reflections, Rotations and Enlargements | |

Objective: To reflect, rotate and enlarge geometric shapes using matrix multiplication | |||

77 | Matrices | Vectors | |

Objective: To use vectors to find resultant speeds and displacements | |||

78 | Matrices – Linear systems | Number of Solutions | |

Objective: To determine solutions to systems of equations | |||

79 | Matrices – Linear systems | Vector Addition in 2 and 3D | |

Objective: To represent, add, subtract and determine the direction of vectors | |||

80 | Matrices – Linear systems | Optimal Solutions | |

Objective: To use linear programming to maximise or minimise an objective function | |||

81 | Matrices – Linear systems | Linear Systems with Matrices | |

Objective: To identify and describe matrices and perform row operations in matrices | |||

82 | Matrices – Linear systems | Row Echelon Form | |

Objective: To identify and create matrices in row echelon form and to solve systems of equations | |||

83 | Matrices – Linear systems | Gauss Jordan Elimination | |

Objective: To use the Gauss Jordan Elimination Method to solve systems of linear equations | |||

84 | Co-ordinate geometry part 2 | Intercept form of a straight line: find the equation when given x and y | |

Objective: To find the equation of a line given the x-axis and y-axis intercepts | |||

85 | Co-ordinate geometry part 2 | Parallel Lines: identify equation of a line parallel to another | |

Objective: To change the standard form of a straight line equation to the y = mx + b form | |||

86 | Co-ordinate geometry part 2 | Perpendicular Lines | |

Objective: To identify the equation of a line that is perpendicular to a given linear equation | |||

87 | Co-ordinate geometry part 2 | Inequalities on the Number Plane | |

Objective: To identify the graph which matches a given inequality | |||

88 | Co-ordinate geometry part 2 | Perpendicular Distance | |

Objective: To calculate the perpendicular distance from a point to a line and between lines | |||

89 | Co-ordinate geometry part 2 | Line through the intersection of two given lines | |

Objective: To determine the equation of a line passing through the intersection of two lines | |||

90 | Co-ordinate geometry part 2 | Angles between two lines | |

Objective: To find the angle between two given straight lines | |||

91 | Co-ordinate geometry part 2 | Internal and external division of an interval | |

Objective: To find the value of k given the interval AB is divided at point P in the ratio of k to some value | |||

92 | Series and sequences part 1 | General Sequences | |

Objective: To use the general form of the n’th term of a sequence to find the first 3 terms | |||

93 | Series and sequences part 1 | Finding Tn Given Sn | |

Objective: To find the value of the n’th term in a sequence given the sum of the first n terms | |||

94 | Series and sequences part 1 | The Arithmetic Progression | |

Objective: To find the common difference of a given arithmetic progression | |||

95 | Series and sequences part 1 | Finding the position of a term in an A.P. | |

Objective: To find the position of a term in a sequence, given an arithmetic progression and a value term | |||

96 | Series and sequences part 1 | Given two terms of A.P. find the sequence | |

Objective: To find the first term and the common difference in an A.P. given the values and positions of two terms | |||

97 | Series and sequences part 1 | Arithmetic Means | |

Objective: To find the arithmetic mean of two values | |||

98 | Series and sequences part 1 | The sum to n terms of an A.P. | |

Objective: To find the sum of n terms of an arithmetic progression given the first three terms | |||

99 | Series and sequences part 1 | The Geometric Progression | |

Objective: To find the common ratio of a given geometric progression | |||

100 | Series and sequences part 1 | Finding the position of a term in a G.P. | |

Objective: To find the place of a term in a given geometric progression | |||

101 | Series and sequences part 1 | Given two terms of G.P. find the sequence | |

Objective: To find the first term given two terms of a geometric progression | |||

102 | Logic | Mathematical induction | |

Objective: To use proof by mathematical induction | |||

103 | Series and sequences part 2 | Geometric Means | |

Objective: To find geometric means of a and b and insert geometric means between 2 endpoints | |||

104 | Series and sequences part 2 | The sum to n terms of a G.P. | |

Objective: To find the sum of n terms of a sequence | |||

105 | Series and sequences part 2 | Sigma notation | |

Objective: To evaluate progressions using sigma notation | |||

106 | Series and sequences part 2 | Limiting Sum or Sum to Infinity | |

Objective: To find the limiting sum of a sequence | |||

107 | Series and sequences part 2 | Recurring Decimals and the Infinite G.P. | |

Objective: To express recurring decimals as a G.P. and to express the limiting sum as a fraction | |||

108 | Series and sequences part 2 | Compound Interest | |

Objective: To calculate the compound interest of an investment using A=P(1+r/100)^n | |||

109 | Series and sequences part 2 | Superannuation | |

Objective: To calculate the end value of adding a regular amount to a fund with stable interest paid over time | |||

110 | Series and sequences part 2 | Time Payments | |

Objective: To calculate the payments required to pay off a loan | |||

111 | Series and sequences part 2 | Applications of arithmetic sequences | |

Objective: To learn about practical situations with arithmetic series | |||

112 | Conic sections | Introduction to Conic Sections and Their General Equation | |

Objective: To identify the conic from its equation by examining the coefficients of x^2 and y^2 | |||

113 | Probability | Counting techniques and ordered selections | |

Objective: To use counting techniques in probability | |||

114 | Probability | Unordered selections – combinations | |

Objective: To use the nCr formula to solve problems where unordered selections occur | |||

115 | Conic sections | The Parabola | |

Objective: To examine the properties of parabolas of the forms x^2 = 4py and y^2 = 4px | |||

116 | Conic sections | Circles | |

Objective: To graph circles of the form x^2 + y^2 = r^2 and to form the equation of the given circles | |||

117 | Conic sections | The Ellipsis | |

Objective: To identify ellipses of the form x^2/a^2 + y^2/b^2 = 1 and to find the equation of ellipses | |||

118 | Conic sections | The Hyperbola | |

Objective: To find the equation of a hyperbola and to derive properties (e.g. vertex) from its equation | |||

119 | Polar coordinates | Polar Coordinates – Plotting and Converting | |

Objective: To plot polar points and convert polar coordinates to rectangular coordinates | |||

120 | Polar coordinates | Converting Rectangular Coordinates to Polar Form | |

Objective: To convert rectangular to polar coordinates | |||

121 | Polar coordinates | Graphing Polar Functions | |

Objective: To write the polar coordinates of a point for selected argument ranges | |||

122 | Calculus part 1 | Limits | |

Objective: To find the limit value of a function as x approaches n | |||

123 | Calculus part 1 | Differentiation from First Principles | |

Objective: To differentiate functions from first principles | |||

124 | Calculus part 1 | Differentiation of y = x to the power of n | |

Objective: To differentiate algebraic functions using the laws of differentiation | |||

125 | Calculus part 1 | Meaning of dy over dx – Equations of Tangents and Normals | |

Objective: To find and use the slope of tangents and normals | |||

126 | Exam | Exam – Grades 11 – 12: Pre-Calculus | |

Objective: Exam |