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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

# 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
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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
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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
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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
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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
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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
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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
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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
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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
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
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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
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height
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
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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
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height
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
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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
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign
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
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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
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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
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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
Objective: To use diagrams, number lines and equivalent fractions to compare and order 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
Objective: To use and understand place value to show whole numbers, tenths and hundredths as decimals
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
Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign
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
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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
Objective: To solve algebraic inequalities requiring (at times) change of direction of inequality sign
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
Objective: On completion of the lesson the student will be aware of common factors and recognize the difference of two squares.
69 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.
70 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.
71 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.
72 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.
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
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
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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
Objective: To calculate the areas of rectangles and parallelograms using Area of Rectangle = Length x Height and Area of Parallelogram = Base x Height
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
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Grades 11 - 12: Probability - Statistics Mathematics

# TOPIC TITLE
1 Self Assessment Self Assessment – Grades 11 – 12: Probability – Statistics
Objective: Assessment
2 Probability Simple events
Objective: To find the probability of events using sample space and event set (E) and P(E) = n(E)/n(S)
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
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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
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Literacy

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