# General Preliminary Year 11 Mathematics – New South Wales (NSW)

### NSW General Preliminary Year 11 Mathematics

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

1 | Study Plan | Study plan – Year 11 | |

Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. | |||

2 | Statistics | Frequency distribution table | |

Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. | |||

3 | Statistics | Frequency histograms and polygons | |

Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. | |||

4 | Statistics | Relative frequency | |

Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. | |||

5 | Statistics | The range. | |

Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. | |||

6 | Statistic-probability | The mode | |

Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. | |||

7 | Statistic-probability | The mean | |

Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. | |||

8 | Statistic-probability | The median | |

Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores | |||

9 | Statistic-probability | Cumulative frequency | |

Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. | |||

10 | Statistic-probability | Calculating the median from a frequency distribution | |

Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. | |||

11 | Statistics | Stem and Leaf Plots along with Box and Whisker Plots | |

Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. | |||

12 | Area | Finding the area of a triangle and other composite shapes. | |

Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas. | |||

13 | Area | Larger areas: square metre, hectare, square kilometre. | |

Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. | |||

14 | Area | Area of a trapezium. | |

Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. | |||

15 | Area | Area of a rhombus. | |

Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. | |||

16 | Area | Area of a circle. | |

Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. | |||

17 | Surface area | Surface area of a cube/rectangular prism. | |

Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. | |||

18 | Surface area | Surface area of a triangular/trapezoidal prism. | |

Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. | |||

19 | Surface area | Surface area of pyramids | |

Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. | |||

20 | Capacity | Converting between volume and capacity using millilitres and litres | |

Objective: On completion of the lesson the student will be able to convert between units of capacity. | |||

21 | Weight/mass | The tonne – converting units and problems | |

Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. | |||

22 | Volume | Finding the volume of prisms | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. | |||

23 | Volume | Volume of a cylinder and sphere. | |

Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. | |||

24 | Volume | Volume of pyramids and cones. | |

Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. | |||

25 | Pythagoras | Find the hypotenuse | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. | |||

26 | Pythagoras | Pythagorean triples | |

Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. | |||

27 | Pythagoras | Find the hypotenuse Part 2 | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. | |||

28 | Pythagoras | Calculating a leg of a right-angled triangle | |

Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. | |||

29 | Trigonometry-ratios | Trigonometric ratios. | |

Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op | |||

30 | Trigonometry-ratios | Using the calculator. | |

Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. | |||

31 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 1 Sine]. | |

Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. | |||

32 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. | |

Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. | |||

33 | Trigonometry-ratios | Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. | |

Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. | |||

34 | Trigonometry-ratios | Unknown in the denominator. [Case 4]. | |

Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. | |||

35 | Trigonometry-compass | Bearings – the compass. | |

Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. | |||

36 | Trigonometry-elevation | Angles of elevation and depression. | |

Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. | |||

37 | Trigonometry-practical | Trigonometric ratios in practical situations. | |

Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. | |||

38 | Trigonometry-ratios | Using the calculator to find an angle given a trigonometric ratio. | |

Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. | |||

39 | Trigonometry- ratios | Using the trigonometric ratios to find an angle in a right-angled triangle. | |

Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. | |||

40 | Trigonometry-exact ratios | Trigonometric ratios of 30., 45. and 60. – exact ratios. | |

Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. | |||

41 | Scientific notation | Scientific notation with larger numbers | |

Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. | |||

42 | Scientific notation | Scientific notation with small numbers | |

Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. | |||

43 | Scientific notation | Changing scientific notation to numerals | |

Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. | |||

44 | Significant figures | Significant figures | |

Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. | |||

45 | Algebraic expressions | Expanding algebraic expressions: negative multiplier | |

Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. | |||

46 | Algebraic expressions | Expanding and simplifying algebraic expressions | |

Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. | |||

47 | Algebraic expressions-products | Products in simplification of algebraic expressions | |

Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. | |||

48 | Algebraic equations | Solving two step equations | |

Objective: On completion of the lesson the student will be able to solve two step equations. | |||

49 | Algebraic equations | Solving equations containing binomial expressions | |

Objective: On completion of the lesson the student will be able to move terms in binomial equations. | |||

50 | Algebraic equations | Equations involving grouping symbols. | |

Objective: On completion of the lesson the student will be able to solve equations using grouping symbols | |||

51 | Algebraic equations | Equations involving fractions. | |

Objective: On completion of the lesson the student will know how to solve equations using fractions. | |||

52 | Algebra-factorising | Simplifying easy algebraic fractions. | |

Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. | |||

53 | Algebraic fractions | Simplifying algebraic fractions using the index laws. | |

Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. | |||

54 | Algebra- formulae | Equations resulting from substitution into formulae. | |

Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. | |||

55 | Simultaneous equns | Simultaneous equations | |

Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. | |||

56 | Coordinate Geometry-straight line | The straight line. | |

Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. | |||

57 | Coordinate Geometry-slope, etc. | Lines through the origin. | |

Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. | |||

58 | Coordinate Geometry-intercept | Slope intercept form of a line. | |

Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. | |||

59 | Co-ordinate Geometry-Intercept form | Intercept form of a straight line: find the equation when given x and y | |

Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. | |||

60 | Similar triangles | Similar triangles | |

Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. | |||

61 | Similar triangles | Using similar triangles to calculate lengths | |

Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. | |||

62 | Overlapping triangles | Examples involving overlapping triangles | |

Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. | |||

63 | Statistic-probability | Probability of Simple Events | |

Objective: On completion of the lesson the student will be able to understand the probability of simple events. | |||

64 | Statistic-probability | Rolling a pair of dice | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. | |||

65 | Statistic-probability | Experimental probability | |

Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. | |||

66 | Statistic-probability | The complementary result .. | |

Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. | |||

67 | Statistic-probability | P[A or B] When A and B are both mutually and NOT mutually exclusive | |

Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. | |||

68 | Sequences and Series-Compound interest | Compound interest | |

Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. | |||

69 | Exam | Exam – Year 11 – Stage 6 – General Mathematics Preliminary | |

Objective: Exam |