# Unit 3AMAS – Year 11 Specialist Mathematics – Western Australia

### Unit 3AMAS – Year 11 Specialist Mathematics

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

1 | Study Plan | Self Assessment – Unit 3AMAS – Year 11 Specialist | |

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

2 | Absolute value or modulus | Simplifying absolute values | |

Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers. | |||

3 | Uniform motion | Average speed | |

Objective: On completion of the lesson the student will be able to convert units for speed, distance and time. | |||

4 | Uniform motion | Using subscripted variables | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, distance and time. | |||

5 | Uniform motion | Uniform motion with equal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, equal distances and time. | |||

6 | Uniform motion | Uniform motion adding the distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, adding distances for total distance and time. | |||

7 | Uniform motion | Uniform motion with unequal distances | |

Objective: On completion of the lesson the student will use subscripted variables for calculations of speed, unequal distances and time. | |||

8 | Uniform motion | Uniform motion of all types | |

Objective: On completion of the lesson the student will use all types of subscripted variables for calculations to determine speed, distance and time. | |||

9 | Geometry – triangles | Triangle inequality theorem | |

Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. | |||

10 | Vectors | Vectors | |

Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. | |||

11 | Simultaneous equations | Number of solutions (Stage 2) | |

Objective: On completion of the lesson of the lesson the student will identify simultaneous equations that are consistent, inconsistent or the same. | |||

12 | Vectors | 2 vector addition in 2 and 3D (stage 2) | |

Objective: On completion of the lesson the student will understand and use component forms for vector resolution. | |||

13 | Linear systems | Optimal solutions (Stage 2) – Vectors | |

Objective: On completion of the lesson the student will understand the process of linear programming to find optimal solutions. | |||

14 | Polar coordinates | Plotting polar coordinates and converting polar to rectangular | |

Objective: On completion of the lesson the student will understand the polar coordinate system and relate this to the rectangular coordinate system. | |||

15 | Polar coordinates | Converting rectangular coordinates to polar form | |

Objective: On completion of the lesson the student will understand the polar coordinate system and report these from rectangular coordinates. | |||

16 | Polar coordinates | Write and graph points in polar form with negative vectors (Stage 2) | |

Objective: On completion of the lesson the student will be using negative angles and negative vector lengths. | |||

17 | Geometry-quadrilaterals | Midsegments of Triangles | |

Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. | |||

18 | 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 | |||

19 | 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. | |||

20 | 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. | |||

21 | 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. | |||

22 | 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. | |||

23 | 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. | |||

24 | 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. | |||

25 | 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. | |||

26 | 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. | |||

27 | 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. | |||

28 | 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. | |||

29 | 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. | |||

30 | Trigonometry-cosine rule | The cosine rule to find an unknown side. [Case 1 SAS]. | |

Objective: On completion of the lesson the student will be able to use the cosine rule to find the length of an unknown side of a triangle knowing 2 sides and the included angle. | |||

31 | Trigonometry-cosine rule | The cosine rule to find an unknown angle. [Case 2 SSS]. | |

Objective: On completion of the lesson the student will be able to find the size of an unknown angle of a triangle using the cosine rule given the lengths of the 3 sides. | |||

32 | Trigonometry-sine rule | The sine rule to find an unknown side. Case 1. | |

Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides. | |||

33 | Trigonometry-sine rule | The sine rule to find an unknown angle. Case 2. | |

Objective: On completion of the lesson the student will be able to use the sine rule to find an unknown angle when given 2 sides and a non-included angle. | |||

34 | Trigonometry-areas | The area formula | |

Objective: On completion of the lesson the student will be able to use the sine formula for finding the area of a triangle given 2 sides and the included angle. | |||

35 | Rules for indices/exponents | Adding indices when multiplying terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. | |||

36 | Rules for indices/exponents | Subtracting indices when dividing terms with the same base | |

Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. | |||

37 | Rules for indices/exponents | Multiplying indices when raising a power to a power | |

Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. | |||

38 | Rules for indices/exponents | Multiplying indices when raising to more than one term | |

Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. | |||

39 | Rules for indices/exponents | Terms raised to the power of zero | |

Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. | |||

40 | Rules for indices/exponents | Negative Indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. | |||

41 | Fractional indices/exponents | Fractional indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. | |||

42 | Fractional indices/exponents | Complex fractions as indices | |

Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. | |||

43 | Logarithms-Log laws | Laws of logarithms. | |

Objective: On completion of the lesson the student will be familiar with 5 logarithm laws. | |||

44 | Logarithms-Log laws expansion | Using the log laws to expand logarithmic expressions. | |

Objective: On completion of the lesson the student will be able to use the log laws to expand logarithmic expressions. | |||

45 | Logarithms-Log laws simplifying | Using the log laws to simplify expressions involving logarithms. | |

Objective: On completion of the lesson the student will be able to simplify logarithmic expressions using the log laws. | |||

46 | Logarithms-Log laws numbers | Using the log laws to find the logarithms of numbers. | |

Objective: On completion of the lesson the student will have an enhanced understanding of the use of the log laws and be able to do more applications with numerical examples. | |||

47 | Logarithms-Equations and logs | Equations involving logarithms. | |

Objective: On completion of the lesson the student will be able to solve equations with log terms. | |||

48 | Logarithms-Logs to solve equations | Using logarithms to solve equations. | |

Objective: On completion of the lesson the student will be able to use logarithms to solve index equations with the assistance of a calculator. | |||

49 | Logarithms-Change base formula | Change of base formula | |

Objective: On completion of the lesson the student will have seen the change of base formula for logarithms and be capable of using it to change the logarithm of one base to another base. | |||

50 | Logarithms-Graph-log curve | The graph of the logarithmic curve | |

Objective: On completion of the lesson the student will be able to draw a logarithmic curve to a given base and know the general properties of log curves. | |||

51 | Logarithms-Log curves | Working with log curves. | |

Objective: On completion of the lesson the student will be able to solve problems with log curves | |||

52 | Exponential function | The exponential function. | |

Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. | |||

53 | Log functions | Logarithmic functions. | |

Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit | |||

54 | Absolute value or modulus | Solving for the variable | |

Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. | |||

55 | Absolute value or modulus | Solving and graphing inequalities | |

Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. | |||

56 | Graphing-polynomials | Graphing complex polynomials: quadratics with no real roots | |

Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. | |||

57 | Graphing-polynomials | General equation of a circle: determine and graph the equation | |

Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning. | |||

58 | Graphing-cubic curves | Graphing cubic curves | |

Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. | |||

59 | Absolute value equations | Absolute value equations | |

Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio | |||

60 | Rect.hyperbola | The rectangular hyperbola. | |

Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. | |||

61 | Functions | Definition, domain and range | |

Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. | |||

62 | Functions | Notation and evaluations | |

Objective: On completion of the lesson the student will be understand different notations for functions. | |||

63 | Functions | More on domain and range | |

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. | |||

64 | Functions | Domain and range from graphical representations | |

Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. | |||

65 | Functions | Evaluating and graphing piecewise functions | |

Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. | |||

66 | Functions | Functions combinations | |

Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. | |||

67 | Functions | Composition of functions | |

Objective: On completion of the lesson the student will understand composition of functions or a function of a function. | |||

68 | Functions | Inverse functions | |

Objective: On completion of the lesson the student will be able to find inverse functions, use the notation correctly and the horizontal line test will be used. | |||

69 | Functions | Rational functions Part 1 | |

Objective: On completion of the lesson the student will be able to work with the division of functions and to interpret this on the coordinate number plane showing vertical and horizontal asymptotes. | |||

70 | Functions | Rational functions Part 2 | |

Objective: On completion of the lesson the student will be able to use the degree of polynomials and polynomial division to assist in graphing rational functions on the coordinate number plane showing vertical, horizontal and slant asymptotes. | |||

71 | Sequences and Series | General sequences. | |

Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. | |||

72 | Sequences and Series | Finding Tn given Sn. | |

Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. | |||

73 | Arithmetic Progression | The arithmetic progression | |

Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts. | |||

74 | Arithmetic Progression | Finding the position of a term in an A.P. | |

Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. | |||

75 | Arithmetic Progression | Given two terms of A.P., find the sequence. | |

Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms | |||

76 | Arithmetic Progression | Arithmetic means | |

Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means. | |||

77 | Arithmetic Progression | The sum to n terms of an A.P. | |

Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems. | |||

78 | Geometric Progression | The geometric progression. | |

Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts. | |||

79 | Geometric Progression | Finding the position of a term in a G.P. | |

Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems. | |||

80 | Exam | Exam – Unit 3AMAS – Year 11 Specialist | |

Objective: Exam |