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

### Unit 3BMAS – Year 11 Specialist Mathematics

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

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

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

2 | 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. | |||

3 | 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. | |||

4 | 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. | |||

5 | 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. | |||

6 | 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. | |||

7 | 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. | |||

8 | 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. | |||

9 | Trig-reciprocal ratios | Reciprocal ratios. | |

Objective: On completion of the lesson the student will be able to identify and use the reciprocal trigonometric ratios of sine, cosine and tan, that is, the cosecant, secant and cotangent ratios. | |||

10 | Trig complementary angles | Complementary angle results. | |

Objective: On completion of the lesson the student will understand how to establish the complementary angle results for the sine and cosine ratios and then how to use these results to solve trig equations. | |||

11 | Trig identities | Trigonometric identities | |

Objective: On completion of the lesson the student will be able to simplify trigonometrical expressions and solve trigonometry equations using the knowledge of trig identities. | |||

12 | Trig larger angles | Angles of any magnitude | |

Objective: On completion of the lesson the student will be able to find the trigonometric values of angles of any magnitude by assigning angles to the four quadrants of the circle. | |||

13 | Trig larger angles | Trigonometric ratios of 0°, 90°, 180°, 270° and 360° | |

Objective: On completion of the lesson the student will learn how to find the Trigonometric Ratios of 0, 90, 180, 270 and 360 degrees. | |||

14 | Graph sine | Graphing the trigonometric ratios – I Sine curve. | |

Objective: On completion of the lesson the student will recognise and draw the sine curve exploring changes in amplitude and period. | |||

15 | Graph cosine | Graphing the trigonometric ratios – II Cosine curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the cosine curve exploring changes in amplitude and period. | |||

16 | Graphs tan curve | Graphing the trigonometric ratios – III Tangent curve. | |

Objective: On completion of the lesson the student will know how to recognise and draw the tan curve. | |||

17 | Graph reciprocals | Graphing the trigonometric ratios – IV Reciprocal ratios. | |

Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot. | |||

18 | Trig larger angles | Using one ratio to find another. | |

Objective: On completion of the lesson the student will find other trig ratios given one trig ratio and to work with angles of any magnitude. | |||

19 | Trig equations | Solving trigonometric equations – Type I. | |

Objective: On completion of the lesson the student will solve simple trig equations with restricted domains. | |||

20 | Trig equations | Solving trigonometric equations – Type II. | |

Objective: On completion of the lesson the student will solve trig equations with multiples of theta and restricted domains. | |||

21 | Trig equations | Solving trigonometric equations – Type III. | |

Objective: On completion of the lesson the student will solve trig equations with two trig ratios and restricted domains. | |||

22 | Trigonometry | Sin(A+B) etc sum and difference identities (Stage 2) | |

Objective: On completion of the lesson the student will be using the reference triangles for 30, 45 and 60 degrees with the sum and difference of angles to find additional exact values of trigonometric ratios. | |||

23 | Trigonometry | Double angle formulas (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the double angle trig identities. | |||

24 | Trigonometry | Half angle identities (Stage 2) | |

Objective: On completion of the lesson the student will derive and use the power reducing formulas and the half angle trig identities. | |||

25 | 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. | |||

26 | Sequences and Series-Sum of gp | The sum to n terms of a G.P. | |

Objective: On completion of the lesson the student will understand the formulas and how to use them to solve problems in summing terms of a Geometric Progression (G.P). | |||

27 | Sequences and Series-Sigma notation | Sigma notation | |

Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates. | |||

28 | Sequences and Series-Sum-infinity | Limiting sum or sum to infinity. | |

Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. | |||

29 | Sequences and Series-Recurring decimal infinity | Recurring decimals and the infinite G.P. | |

Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. | |||

30 | 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. | |||

31 | Functions | Notation and evaluations | |

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

32 | 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. | |||

33 | 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. | |||

34 | Functions | Evaluating and graphing piecewise functions | |

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

35 | Functions | Functions combinations | |

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

36 | Functions | Composition of functions | |

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

37 | 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. | |||

38 | 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. | |||

39 | 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. | |||

40 | Functions | Parametric equations (Stage 2) | |

Objective: On completion of the lesson the student will be able to eliminate the parameter from a set of equations and identify appropriate restrictions on the domain and range. | |||

41 | Functions | Polynomial addition etc in combining and simplifying functions (Stage 2) | |

Objective: On completion of the lesson the student will have multiple techniques to understand and construct graphs using algebra. | |||

42 | Calculus | Limits | |

Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule. | |||

43 | Calculus=1st prin | Differentiation from first principles. | |

Objective: On completion of the lesson the student will be able apply the first principles (calculus) formula to find the gradient of a tangent at any point on a continuous curve. | |||

44 | Calculus=1st prin | Differentiation of y = x to the power of n. | |

Objective: On completion of the Calculus lesson the student will be able to differentiate a number of expressions involving x raised to the power of n. | |||

45 | Calculus-differential, integ | Meaning of dy over dx – equations of tangents and normals. | |

Objective: On completion of the Calculus lesson the student will be able to apply differentiation and algebra skills to find the equation of the tangent and the normal to a point on a curve. | |||

46 | Calculus-differential, integ | Function of a function rule, product rule, quotient rule. | |

Objective: On completion of the Calculus lesson the student will understand how to use the chain rule, the product rule and the quotient rule. | |||

47 | Calculus-differential, integ | Increasing, decreasing and stationary functions. | |

Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions. | |||

48 | Calculus | First Derivative – turning points and curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first derivative to find and identify the nature of stationary points on a curve. | |||

49 | Calculus-2nd derivative | The second derivative – concavity. | |

Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion. | |||

50 | Calculus – Curve sketching | Curve sketching | |

Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve. | |||

51 | Calculus – Maxima minima | Practical applications of maxima and minima | |

Objective: On completion of the lesson the student will be able to apply calculus to a suite of simple maxima or minima problems. | |||

52 | Calculus – Integration | Integration – anti-differentiation, primitive function | |

Objective: On completion of the Calculus lesson the student will be able to use rules of integration to find primitives of some simple functions. | |||

53 | Calculus – Computation area | Computation of an area | |

Objective: On completion of the Calculus lesson the student will be able to select an appropriate formula to calculate an area, re-arrange an expression to suit the formula, and use correct limits in the formula to evaluate an area. | |||

54 | Logarithms-Complex numbers | Imaginary numbers and standard form | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for addition and subtraction. | |||

55 | Logarithms-Complex numbers | Complex numbers – multiplication and division | |

Objective: On completion of the lesson the student will use the a+bi form of complex numbers for multiplication and division. | |||

56 | Logarithms-Complex numbers | Plotting complex number and graphical representation | |

Objective: On completion of the lesson the student will use the argand diagram to assist in the addition and subtraction of complex numbers. | |||

57 | Logarithms-Complex numbers | Absolute value | |

Objective: On completion of the lesson the student will use the absolute value or modulus of complex numbers | |||

58 | Exam | Exam – Unit 3BMAS – Year 11 Specialist | |

Objective: Exam |