# Year 12 B and C Mathematics – Queensland

### QLD Year 12 B and C Mathematics

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

1 | Study Plan | Study plan – Year 12 |

2 | Geometry-parabola | The parabola: to describe properties of a parabola from its equation |

3 | Functions and graphs | Quadratic polynomials of the form y = ax. + bx + c. |

4 | Functions and graphs | Graphing perfect squares: y=(a-x) squared |

5 | Graphing roots | Graphing irrational roots |

6 | Factors by grouping | Factors by grouping. |

7 | Difference of 2 squares | Difference of two squares |

8 | Common fact and diff | Common factor and the difference of two squares |

9 | Quadratic trinomials | Quadratic trinomials [monic] – Case 1. |

10 | Factorising quads | Factorising quadratic trinomials [monic] – Case 2. |

11 | Factorising quads | Factorising quadratic trinomials [monic] – Case 3. |

12 | Factorising quads | Factorising quadratic trinomials [monic] – Case 4. |

13 | Factorising quads | Factorisation of non-monic quadratic trinomials |

14 | Factorising quads | Factorisation of non-monic quadratic trinomials – moon method |

15 | Sum/diff 2 cubes | Sum and difference of two cubes. |

16 | Algebraic fractions | Simplifying algebraic fractions. |

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

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

19 | Graphing-cubic curves | Graphing cubic curves |

20 | Absolute value equations | Absolute value equations |

21 | Rect.hyperbola | The rectangular hyperbola. |

22 | Exponential function | The exponential function. |

23 | Log functions | Logarithmic functions. |

24 | Functions | Definition, domain and range |

25 | Functions | Notation and evaluations |

26 | Functions | More on domain and range |

27 | Functions | Domain and range from graphical representations |

28 | Functions | Evaluating and graphing piecewise functions |

29 | Functions | Functions combinations |

30 | Functions | Composition of functions |

31 | Functions | Inverse functions |

32 | Functions | Rational functions Part 1 |

33 | Functions | Rational functions Part 2 |

34 | Functions | Parametric equations (Stage 2) |

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

36 | Functions | Parametric functions (Stage 2) |

37 | Algebra-polynomials | Introduction to polynomials |

38 | Algebra-polynomials | The sum, difference and product of two polynomials. |

39 | Algebra-polynomials | Polynomials and long division. |

40 | Remainder theorem | The remainder theorem. |

41 | Remainder theorem | More on remainder theorem |

42 | Factor theorem | The factor theorem |

43 | Factor theorem | More on the factor theorem |

44 | Factor theorem | Complete factorisations using the factor theorem |

45 | Polynomial equations | Polynomial equations |

46 | Graphs, polynomials | Graphs of polynomials |

47 | Calculus | 10508/Limits”>Limits |

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

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

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

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

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

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

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

55 | Calculus – Curve sketching | Curve sketching |

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

57 | Logarithms-Power of 2 | Powers of 2. |

58 | Logarithms-Equations and logs | Equations of type log x to the base 3 = 4. |

59 | Logarithms-Equations and logs | Equations of type log 32 to the base x = 5. |

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

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

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

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

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

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

66 | Logarithms-Change base formula | Change of base formula |

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

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

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

70 | Sequences and Series-Compound interest | Compound interest |

71 | Sequences and Series-Superannuation | Superannuation. |

72 | Sequences and Series-Time payments | Time payments. |

73 | Sequences and Series | Applications of arithmetic sequences |

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

75 | Calculus – Computation area | Computation of an area |

76 | Calculus – Computation volumes | Computation of volumes of revolution |

77 | Calculus – Trapezoidal and Simpson’s rules | The Trapezium rule and Simpson’s rule |

78 | Statistics – Spread | Measures of spread |

79 | Statistics – Standard deviation | Standard deviation applications |

80 | Statistics – Standard deviation | Normal distribution |

81 | Statistics – Interquartile range | Measures of spread: the interquartile range |

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

83 | Statistics | Scatter Diagrams |

84 | Number theory – sets | Number sets and their members |

85 | Number theory – operations | Properties of real numbers using addition and multiplication |

86 | Number theory – equations | Transformations that produce equivalent equations |

87 | Logic | Inductive and deductive reasoning |

88 | Logic | Definition and use of counter examples |

89 | Logic | Indirect proofs |

90 | Logic | Mathematical induction |

91 | Logic | Conditional statements (converse, inverse and contrapositive) (Stage 2) |

92 | Translations | Transformations – reflections |

93 | Geometric transformations | Geometry transformations without matrices: reflection (Stage 2) |

94 | Geometric transformations | Geometry transformations without matrices: translation (Stage 2) |

95 | Geometric transformations | Geometry transformations without matrices: rotation (Stage 2) |

96 | Geometric transformations | Geometry transformations without matrices: dilation or enlargement (Stage 2) |

97 | Geometric transformations | The definition and concept of combined transformations resulting in an equivalent single transformation. |

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

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

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

101 | Logarithms-Complex numbers | 10467/Absolute+value”>Absolute value |

102 | Logarithms-Complex numbers | Trigonometric form of a complex number |

103 | Logarithms-Complex numbers | Multiplication and division of complex numbers in trig form (Stage 2) |

104 | Logarithms-Complex numbers | DeMoivre’s theorem (Stage 2) |

105 | Logarithms-Complex numbers | The nth root of real and complex numbers (Stage 2) |

106 | Logarithms-Complex numbers | Fundamental theorem of algebra (Stage 2) |

107 | Matrices | Basic concepts – Matrices |

108 | Matrices | Addition and subtraction of matrices |

109 | Matrices | Scalar matrix multiplication |

110 | Matrices | Multiplication of one matrix by another matrix |

111 | Matrices | Translation in the number plane |

112 | Matrices | Translation by matrix multiplication |

113 | Transformations | Special transformations – reflections, rotations and enlargements. |

114 | Vectors | Vectors |

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

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

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

118 | Linear systems | Linear systems with matrices (Stage 2) |

119 | Linear systems | Row-echelon form (Stage 2) |

120 | Linear systems | Gauss Jordan elimination method (Stage 2) |

121 | Conic sections | Introduction to conic sections and their general equation |

122 | Conic sections | The parabola x. = 4ay |

123 | Conic sections | Circles |

124 | Conic sections | Ellipses |

125 | Conic sections | Hyperbola |

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

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

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

129 | Trigonometry | t Formulas (Stage 2) |

130 | Exam | Exam – Year 12 – Maths B & C |