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### 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
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
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