# Year 12 Maths and Specialist Studies Mathematics – South Australia

### SA Year 12 Maths and Specialist Studies Mathematics

# | TOPIC | TITLE | |
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1 | Study Plan | Study plan – Year 12 Maths and Specialist Studies | |

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

2 | Data | Bar Charts | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in column graphs. | |||

3 | Data | Line graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in line graphs. | |||

4 | Data | Pie and bar graphs. | |

Objective: On completion of the lesson the student will be able to organise, read and summarise information in pie and bar graphs. | |||

5 | 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. | |||

6 | Statistics | Frequency histograms and polygons | |

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

7 | Statistics | Relative frequency | |

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

8 | 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. | |||

9 | 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. | |||

10 | 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. | |||

11 | 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 | |||

12 | Statistic-probability | Cumulative frequency | |

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

13 | 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. | |||

14 | Statistics – grouped data | Calculating mean, mode and median from grouped data | |

Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. | |||

15 | Statistics using a calculator | Statistics and the student calculator | |

Objective: On completion of the lesson the student will be capable of using a scientific calculator in statistics mode to calculate answers to statistical problems. | |||

16 | Statistics – Range and dispersion | Range as a measure of dispersion | |

Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. | |||

17 | Statistics – Spread | Measures of spread | |

Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. | |||

18 | Statistics – Standard deviation | Standard deviation applications | |

Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. | |||

19 | Statistics – Standard deviation | Normal distribution | |

Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. | |||

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

Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range | |||

21 | 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. | |||

22 | Statistics | Scatter Diagrams | |

Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. | |||

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

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

24 | 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. | |||

25 | Statistic-probability | Experimental probability | |

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

26 | Statistic-probability | Tree diagrams – not depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. | |||

27 | Statistic-probability | Tree diagrams – depending on previous outcomes | |

Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. | |||

28 | 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. | |||

29 | 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. | |||

30 | Statistic-probability | Binomial Theorem – Pascal’s Triangle | |

Objective: On completion of this lesson the student will use Pascal’s triangle and the binomial theorem to write the expansion of binomial expressions raised to integer powers. | |||

31 | Statistic-probability | Binomial probabilities using the Binomial Theorem | |

Objective: On completion of the lesson the student will be able to solve certain types of probability questions using the binomial theorem | |||

32 | Statistic-probability | Counting techniques and ordered selections – permutations | |

Objective: On completion of this lesson the student will be competent in using some new counting techniques used for solving probability. | |||

33 | Statistic-probability | Unordered selections – combinations | |

Objective: On completion of the lesson the student will be able to use the formula, n c r both with and without a calculator and be able to use it to solve probability problems where unordered selections happen. | |||

34 | Coordinate Geometry-gradient | Gradient | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. | |||

35 | Coordinate Geometry-gradient | Gradient formula. | |

Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. | |||

36 | 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. | |||

37 | 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. | |||

38 | Coordinate Geometry-equation of line | General form of a line and the x and y Intercepts. | |

Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. | |||

39 | 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. | |||

40 | Coordinate Geometry-point slope | Point slope form of a line | |

Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. | |||

41 | Co-ordinate Geometry-Two point formula | Two point formula: equation of a line which joins a pair of points. | |

Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. | |||

42 | 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. | |||

43 | 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 | |||

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

Objective: On completion of the lesson the student should be able to convert between logarithmic statements and index statements to the power of 2. | |||

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

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the number from which the logarithm evolves. | |||

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

Objective: On completion of the lesson the student will have an enhanced understanding of the definition of a logarithm and how to use it to find an unknown variable which in this case is the base from which the number came. | |||

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

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

48 | 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. | |||

49 | 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. | |||

50 | 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. | |||

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

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

52 | 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. | |||

53 | 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. | |||

54 | 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. | |||

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

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

56 | Calculus | Limits | |

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

57 | 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. | |||

58 | 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. | |||

59 | 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. | |||

60 | 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. | |||

61 | 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. | |||

62 | 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. | |||

63 | 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. | |||

64 | 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. | |||

65 | 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. | |||

66 | 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. | |||

67 | 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. | |||

68 | Calculus – Computation volumes | Computation of volumes of revolution | |

Objective: On completion of the Calculus lesson the student will know how to choose an appropriate volume formula, re-arrange an expression to suit the formula, and then calculate a result to a prescribed accuracy. | |||

69 | Matrices | Basic concepts – Matrices | |

Objective: On completion of the lesson the student will have had an introduction to matrices | |||

70 | Matrices | Addition and subtraction of matrices | |

Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations. | |||

71 | Matrices | Scalar matrix multiplication | |

Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. | |||

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

Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. | |||

73 | Matrices | Translation in the number plane | |

Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. | |||

74 | Matrices | Translation by matrix multiplication | |

Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. | |||

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

Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. | |||

76 | 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. | |||

77 | 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. | |||

78 | 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. | |||

79 | 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. | |||

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

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations. | |||

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

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the row-echelon form. | |||

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

Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the Gauss Jordan elimination method. | |||

83 | 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. | |||

84 | 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. | |||

85 | 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. | |||

86 | 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. | |||

87 | 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. | |||

88 | 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. | |||

89 | 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. | |||

90 | 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. | |||

91 | 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. | |||

92 | 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. | |||

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

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

94 | 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. | |||

95 | 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. | |||

96 | 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. | |||

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

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

98 | 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. | |||

99 | Trigonometry | t Formulas (Stage 2) | |

Objective: On completion of the lesson the student will solve trig equations using the t substitution. | |||

100 | 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. | |||

101 | 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. | |||

102 | 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. | |||

103 | Logarithms-Complex numbers | Absolute value | |

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

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

Objective: On completion of the lesson the student will write complex numbers in trigonometric or polar form. This may also be known as mod-ard form. | |||

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

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

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

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find powers of complex numbers in trig form. | |||

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

Objective: On completion of the lesson the student will use DeMoivre’s theorem to find roots of complex numbers in trig form. | |||

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

Objective: On completion of the lesson the student will recognise and use the fundamental theorem of algebra to find factors for polynomials with real coefficients over the complex number field. | |||

109 | Logic | Inductive and deductive reasoning | |

Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. | |||

110 | Logic | Definition and use of counter examples | |

Objective: On completion of this lesson the student will be able to create counter examples to statements. | |||

111 | Logic | Indirect proofs | |

Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved. | |||

112 | Logic | Mathematical induction | |

Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series. | |||

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

Objective: On completion of the lesson the student will be able to form related conditional statements. | |||

114 | Geometry – triangles | Triangle inequality theorem | |

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

115 | 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. | |||

116 | 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. | |||

117 | 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. | |||

118 | Algebra-polynomials | Introduction to polynomials | |

Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. | |||

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

Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. | |||

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

Objective: On completion of the lesson the student will understand the long division process with polynomials. | |||

121 | Remainder theorem | The remainder theorem. | |

Objective: On completion of the lesson the student will understand how the remainder theorem works and how it can be applied. | |||

122 | Remainder theorem | More on remainder theorem | |

Objective: On completion of the lesson the student will understand the remainder theorem and how it can be applied to solve some interesting questions on finding unknown coefficients of polynomials. | |||

123 | Factor theorem | The factor theorem | |

Objective: On completion of the lesson the student will be able to use the factor theorem and determine if a term in the form of x minus a is a factor of a given polynomial. | |||

124 | Factor theorem | More on the factor theorem | |

Objective: On completion of the lesson the student will fully understand the factor theorem and how it can be applied to solve some questions on finding unknown coefficients of polynomials. | |||

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

Objective: On completion of the lesson the student will be able to factorise polynomials of a higher degree than 2 and to find their zeros. | |||

126 | Polynomial equations | Polynomial equations | |

Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms. | |||

127 | Graphs, polynomials | Graphs of polynomials | |

Objective: On completion of the lesson the student will understand how to graph polynomials using the zeros of polynomials, the y intercepts and the direction of the curves. | |||

128 | Circle Geometry | Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs. | |

Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro | |||

129 | Circle Geometry | Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. | |

Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’ | |||

130 | Circle Geometry | Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal. | |

Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre. | |||

131 | Circle Geometry | Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |

Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. | |||

132 | Circle Geometry | Theorem – Angles in the same segment of a circle are equal. | |

Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. | |||

133 | Circle Geometry | Theorem – The angle of a semi-circle is a right angle. | |

Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ | |||

134 | Circle Geometry | Theorem – The opposite angles of a cyclic quadrilateral are supplementary. | |

Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. | |||

135 | Circle Geometry | Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle. | |

Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite. | |||

136 | Circle Geometry | Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. | |

Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. | |||

137 | Circle Geometry | Theorem – Tangents to a circle from an external point are equal. | |

Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. | |||

138 | Circle Geometry | Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |

Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. | |||

139 | Circle Geometry-cyclic quads | Theorem – If the opposite angles in a quadrilateral are supplementary then the quadrilateral is cyclic. | |

Objective: On completion of the lesson the student will be able to prove that a quadrilateral is cyclic using the supplementary angles theorem. | |||

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

Objective: On completion of the Calculus lesson the student will know how to calculate sub-intervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve. | |||

141 | Functions | Functions combinations | |

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

142 | Functions | Composition of functions | |

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

143 | 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. | |||

144 | 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. | |||

145 | 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. | |||

146 | 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. | |||

147 | 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. | |||

148 | Functions | Parametric functions (Stage 2) | |

Objective: On completion of the lesson the student will understand some standard parametric forms using trigonometric identities, appreciate the beauty of the the graphs that can be generated and an application to projectile motion. | |||

149 | Exam | Exam – Year 12 Maths and Specialist Studies | |

Objective: Exam |