### SA Year 11 Specialist Mathematics

# TOPIC TITLE
1 Study Plan Study plan – Year 11 Specialist
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.
2 Length Using the formal unit of the centimetre to measure length and perimeter
Objective: On completion of the lesson the student will be able to measure length and perimeter in centimetres.
3 Area Area of a circle.
Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle.
4 Area Area of regular polygons and composite figures.
Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula.
5 Tessellating 2-D shapes Use grids to enlarge/reduce 2D shapes
Objective: On completion of the lesson the student will be able to use grids to enlarge or reduce two dimensional shapes and also to recognise shapes that will and won’t tessellate.
6 Geometry-angles Measuring angles
Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is.
7 Geometry-constructions Geometric constructions
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.
8 Pythagoras Find the hypotenuse
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse.
9 Pythagoras Pythagorean triples
Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple.
10 Pythagoras Find the hypotenuse Part 2
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds.
11 Pythagoras Calculating a leg of a right-angled triangle
Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle.
12 Factors by grouping Factors by grouping.
Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression.
13 Difference of 2 squares Difference of two squares
Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors.
14 Common fact and diff Common factor and the difference of two squares
Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares.
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.
Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative.
Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative.
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.
21 Sum/diff 2 cubes Sum and difference of two cubes.
Objective: On completion of the lesson the student will be cognisant of the sum and difference of 2 cubes and be capable of factorising them.
22 Surds Binomial expansions
Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds.
23 Surds Conjugate binomials with surds
Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds.
24 Surds Rationalising the denominator
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds.
25 Surds Rationalising binomial denominators
Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions.
Objective: On completion of the lesson the student will understand simple quadratic equations.
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.
29 Quadratic equations Completing the square
Objective: On completion of the lesson the student will understand the process of completing the square.
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.
Objective: On completion of the lesson the student will be familiar with the quadratic formula.
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.
Objective: On completion of the lesson the student will better understand why quadratic equations have two solutions and will be capable of solving quadratic equations and problems graphically..
34 Geometry-parabola The parabola: to describe properties of a parabola from its equation
Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions.
35 Functions and graphs Quadratic polynomials of the form y = ax. + bx + c.
Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis.
36 Functions and graphs Graphing perfect squares: y=(a-x) squared
Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve.
37 Graphing roots Graphing irrational roots
Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational.
38 Coordinate geometry Solve by graphing
Objective: On completion of the lesson students will use the slope intercept form of a line to create graphs and find points of intersection.
39 Geometry To identify collinear points, coplanar lines and points in 2 and 3 dimensions
Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays.
40 Geometry – angles To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra
Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles.
41 Geometry-constructions Angle bisector construction and its properties (Stage 2)
Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge.
42 Geometry-constructions Circumcentre and incentre (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values.
43 Geometry-constructions Orthocentre and centroids (Stage 2)
Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values.
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.
46 Geometry-quadrilaterals Using the Properties of a Parallelogram
Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram.
47 Geometry-quadrilaterals Proving a Shape is a Parallelogram
Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram.
48 Geometry-quadrilaterals Properties of the Rectangle, Square and Rhombus
Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values.
49 Geometry-quadrilaterals Properties of the Trapezium and Kite
Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values.
Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.
51 Geometry-locus Constructions and loci – single condition
Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition.
52 Geometry-locus Constructions and loci – multiple conditions
Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane.
Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems.
54 Geometry-angles Complementary and supplementary angles
Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems.
55 Geometry-angles Vertically opposite angles
Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems.
56 Geometry-angles Parallel Lines.
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles.
57 Geometry-problems Additional questions involving parallel lines
Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them.
58 Special triangles Special triangles
Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles.
59 Geometry-congruence Congruent triangles, Test 1 and 2
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent.
60 Geometry-congruence Congruent triangles, Test 3 and 4
Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent.
61 Geometry-congruence Proofs and congruent triangles.
Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent.
62 Similar triangles Similar triangles
Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar.
63 Similar triangles Using similar triangles to calculate lengths
Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles.
64 Overlapping triangles Examples involving overlapping triangles
Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles.
65 Geometry – triangles Triangle inequality theorem
Objective: On completion of the lesson the student will understand and use the triangle inequality theorem.
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
67 Simultaneous equns Simultaneous equations
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method.
68 Simultaneous equns Elimination method
Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method.
69 Simultaneous equns Elimination method part 2
Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method.
70 Simultaneous equns Applications of simultaneous equations
Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations.
71 Coordinate Geometry-the plane Distance formula.
Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results.
72 Coordinate Geometry-midpoint, slope Mid-point formula
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.
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.
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.
75 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.
76 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.
77 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.
78 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.
79 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.
80 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
81 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.
82 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.
83 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.
84 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.
85 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.
86 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.
87 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.
88 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.
89 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.
90 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.
91 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.
92 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.
93 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.
94 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.
95 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.
96 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.
97 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.
98 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.
99 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.
100 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.
101 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.
102 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.
103 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.
104 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.
105 Trig equations Solving trigonometric equations – Type I.
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.
106 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.
107 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.
108 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.
109 Trigonometry Double angle formulas (Stage 2)
Objective: On completion of the lesson the student will derive and use the double angle trig identities.
110 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.
111 Trigonometry t Formulas (Stage 2)
Objective: On completion of the lesson the student will solve trig equations using the t substitution.
112 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.
113 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.
114 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.
115 Logarithms-Log laws Laws of logarithms.
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.
116 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.
117 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.
118 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.
119 Logarithms-Equations and logs Equations involving logarithms.
Objective: On completion of the lesson the student will be able to solve equations with log terms.
120 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.
121 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.
122 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.
123 Logarithms-Log curves Working with log curves.
Objective: On completion of the lesson the student will be able to solve problems with log curves
124 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.
125 Co-ordinate Geometry-Intercept form Intercept form of a straight line: find the equation when given x and y
Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line.
126 Co-ordinate Geometry-Parallel lines equations Parallel lines: identify equation of a line parallel to another
Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines.
127 Co-ordinate Geometry-Perpendicular lines Perpendicular lines.
Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line.
128 Co-ordinate Geometry-Inequalities Inequalities on the number plane.
Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities.
129 Co-ordinate Geometry-Theorems Perpendicular distance
Objective: On completion of the lesson the student will be able to derive the formula to calculate the distance between a given point and a given line. The student will also be able to calculate the distance between parallel lines.
130 Co-ordinate Geometry-Theorems Line through intersection of two given lines
Objective: On completion of the lesson the student will be able to calculate the equation of a line which goes through the intersection of two given lines and also through another named point or satisfies some other specified condition.
131 Co-ordinate Geometry-Theorems Internal and external division of an interval
Objective: On completion of the lesson the student will be able to divide an interval according to a given ratio and to calculate what point divides an interval in a given ratio for both internal and external divisions.
132 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.
133 Functions Notation and evaluations
Objective: On completion of the lesson the student will be understand different notations for functions.
134 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.
135 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.
136 Functions Evaluating and graphing piecewise functions
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.
137 Functions Functions combinations
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.
138 Functions Composition of functions
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.
139 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.
140 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.
141 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.
142 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.
143 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
144 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.
145 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.
146 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
147 Conic sections Introduction to conic sections and their general equation
Objective: On completion of the lesson the student will identify the conic section from the coefficients of the equation.
148 Conic sections The parabola x. = 4ay
Objective: On completion of the lesson the student will identify the focus and directrix for a parabola given in standard form.
149 Conic sections Circles
Objective: On completion of the lesson the student will identify the radius of a circle given in standard form.
150 Conic sections Ellipses
Objective: On completion of the lesson the student will identify focus, vertices and axes of an ellipse.
151 Conic sections Hyperbola
Objective: On completion of the lesson the student will identify focus, vertices, axes and asymptotes of a hyperbola.
152 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.
153 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.
154 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.
155 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.
156 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.
157 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.
158 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.
159 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.
160 Logic Inductive and deductive reasoning
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.
161 Logic Definition and use of counter examples
Objective: On completion of this lesson the student will be able to create counter examples to statements.
162 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.
163 Logic Mathematical induction
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.
164 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.
165 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
166 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’
167 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.
168 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.
169 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.
170 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.’
171 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.
172 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.
173 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.
174 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.
175 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.
176 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.
177 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.
178 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.
179 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.
180 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.
181 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
182 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.
183 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.
184 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.
185 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.
186 Geometric Progression Given two terms of G.P., find the sequence.
Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression.
187 Sequences and Series-Geometric means Geometric means.
Objective: On completion of the lesson the student will be able to make a geometric progression between two given terms. This could involve finding one, two, or even larger number of geometric means.
188 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).
189 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.
190 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.
191 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.
192 Sequences and Series-Compound interest Compound interest
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
193 Sequences and Series-Superannuation Superannuation.
Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P.
194 Sequences and Series-Time payments Time payments.
Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan.
195 Sequences and Series Applications of arithmetic sequences
Objective: On completion of the lesson the student will be capable of problems involving practical situations with arithmetic series.
196 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.
197 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.
198 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.
199 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.
200 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.
201 Algebra-polynomials Polynomials and long division.
Objective: On completion of the lesson the student will understand the long division process with polynomials.
202 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.
203 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.
204 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.
205 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.
206 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.
207 Polynomial equations Polynomial equations
Objective: On completion of the lesson the student will be capable of solving polynomial equations given in different forms.
208 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.
209 Roots quad equations Sum and product of roots of quadratic equations
Objective: On completion of the lesson the student will understand the formulas for the sum and product of roots of quadratic polynomials and how to use them. The student will understand how to form a quadratic equation given its roots.
210 Roots quad equations Sum and product of roots of cubic and quartic equations
Objective: On completion of the lesson the student will be able to do problems on the sum and products of roots of cubic and quartic equations.
211 Exam Exam – Year 11 Specialist
Objective: Exam