Year 11 (NCEA) Mathematics – New Zealand
Year 11 (NCEA) Mathematics
#  TOPIC  TITLE  

1  Study Plan  Study plan – Year 11  
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.  
2  Pythagoras  Pythagorean triples  
Objective: On completion of the lesson the student will be able to use the 345 Pythagorean triple.  
3  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.  
4  Pythagoras  Calculating a leg of a rightangled 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.  
5  Pythagoras  Proofs of Pythagoras theorem  
Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem  
6  Surds  Introducing surds  
Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers.  
7  Surds  Some rules for the operations with surds  
Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds.  
8  Surds  Simplifying surds  
Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication.  
9  Surds  Creating entire surds  
Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds  
10  Surds  Adding and subtracting like surds  
Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds.  
11  Surds  Expanding surds  
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.  
12  Surface area  Surface area of a triangular/trapezoidal prism.  
Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula.  
13  Surface area  Surface area of a cylinder and sphere.  
Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula.  
14  Surface area  Surface area of pyramids  
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.  
15  Surface area  Surface area of cones  
Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul  
16  Surface area  Surface area of composite solids  
Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids.  
17  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.  
18  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.  
19  Volume  Finding the volume of prisms  
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.  
20  Volume  Volume of a cylinder and sphere.  
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.  
21  Volume  Volume of pyramids and cones.  
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones.  
22  Volume  Composite solids.  
Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.  
23  Scientific notation  Scientific notation with larger numbers  
Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation.  
24  Scientific notation  Scientific notation with small numbers  
Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation.  
25  Scientific notation  Changing scientific notation to numerals  
Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation.  
26  Significant figures  Significant figures  
Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures.  
27  Trigonometryratios  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  
28  Trigonometryratios  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.  
29  Trigonometryratios  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.  
30  Trigonometryratios  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.  
31  Trigonometryratios  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.  
32  Trigonometryratios  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.  
33  Trigonometryelevation  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.  
34  Trigonometrypractical  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.  
35  Trigonometryratios  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.  
36  Trigonometry ratios  Using the trigonometric ratios to find an angle in a rightangled 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.  
37  Number theory – sets  Number sets and their members  
Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system.  
38  Number theory – operations  Properties of real numbers using addition and multiplication  
Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication.  
39  Number theory – equations  Transformations that produce equivalent equations  
Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations.  
40  Geometryangles  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.  
41  Geometryangles  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.  
42  Geometryangles  Angles at a Point.  
Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems.  
43  Geometryangles  Parallel Lines.  
Objective: On completion of the lesson the student will able to identify corresponding, cointerior and alternate angles.  
44  Geometryproblems  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.  
45  Geometrytriangles  Exterior angle theorem  
Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions.  
46  Geometryconstructions  Geometric constructions  
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.  
47  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.  
48  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.  
49  Geometryconstructions  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.  
50  Geometryconstructions  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.  
51  Geometryconstructions  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.  
52  Geometryquadrilaterals  Midsegments of Triangles  
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.  
53  Geometryquadrilaterals  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.  
54  Geometryquadrilaterals  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.  
55  Geometryquadrilaterals  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.  
56  Geometryquadrilaterals  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.  
57  Geometryquadrilaterals  The quadrilateral family and coordinate methods in geometry  
Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties.  
58  Geometrylocus  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.  
59  Geometrylocus  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.  
60  Geometry problems  More difficult exercises involving parallel lines  
Objective: On completion of the lesson the student will able to identify corresponding, cointerior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log  
61  Geometryreasoning  Further difficult exercises involving formal reasoning  
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.  
62  Geometrypolygons  Angles of regular polygons  
Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees.  
63  Geometrycongruence  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.  
64  Geometrycongruence  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.  
65  Geometrycongruence  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.  
66  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.  
67  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.  
68  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.  
69  Quadratic equations  Introduction to quadratic equations.  
Objective: On completion of the lesson the student will understand simple quadratic equations.  
70  Quadratic equations  Quadratic equations with factorisation.  
Objective: On completion of the lesson the student will be able to find both roots of a quadratic equation by factorising.  
71  Quadratic equations  Solving quadratic equations.  
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.  
72  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.  
73  Statisticprobability  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.  
74  Statisticprobability  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.  
75  Statisticprobability  The median  
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores  
76  Statisticprobability  Cumulative frequency  
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.  
77  Statisticprobability  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.  
78  Statisticprobability  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.  
79  Statisticprobability  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.  
80  Statisticprobability  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.  
81  Statisticprobability  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.  
82  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.  
83  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.  
84  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.  
85  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.  
86  Translations  Transformations – reflections  
Objective: On completion of the lesson the student will be able to take a preimage and using the appropriate techniques, accurately show its image after reflection.  
87  Geometric transformations  Geometry transformations without matrices: reflection (Stage 2)  
Objective: On completion of this lesson the student will use and understand the language used in geometric transformations and perform reflections in a number plane.  
88  Geometric transformations  Geometry transformations without matrices: translation (Stage 2)  
Objective: On completion of this lesson the student will perform translations in a number plane.  
89  Geometric transformations  Geometry transformations without matrices: rotation (Stage 2)  
Objective: On completion of this lesson the student will perform and construct rotations.  
90  Geometric transformations  Geometry transformations without matrices: dilation or enlargement (Stage 2)  
Objective: On completion of this lesson the student will perform the noncongruent transformation of dilation or emlargement and calculate scale factor.  
91  Geometric transformations  The definition and concept of combined transformations resulting in an equivalent single transformation.  
Objective: On completion of this lesson the student will combine reflections and glide transformations to produce single isometric transformations.  
92  Algebraic equations  Solving two step equations  
Objective: On completion of the lesson the student will be able to solve two step equations.  
93  Algebraic equations  Solving equations containing binomial expressions  
Objective: On completion of the lesson the student will be able to move terms in binomial equations.  
94  Algebraic equations  Equations involving grouping symbols.  
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols  
95  Rules for indices/exponents  Adding indices when multiplying terms with the same base  
Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base.  
96  Rules for indices/exponents  Subtracting indices when dividing terms with the same base  
Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base.  
97  Rules for indices/exponents  Multiplying indices when raising a power to a power  
Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power.  
98  Rules for indices/exponents  Multiplying indices when raising to more than one term  
Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power.  
99  Rules for indices/exponents  Terms raised to the power of zero  
Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero.  
100  Rules for indices/exponents  Negative Indices  
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices.  
101  Fractional indices/exponents  Fractional indices  
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.  
102  Fractional indices/exponents  Complex fractions as indices  
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices.  
103  Algebraic equations  Equations involving fractions.  
Objective: On completion of the lesson the student will know how to solve equations using fractions.  
104  Algebra formulae  Equations resulting from substitution into formulae.  
Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations.  
105  Algebra formulae  Changing the subject of the formula.  
Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously.  
106  Algebrainequalities  Solving Inequalities.  
Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities.  
107  Algebrafactorising  Simplifying easy algebraic fractions.  
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.  
108  Algebraic fractions  Simplifying algebraic fractions using the index laws.  
Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies.  
109  Algebranegative indices  Algebraic fractions resulting in negative indices.  
Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index.  
110  Factorisation  Factorisation of algebraic fractions including binomials.  
Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods.  
111  Algebraic fractionsbinomial  Cancelling binomial factors in algebraic fractions.  
Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions.  
112  Absolute value or modulus  Simplifying absolute values  
Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers.  
113  Absolute value or modulus  Solving for the variable  
Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value.  
114  Absolute value or modulus  Solving and graphing inequalities  
Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value.  
115  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.  
116  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.  
117  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.  
118  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.  
119  Geometrycircles  The equation of a circle: to find radii of circles  
Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius.  
120  Geometrycircles  The semicircle: to select the equation given the semi circle and vice versa  
Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle.  
121  Geometryparabola  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.  
122  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.  
123  Functions and graphs  Graphing perfect squares: y=(ax) 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.  
124  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.  
125  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.  
126  Graphingpolynomials  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.  
127  Graphingpolynomials  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.  
128  Graphingcubic 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.  
129  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  
130  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.  
131  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.  
132  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  
133  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  
134  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 midpoint 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 midpoint of the chord is perpendicular’  
135  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.  
136  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.  
137  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.  
138  Circle Geometry  Theorem – The angle of a semicircle is a right angle.  
Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semicircle is a rightangle.’  
139  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.  
140  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.  
141  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.  
142  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.  
143  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.  
144  Coordinate GeometryTwo 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.  
145  Coordinate GeometryIntercept 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.  
146  Coordinate GeometryParallel 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.  
147  Coordinate GeometryPerpendicular 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.  
148  Coordinate GeometryInequalities  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.  
149  Coordinate GeometryTheorems  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.  
150  Coordinate GeometryTheorems  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.  
151  Coordinate GeometryTheorems  Angles between two lines  
Objective: On completion of the lesson the student will be able to calculate the angle between given lines and derive the equation of a line given its angle to another line.  
152  Coordinate GeometryTheorems  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.  
153  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.  
154  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.  
155  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  
156  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.  
157  Statistics  Scatter Diagrams  
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.  
158  Trigonometryexact 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.  
159  Trigonometrycosine 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.  
160  Trigonometrycosine 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.  
161  Trigonometrysine 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.  
162  Trigonometrysine 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 nonincluded angle.  
163  Trigonometryareas  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.  
164  Graphing binomials  Binomial products.  
Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression.  
165  Graphing binomials  Binomial products with negative multiplier  
Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products.  
166  Graphing binomials  Binomial products [nonmonic].  
Objective: On completion of the lesson, the student will have examined more complex examples with binomial products.  
167  Squaring binomial  Squaring a binomial. [monic]  
Objective: On completion of the lesson the student should understand the simple onestep process of squaring a monic binomial.  
168  Squaring binomial  Squaring a binomial [nonmonic].  
Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials.  
169  Factorising  Expansions leading to the difference of two squares  
Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares.  
170  Algebraic expressionsproducts  Products in simplification of algebraic expressions  
Objective: On completion of the lesson the student will understand simplification of algebraic expressions in stepbystep processing.  
171  Algebraic expressionslarger expansions  Algebraic Expressions – Larger expansions.  
Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions.  
172  Algebrahighest common factor  Highest common factor.  
Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression.  
173  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.  
174  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.  
175  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.  
176  Quadratic trinomials  Quadratic trinomials [monic] – Case 1.  
Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive.  
177  Factorising quads  Factorising quadratic trinomials [monic] – Case 2.  
Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative.  
178  Factorising quads  Factorising quadratic trinomials [monic] – Case 3.  
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.  
179  Factorising quads  Factorising quadratic trinomials [monic] – Case 4.  
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.  
180  Factorising quads  Factorisation of nonmonic quadratic trinomials  
Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial.  
181  Factorising quads  Factorisation of nonmonic quadratic trinomials – moon method  
Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method.  
182  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.  
183  Algebraic fractions  Simplifying algebraic fractions.  
Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point.  
184  Logic  Inductive and deductive reasoning  
Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive.  
185  Logic  Definition and use of counter examples  
Objective: On completion of this lesson the student will be able to create counter examples to statements.  
186  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.  
187  Logic  Mathematical induction  
Objective: On completion of the lesson the student will be able to perform the process of mathematical induction for simple series.  
188  Quadratic equations  Completing the square  
Objective: On completion of the lesson the student will understand the process of completing the square.  
189  Quadratic equations  Solving quadratic equations by completing the square  
Objective: On completion of the lesson the student will understand the reasoning behind completing the square.  
190  Quadratic equations  The quadratic formula  
Objective: On completion of the lesson the student will be familiar with the quadratic formula.  
191  Quadratic equations  Problem solving with quadratic equations  
Objective: On completion of the lesson the student will be able to express a problem as a quadratic equation and then solve it.  
192  Quadratic equations  Solving simultaneous quadratic equations graphically  
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..  
193  Coordinate Geometrythe 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.  
194  Coordinate Geometrymidpoint, slope  Midpoint formula  
Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically.  
195  Coordinate Geometrygradient  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 xaxis; or its rise and run.  
196  Coordinate Geometrygradient  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.  
197  Coordinate Geometrystraight 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.  
198  Coordinate Geometryslope, 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.  
199  Coordinate Geometryequation 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.  
200  Coordinate Geometryintercept  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.  
201  Coordinate Geometrypoint 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.  
202  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.  
203  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.  
204  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.  
205  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.  
206  Linear systems  Rowechelon form (Stage 2)  
Objective: On completion of the lesson the student will process matrices formed from linear systems of equations using the rowechelon form.  
207  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.  
208  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.  
209  Functions  Notation and evaluations  
Objective: On completion of the lesson the student will be understand different notations for functions.  
210  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.  
211  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.  
212  Functions  Evaluating and graphing piecewise functions  
Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions.  
213  Functions  Functions combinations  
Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains.  
214  Functions  Composition of functions  
Objective: On completion of the lesson the student will understand composition of functions or a function of a function.  
215  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.  
216  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.  
217  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.  
218  Trigreciprocal 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.  
219  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.  
220  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.  
221  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.  
222  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.  
223  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.  
224  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.  
225  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.  
226  Graph reciprocals  Graphing the trigonometric ratios – IV Reciprocal ratios.  
Objective: On completion of the lesson the student will know how to recognise and draw the curves of the reciprocal ratios: cosec, sec and cot.  
227  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.  
228  Trig equations  Solving trigonometric equations – Type I.  
Objective: On completion of the lesson the student will solve simple trig equations with restricted domains.  
229  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.  
230  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.  
231  LogarithmsPower 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.  
232  LogarithmsEquations 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.  
233  LogarithmsEquations 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.  
234  LogarithmsLog laws  Laws of logarithms.  
Objective: On completion of the lesson the student will be familiar with 5 logarithm laws.  
235  LogarithmsLog 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.  
236  LogarithmsLog 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.  
237  LogarithmsLog 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.  
238  LogarithmsEquations and logs  Equations involving logarithms.  
Objective: On completion of the lesson the student will be able to solve equations with log terms.  
239  LogarithmsLogs 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.  
240  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.  
241  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.  
242  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.  
243  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.  
244  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  
245  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.  
246  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.  
247  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.  
248  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.  
249  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.  
250  Calculus  Limits  
Objective: On completion of the lesson the student will be able to solve problems using limiting sum rule.  
251  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.  
252  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.  
253  Calculusdifferential, 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.  
254  Calculusdifferential, 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.  
255  Calculusdifferential, 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.  
256  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.  
257  Calculus2nd 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.  
258  Sequences and SeriesGeometric 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.  
259  Sequences and SeriesSum 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).  
260  Sequences and SeriesSigma notation  Sigma notation  
Objective: On completion of the G.P. lesson the student will be familiar with the sigma notation and how it operates.  
261  Sequences and SeriesSuminfinity  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.  
262  Sequences and SeriesRecurring 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.  
263  Sequences and SeriesCompound 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.  
264  Sequences and SeriesSuperannuation  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.  
265  Sequences and SeriesTime 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.  
266  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.  
267  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.  
268  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.  
269  Calculus – Integration  Integration – antidifferentiation, 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.  
270  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, rearrange an expression to suit the formula, and use correct limits in the formula to evaluate an area.  
271  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, rearrange an expression to suit the formula, and then calculate a result to a prescribed accuracy.  
272  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 subintervals, set up a table of values, then apply the Trapezoidal Rule, or Simpson’s Rule to approximate an area beneath a curve.  
273  Exam  Exam – Year 11  
Objective: Exam 