Year 10 (NCEA) Mathematics – New Zealand
Year 10 (NCEA) Mathematics
#  TOPIC  TITLE  

1  Study Plan  Study plan – Year 10  
Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision.  
2  Subtraction  Subtraction with borrowing  
Objective: On completion of the lesson the student will be able to record subtraction number sentences and will understand the need to trade between place value columns using the renaming method  
3  Subtraction  Subtraction of twodigit numbers Involving comparison.  
Objective: On completion of the lesson the student will know how to solve and record the answer to word problems and will understand how estimation helps to find out if an answer is correct.  
4  Subtraction  Subtraction up to the number 999 using the renaming method  
Objective: On completion of the lesson the student will know another way to trade between columns in subtraction using the renaming method. The student will also learn how to solve number sentences with missing numbers.  
5  Subtraction  Subtraction involving four digit numbers and beyond using the renaming method.  
Objective: On completion of the lesson the student will be able to use written methods to solve subtraction problems involving 4 and 5 digit whole numbers.  
6  Area  Finding the area of a triangle and other composite shapes.  
Objective: On completion of the lesson the student will be able calculate areas of triangles and shapes based on triangles, rectangles and parallelograms using given formulas.  
7  Area  Larger areas: square metre, hectare, square kilometre.  
Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit.  
8  Volume  Solving Problems about Volume – Part 2.  
Objective: On completion of the lesson the student will be able to apply strategies to solve problems using rectangular prisms and larger unit.  
9  Capacity  Converting between volume and capacity using millilitres and litres  
Objective: On completion of the lesson the student will be able to convert between units of capacity.  
10  Weight/mass  The tonne – converting units and problems  
Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another.  
11  Area  Area of a trapezium.  
Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula.  
12  Area  Area of a rhombus.  
Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems.  
13  Fractions  Adding and subtracting fractions with different denominators  
Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other.  
14  Fractions  Multiplying mixed numbers (mixed numerals)  
Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form.  
15  Fractions  Finding reciprocals of fractions and mixed numbers (mixed numerals)  
Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals).  
16  Fractions  Dividing fractions  
Objective: On completion of the lesson the student will be able to divide fractions.  
17  Fractions  Dividing mixed numbers (mixed numerals)  
Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals).  
18  Rules properties  Using Order of Operation procedures (BIDMAS) with Fractions  
Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions.  
19  Decimals  Dividing decimals by 10, 100 and 1000  
Objective: On completion of the lesson the student will be able to divide decimal numbers by one hundred and recognise the pattern formed when decimals are divided by ten, one hundred and one thousand.  
20  Decimals  Dividing decimal fractions by whole numbers  
Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers.  
21  Decimals  Dividing numbers by a decimal fraction  
Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction.  
22  Percentages  One quantity as a percentage of another  
Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another.  
23  Time zones  Time zones  
Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions.  
24  Time, distance, speed  Average speed  
Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object.  
25  3D shapes  Recognise nets for prisms, pyramids, cubes and cones  
Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones.  
26  Equations  Problem solving strategies  
Objective: On completion of the lesson the student will be able to recall the steps in a strategy for solving word problems.  
27  Number problems  Problems with numbers.  
Objective: On completion of the lesson the student will be able to solve problems with numbers using a problem solving strategy.  
28  Money  Problems involving money  
Objective: On completion of the lesson the student will be able to solve problems with money.  
29  Length  Problems with length.  
Objective: On completion of the lesson the student will be able to solve problems with length.  
30  Mass  Problems with mass.  
Objective: On completion of the lesson the student will be able to solve problems with mass.  
31  Area  Problems with area.  
Objective: On completion of the lesson the student will be able to solve problems with area.  
32  Volume/capacity  Problems with volume/capacity.  
Objective: Problem Solving: problems involving volume/capacity  
33  Surface area  Surface area of a cube/rectangular prism.  
Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula.  
34  Algebraic expressions  Algebraic expressions.  
Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand.  
35  Algebraic expressions  Substitution into algebraic expressions.  
Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations.  
36  Algebraic expressions  Directed numbers: addition and subtraction.  
Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals.  
37  Algebraic expressions  Directed numbers: multiplication and division.  
Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer.  
38  Algebraic expressions  Simplifying algebraic expressions: adding like terms.  
Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms.  
39  Algebraic expressions  Simplifying algebraic Expressions: subtracting like terms.  
Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction.  
40  Algebraic expressions  Simplifying Algebraic expressions: combining addition and subtraction.  
Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes.  
41  Algebraic expressions  Simplifying algebraic expressions: multiplication  
Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form.  
42  Algebraic expressions  Simplifying algebraic expressions: division  
Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions.  
43  Algebraic expressions  Expanding algebraic expressions: multiplication  
Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step.  
44  Algebraic expressions  Expanding algebraic expressions: negative multiplier  
Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier.  
45  Algebraic expressions  Expanding and simplifying algebraic expressions  
Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions.  
46  Algebraic equations  Solving equations containing addition and subtraction  
Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side.  
47  Algebraic equations  Solving equations containing multiplication and division  
Objective: On completion of the lesson the student will be able to solve simple equations involving all operations.  
48  Trigonometrycompass  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.  
49  Geometryangles  Adjacent angles  
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.  
50  Geometrytriangles  Angle sum of a triangle  
Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems.  
51  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.  
52  Geometryquadrilaterals  Quadrilaterals 

Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees.  
53  Geometryquadrilaterals  Classifying Quadrilaterals  
Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals.  
54  Statistics  Frequency distribution table  
Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table.  
55  Statistics  Frequency histograms and polygons  
Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons.  
56  Statistics  Relative frequency  
Objective: On completion of the lesson the student will be able to collect, display and make judgements about data.  
57  Statisticprobability  Probability of Simple Events  
Objective: On completion of the lesson the student will be able to understand the probability of simple events.  
58  Statisticprobability  Rolling a pair of dice  
Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously.  
59  Statisticprobability  Experimental probability  
Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial.  
60  Pythagoras  Pythagorean triples  
Objective: On completion of the lesson the student will be able to use the 345 Pythagorean triple.  
61  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.  
62  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.  
63  Pythagoras  Proofs of Pythagoras theorem  
Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem  
64  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.  
65  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.  
66  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.  
67  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  
68  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.  
69  Surds  Expanding surds  
Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds.  
70  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.  
71  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.  
72  Surface area  Surface area of pyramids  
Objective: On completion of the lesson the student will be able to find the surface areas of pyramids.  
73  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  
74  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.  
75  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.  
76  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.  
77  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.  
78  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.  
79  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.  
80  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.  
81  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.  
82  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.  
83  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.  
84  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.  
85  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  
86  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.  
87  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.  
88  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.  
89  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.  
90  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.  
91  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.  
92  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.  
93  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.  
94  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.  
95  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.  
96  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.  
97  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.  
98  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.  
99  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.  
100  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.  
101  Geometryangles  Parallel Lines.  
Objective: On completion of the lesson the student will able to identify corresponding, cointerior and alternate angles.  
102  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.  
103  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.  
104  Geometryconstructions  Geometric constructions  
Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses.  
105  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.  
106  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.  
107  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.  
108  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.  
109  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.  
110  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.  
111  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.  
112  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.  
113  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.  
114  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.  
115  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.  
116  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.  
117  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.  
118  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  
119  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.  
120  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.  
121  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.  
122  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.  
123  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.  
124  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.  
125  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.  
126  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.  
127  Quadratic equations  Introduction to quadratic equations.  
Objective: On completion of the lesson the student will understand simple quadratic equations.  
128  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.  
129  Quadratic equations  Solving quadratic equations.  
Objective: On completion of the lesson the student will have gained more confidence in working with quadratic equations.  
130  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.  
131  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.  
132  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.  
133  Statisticprobability  The median  
Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores  
134  Statisticprobability  Cumulative frequency  
Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons.  
135  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.  
136  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.  
137  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.  
138  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.  
139  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.  
140  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.  
141  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.  
142  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.  
143  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.  
144  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.  
145  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.  
146  Geometric transformations  Geometry transformations without matrices: translation (Stage 2)  
Objective: On completion of this lesson the student will perform translations in a number plane.  
147  Geometric transformations  Geometry transformations without matrices: rotation (Stage 2)  
Objective: On completion of this lesson the student will perform and construct rotations.  
148  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.  
149  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.  
150  Algebraic equations  Solving two step equations  
Objective: On completion of the lesson the student will be able to solve two step equations.  
151  Algebraic equations  Solving equations containing binomial expressions  
Objective: On completion of the lesson the student will be able to move terms in binomial equations.  
152  Algebraic equations  Equations involving grouping symbols.  
Objective: On completion of the lesson the student will be able to solve equations using grouping symbols  
153  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.  
154  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.  
155  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.  
156  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.  
157  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.  
158  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.  
159  Fractional indices/exponents  Fractional indices  
Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices.  
160  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.  
161  Algebraic equations  Equations involving fractions.  
Objective: On completion of the lesson the student will know how to solve equations using fractions.  
162  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.  
163  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.  
164  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.  
165  Algebrafactorising  Simplifying easy algebraic fractions.  
Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising.  
166  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.  
167  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.  
168  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.  
169  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.  
170  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.  
171  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.  
172  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.  
173  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.  
174  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.  
175  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.  
176  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.  
177  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.  
178  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.  
179  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.  
180  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.  
181  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.  
182  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.  
183  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.  
184  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.  
185  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.  
186  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.  
187  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  
188  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.  
189  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.  
190  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  
191  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  
192  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’  
193  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.  
194  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.  
195  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.  
196  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.’  
197  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.  
198  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.  
199  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.  
200  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.  
201  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.  
202  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.  
203  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.  
204  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.  
205  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.  
206  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.  
207  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.  
208  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.  
209  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.  
210  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.  
211  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.  
212  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.  
213  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  
214  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.  
215  Statistics  Scatter Diagrams  
Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these.  
216  Exam  Exam – Year 10  
Objective: Exam 