Chapter 1

65

Define the types of numbers (natural numbers, integers, prime numbers and composite numbers, real numbers, rational and irrational numbers)

Factors and multiples

Prime factors

Highest common factor and lowest common multiple

Prime numbers and composite numbers

Squares and square roots

Cubes and cube roots

Using a number line

Adding and subtracting integers

Word problems - Integers

Rounding whole numbers

Rounding decimals

Significant figures

Estimate answers to calculations (e.g. 57 x 246)

Upper and lower bounds

Calculating with upper and lower bounds

Explanation of different mathematical symbols

Place values and comparing decimals

Comparing fractions

Using a scientific calculator to do simple calculations

Types of fractions

Mixed to improper

Improper to mixed

Convert decimals to fractions

Fractions to percentages

Percentages to fractions

Recurring decimals to fractions

Multiplication and division

Long division

Order of operations

Addition and subtraction of fractions

Addition and subtraction of mixed fractions

Simplifying fractions

Multiplication and division of fractions

Multiplication and division of mixed fractions

Convert fraction to a decimal

Percentage of a quantity

Express one quantity as a percentage of another

Percentage increases and decreases

Reverse percentages

Dividing a quantity in a given ratio

Proportion

Word problems

Increase and decrease a quantity by a given ratio

Introduction to indices

First index law

Second index law

Third index law

Fourth index law

Fifth index law

Sixth index law

Seventh index law (Negative indices)

Exponential functions

Standard form (positive and negative indices)

Fractional indices

Currency conversions

Earnings

Profit and loss

Percentage profit and loss

Simple interest

Compound interest

24-hour and 12-hour clocks

Defining sets and subsets

Set notation and venn diagrams

Word problems - Venn diagrams

Chapter 2

53

Using variables

Transform simple formulae

Substituting positive and negative numbers

Simplifying expressions

Transforming complex formulae

Expanding a pair of brackets

Expanding brackets

Factorising

Difference of two squares

Factorisation by grouping

Factorising quadratic equations - part 1

Factorising quadratic equations - part 2

Simplifying algebraic fractions

Adding and subtracting algebraic fractions

Simplifying complex algebraic fractions

First index law (same as above)

Second index law (same as above)

Third index law (same as above)

Fourth index law (same as above)

Seventh Index Law (same as above)

Fractional indices (same as above)

Solving one-step linear equations

Solving two-step linear equations

Solving equations with brackets

Solving equations with the unknown on both sides

Solving simultaneous equations using substitution

Solving simultaneous equations using elimination

Problems solving using simultaneous equations

Solve quadratic equations by factorisation

Quadratic formula

Completing the square

Solving linear inequations

Sketching linear inequations

Solving simultaneous linear inequations

Arithmetic sequences

Sequences with quadratic rules

Sequences with cubic rules

Geometric sequences

Direct variation

Inverse variation

Conversion graphs

Speed, distance and time

Travel graphs

Speed-time graphs, acceleration and deceleration

Area under a speed-time graph

Introduction to quadratic functions

Graphical solution of a quadratic function

The reciprocal function

Exponential functions

Gradients of curves

Functions

Inverse functions

Composite functions

Chapter 3

32

Angles and lines

Types of triangles

Congruent and Similar triangles

Circles

Types of quadrilaterals

Polygons

Nets

Constructing triangles - part 1

Constructing triangles - part 2

Constructing simple geometric shapes - part 1

Constructing simple geometric shapes - part 2

Constructing perpendicular bisectors - part 1

Constructing perpendicular bisectors - part 2

Scale drawings

Calculate lengths of similar figures

Area and volume of similar shapes

Symmetry and 2D shapes

Symmetry and 3D shapes

Circle properties

Angles at a point and on a line

Angles formed within parallel lines

Angles in a triangle

Angles in a quadrilateral

Sum of the interior angles of a polygon

Sum of the exterior angles of a polygon

Angles in a semi-circle

Angle between tangent and radius of a circle

Angle properties of irregular polygons

Angle at the centre of a circle

Angle in the same segment

Loci - part 1

Loci - part 2

Chapter 4

16

Basic unit conversions

Area and volume conversions

Perimeter of square, rectangle, triangle and trapezium

Area of square, rectangle, triangle and trapezium

Perimeter and area of parallelograms

Circumference of a circle

Area of a circle

Length of an arc

Area of a sector

Surface area and volume of a cuboid

Surface area and volume of a cylinder

Surface area and volume of a sphere

Surface area and volume of a pyramid

Surface area and volume of a cone

Area of compound shapes

Volume of compound shapes

Chapter 5

9

Cartesian plane in two-dimensions

Plotting linear graphs

Finding gradients from graphs

Sketching linear graphs

General equation of a straight line

Midpoints and distance between two points

Graphing solution of simultaneous linear equations

Determining linear rules

Parallel and perpendicular lines

Chapter 6

14

True bearings

Pythagoras’ theorem

Finding the hypotenuse

Finding the other sides

Introduction to SOH CAH TOA

Calculating unknown side lengths

Calculating unknown angles

Angles of elevation and depression

Angles between 0 and 180

Sine rule

Cosine rule

Area of triangle using heron's formula

Pythagoras’ theorem in 3-Dimensions part 1

Pythagoras’ theorem in 3-Dimensions part 2

Chapter 7

23

Translation

Addition and subtraction of vectors

Multiplying a vector by a scalar

Magnitude of a vector

Position vectors

Vector geometry

Introduction to matrices

Adding and subtracting matrices

Multiplying matrices by a scalar quantity

Multiplying a matrix by another matrix

Identity matrix

The zero matrix

The determinant of a 2 x 2 matrix

The inverse of a matrix

Reflection

Rotation around the origin

Rotation around other points

Translation

Enlargement

Negative enlargement

Combinations of transformations

Transformations and matrices

Transformations and inverse matrices

Chapter 8

5

Simple probability

Probability scale

Probability of an event occurring = 1 – the probability of the event not occurring.

Using a two-way table

Tree diagrams

Chapter 9

6

Calculate mean, median, mode and range

The mean for grouped data and modal class

Collecting data

Histogram

Scatter diagrams, types of correlation and line of best fit

Cumulative frequency