BASIC ARITHMETIC TOPICS

Basic Arithmetic

The Four Basic Rules

Addition

Subtraction

Multiplication

Division

Fractions

Addition and Subtraction of Vulgar

Fractions

Multiplication and Division of Vulgar

Fractions

Expressing Division of Whole numbers in

Terms of a Fraction

Cancelling and Equivalent Fractions

Improper Fractions

Mixed Fractions

Decimals

Addition and Subtraction of Decimals

Multiplication of Decimals

Multiplication by Powers of 10, 100, 1000

Multiplication of Decimals by Whole

Numbers or Decimals

Division of Decimals

Conversion of Fractions to Decimals

Recurring Numbers

Conversion of Decimals to Fractions

Shortening of Numbers – Decimal Place

Significant Figures

Percentages

Working out percentages from the Original Number

Applications of Percentages

Simple Interest (SI)

Hire Purchase

Compound Interest (CI)

Ratios

Comparing Numbers

Ratios in Proportion

Squares of Numbers

Cubes of Numbers

Square Roots and Cube Roots of Numbers

Square Roots of Numbers

Cube Roots of Numbers

Indices

Multiplying and Dividing Indices

Standard Form

Practical Applications of Working with

Numbers

Estimation

Adding Back

Rounding Numbers and Money

Exchange Rates

Upper and Lower Bounds, Accuracy of

Answers and Range

Calculating Maximum/Minimum Answers

Time

The Metric System weight and length

‘Bodmas’ – Order of Working Out Problems

Factors

Highest Common Factor (HCF)

Multiples

Common Multiples and Lowest Common

Multiples

Prime Numbers and Prime Factors

Prime Factors

Flow Charts

Scales

Inequalities

Definitions of Various Types of Numbers

Showing Inequalities on a Number Line

Number Sequences

The Arithmetic Progression (A.P.)

The Geometrical Progression (G.P.)

Fibonacci Sequences

Triangular Sequences

Reading Values on Instruments and Dials

Calculations Involving Surds

Addition and Subtraction of Surds

Multiplication and Division

Division of Surds

Rationalising the Denominator

Simplifying Surds

Degree of Accuracy

Areas

Squares and Rectangles

Parallelogram Rhombus and Triangle

Trapezium and Kite

Properties of Quadrilaterals

Areas of Circles

Areas of Shapes with Mixed Units

Areas of Figures Built up From Basic Shapes

Areas of Borders and Shaded Parts

Perimeters

Volumes

Prisms

Pyramid

Cone and Sphere

Volumes of Figures Built up From Basic Shapes

Volumes of Shapes with Mixed Units

Ratios of Areas and Volumes of Similar Shapes

Surface Area and Nets
SHAPE & SPACE TOPICS
GEOMETRY TOPICS

Measurement of Angles

Standard Properties of Angles

Types of Angles

Exterior Angles of a Polygon

Interior Angles of a Polygon

Properties of Parallel Lines

Circles – Arcs and Sectors of Circles

Arcs

Sectors

Circle Theorems

Tangent Properties

Triangles

Pythagoras’ Theorem

Standard Triangles

Trigonometry

Standard Trigonometric Ratios

Sine and Cosine Rule

Sine Rule

Cosine Rule

Graphs of Sine, Cosine and Tangent

Sine Graph

3D Trigonometry (Solid Geometry)

Angle of Elevation/Depression

Bearings

Congruency and Similarity of Shapes

Congruency

Similarity

Symmetry

Tessellations

Constructions

Constructing Triangles

Constructions

Constructing Triangles

Geometrical Constructions

Loci

Geometrical Transformations

Reflections

Rotations

Translations

Enlargements

Matrices

Types of Matrices

Multiplication of a Matrix by a Number

Multiplication of a Matrix by a Matrix

Transformations Using Matrices

Vectors

Addition of Vectors

Multiplication of a Vector by a Scalar

Column Vectors

Addition of Vectors Using Column Vectors

Subtraction

Multiplication of Column Vectors by a Scalar Quantity

The Modulus of a Vector

Area of a Triangle Using Sine Function

The Trigonometric Functions of Obtuse Angles

Shear and Stretch Transformations

Shear Transformations Stretch Transformations
STATISTICS & PROBABILITY TOPICS

Representation of Data

Ways of Representing Data

Block Charts

Drawing or Plotting Statistical Charts

Bar Charts

Proportionate Bar Charts

Chronological Bar Charts

Pictograms

Histograms

Histograms with Unequal Widths

Pie Charts

Interpreting Data from Block Charts and Pie Charts

Mean, Median and Mode

Frequency Tables

Cumulative Frequency

Sets and Venn Diagrams

Constructing Venn Diagrams to Solve Problems

Describing the Shaded Regions on Venn Diagrams

Probability

Equiprobable Probability

Experimental Probability

Expected and Observed Frequencies

Complement of Probability

Mutually Exclusive Probability

Independent Probability

Tree Diagrams
ALGEBRA TOPICS

Formulae

Speed, Distance and Time

Aspects of Algebra

Directed Numbers

Addition/Subtraction

Multiplication/Division

Substitution

Removal of Brackets

Transposing Formulae

Numbers/Letters Added

Numbers/Letters Subtracted

Numbers/Letters Multiplied

Numbers/Letters Divided

Factorising

Splitting Into Pairs

Factorising Quadratic Expressions

Factorising Quadratic Equations

Quadratic Equations Which Will Factorise

Quadratic Equations Which Will Not Factorise

Simultaneous Equations

Constructing Equations

Solving linear Inequalities

Algebra Contents

Proportion

Direct Proportion

Inverse Proportion

Quadratic Inequalities

Solving Quadratic Inequalities

Functions

The Inverse of a Function

Composite Functions

Calculating Composite Functions

Mapping Functions, Range and Domain

Mapping Functions

Domain and Range of Functions

Differentiation (Calculus)

The Process of Differentiation

Applications of Differentiation

Maxima and Minima

Differentiation Using Units

Constructing Equations and the nth Term of Number Sequences

Constructing NonLinear Equations

Making Equations from Numbers by Comparison

The General Case of Number Sequences (nth term)

The Fibonacci Sequence

Iteration (Iterative Processes)

Constructing Equations from First Principles
GRAPHS TOPICS

Types of Graphs

Coordinates of a Point

Straight Line Graphs  Plotting (Drawing)

Reading Values from a Graph

Choosing Scales for Axes on Graphs

Choosing the Correct Scales

Equations of Straight Line Graphs

Finding the Equation of a Straight Line Graph

Curved Graphs

Gradients of Curved Graphs

Distance – Time Graphs

Velocity – Time Graphs

Graphs Obtained From Experimental Data

Line of Best Fit and Correlation

Intersecting Graphs

Standard Graphs

Recognising Equations

Graphs of Inequalities

Graphs of a Circle

Plotting Curved Graphs (Polynomials)

Plotting Asymptotic Graphs

General Shapes of Graphs and the Effects of Graph Shifting

Parallel Graphs

Determining the Equation of a Parallel Straight Line Graph

Intersecting Graphs at Right Angles to Each Other

Graphs and Proportion