## BASIC ARITHMETIC TOPICS

• Basic Arithmetic

• The Four Basic Rules

• 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

• Rounding Numbers and Money

• Exchange Rates

• Upper and Lower Bounds, Accuracy of

• 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

• 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

## 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

• 3-D 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

• 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

• Multiplication/Division

• Substitution

• Removal of Brackets

• Transposing Formulae

• Numbers/Letters Subtracted

• Numbers/Letters Multiplied

• Numbers/Letters Divided

• Factorising

• Splitting Into Pairs

• 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

• 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 Non-Linear 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

• Co-ordinates 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

• 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