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

  • 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

  • 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 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

  • 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

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