NUMBER UNIT TOPICS

  • Number Unit Introduction

  • Numbers and Place Value

  • Definitions of Various Types of Numbers

  • Inequalities

  • The Four Basic Rules of Number

  • Addition

  • Subtraction

  • Multiplication

  • Division

  • Biggest and Smallest Numbers

  • Questions Involving Basic Operations & Whole Numbers

  • Numbers Based on a Multiplication Calculation

  • Rounding Numbers

  • Rounding up money

  • Estimation

  • Bidmas- Order of Working out Problems

  • Accuracy, Upper and Lower Bounds of Answers and Range of Numbers

  • Range

  • Upper and Lower Bounds

  • Calculating Maximum/Minimum Answers

  • Error Intervals

  • Truncated Numbers

  • Systematic Listing

  • Product Rule for Counting

  • Squares of Numbers

  • Cubes of Numbers

  • Square Roots and Cube Roots of Numbers

  • Square root of Numbers

  • Cube Root of Numbers

  • Factors

  • Highest Common Factor (HCF)

  • Multiples

  • Common Multiples and Lowest Common Multiples

  • Prime Numbers and Prime Factors

  • Prime Factors

  • Calculating Prime Factors Using Prime Factor Trees

  • Using Prime Factor Trees to Calculate LCM and HCF

  • Lowest (Least) Common Multiple – LCM

  • Highest Common Factor – HCF

  • Calculating a Pair of Numbers from Their HCF and LCM Values

  • Applications of HCF and LCM

  • Standard Form and Writing Numbers in Standard Form

  • Fractions, Decimals and Percentages

  • 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

  • Conversion of Decimals to Fractions

  • Recurring Numbers

  • Converting a Recurring Decimal into a Fraction

  • Shortening of Numbers – Decimal Place

  • Significant Figures

  • Percentages

  • Working out Percentages from the Original Number

  • Reverse Percentages

  • Percentage Changes Using a Multiplier

  • The percentage Added

  • The Percentage Subtracted

  • Applications of Percentages

  • Simple Interest

  • Hire Purchase

  • Compound Interest

  • Common Fraction, Decimal and Percentage Equivalents

  • Powers and Roots of Fractions and Decimals

  • Find Powers and Roots (without a calculator)

  • Using Percentages to Compare Numbers

  • Putting Numbers into Numerical Order

  • Indices

  • Whole Number Indices

  • Fractional Number Indices

  • Negative Index Numbers

  • Laws of Indices

  • Indices Containing Brackets

  • Directed Numbers

  • Addition/Subtraction of Directed Numbers

  • Multiplication/Division of Directed Numbers

  • Exchange Rates

RATIO & PROPORTIONS UNIT TOPICS

  • Ratio and Proportion Introduction

  • Ratios

  • Measure - The Metric System

  • The Basic Units of Measure

  • Making Estimates of Measures

  • Changing Between Related Units

  • Length

  • Weight

  • Volume of Liquids (Capacity)

  • Time

  • Scale and Scale Drawings

  • Scales

  • Scale Drawings

  • Ratios of Perimeters, Areas and Volume of Similar Shapes and Scales

  • Reading Values on Instruments and Dials (Scales)

  • Proportion

  • Further Direct and Inverse Proportion

  • Direct Proportion

  • Inverse Proportion

  • Constructing Equations for Questions Involving Proportion

  • Graphs and Proportion

  • Best Buys

  • Compound Units

  • Triangle Method

  • Speed, Distance and Time (SDT)

  • Converting SDT Units

  • Density

  • Pressure

  • Simple and Compound Interest

  • Simple Interest

  • Compound Interest

  • Using a Calculator for Powers (Repetition function)

  • Growth and Decay

  • Decay

STATISTICS UNIT TOPICS

  • Statistics Introduction

  • Data Collection

  • Types of Data

  • Quantitative Data

  • Qualitative Data

  • Primary Data

  • Secondary Data

  • Biased Data

  • Hypothesis and Experiments

  • Questionnaires

  • Types of Questions

  • Sampling

  • Data Presentation and Analysis

  • Representation of Data – Tables (Tabulated Data)

  • Double Tables (Two Way Tables)

  • Analysing Double Tables

  • Stratified Data/Sampling

  • Ways of Representing Data (Charts)

  • Block Charts

  • Drawing or Plotting Statistical Charts

  • Pictograms

  • Simple bar Charts

  • Dual (Comparative) Bar Charts- Multiple Bar ChartsLine of Best Fit, Correlation and Scatter Graphs

  • Mean, Median and Mode (ungrouped data)

  • Mean (Average)

  • Stacked Bar Charts (Composite Bar Charts)

  • Pie Charts

  • Using Sectors to Work out Pie Charts

  • Interpreting Data from Block Charts and Pie Charts

  • Choosing the Correct Type of Chart

  • Histograms

  • Grouping Data

  • Histograms with Unequal Widths (Unequal Class Intervals)

  • Working Out Histograms Using Areas

  • Line Graphs

  • Plotting Line Graphs

  • Co-ordinates of a Point(s)

  • Line Graphs –Plotting (Drawing)

  • Graphs Where the Axis Does Not Start at Zero

  • Multiple Line Graphs

  • Scatter Graphs

  • Median and Mode

  • Frequency tables

  • Calculating the Mean from Grouped Data and Tables

  • Calculating the Median (Median Class) from Grouped Data

  • Calculating the Mode (Modal Class) from Grouped Data

  • Frequency Polygons

  • Cumulative Frequency and Cumulative Frequency Diagrams

  • Grouping Frequencies

  • Cumulative Frequency

  • Cumulative Frequency Diagrams

  • Median, Percentiles, Quartiles and Interquartile Range

  • Finding the Median from a Cumulative Frequency Diagram

  • Percentiles

  • Quartiles

  • Interquartile Range

  • Box Plots (Box and Whisker Plots)

PROBABILITY UNIT TOPICS

  • Probability Introduction

  • Probability Scale

  • Probability (of an Event Happening)

  • Using data Sources to Work out Probabilities

  • Tables

  • Frequency Trees

  • Calculating Probabilities from Frequency Trees

  • Creating Tree Diagrams from Two Way Tables

  • Experimental Probability

  • Expected and Observed Frequencies

  • Complement of Probability

  • Relative Frequency (Experimental Data)

  • Mutually Exclusive Probability

  • Independent Probability

  • Probability with and Without Replacement

  • Sets and Venn Diagrams

  • Working with Venn Diagrams

  • Completing Numbers Within the Set

  • Extracting Data from the Set Using Symbols

  • Shading in Venn Diagrams and the Language of Sets

  • Using Venn Diagrams to Solve Probability Problems

  • Tree Diagrams

GEOMETRY UNIT TOPICS

  • Geometry and Measures

  • Properties of Angles and Shapes

  • Standard Properties of Angles

  • Types of Angles

  • Angles on a Straight Line

  • Angles at a Point

  • Angles in a Polygon

  • Exterior Angles of a Polygon

  • Interior Angles of a Polygon

  • Triangles

  • Properties of Parallel Lines

  • Properties of Quadrilaterals

  • Circles

  • Circle Theorems

  • Tangent Properties

  • Symmetry

  • Geometrical Transformations

  • Reflections

  • Rotations

  • Translations

  • Enlargements (Positive Whole Number Scale Factor)

  • Enlargements with a Fractional Scale Factor

  • Enlargements with a Negative Scale Factor

  • Invariant Points

  • Congruency and Similarity

  • Congruency

  • Similarity

  • Pythagoras’ Theorem (Right Angled Triangles)

  • Standard Triangles

  • Trigonometry (Right-angled Triangles only)

  • Standard Trigonometrical Ratios

  • Sine and Cosine Rule

  • Sine Rule

  • Cosine Rule

  • Graphs of Sine Cosine and Tangent

  • Sine Graph

  • Variations on the Sine Curve

  • Cosine Graph

  • Tangent Graph

  • 3-D Trigonometry (Solid Trigonometry)

  • Geometrical Proofs

  • Angles in a Triangle Add up to 180o

  • Angle in a Semicircle (90 o)

  • Alternate Segment Theorem

  • Angle at the Centre (Twice Angle at Circumference)

  • Plan, Front and Side Elevations of 3-D Shapes

  • Surface Area and Nets

  • Angle of Elevation and Angle of Depression

  • Bearings

  • Measurement of Angles

  • Constructions

  • Drawing Triangles and Other Shapes

  • Geometrical Constructions

  • Loci

  • Practical Applications of Loci

  • Mensuration

  • Perimeters of Shapes

  • Perimeters of Basic Shapes

  • Perimeter of a Circle (Circumference)

  • Perimeters of Compound Shapes

  • Areas

  • Areas of Circles

  • Areas of Shapes with Mixed Units

  • Circles – Arc Length and Area of Sectors

  • Arc Length

  • Area of Sectors

  • Areas of Compound Shapes (Figures Built up from Basic Shapes)

  • Areas of Borders and Shaded Parts

  • Area of a Triangle using Sine Function

  • Areas of Shapes without Using Formulae (‘Counting Squares’)

  • Calculating Surface Areas from Nets

  • Areas of Similar Shapes

  • Volumes

  • Prisms

  • Pyramids

  • A Cone

  • A Sphere

  • A Truncated Cone (Frustum)

  • Volumes of Compound Shapes

  • Volumes of shapes with Mixed Units

  • Volumes of Similar Shapes

  • Vectors

  • Addition of Vectors Graphically

  • Vector Problems without a Grid

  • Dividing Vectors by a Given Ratio

  • Column Vectors

  • Addition of Vectors Using Column Vectors

  • Subtraction of Vectors Using Column Vectors

  • Multiplication of Column Vectors by a Scalar Quantity

  • The Modulus of a Vector

ALGEBRA UNIT TOPICS

  • Algebra Introduction

  • ·Equations, Formula, Expression and Terms

  • Working with Formulae

  • Speed, Distance and Time

  • Aspects of Algebra

  • Substitution

  • Removal of Brackets

  • Multiplying Three Sets of Binomials Together

  • Surds

  • Calculations Involving Surds

  • Simplifying Surds

  • Factorising

  • Splitting into Pairs

  • Factorising Quadratic Expressions

  • Factorising Quadratic Equations

  • Quadratic Equations Which Will Factorise

  • Quadratic Equations Which Will Not Factorise

  • The Discriminant

  • Completing the Square

  • Solving Quadratic Equations by Completing the Square

  • Algebraic Fractions

  • Simultaneous Equations

  • Substitution method

  • Elimination method

  • Constructing Equations

  • Transposing Formulae

  • Solving Linear Inequalities

  • Showing Inequalities on a Number Line

  • Number (Function) Machines

  • Functions (Function Notation)

  • Inverse and Composite Functions Using Function Notation

  • The Inverse of a Function

  • Iteration (Iterative Processes)
  • Using the ANS button for Iteration

  • Making Iterative Formulae

  • Sequences, Functions and Graphs

  • Number Sequences

  • ·Arithmetic Number Sequences

  • Number Sequence Rules (Arithmetic Number Sequences)

  • Term-to-term Rule

  • Finding the nth Term of an Arithmetic Sequence

  • Geometric Sequences

  • Quadratic Sequences

  • Finding the nth Term of a Quadratic Sequence

  • Sequences Formed Using Shapes

  • Even Numbers, Odd Numbers and Consecutive Numbers

  • Other Sequences (types of numbers)

  • Graphs

  • Types of Graphs

  • Co-ordinates of a Point(s)

  • Straight Line Graphs – Plotting (Drawing)

  • Choosing Scales for Axes on Graphs

  • Choosing the Correct Scale

  • Straight Line Graphs and Gradients of Graphs

  • Gradients of Straight Line Graphs

  • Equations of Straight Line Graphs

  • Straight Line Graphs – Finding the values of ‘m’ and ‘c’

  • Finding the Equation of a Straight Line Graph from Two Points

  • Line Segment and Midpoint

  • Parallel Graphs

  • Determining the Equation of a Parallel Straight Line Graph

  • Graphs which Intersect at Right Angles (Perpendicular Graphs)
  • Practical Graphs

  • Graphs with a Standard (fixed) Charge

  • Plotting Curved Graphs

  • Intersecting Graphs (Solving Equations Graphically)

  • Standard Graphs

  • Gradients of Curved Graphs

  • Turning Point of Quadratic Graphs

  • Identifying Important Points from a Quadratic Graph

  • Finding Roots by Symmetry

  • Finding the Turning Point by Completing the Square

  • Exponential Graphs

  • Exponential Graphs Multiplied by a Number

  • Distance-Time and Velocity-Time Graphs

  • Velocity-Time Graphs (Speed-Time Graphs)

  • Velocity-Time Graphs – Straight lines

  • Area Under a Curve (Graph)

  • Velocity-Time Graphs – Curved lines

  • Sketch Graphs and the Effects of Graph Shifting

  • Graph Stretching of Sine and Cosine Graphs

  • Graphs from Real Life Situations

  • Experimental Graphs

  • Shading Graphs to Represent Inequalities

  • Graphs of Circle

  • Finding the Equation of the Tangent to the Circle at a Given Point

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