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

Coordinates 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 (Rightangled 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

3D 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 3D 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)

Termtoterm 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

Coordinates 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

DistanceTime and VelocityTime Graphs

VelocityTime Graphs (SpeedTime Graphs)

VelocityTime Graphs – Straight lines

Area Under a Curve (Graph)

VelocityTime 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