## NUMBER UNIT TOPICS

• Number Unit Introduction

• Numbers and Place Value

• Definitions of Various Types of Numbers

• Inequalities

• The Four Basic Rules of Number

• 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

• 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 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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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