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Learning Materials

Structured explanations, one concept at a time.

Mathematics

GCSE

Numbers

Number & Rounding

Things you’ll need for GCSE Maths

Reading and Writing Numbers of Any Size

Rounding Whole Numbers

Understanding Place Value in Whole Numbers and Decimals

Rounding Decimals

Rounding to Significant Figures

Directed Numbers

Rounding Up or Down in Context

Checking Methods and Solutions

Estimating Solutions Using Approximations

Number properties including prime factor decomposition

Common Properties of Numbers

Squares, Cubes, and Their Roots

Prime Factorisation (Index Form)

Highest Common Factor (HCF) and Lowest Common Multiple (LCM)

Using Prime Factor Decomposition in Numerical Problems

Index laws including standard form

Positive Integral Indices

Zero and Negative Indices ⭐

Fractional Indices ⭐

Using the Rules of Indices (Positive Integral Indices)

Using the Rules of Indices (Positive, Negative and Fractional Indices) ⭐

Converting Numbers Into and Out of Standard Form ⭐

Using Numbers Written in Standard Form ⭐

Fractions, decimals percentages and ratios

How to Find Equivalent Fractions

Equivalences Between Fractions, Decimals and Percentages

Converting Numbers From One Form Into Another

Ordering and Comparing Whole Numbers, Decimals, Fractions and Percentages

Simplifying Fractions

Expressing One Number as a Fraction or Percentage of Another

Finding a Fraction or Percentage of a Quantity

Calculating Fractional and Percentage Changes (Increase and Decrease)

Understanding and Using Multipliers

Solving Problems with Repeated Proportional Changes

Calculating Using Ratios in a Variety of Situations

Solving Numerical Problems Involving Direct and Inverse Proportion ⭐

Finding the Original Quantity After a Proportional Change ⭐

Proficiency in calculations

Understanding and Using Number Operations and Their Relationships

Adding, Subtracting, Multiplying and Dividing Whole Numbers (Including Large Whole Numbers)

Adding, Subtracting, Multiplying and Dividing Decimals, Fractions and Negative Numbers

Understanding and Using Negative Numbers with Number Machines

Using a Calculator Efficiently and Effectively

Using a Calculator Efficiently and Effectively for Standard Form ⭐

Using Trigonometric Functions on a Calculator Efficiently and Effectively ⭐

Limits of accuracy

Rounding an Answer to a Reasonable Degree of Accuracy

Recognising That Measurements Are Approximate

Determining Upper and Lower Bounds ⭐

Calculating Upper and Lower Bounds in Calculations ⭐

Premature Rounding in Multi Step Calculations

Extraction, interpretation and presentation of information

Interpreting and Using Mathematical Information

Creating Plans and Schedules

Using, Interpreting and Producing Venn Diagrams

Personal/household finance and enterprise

Calculations Involving Money

Understanding Personal and Household Finance and Enterprise

Simple and Compound Interest

Calculations Involving Multiple Rates ⭐

Annual Equivalent Rate (AER) ⭐

Annual Percentage Rate (APR) ⭐

Rational and irrational numbers

Recurring Decimals and Exact Fractions

Converting Recurring Decimals to Fractions ⭐

Rational and Irrational Numbers ⭐

Manipulating and Simplifying Expressions Involving Surds ⭐

Manipulating and Simplifying More Complex Expressions Involving Surds ⭐

Using Surds in Exact Calculations ⭐

Algebra

Algebraic conventions and manipulation of expressions and formulae

Basic Conventions of Algebra

Substituting Values into Formulae and Expressions

Equations, Expressions and Formulae

Identities, Equations, Expressions and Formulae ⭐

Forming and Simplifying Expressions

Collecting Like Terms

Expanding Expressions with a Single Bracket

Multiplying and Dividing Terms Using the Rules of Indices

Simplifying Algebraic Fractions

Simplifying More Complex Algebraic Fractions ⭐

Expanding Two Linear Expressions ⭐

Expanding a Linear Expression and a Quadratic Expression ⭐

Factorising Linear and Quadratic Expressions with a Common Factor

Factorising More Complex Expressions by Extracting Common Factors ⭐

Factorising Quadratic Expressions ⭐

Changing the Subject of a Formula (Subject in One Term)

Changing the Subject of a Formula (Subject in More Than One Term) ⭐

Equations and inequalities – algebraic method

Forming, Manipulating and Solving Linear and Simple Equations

Forming, Manipulating and Solving More Complex Linear Equations ⭐

Forming, Manipulating and Solving Simple Linear Inequalities

Forming, Manipulating and Solving Linear Inequalities (Variable on Both Sides and Double Inequalities) ⭐

Solving Quadratic Equations by Factorisation ⭐

Solving Simultaneous Linear Equations by Algebra ⭐

Solving Equations Involving Fractions with Linear Denominators ⭐

Solving Quadratic Equations Using a Formula ⭐

Solving Cubic Equations by Trial and Improvement

Direct and Inverse Proportion ⭐

Sequences

Recognising, Describing and Continuing Number Patterns

Describing the Rule for the Next Term of a Sequence

Generating Linear and Non Linear Sequences from the nth Term Rule

Finding the nth Term of a Linear Sequence

Finding the nth Term of a Quadratic Sequence ⭐

Coordinates, linear and non-linear graphs

Using Coordinates in All Four Quadrants

Drawing and Interpreting Straight Line Graphs

Using the Form y = mx + c

Drawing and Interpreting Quadratic Graphs and Solving Using y = k

Using Straight Line Graphs to Locate Regions Defined by Inequalities ⭐

Identifying Equations of Parallel and Perpendicular Lines ⭐

Solving Simultaneous Linear Equations by Graphs ⭐

Drawing and Interpreting Non Linear Graphs ⭐

Drawing and Interpreting Cubic Graphs ⭐

Using Graphs to Solve Equations Involving Quadratics and Cubics ⭐

Drawing and Interpreting Implicitly Defined Graphs ⭐

Real-life graphs

Drawing and Interpreting Real Life Graphs

Interpreting Graphs Used in the Media

Constructing and Using Tangents to Estimate Rates of Change ⭐

Interpreting the Area Under a Graph ⭐

Using the Trapezium Rule to Estimate the Area Under a Curve ⭐

Geometry and measures

Geometric terms, vocabulary and properties of shape

Geometric Terms

Vocabulary and Properties of 2-D Shapes

Vocabulary and Properties of 3-D Shapes

Use of mathematical equipment for measurement and accurate drawing

Measuring and Accurately Drawing Geometric Figures

Accurate Constructions Using Ruler, Protractor and Compasses

Solving Problems Involving Intersecting Loci

Maps, scale drawings, bearings and 2-D representation of 3-D shapes

Reading and Interpreting Scales

Using and Interpreting Maps

Interpreting and Producing Scale Drawings

Understanding and Using 3 Figure Bearings

Interpreting Plans and Elevations of 3-D Shapes

Interpreting 2-D Representations of 3-D Shapes on Isometric Paper

Interpreting Nets of 3-D Shapes

Angle facts

Angle Properties

Angle Properties of Triangles and Quadrilaterals

Circle Theorems ⭐

Constructing Geometric Proofs Using Angle Properties and Circle Theorems ⭐

Units and measure

Carrying Out Calculations Involving Time

Converting Between Units of Time

Making Sensible Estimates of Metric Measurements

Converting Between Metric and Imperial Units

Compound Measures for Speed and Fuel Consumption

Compound Measures: Density, Population Density and Flow Rates

Converting Between Units of Area and Volume ⭐

Perimeter, area and volume

Area and Perimeter of 2-D Shapes

Circular Measures in 2-D Shapes ⭐

Surface Area, Volume and Capacity of 3-D Shapes

Surface Area and Capacity of 3-D Shapes (Continued) ⭐

Pythagoras’ theorem and trigonometry

Using Pythagoras’ Theorem in 2-D

Using Pythagoras’ Theorem in 3-D ⭐

Using Trigonometric Relationships in Right Angled Triangles ⭐

Calculating Sides and Angles in Right Angled Triangles in 2-D and 3-D ⭐

Extending Trigonometry to Angles of Any Size ⭐

Applying Trigonometry with Angles of Any Size in 2-D and 3-D ⭐

Using the Formula for the Area of a Triangle ⭐

Graphs of Trigonometric Functions ⭐

Position, symmetry and transformations

Finding Coordinates from Geometrical Information

Drawing Lines of Symmetry

Rotational Symmetry

Transformations

Enlargement with a Negative Scale Factor ⭐

Describing and Drawing Two Successive Transformations ⭐

Similar shapes and congruence

Identifying Congruent and Similar Shapes

Similar Shapes as Enlargements

Corresponding Dimensions in Similar Shapes ⭐

Corresponding Angles in Similar and Congruent Shapes ⭐

Relationships Between Length, Area, Volume and Capacity in Similar Shapes ⭐

Triangle Congruence Conditions ⭐

Statistics and probability

Data handling cycle – collection methods

The Statistical Problem Solving Process

Specifying and Testing Hypotheses

Designing and Criticising Questionnaire Questions

Reliability of Data and Conclusions

Tallying Methods

Frequency Tables

Sorting, Classifying and Tabulating Data

Grouping Data into Class Intervals

Specifying Data and Considering Sampling Methods ⭐

Sampling Techniques ⭐

Data handling cycle – represent, interpret and display results

Pictograms, Bar Charts and Pie Charts

Vertical Line Diagrams for Discrete Data

Line Graphs Over Time

Scatter Diagrams for Paired Variables

Lines of Best Fit

Interpreting Scatter Diagrams and Drawing Conclusions

Correlation and Causality

Finding the Mean, Median, Mode and Range

Grouped Frequency Diagrams and Frequency Polygons

Mean, Median, Mode and Range from a Discrete Frequency Distribution

Estimating the Mean of a Grouped Frequency Distribution

Estimating the Median of a Grouped Frequency Distribution ⭐

Modal Category and Modal Class

Determining the Group Containing the Median

Selecting and Using Measures of Central Tendency

Comparing Data Distributions

Selecting and Using Measures of Spread ⭐

Cumulative Frequency Tables and Diagrams ⭐

Box and Whisker Diagrams ⭐

Histograms with Unequal Class Widths ⭐

Misleading Graphs

Finding Patterns and Exceptions in Data

Drawing Inferences and Conclusions from Data

Probability – single event/experiment

The Vocabulary of Probability

Probability Vocabulary

The Probability Scale

Expressing Probability

Total Probability of an Experiment

Calculating Theoretical Probability

Estimating Probability Using Experimental Evidence

Relative Frequency and Number of Trials

Comparing Experimental and Theoretical Probability

Expected Number of Successes

Probability – more than one event/experiment

Mutually Exclusive Events

Independent Events

Identifying Outcomes of Combined Experiments

Choosing Between Adding and Multiplying Probabilities

Three Independent Events ⭐

Dependent Events ⭐

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