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GCSEMathsAQAHigherRevision Notes

AQA GCSE Maths: Higher Revision Notes

Exam code: 8300

Concise resources for the AQA GCSE Maths: Higher course.

1. Number

Mathematical Symbols

Order of Operations (BIDMAS/BODMAS)

Irrational Numbers

Negative Numbers

Money Calculations

Addition & Subtraction

Multiplication & Division

Related Calculations

Systematic Lists

Product Rule for Counting

Types of Numbers

Prime Factor Decomposition

Uses of Prime Factor Decomposition

Laws of Indices

Converting to & from Standard Form

Operations with Standard Form

Basic Fractions

Mixed Numbers & Improper Fractions

Adding & Subtracting Fractions

Multiplying & Dividing Fractions

Basic Percentages

Percentage Increases & Decreases

Reverse Percentages

Simple Interest

Compound Interest

Exponential Growth & Decay

Converting Fractions, Decimals & Percentages

Recurring Decimals

Ordering Fractions, Decimals & Percentages

Rounding & Estimation

Upper & Lower Bounds

Simplifying Surds

Rationalising Denominators

Using a Calculator

2. Algebra

Algebraic Notation

Algebraic Vocabulary

Collecting Like Terms

Algebraic Roots & Indices

Expanding & Simplifying Single Brackets

Expanding Double Brackets

Expanding Triple Brackets

Factorising Out Terms

Factorising by Grouping

Factorising Simple Quadratics

Factorising Harder Quadratics

Difference of Two Squares

Deciding the Factorisation Method

Completing the Square

Simplifying Algebraic Fractions

Adding & Subtracting Algebraic Fractions

Multiplying & Dividing Algebraic Fractions

Solving Equations with Algebraic Fractions

Formulas where Subject Appears Once

Formulas where Subject Appears Twice

Algebraic Proof

Solving Linear Equations

Solving Quadratics by Factorising

The Quadratic Formula

Completing the Square

Deciding the Quadratic Method

Linear Simultaneous Equations

Quadratic Simultaneous Equations

Forming Equations from Words

Forming Equations from Shapes

Problem Solving with Equations

Introduction to Functions

Composite Functions

Inverse Functions

Midpoint of a Line

Gradient of a Line

Length of a Line

Equations of Straight Lines (y = mx + c)

Drawing Straight Line Graphs

Perpendicular Lines

Types of Graphs

Quadratic Graphs

Drawing Graphs from Tables

Solving Equations Using Graphs

Trigonometric Graphs

Solving Trig Equations

Equation of a Circle

Equation of a Tangent

Finding Gradients of Tangents

Finding Areas under Graphs

Distance-Time Graphs

Speed-Time Graphs

Conversion Graphs

Rates of Change of Graphs

Solving Linear Inequalities

Solving Quadratic Inequalities

Representing Inequalities as Regions

Finding Inequalities from Regions

Translations of Graphs

Reflections of Graphs

Introduction to Sequences

Types of Sequences

nth Terms of Linear Sequences

Quadratic Sequences

3. Ratio, Proportion & Rates of Change

Introduction to Ratios

Sharing in a Ratio

Working with Proportion

Ratios with Fractions, Decimals & Percentages

Multiple Ratios

Direct Proportion

Inverse Proportion

Converting between Units

Squared & Cubic Units

Compound Measures

Speed, Density & Pressure

4. Geometry & Measures

Rotational Symmetry

Lines of Symmetry

Planes of Symmetry

Plans & Elevations

Basic Angle Properties

Angles in Polygons

Angles in Parallel Lines

Constructing Triangles

Angles at Centre & Circumference

Angle in a Semicircle

Theorems with Chords & Tangents

Angles in Cyclic Quadrilaterals

Angles in the Same Segment

The Alternate Segment Theorem

Circle Theorem Proofs

Adding & Subtracting Areas

Problem Solving with Areas

Area & Circumference of Circles

Arc Lengths & Sector Areas

Problem Solving with Volumes

Congruent Triangles

Similar Lengths

Geometrical Proof

Similar Areas & Volumes

Pythagoras Theorem

Angles of Elevation & Depression

Exact Trig Values

The Cosine Rule

Area of a Triangle

Deciding the Trigonometric Rule

3D Pythagoras & Trigonometry

Introduction to Column Vectors

Representing Vectors as Diagrams

Length of a Vector

Position & Displacement Vectors

Finding Vector Paths

Problem Solving with Vectors

Combination of Transformations

5. Probability

Basic Probability

Sample Space Diagrams

Relative & Expected Frequency

Frequency Trees

Set Notation & Venn Diagrams

Probability Tree Diagrams

Combined Probabilities

Conditional Probability

Combined Conditional Probabilities

Exam boards

Study tools

Related links