Course:
Full GCSE Mathematics Course
GCSE Mathematics Course Topics
Section 1: Number
Chapter 1: Type of numbers
1.2. Factors and Multiples
1.3. LCM and HCF
1.4. Rounding and Estimating
Chapter 2: Fractions
Chapter 3: Decimals
Chapter 4: Standard Form or Scientific Notation
Chapter 5: Bounds
Chapter 6: Unit Conversions
6.2. Speed, Density and Pressure
Chapter 7: Percentages
7.2. Compound Growth & Decay
Chapter 8: Proportions
Chapter 9: Ratios
Section 2: Algebra
Chapter 1: Algebra Basics
Chapter 2: Power and Roots
Chapter 3: Multiplying Out Brackets
Chapter 4: Factorising Basics
Chapter 5: Surds
Chapter 6: Rearranging Formulas
Chapter 7: Solving Equations
Chapter 8: Quadratic Equations
Chapter 9: Algebraic Fractions
Chapter 10: Algebraic Proofs
Chapter 11: Algebraic Identity
Chapter 12: Sequences
Chapter 13: Inequalities
Chapter 14: Simultaneous Equations
Chapter 15: Functions
Chapter 16: Iterative Methods
Section 3: Graphs
Chapter 1: Straight Line and Gradients
1.1. Drawing Straight line graphs
1.2. Equation of a Straight Line Simple
1.3. Gradient of a Straight Line
1.3.1. Parallel and Perpendicular Lines
1.4. Find Equation of a Line Ad-vanced
1.5. Proving a Coordinate Lies on a graph
1.6. Coordinates and Ratios
1.7. Equation of tangent to circle
Chapter 2: Quadratic Graphs
Chapter 3: Solving Equations with Graphs
3.1. Simultaneous equations
3.2. Solving Simultaneous Equations Linear and Non-Linear with Graphs
3.3. Solving Harder Equation with Graphs
3.4. Solving Inequalities with Graphs
Chapter 4: Distance – Time Graphs
Chapter 5: Graph Transformation
Chapter 6: 10 Common Graphs Shapes
Section 4: Measures and Geometry
Chapter 1: Measures
1.1. Locus of Points and Construction#
1.1.1. Locus from a Single Fixed Point
1.1.2. Locus from One Line
1.1.3. Locus from Two Lines
1.1.4. Locus from Two Given Points
1.2. Bearings
1.3. Congruent Triangles
1.3.1. SSS – Side Side Side
1.3.2. SAS – Side Angle Side
1.3.3. ASA – Angle Side Angle
1.3.4. RHS – Right Angle Hypotenuse Side
1.4. Similar Shapes
1.4.1. Levels of Scale Factor
Chapter 2: Geometry
2.1. Introduction
2.2. Types of Angles
2.3. Some Important Rules
2.3.1. Important Triangles
2.3.2. Important Quadrilaterals
2.4. Parallel Lines
2.4.1. Alternate, Allied and Corresponding Angles
2.5. Polygons
2.5.1. Examples of Polygons
2.5.2. Interior and Exterior Angles
2.6. Circle Geometry
2.6.1. Circle Theorems
2.7. Transformations
Section 5: Pythagoras and Trigonometry
Chapter 1: Pythagoras Theorem
1.1. Properties of Triangles
1.2. Pythagoras
1.3. 3D Pythagoras
1.3.1. Prisms
1.3.2. 3D Pythagoras for Cuboids
Chapter 2: Trigonometry
2.1. Sin, Cos and Tan
2.2. Common Values
2.3. Properties of Non-Right Angle Trian-gles
2.4. The Sine Rule
2.5. The Cosine Rule
2.6. Tips and Tricks
2.7. 3D Trigonometry
Chapter 3: Vectors
3.1. Definitions
3.2. Vector Addition/Subtraction/Multiplication
3.3. Finding Magnitude of Vectors
3.4. Finding Resultant of Vectors
3.5. Finding Vectors on a Straight Line
3.6. Finding Vectors with Ratios
3.7. Proof: Vectors and Identities
Section 6: Probability
Chapter 1: Probability Basics
1.1. Terminology
1.2. Finding Probabilities
1.3. Sample Space
1.4. Product Rule to Count Outcomes
1.5. Probability of Events Not Happening
Chapter 2: Relative Frequency
2.2. Frequency Trees
2.3. Expected Frequency
2.4. Independent Events
2.4.1. Probability Trees
2.5. Dependent Events
2.5.1. Probability Trees
Chapter 3: Venn Diagrams
Section 7: Statistics
Chapter 1: Statistics Basics
1.1. Terminology, Sample and Data Collection
1.2. Mean, Median, Most and Range
1.3. Discrete: Frequency Tables
1.4. Continuous: Frequency Tables
1.5. Cumulative Frequency
Chapter 2: Histograms and Frequency Density
2.1. Histogram
2.2. Scatter Graph
2.3. Frequency Polygon
2.4. Stem and Leaf
2.5. Pie Chart
2.6. Time Series
