GCSE Maths Higher

GCSE maths – Year 10 Key Topics

⚡ 1. Number

• Structure and calculation
  • Ordering Numbers
  • Four Operations and Place Value
  • Relationships Between Operations
  • Factors, Multiples and Prime Numbers
  • Systematic Listing
  • Powers and Roots
  • Indices
  • Exact Calculations and Surds
  • Standard Form
• Fractions, decimals and percentages
  • Fractions and Decimals
  • Fractions in Ratio Problems
  • Fractions and Percentages as Operators
• Measures and accuracy
  • Units and Measures
  • Estimation
  • Rounding and Error Intervals
  • Limits of Accuracy

⚡ 2. Algebra

• Notation, vocabulary and manipulation
  • Algebraic Notation
  • Substitution
  • Algebra Vocabulary
  • Simplifying Expressions & Advanced Manipulation
  • Formulae
  • Identities and Proof
  • Functions
• Graphs
  • Coordinates
  • Straight Line Graphs
  • Gradients and Intercepts
  • Quadratic Graphs
  • Recognising Graphs & Advanced Graphs
  • Transformations of Graphs
  • Graphs in Context & Advanced Graph Interpretation
  • Gradients and Areas
  • Circle Graphs
• Solving equations and inequalities
  • Linear Equations
  • Quadratic Equations
  • Simultaneous Equations
  • Iteration
  • Algebraic Modelling
  • Inequalities
• Sequences
  • Generating Sequences
  • Number Sequences & Advanced Sequences
  • nth Term

⚡ 3. Ratio, proportion and rates of change

• Ratio, proportion and rates of change
  • Units and Conversions
  • Scale Factors, Maps and Diagrams
  • Fractions and Ratios
  • Percentages
  • Direct and Inverse Proportion
  • Compound Units
  • Ratios, Scale Factors and Similarity
  • Algebraic Direct and Inverse Proportion
  • Graphs and Rates of Change
  • Instantaneous Rate of Change
  • Growth, Decay and Compound Interest

⚡ 4. Geometry and measures

• Properties and constructions
  • Geometric Language and Notation
  • Constructions and Loci
  • Angles
  • Properties of Shapes
  • Congruence and Similarity
  • Geometric Reasoning and Proof
  • Circles
  • Coordinate Geometry
  • 3D Shapes
  • Plans and Elevations
  • Advanced Transformations
  • Circle Theorems
• Mensuration and calculation
  • Units and Measures
  • Measuring and Bearings
  • Area and Volume Formulae
  • Circles and Composite Shapes
  • Sectors and Arcs
  • Similarity
  • Pythagoras and Trigonometry
  • Advanced Trigonometry
  • Sine Rule
  • Cosine Rule
  • Area of Any Triangle
• Vectors
  • Vector Basics
  • Vector Arithmetic
  • Vector Proofs

⚡ 5. Probability

• Probability
  • Recording Probability Experiments
  • Randomness and Fairness
  • Relative Frequency and Theoretical Probability
  • Probability Rules
  • Experimental Probability
  • Systematic Listing
  • Theoretical Probability
  • Combined Events
  • Conditional Probability
  • Two-Way Tables
  • Tree Diagrams
  • Venn Diagrams
  • Expected Frequencies

⚡ 6. Statistics

• Statistics
  • Sampling and Populations
  • Types of Data
  • Tables, Charts and Diagrams
  • Statistical Diagrams and Choosing Appropriate Graphs
  • Analysing Data Sets
  • Scatter Graphs and Correlation
  • Grouped Data
  • Cumulative Frequency Graphs
  • Box Plots (Box-and-Whisker Diagrams)
  • Quartiles and Interquartile Range (IQR)
  • Scatter Graph Extension (Higher)
  • Correlation vs Causation

What We Focus On In Tuition

• Practice with real GCSE exam questions
• Support for both Foundation & Higher tiers
• Confidence building for Grade 5–9 success