73 Topics

Every GCSE Maths Topic — Explained

Step-by-step guides, worked examples and practice questions for every topic on the AQA, Edexcel and OCR GCSE Maths specification.

🔢

Number

10 topics

1. Fractions –

Master fractions for GCSE Maths with step-by-step methods, worked examples, and practice questions for Foundation and Higher tiers.

2. Decimals –

Learn how to work with decimals in GCSE Maths including ordering, rounding, and the four operations with clear examples.

3. Percentages –

Complete guide to GCSE Maths percentages covering percentage change, reverse percentages, and compound interest with worked examples.

4. Powers and Roots –

Understand squares, cubes, square roots, and cube roots for GCSE Maths with clear methods and exam-style practice questions.

5. Standard Form –

Master standard form for GCSE Maths with step-by-step methods for writing, calculating, and converting standard form numbers.

6. Surds –

Learn how to simplify, add, multiply, and rationalise surds for GCSE Maths Higher tier with step-by-step examples.

H

7. Bounds and Error Intervals –

Master bounds and error intervals for GCSE Maths Higher tier with clear rules for upper and lower bounds in calculations.

H

8. Indices and Index Laws –

Complete guide to index laws for GCSE Maths covering multiplying, dividing, negative and fractional indices with worked examples.

9. Prime Factorisation, HCF and LCM –

Learn prime factorisation, HCF and LCM for GCSE Maths with factor trees, Venn diagrams, and step-by-step worked examples.

10. Order of Operations (BIDMAS) –

Master BIDMAS for GCSE Maths with clear explanations of operation order, worked examples, and common exam pitfalls to avoid.

📐

Algebra

22 topics

11. Simplifying Expressions –

Learn how to simplify algebraic expressions for GCSE Maths by collecting like terms and using index laws with worked examples.

12. Expanding Brackets –

Master expanding single and double brackets in GCSE Maths with step-by-step methods, worked examples, and practice questions.

13. Factorising Expressions –

Learn how to factorise algebraic expressions at GCSE level with worked examples, step-by-step methods, and practice questions.

14. Solving Linear Equations –

Master solving linear equations for GCSE Maths with clear steps, worked examples, and practice questions for Foundation and Higher tiers.

15. Solving Inequalities –

Learn how to solve linear inequalities for GCSE Maths with step-by-step methods, number line diagrams, and exam-style practice questions.

16. Forming and Solving Equations –

Learn how to form and solve equations from word problems for GCSE Maths with worked examples, methods, and practice questions.

17. Sequences and Nth Term –

Master arithmetic sequences and the nth term rule for GCSE Maths with clear methods, worked examples, and practice questions.

18. Quadratic Sequences & Nth Term –

Learn how to find the nth term of a quadratic sequence for GCSE Maths Higher tier with step-by-step methods and worked examples.

H

19. Solving Quadratics by Factorising –

Learn how to solve quadratic equations by factorising for GCSE Maths with step-by-step methods, worked examples, and practice questions.

20. Quadratic Formula –

Master the quadratic formula for GCSE Maths Higher tier with clear steps, worked examples, discriminant explanation, and practice questions.

H

21. Completing the Square –

Learn completing the square for GCSE Maths Higher tier with step-by-step methods, turning points, worked examples, and practice questions.

H

22. Algebraic Fractions –

Master algebraic fractions for GCSE Maths Higher tier including simplifying, adding, subtracting, multiplying, and solving equations.

H

23. Simultaneous Equations: Elimination –

Learn how to solve simultaneous equations using the elimination method for GCSE Maths with worked examples and practice questions.

24. Simultaneous Equations: Substitution –

Learn the substitution method for simultaneous equations at GCSE with step-by-step examples for linear and non-linear systems.

25. Linear Graphs & Equation of a Line –

Master linear graphs and the equation of a line for GCSE Maths. Learn y = mx + c, gradient, intercept, and parallel/perpendicular lines with worked examples.

26. Quadratic Graphs

Learn how to plot quadratic graphs, find turning points, roots and the line of symmetry for GCSE Maths. Includes worked examples and practice questions.

27. Cubic, Reciprocal & Exponential Graphs –

Recognise and sketch cubic, reciprocal and exponential graphs for GCSE Maths Higher tier. Key features, shapes and worked examples explained.

H

28. Graph Transformations

Master graph transformations for GCSE Maths Higher tier. Learn translations, reflections, stretches with f(x) notation and worked examples.

H

29. Functions & Function Notation –

Understand functions and function notation for GCSE Maths Higher tier. Learn f(x), domain, range, inputs and outputs with clear worked examples.

H

30. Inverse & Composite Functions –

Learn inverse and composite functions for GCSE Maths Higher tier. Step-by-step methods for f⁻¹(x) and fg(x) with worked examples and practice.

H

31. Algebraic Proof

Master algebraic proof for GCSE Maths Higher tier. Learn how to prove statements about odd, even and consecutive numbers with worked examples.

H

32. Iteration

Learn the iteration method for GCSE Maths Higher tier. Solve equations using iterative formulas with worked examples and exam tips.

H
⚖️

Ratio, Proportion & Rates of Change

5 topics

33. Ratio Basics & Sharing in a Ratio –

Learn ratio basics and how to share amounts in a given ratio for GCSE Maths. Simplifying ratios, sharing and worked examples for Foundation & Higher.

34. Ratio Problem Solving in Context –

Solve ratio problems in real-life contexts for GCSE Maths. Recipes, best buys, scaling and multi-step ratio questions with worked examples.

35. Direct & Inverse Proportion –

Learn direct and inverse proportion for GCSE Maths. Formulas, graphs, worked examples and practice questions for Foundation and Higher tier.

36. Percentages: Increase & Decrease –

Master percentage increase and decrease for GCSE Maths. Multipliers, compound interest, repeated change and worked examples for all exam boards.

37. Reverse Percentages

Master reverse percentages for GCSE Maths. Learn how to find the original amount before a percentage increase or decrease with worked examples.

📏

Geometry & Measures

12 topics

51. Trigonometry in 3D –

Master 3D trigonometry for GCSE Maths Higher tier with step-by-step methods, worked examples, and practice questions.

H

52. Circle Theorems –

Learn all circle theorems for GCSE Maths Higher tier with clear diagrams, worked examples, and exam-style practice questions.

H

53. Arc Length and Sector Area –

Master arc length and sector area for GCSE Maths with clear formulas, worked examples at Foundation and Higher, and practice questions.

54. Angles: Basic Rules & Parallel Lines –

Learn angle rules and parallel line angles for GCSE Maths with step-by-step methods, worked examples, and practice questions.

55. Angles in Polygons –

Learn interior and exterior angles in polygons for GCSE Maths with formulas, worked examples, and practice questions.

56. Vectors –

Master vectors for GCSE Maths Higher tier with clear notation, worked examples, and exam-style practice questions.

H

57. Transformations: Reflection, Rotation, Translation

Master reflections, rotations, and translations for GCSE Maths with step-by-step methods, worked examples, and practice questions.

58. Enlargement & Scale Factor –

Learn enlargement and scale factor for GCSE Maths with step-by-step methods, fractional and negative scale factors, and practice questions.

59. Congruence and Similarity –

Master congruence and similarity for GCSE Maths with congruence conditions, similar shapes, area and volume scale factors, and practice questions.

60. Constructions and Loci –

Learn constructions and loci for GCSE Maths with step-by-step compass and ruler methods, worked examples, and practice questions.

61. Bearings –

Master bearings for GCSE Maths with three-figure notation, step-by-step methods, worked examples, and practice questions.

62. Plans and Elevations –

Learn plans and elevations for GCSE Maths Foundation with step-by-step methods, worked examples, and practice questions.

📊

Statistics & Probability

11 topics

63. Mean Median Mode and Range –

Learn how to calculate the mean, median, mode and range for GCSE Maths with worked examples, exam tips and practice questions.

64. Frequency Tables and Grouped Data –

Master frequency tables and grouped data for GCSE Maths with step-by-step methods, worked examples and practice questions.

65. Bar Charts Pie Charts and Pictograms –

Master bar charts, pie charts and pictograms for GCSE Maths Foundation with clear methods, worked examples and practice questions.

66. Histograms –

Learn how to draw and interpret histograms for GCSE Maths Higher with frequency density, worked examples and practice questions.

H

67. Cumulative Frequency and Box Plots –

Master cumulative frequency diagrams and box plots for GCSE Maths Higher with step-by-step methods, worked examples and practice questions.

H

68. Scatter Graphs and Correlation –

Learn scatter graphs and correlation for GCSE Maths with lines of best fit, worked examples and practice questions for Foundation and Higher.

69. Probability Basics and Relative Frequency –

Master probability basics and relative frequency for GCSE Maths with clear methods, worked examples and practice questions.

70. Probability Tree Diagrams –

Learn how to draw and use probability tree diagrams for GCSE Maths with worked examples, exam tips and practice questions.

71. Venn Diagrams –

Master Venn diagrams for GCSE Maths with set notation, worked examples and practice questions for Foundation and Higher tiers.

72. Conditional Probability –

Master conditional probability for GCSE Maths Higher with tree diagrams, Venn diagrams, worked examples and practice questions.

H

73. Sampling Methods –

Learn sampling methods for GCSE Maths including random, systematic and stratified sampling with worked examples and practice questions.

Ready to practise?

Get AI-marked practice questions on any topic — with instant feedback and step-by-step solutions.

Start free →
BlogStudy NotesPast Papers← Home