GCSE Maths worksheets with answers

Number

1. Place value, ordering and decimal operations
2. Signed arithmetic and number lines
3. Operation order, inverses and reciprocals
4. Primes, factor trees, HCF and LCM
5. Systematic lists and combinations
6. Integer powers and roots
7. Equivalent fractions and mixed numbers
8. Fraction arithmetic and exact answers
9. Decimals, fractions and percentages
10. Metric units, money and dimensional conversion
11. Estimation and sense checks
12. Rounding, significant figures and error intervals
13. Standard form and calculator entry

Ratio, proportion and rates of change

1. Ratio notation and multiplicative comparison
2. Fractions within ratio problems
3. Sharing quantities and equivalent ratios
4. Scale factors, scale drawings and maps
5. Percentages, changes and multipliers
6. Original values, profit and simple interest
7. Compound growth and decay
8. Direct and inverse proportion: tables and relationships
9. Speed, density, pressure and unit pricing
10. Proportional graphs and rates of change

Algebra

1. Algebraic language and notation
2. Substitution and calculator brackets
3. Like terms and algebraic index rules
4. Single brackets and common factors
5. Expanding two binomials
6. Monic quadratics and difference of squares
7. Formulae and changing the subject
8. Identities and algebraic reasoning
9. Input/output and inverse number machines
10. Linear equations, including both sides
11. Forming equations from situations
12. One-variable linear inequalities
13. Two linear simultaneous equations
14. Solving monic quadratics by factorisation
15. Coordinates and geometric problems on axes
16. Plotting lines, gradient and intercept
17. Equations of lines and parallel lines
18. Quadratic graphs, roots and turning points
19. Cubic, reciprocal and contextual graphs
20. Term rules, special and geometric sequences
21. The nth term of a linear sequence

Geometry and measures

1. Shape vocabulary, symmetry and quadrilaterals
2. Angles at points, lines and parallel lines
3. Triangles, interior and exterior polygon angles
4. Congruence criteria and geometric deductions
5. Compass constructions and loci
6. Reflections, rotations and translations
7. Positive and fractional enlargements
8. Column vectors and vector arithmetic
9. Solids, plans and elevations
10. Circle vocabulary and perimeter
11. Areas of triangles, quadrilaterals and composites
12. Prisms, cylinders and surface area
13. Pyramids, cones, spheres and composite solids
14. Arc lengths and sectors
15. Similar figures and length ratios
16. Pythagoras in two dimensions
17. Right-triangle trigonometry in two dimensions
18. Exact trigonometric values
19. Bearings and geometric modelling

Probability and statistics

1. Probability language, frequency trees and expectation
2. Exhaustive outcomes and experimental probability
3. Sets, Venn diagrams and sample spaces
4. Independent and dependent event trees
5. Samples, populations and statistical claims
6. Data tables, bar/pie/time-series charts and frequency polygons
7. Ordered stem-and-leaf, averages, spread and grouped means
8. Scatter graphs and predictions
9. Linked representations and multistep reasoning

Foundation only

1. Foundation numerical fluency clinic
2. Foundation ratio and percentage problems
3. Foundation algebra and graph clinic
4. Foundation geometry and equipment clinic
5. Foundation statistics and probability clinic

Higher only: number, algebra and proportion

1. Product counting and estimating powers/roots
2. Fractional and negative indices
3. Surds, exact calculations and rationalising
4. Recurring decimals as fractions
5. Upper/lower bounds in calculations
6. Algebraic fractions and rational equations
7. Three binomials and non-monic factorisation
8. General algebraic proofs
9. Formal, inverse and composite functions
10. Translations and reflections of function graphs
11. Perpendicular gradients and line equations
12. Origin-centred circles and tangents
13. Completing the square and turning points
14. Quadratic formula and rearranged quadratics
15. Linear/quadratic simultaneous equations
16. Quadratic and two-variable inequalities
17. Exponential and trigonometric graphs
18. Graph gradients and areas
19. Average and instantaneous rates of change
20. Iterative formulae, roots and growth models
21. Quadratic sequence nth terms
22. Geometric sequences with surds and other patterns
23. Constructing direct/inverse proportional equations

Higher only: geometry and measures

1. Negative-scale-factor enlargement
2. Combined transformations and invariance
3. Area and volume in similar figures
4. Circle theorems and angle chains
5. Circle theorem proofs and linked geometry
6. Three-dimensional Pythagoras and trigonometry
7. Sine rule and the ambiguous case
8. Cosine rule for sides and angles
9. Area of any triangle and mixed trigonometry
10. Vector geometric arguments and proofs

Higher only: probability and statistics

1. Conditional probability in tables, trees and Venn diagrams
2. Algebraic probability and linked events
3. Histograms with unequal widths
4. Cumulative frequency and quantiles
5. Box plots and distribution comparisons
6. Capture–recapture and sampling assumptions

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