GCSE topic mastery
Build understanding.
Then tackle the hard questions.
A GCSE Maths resource library with gradually more demanding questions and separate worked solutions. Find your starting point, practise with purpose, and develop the reasoning behind the method.
Start here: how to get the most from the packs
- Find your starting point.
Try the six diagnostic questions, D1–D6, before looking at the solutions. Use what you find to choose a starting stage. An error is useful information about what to practise next.
- Practise a small set properly.
Work for about 20–30 minutes on a manageable selection, rather than rushing a whole booklet. Show your working and explain your decisions. If a method is unfamiliar, use the reference page or a relevant video, then try fresh questions independently.
- Check, explain, then retry.
Open the solutions after a genuine attempt. Compare the reasoning, not just the final answer. Record the question, your error and the change you need to make. Close the solution and redo the question from the beginning.
- Come back to it.
Retry mistakes in a later session. Attempt R1–R6 at least a week later with your earlier work closed, then mix in older topics. Use past papers too, so you practise recognising which method a new problem needs.
Choose challenge thoughtfully. You do not need to finish every pack in one sitting. Follow each booklet’s calculator and accuracy instructions, and print it or annotate it on a tablet. Grade bands describe intended difficulty, not a guaranteed exam grade; some final tasks are deliberate extensions. The PDFs open in a new tab, where you can save or print them using your browser.
For parents and teachers
Use the diagnostic to select practice, then allocate a small set with a clear purpose. Ask students to explain why a method works and to retry errors without the solution visible. The worked solutions support feedback; these are topic practice packs rather than timed exam papers or official exam-board mark schemes.
Choose your next step
Find a topic. Build it properly.
Each pack contains 60 main questions, six diagnostic tasks and six retrieval tasks. Start with the questions; keep the worked solutions for checking and feedback.
Linear equations
Build equations, handle brackets and fractions, then explain and generalise your methods.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Percentages
Work with multipliers, reverse percentages and connected percentage problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Ratio
Simplify, share and recover quantities before tackling changing groups and linked ratios.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Direct & inverse proportion
Build proportional models and connect powers, roots and change factors.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Indices
Develop index laws, including zero, negative and fractional powers, and use them in equations.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Rearranging formulae
Change the subject using inverse operations, factorisation and valid branches.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Expanding & factorising
Move from brackets and common factors to quadratic structure and algebraic proof.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Straight-line graphs
Connect gradients, equations, perpendicular lines and intersections with geometric reasoning.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Quadratic equations
Choose a method, solve hidden quadratics and check restrictions on your solutions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Simultaneous equations
Use elimination and substitution, form models and find complete solution sets.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Quadratic graphs
Plot and interpret parabolas, then connect roots, symmetry and turning points.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Similarity & scale factors
Match corresponding lengths and connect scale factors with area, volume and proof.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Pythagoras
Build reliable right-triangle reasoning and combine exact lengths with unfamiliar geometry.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Right-angled trigonometry
Use sine, cosine and tangent with exact values and connected right-triangle problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Sine rule, cosine rule & triangle area
Choose and combine non-right-triangle methods, including exact area calculations.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Circle theorems & proof
Connect angle facts and circle theorems, giving clear reasons for each step.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Vectors & geometric proof
Use vector relationships to solve geometry problems and justify conclusions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Probability trees & conditional probability
Organise outcomes, build tree models and choose the correct conditional probabilities.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Averages, spread & statistical problems
Use averages and measures of spread to compare, reconstruct and reason about data.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Histograms & frequency density
Connect class width, area and frequency, then work backwards from incomplete information.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Cumulative frequency & box plots
Read and construct summaries, compare distributions and interpret quartiles carefully.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Bounds, error intervals & accuracy
Interpret rounding intervals and use them to justify calculations and accuracy claims.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Surds & exact calculations
Simplify and combine surds while preserving exact values in connected problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Algebraic fractions
Simplify, combine and solve while keeping excluded values and valid solutions in view.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Sequences & nth-term problems
Find and use sequence rules, recover missing information and explain general patterns.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Inequalities & regions
Solve inequalities and interpret boundaries, solution sets and feasible regions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Functions & graph transformations
Work with functions, their combinations and transformations, checking valid inputs.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Algebraic proof & number reasoning
Represent number properties algebraically and build arguments that cover every case.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Perimeter, area & compound shapes
Separate boundary from area and combine familiar shapes in multi-step problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Circles, arcs & sectors
Connect circumference, arc length, sector area and exact circular geometry.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Volume & surface area
Model solids and combine dimensions, capacity and material area accurately.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Compound measures
Connect quantities and units in speed, density, pressure and other rate problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Transformations & invariance
Describe and combine transformations, then identify what changes and what stays fixed.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Constructions & loci
Use precise constructions and interpret sets of points satisfying geometric conditions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Bearings, scale drawings & navigation
Link directions and scale with distances, angles and multi-step journeys.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Angles, parallel lines & polygons
Build angle reasoning from line facts to polygons and connected geometric arguments.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Congruence & geometric proof
Identify sufficient information and construct clear, complete geometric proofs.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
3D geometry: Pythagoras & trigonometry
Find the right triangles inside solids and combine exact lengths with spatial reasoning.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Standard form & estimation
Work with very large and small numbers and use estimates to check conclusions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Fractions, decimals & recurring decimals
Connect exact representations and use fractions and recurring decimals in reasoning.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Prime factors, HCF, LCM & divisibility
Use prime structure to solve factor, multiple and reverse-number problems.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Sets & Venn diagrams
Use precise set language, reconstruct regions and reason about overlaps and selection.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Systematic listing & the product rule
Organise choices, handle restrictions and prove that a counting method is complete.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Plans, elevations & spatial reasoning
Read views, reconstruct solids and reason about hidden cubes and exposed faces.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Real-life graphs & rates of change
Connect gradients and areas with journeys, motion and changing rates.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Numerical methods & iteration
Use systematic trials and brackets, then interpret iterative rules and rounding claims.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Scatter graphs & correlation
Plot paired data, interpret estimates and challenge claims about statistical models.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Sampling, bias & population estimates
Design samples and assess weighting, missing responses and population estimates.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Two-way tables & frequency trees
Complete counts, choose reference groups and reconstruct missing conditional information.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Statistical diagrams & comparisons
Construct and compare charts while checking scales, changing totals and misleading displays.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Growth, decay & repeated change
Compose multipliers and reason backwards through repeated percentage models.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Forming equations & modelling
Translate words and diagrams into models, then check assumptions and feasible answers.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Coordinate geometry & reasoning
Combine coordinates, distances, gradients and midpoints to reconstruct and prove shapes.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Non-linear graphs
Explore cubic, reciprocal and exponential families, intersections and domain restrictions.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Trigonometric graphs & equations
Connect sine, cosine and tangent graphs with exact values and complete solution sets.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Equations of circles & tangents
Combine radius, coordinates and perpendicular gradients with exact intersections and proof.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
Optimisation: maximum & minimum
Build objectives, apply constraints and prove optimal results without calculus.
60 main questions + diagnostic & retrieval
Video lesson Lesson to follow
You can start with the questions and use the worked solutions to check your reasoning.
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