Free practice · 2022–2026
132 original past-paper questions and language tasks for Higher Mathematics. Choose a topic and read each question right here, with screen-friendly wording and its original equations and diagrams. Rarity shows how often its question type was found in the last five exam years—not how difficult it is.
41 matching entries · Higher · showing 1–24. Mixed questions appear in every relevant topic filter, but are counted once.
Higher Mathematics
Paper 1 Non-calculator
PDF page 3 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 5 · check any continuation
Tangent equations to curves · Trigonometric equations · 2 more skills
Differentiate to find the gradient, then use the point to form the tangent equation.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 6 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 4 · check any continuation
Domains, ranges and transformations · Stationary points and optimisation
Track how inputs, outputs and key coordinates change.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 5 · check any continuation
Areas under and between curves
Find the boundaries, integrate the difference and account for areas below the axis.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 6 · check any continuation
Increasing and decreasing functions
Use the sign of the derivative to justify intervals of behaviour.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 7 · check any continuation
Stationary points and optimisation
Find critical values and justify their nature or practical relevance.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 3 · check any continuation
Tangent equations to curves
Differentiate to find the gradient, then use the point to form the tangent equation.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 3 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 4 · check any continuation
Domains, ranges and transformations · Stationary points and optimisation
Track how inputs, outputs and key coordinates change.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 6 · check any continuation
Differentiation and rates of change · Integration and definite integrals
Differentiate the supplied function and apply the result in context.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 7 · check any continuation
Polynomial division and factor theorem · Differentiation and rates of change · 2 more skills
Use a known factor or remainder to reduce a polynomial problem.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 4 · check any continuation
Areas under and between curves
Find the boundaries, integrate the difference and account for areas below the axis.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 5 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 6 · check any continuation
Triangle trigonometry and bearings · Stationary points and optimisation
Choose the right trigonometric relationship and use the stated angle units.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 3 · check any continuation
Differentiation and rates of change · Integration and definite integrals
Differentiate the supplied function and apply the result in context.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 5 · check any continuation
Differentiation and rates of change
Differentiate the supplied function and apply the result in context.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 3 · check any continuation
Tangent equations to curves
Differentiate to find the gradient, then use the point to form the tangent equation.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 4 · check any continuation
Domains, ranges and transformations · Quadratic equations and graphs · 1 more skills
Track how inputs, outputs and key coordinates change.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 5 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 6 · check any continuation
Areas under and between curves
Find the boundaries, integrate the difference and account for areas below the axis.
Published marking linked · general strategy, not a model answer
Paper 2
PDF page 6 · check any continuation
Stationary points and optimisation
Find critical values and justify their nature or practical relevance.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 3 · check any continuation
Differentiation and rates of change · Integration and definite integrals
Differentiate the supplied function and apply the result in context.
Published marking linked · general strategy, not a model answer
Paper 1 Non-calculator
PDF page 4 · check any continuation
Integration and definite integrals
Find an antiderivative and use limits or a supplied condition correctly.
Published marking linked · general strategy, not a model answer
132 numbered questions or named language tasks across 10 source PDFs in this subject/level selection. Repeated copies of the same extracted question are grouped once. 9 entries still need topic classification. Optional essay and text choices are included; these counts are not the number you must answer in an exam.
Question anchors and printed allocations are extracted from SHA-256-verified source PDFs. Optional alternatives are not added together. Applicable all-question paper totals are reconciled with the printed rubric; mismatches withhold automatic mark totals. A first written-answer marking row is never treated as a whole-question total. Exact marking pages require a section-matched table anchor or a wording- and digest-checked source pair. Topic headings are conservative rule matches and provisional, not independently reviewed or proof of current syllabus coverage. Original questions, diagrams, passages and official answers are not republished in this metadata index. Checked original question pages are rendered on demand in the website without rewriting their wording or diagrams. Scans, extraction gaps and uncertain marks remain visible rather than filled with invented content. Source audit: 2026-10-21. Question index: 2026-10-23. There were no ordinary exam sittings in 2020 or 2021. This is not a claim that every question has been independently checked or that scanned papers are fully indexed.
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