A Level Maths A* Exam Questions

This is a collection of A* questions chosen for one reason: they are genuinely difficult. They are taken from the CIE Pre-U Maths syllabus — a qualification once sat in many top UK private schools as a more challenging alternative to A Level Maths — together with the hardest questions from the OCR B (MEI) 4754 (C4) papers. Every question here remains directly relevant to the current A Level Maths syllabus.

These questions sit beyond Stage 4 of your A Level Maths journey — they are for students who have already worked through the video lessons, practised with exam questions by topic, consolidated their understanding with revision notes, and tested themselves with past papers, but want to push further. They are ideal for students aiming for an A* grade.

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C3 Jun 2005, Q8 (OCR 4753) Further Differentiation, Further Integration Question | Mark Scheme | Solution
C3 Jun 2005, Q9 (OCR 4753) Functions, Further Differentiation, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2006, Q7 (OCR 4753) Further Differentiation, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2006, Q8 (OCR 4753) Functions, Further Differentiation, Integration By Substitution, Transformations Question | Mark Scheme | Solution
C3 Jun 2006, Q7 (OCR 4753) Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2006, Q8 (OCR 4753) Transformations, Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2007, Q7 (OCR 4753) Functions, Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jan 2007, Q8 (OCR 4753) Functions, Further Differentiation, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2007, Q7 (OCR 4753) Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2007, Q8 (OCR 4753) Functions, Further Differentiation, Further Integration Question | Mark Scheme | Solution
C3 Jan 2008, Q7 (OCR 4753) Further Differentiation, Integration By Substitution, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2008, Q8 (OCR 4753) Transformations, Functions Question | Mark Scheme | Solution
C3 Jun 2008, Q8 (OCR 4753) Functions, Further Differentiation, Further Integration Question | Mark Scheme | Solution
C3 Jun 2008, Q9 (OCR 4753) Transformations, Further Differentiation Question | Mark Scheme | Solution
C3 Jan 2009, Q8 (OCR 4753) Further Differentiation, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2009, Q9 (OCR 4753) Functions, Further Differentiation, Transformations Question | Mark Scheme | Solution
C3 Jun 2009, Q8 (OCR 4753) Functions, Exponentials and Logarithms, Further Integration Question | Mark Scheme | Solution
C3 Jun 2009, Q9 (OCR 4753) Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2010, Q8 (OCR 4753) Further Differentiation, Further Integration Question | Mark Scheme | Solution
C3 Jan 2010, Q9 (OCR 4753) Further Differentiation, Functions Question | Mark Scheme | Solution
C3 Jun 2010, Q8 (OCR 4753) Exponentials and Logarithms, Further Integration Question | Mark Scheme | Solution
C3 Jun 2010, Q9 (OCR 4753) Further Differentiation, Functions, Exponentials and Logarithms, Transformations Question | Mark Scheme | Solution
C3 Jan 2011, Q8 (OCR 4753) Integration By Substitution, Further Differentiation, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jan 2011, Q9 (OCR 4753) Further Differentiation, Further Integration, Transformations Question | Mark Scheme | Solution
C3 Jun 2011, Q8 (OCR 4753) Functions, Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2011, Q9 (OCR 4753) Transformations, Functions Question | Mark Scheme | Solution
C3 Jan 2012, Q8 (OCR 4753) Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jan 2012, Q9 (OCR 4753) Exponentials and Logarithms, Functions, Integration By Substitution Question | Mark Scheme | Solution
C3 Jun 2012, Q8 (OCR 4753) Further Differentiation, Further Integration Question | Mark Scheme | Solution
C3 Jun 2012, Q9 (OCR 4753) Transformations, Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jan 2013, Q8 (OCR 4753) Transformations, Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jan 2013, Q9 (OCR 4753) Functions, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2013, Q8 (OCR 4753) Further Differentiation, Further Integration, Transformations, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2013, Q9 (OCR 4753) Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jun 2014, Q8 (OCR 4753) Functions, Further Differentiation Question | Mark Scheme | Solution
C3 Jun 2014, Q9 (OCR 4753) Further Differentiation, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2015, Q8 (OCR 4753) Further Differentiation, Transformations Question | Mark Scheme | Solution
C3 Jun 2015, Q9 (OCR 4753) Further Differentiation, Functions, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2016, Q8 (OCR 4753) Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jun 2016, Q9 (OCR 4753) Further Differentiation, Exponentials and Logarithms, Functions, Transformations Question | Mark Scheme | Solution
C3 Jun 2017, Q8 (OCR 4753) Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jun 2017, Q9 (OCR 4753) Functions, Further Differentiation, Integration By Substitution, Exponentials and Logarithms Question | Mark Scheme | Solution
C3 Jun 2018, Q8 (OCR 4753) Further Differentiation, Integration By Substitution Question | Mark Scheme | Solution
C3 Jun 2018, Q9 (OCR 4753) Transformations, Exponentials and Logarithms, Further Integration Question | Mark Scheme | Solution
C4 Jun 2005, Q7 (OCR 4754) Rational Expressions, Further Integration, Differential Equations, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jan 2006, Q7 (OCR 4754) Trigonometry: Compound and Double Angle Formulae, Further Differentiation, Trigonometry: Secant, Cosecant and Cotangent, Differentiation Question | Mark Scheme | Solution
C4 Jan 2006, Q8 (OCR 4754) Further Differentiation, Rational Expressions, Further Integration, Differential Equations, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2006, Q6 (OCR 4754) Parametric Equations, Trigonometry: Radians, Circle Sectors and Triangles, Trigonometry Question | Mark Scheme | Solution
C4 Jan 2007, Q7 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae, Quadratic Equations Question | Mark Scheme | Solution
C4 Jun 2007, Q7 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2007, Q8 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent Question | Mark Scheme | Solution
C4 Jan 2008, Q8 (OCR 4754) Parametric Equations, Further Differentiation, Differential Equations, Transformations Question | Mark Scheme | Solution
C4 Jun 2008, Q9 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jan 2009, Q7 (OCR 4754) Differential Equations, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jan 2009, Q8 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent Question | Mark Scheme | Solution
C4 Jun 2009, Q8 (OCR 4754) Trigonometry: Compound and Double Angle Formulae, Trigonometry, Quadratic Equations, Surds Question | Mark Scheme | Solution
C4 Jan 2010, Q6 (OCR 4754) Trigonometry: Compound and Double Angle Formulae Question | Mark Scheme | Solution
C4 Jan 2010, Q7 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2010, Q8 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae, Trigonometry Question | Mark Scheme | Solution
C4 Jan 2011, Q7 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jan 2011, Q8 (OCR 4754) Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent Question | Mark Scheme | Solution
C4 Jun 2011, Q8 (OCR 4754) Connected Rates of Change, Differential Equations, Further Integration Question | Mark Scheme | Solution
C4 Jan 2012, Q8 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae Question | Mark Scheme | Solution
C4 Jan 2012, Q9 (OCR 4754) Connected Rates of Change, Differential Equations Question | Mark Scheme | Solution
C4 Jun 2012, Q7 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent Question | Mark Scheme | Solution
C4 Jan 2013, Q8 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2013, Q6 (OCR 4754) Differential Equations, Trigonometry: Compound and Double Angle Formulae Question | Mark Scheme | Solution
C4 Jun 2013, Q7 (OCR 4754) Parametric Equations, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2014, Q8 (OCR 4754) Differential Equations, Rational Expressions Question | Mark Scheme | Solution
C4 Jun 2015, Q7 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2016, Q8 (OCR 4754) Rational Expressions, Differential Equations, Exponentials and Logarithms Question | Mark Scheme | Solution
C4 Jun 2017, Q7 (OCR 4754) Differential Equations, Further Differentiation, Parametric Equations, Trigonometry: Secant, Cosecant and Cotangent, Integration By Substitution Question | Mark Scheme | Solution
C4 Jun 2017, Q8 (OCR 4754) Parametric Equations, Trigonometry: Compound and Double Angle Formulae Question | Mark Scheme | Solution
C4 Jun 2018, Q8 (OCR 4754) Differential Equations, Rational Expressions, Further Integration, Exponentials and Logarithms Question | Mark Scheme | Solution
Mixed Topic A* Questions — Pure Sheet 1 (Cambridge Pre-U) Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent, Parametric Equations, Further Differentiation, Surds Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 2 (Cambridge Pre-U) Connected Rates of Change, Differentiation, Polynomial Division And The Factor Theorem, Rational Expressions, Further Integration, Sequences and Series Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 3 (Cambridge Pre-U) Differential Equations, Trigonometry: Compound and Double Angle Formulae, Trigonometry: Secant, Cosecant and Cotangent, Further Integration Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 4 (Cambridge Pre-U) Trigonometry: Compound and Double Angle Formulae, Functions, Parametric Equations, Further Differentiation, Trigonometry: Radians, Circle Sectors and Triangles Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 5 (Cambridge Pre-U) Parametric Equations, Functions, General Binomial Expansion, Integration By Substitution Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 6 (Cambridge Pre-U) Further Differentiation, Trigonometry: Radians, Circle Sectors and Triangles, Integration By Substitution Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 7 (Cambridge Pre-U) Differentiation, Functions, Trigonometry: Compound and Double Angle Formulae, Connected Rates of Change, Integration By Substitution, Further Differentiation Question | Mark Scheme
Mixed Topic A* Questions — Pure Sheet 8 (Cambridge Pre-U) Sequences and Series, Rational Expressions, Differential Equations, Further Integration, Trigonometry: Compound and Double Angle Formulae, Transformations Question | Mark Scheme
Mixed Topic A* Questions — Stats Sheet 1 (Cambridge Pre-U) Correlation and Regression, The Normal Distribution, Discrete Distributions (inc. Binomial Distribution) Question | Mark Scheme
Mixed Topic A* Questions — Stats Sheet 2 (Cambridge Pre-U) The Normal Distribution, Probability Question | Mark Scheme
Mixed Topic A* Questions — Stats Sheet 3 (Cambridge Pre-U) Discrete Distributions (inc. Binomial Distribution), Binomial Expansion, The Normal Distribution Question | Mark Scheme
Mixed Topic A* Questions — Mech Sheet 1 (Cambridge Pre-U) Newton's Third Law (Objects in Contact and Connected Particles), Coefficient Of Friction, Resolving Non-Perpendicular Forces Question | Mark Scheme
Mixed Topic A* Questions — Mech Sheet 2 (Cambridge Pre-U) Coefficient Of Friction, Resolving Non-Perpendicular Forces, Kinematics: Constant Acceleration (SUVAT), Projectiles, Further Differentiation Question | Mark Scheme
Mixed Topic A* Questions — Mech Sheet 3 (Cambridge Pre-U) Projectiles Question | Mark Scheme