Practice

See where the marks go

Write a full proof, then compare it with the model and a near miss.

Try the 18-mark Core Pure mini-paper

Core Pure: proof and complex numbers

• Induction for sums and divisibilityProof by mathematical induction15 questions · Free
• Complex numbers and quadratic rootsImaginary and complex numbers15 questions · Free
• Conjugate pairs and polynomial rootsComplex conjugation13 questions
• The Argand diagram: modulus and argumentArgand diagrams15 questions
• Loci and regions in the Argand diagramLoci in the Argand diagram13 questions
• De Moivre's theorem: identities and sumsDe Moivre’s theorem14 questions
• Exponential form and nth rootsExponential form of complex numbers14 questions
• Roots of unity and their geometrySolving geometric problems13 questions

Core Pure: matrices

• Matrix arithmetic, identity and zeroIntroduction to matrices14 questions · Free
• Matrices as transformations in 2D and 3DLinear transformations in two dimensions14 questions
• Determinants, invariant points and invariant linesDeterminants14 questions
• Inverse matrices and singular matricesInverting a 2 × 2 matrix14 questions
• Three equations, three planesSolving systems of equations using matrices14 questions
• Induction for matrix powersProof by mathematical induction14 questions

Core Pure: roots, series and expansions

• Roots and coefficients, transformed rootsRoots of a quadratic equation14 questions

Further Statistics 1

• Discrete distributions and the Poisson modelExpected value of a discrete random variable12 questions
• Geometric and negative binomial modelsThe geometric distribution12 questions
• Poisson and geometric hypothesis testsTesting for the mean of a Poisson distribution12 questions
• The central limit theoremThe central limit theorem12 questions
• Chi-squared testsGoodness of fit12 questions
• Probability generating functionsProbability generating functions12 questions
• Type I and Type II errors, size and powerType I and Type II errors12 questions

Further Mechanics 1

• Momentum and impulseMomentum in one direction12 questions
• Work, energy and powerWork done12 questions
• Hooke's law and elastic energyHooke’s law and equilibrium problems12 questions
• Direct collisions and restitutionDirect impact and Newton’s law of restitution12 questions
• Oblique collisionsOblique impact with a fixed surface12 questions