OxfordAQA International AS and A-level Further Mathematics (9665) exam questions and past papers
Free OxfordAQA International A Level Further Maths past papers, with mark schemes and model answers for every paper.
How to use the past papers
Sit each paper under timed conditions, then mark it yourself with the mark scheme. Compare your answers with our model answers to see exactly what a full-mark answer looks like, and note the questions where you lost marks so you know what to revise next.
OxfordAQA International A Level Further Maths exam questions by topic
Every topic on the OxfordAQA International AS and A-level Further Mathematics (9665) specification, grouped by paper. Each pack has full model answers.
FP1: Pure maths (AS)
1.1
Further Algebra and FunctionsRational functions (asymptotes, inequalities), inequalities/modulus, roots & coefficients (quadratic), transformed roots, summation of series, method of differences
QuestionsModel answers
1.2
Further Coordinate GeometryEllipse, hyperbola, parabola, loci (distance from point and line)
QuestionsModel answers
FPSM1: Pure maths, statistics and mechanics (AS)
2.1
MatricesMatrix arithmetic (up to 3x3), 2D/3D transformations (2D incl. shears, invariant points and lines), determinants & inverses (2x2)
QuestionsModel answers
2.2
Numerical MethodsSign change, Newton-Raphson (incl. interval bisection, linear interpolation)
QuestionsModel answers
2.4
Further ProbabilityBayes, probability generating functions, linear combinations of RVs (Bayes, PGFs, linear combinations incl. covariance)
QuestionsModel answers
2.6
Further Kinematics and DynamicsRelative motion (interception, closest approach), dimensional analysis
QuestionsModel answers
2.8
Exponentials and LogarithmsLog-linear graphs (reducing laws to linear form)
QuestionsModel answers
FP2: Pure maths (A2)
3.1
Further Algebra and FunctionsRoots & coefficients (polynomials), summation of series (finite series), Maclaurin/Taylor (Maclaurin, limits)
QuestionsModel answers
3.4
Proof and Mathematical InductionSeries, divisibility (incl. proof of de Moivre)
QuestionsModel answers
3.5
Further CalculusImproper integrals, arc length, surface area (about x-axis), further trig integration (inverse trig)
QuestionsModel answers
3.6
Hyperbolic FunctionsDefinitions & graphs, identities & equations, inverse hyperbolic functions, differentiation & integration
QuestionsModel answers
3.7
Differential EquationsFirst order linear, second order homogeneous, second order non-homogeneous
QuestionsModel answers
3.8
Further Vectors and 3D GeometryScalar product, vector product, lines, planes, intersections, angles, shortest distances (incl. triple scalar product, direction cosines)
QuestionsModel answers
3.9
Matrices2D/3D transformations (3D rotations, reflections), determinants & inverses (3x3), eigenvalues/eigenvectors (real only), simultaneous equations (3 unknowns, geometric interpretation)
QuestionsModel answers
FS2: Statistics (A2)
4.1
Statistical EstimationUnbiased estimators (incl. consistency, efficiency, pooled), confidence intervals (normal, large sample, t)
QuestionsModel answers
4.2
Further Hypothesis TestingType I/II, power, chi-squared goodness of fit, chi-squared contingency (Yates for 2x2), t-tests/means (difference of means, pooled and paired t), variances (chi-squared single variance, F-test)
QuestionsModel answers
4.3
Moment Generating FunctionsDefinition and standard MGFs, moments, sums of independent random variables
QuestionsModel answers
FM2: Mechanics (A2)
5.5
Momentum and CollisionsMomentum & impulse, restitution, oblique collisions (2D, oblique, fixed surfaces)
QuestionsModel answers
5.6
Further Kinematics and DynamicsResistance (a + bv, a + bv^2), variable forces
QuestionsModel answers
StemUp Extreme Papers
Our hardest Further Maths questions, for students aiming for an A*. Every paper comes with full model answers.
A Level papers
Sit them timed, mark with the mark scheme, then compare with our model answers.
More OxfordAQA International A Level subjects
Join the StemUp study community
Be the first to know about new products, new resources and exam tips.
