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AQA A-level Further Maths questions by topic
Original topic questions for AQA A-level Further Maths (7367), set out under the sections of AQA's Further Mathematics specification from Proof to Binary operations, in the order it prints them. Every question has a worked solution, and every set comes as a printable PDF.
Other specifications: Edexcel A-level Maths · Edexcel A-level Further Maths · AQA A-level Maths · OCR A-level Maths A · OCR A-level Further Maths A · OCR MEI A-level Maths · every topic, by unit
Compulsory content
A Proof30 questions2 topics
- Proof by induction: sums and series15 questions · 64 marks · A1 · PDF, 74 KB
- Induction: divisibility and matrices15 questions · 71 marks · A1 · PDF, 55 KB
B Complex numbers121 questions8 topics
- Complex arithmetic and the Argand diagram15 questions · 56 marks · B1, B2, B3, B4 · PDF, 55 KB
- Roots of polynomials15 questions · 68 marks · B1, B3 · PDF, 77 KB
- Modulus, argument and loci16 questions · 67 marks · B4, B5, B6, B7 · PDF, 79 KB
- Further loci and regions in the Argand diagram15 questions · 64 marks · B7 · PDF, 55 KB
- Geometric series15 questions · 59 marks · B8 · PDF, 55 KB
- De Moivre's theorem and trigonometric identities15 questions · 60 marks · B8, B9 · PDF, 77 KB
- Roots of unity and complex roots15 questions · 69 marks · B8, B9, B10, B11 · PDF, 77 KB
- Maclaurin series15 questions · 60 marks · B9 · PDF, 73 KB
B Complex numbers, Compulsory content, on the specification map
C Matrices76 questions5 topics
- Matrix algebra and transformations16 questions · 65 marks · C1, C2, C3, C5 · PDF, 82 KB
- Systems of equations and invariance15 questions · 64 marks · C4, C7, C8 · PDF, 76 KB
- Eigenvalues and eigenvectors15 questions · 67 marks · C4, C10 · PDF, 75 KB
- Determinants and inverses15 questions · 53 marks · C5, C6, C7, C9 · PDF, 74 KB
- Diagonalisation and the Cayley-Hamilton theorem15 questions · 63 marks · C11 · PDF, 78 KB
D Further algebra and functions213 questions14 topics
- Roots of polynomials15 questions · 68 marks · D1, D2 · PDF, 77 KB
- Summing series and the method of differences15 questions · 67 marks · D3, D4 · PDF, 77 KB
- Partial fractions15 questions · 60 marks · D4 · PDF, 52 KB
- Maclaurin series15 questions · 60 marks · D5, D6, D7 · PDF, 73 KB
- The general binomial expansion15 questions · 70 marks · D6 · PDF, 56 KB
- Limits and L'Hôpital's rule15 questions · 59 marks · D7 · PDF, 75 KB
- Simultaneous equations and inequalities15 questions · 60 marks · D8, D14 · PDF, 53 KB
- Graphs, proportion and transformations16 questions · 64 marks · D8, D11, D12, D13 and 2 more · PDF, 63 KB
- Inequalities and inequations15 questions · 61 marks · D8, D9, D10, D12 · PDF, 52 KB
- Functions, inverses and the modulus15 questions · 52 marks · D10, D11, D16 · PDF, 52 KB
- Conic sections15 questions · 60 marks · D13, D15 · PDF, 54 KB
- Quadratic functions15 questions · 56 marks · D14 · PDF, 54 KB
- Tangents, turning points and curve behaviour16 questions · 74 marks · D14 · PDF, 87 KB
- Matrix algebra and transformations16 questions · 65 marks · D16 · PDF, 82 KB
D Further algebra and functions, Compulsory content, on the specification map
E Further calculus121 questions8 topics
- Mean values and improper integrals15 questions · 60 marks · E1, E3, E9 · PDF, 75 KB
- Volumes of revolution16 questions · 65 marks · E2 · PDF, 81 KB
- Partial fractions15 questions · 60 marks · E4 · PDF, 52 KB
- Integrating rational functions15 questions · 62 marks · E4 · PDF, 73 KB
- Calculus with inverse trigonometric functions15 questions · 59 marks · E4, E5, E6 · PDF, 74 KB
- Arc length and surface area15 questions · 64 marks · E7 · PDF, 75 KB
- Reduction formulae15 questions · 69 marks · E8, E9 · PDF, 55 KB
- Limits and L'Hôpital's rule15 questions · 59 marks · E9 · PDF, 75 KB
E Further calculus, Compulsory content, on the specification map
F Further vectors45 questions3 topics
- Lines and planes in three dimensions15 questions · 61 marks · F1, F2, F3, F4 and 1 more · PDF, 75 KB
- Intersections, angles and distances15 questions · 58 marks · F3, F4, F6 · PDF, 77 KB
- The vector product and the scalar triple product15 questions · 56 marks · F4, F5, F6 · PDF, 78 KB
F Further vectors, Compulsory content, on the specification map
G Polar coordinates31 questions2 topics
- Polar curves16 questions · 66 marks · G1, G2 · PDF, 93 KB
- Areas with polar coordinates15 questions · 65 marks · G3 · PDF, 76 KB
G Polar coordinates, Compulsory content, on the specification map
H Hyperbolic functions45 questions3 topics
- Hyperbolic functions and identities15 questions · 60 marks · H1, H3, H4, H6 and 1 more · PDF, 74 KB
- Calculus with hyperbolic functions15 questions · 62 marks · H2, H4, H5, H7 · PDF, 53 KB
- Arc length and surface area15 questions · 64 marks · H7 · PDF, 75 KB
H Hyperbolic functions, Compulsory content, on the specification map
I Differential equations136 questions9 topics
- First order equations and integrating factors15 questions · 68 marks · I1, I2 · PDF, 56 KB
- Solving differential equations12 questions · 56 marks · I2, I3 · PDF, 51 KB
- Second order equations18 questions · 85 marks · I2, I4, I5, I6 · PDF, 78 KB
- Rates of change and building differential equations15 questions · 59 marks · I3 · PDF, 81 KB
- Modelling with differential equations15 questions · 68 marks · I3, I6, I7, I8 and 2 more · PDF, 78 KB
- Simple harmonic motion16 questions · 78 marks · I7, I10 · PDF, 84 KB
- Hooke's law and elastic strings15 questions · 60 marks · I10 · PDF, 80 KB
- Oscillations on strings and springs15 questions · 65 marks · I10 · PDF, 80 KB
- Newton's laws with a variable force15 questions · 65 marks · I11 · PDF, 80 KB
I Differential equations, Compulsory content, on the specification map
J Numerical methods32 questions2 topics
- The trapezium rule16 questions · 68 marks · J1 · PDF, 87 KB
- Numerical methods for differential equations16 questions · 62 marks · J1, J2, J3 · PDF, 85 KB
J Numerical methods, Compulsory content, on the specification map
Optional application 1, mechanics
MA Dimensional analysis15 questions1 topic
- Modelling, quantities and units15 questions · 51 marks · MA1, MA2 · PDF, 76 KB
MA Dimensional analysis, Optional application 1, mechanics, on the specification map
MB Momentum and collisions76 questions5 topics
- Momentum and impulse16 questions · 72 marks · MB1, MB3, MB4 · PDF, 107 KB
- Impulse and momentum as vectors15 questions · 60 marks · MB1, MB3 · PDF, 79 KB
- Direct impact and Newton's law of restitution15 questions · 65 marks · MB2 · PDF, 80 KB
- Oblique impact and impact with a smooth surface15 questions · 62 marks · MB2 · PDF, 81 KB
- Newton's laws with a variable force15 questions · 65 marks · MB4 · PDF, 80 KB
MB Momentum and collisions, Optional application 1, mechanics, on the specification map
MC Work, energy and power90 questions6 topics
- Work, energy and power15 questions · 65 marks · MC1, MC2, MC3, MC5 and 1 more · PDF, 79 KB
- Motion in a vertical circle15 questions · 66 marks · MC2 · PDF, 80 KB
- Elastic potential energy15 questions · 64 marks · MC3, MC5, MC6 · PDF, 80 KB
- Direct impact and Newton's law of restitution15 questions · 65 marks · MC3 · PDF, 80 KB
- Hooke's law and elastic strings15 questions · 60 marks · MC4 · PDF, 80 KB
- Newton's laws with a variable force15 questions · 65 marks · MC5 · PDF, 80 KB
MC Work, energy and power, Optional application 1, mechanics, on the specification map
MD Circular motion60 questions4 topics
- Angular speed and horizontal circular motion15 questions · 69 marks · MD1, MD2, MD3, MD4 and 1 more · PDF, 81 KB
- Radians, arcs and small angles15 questions · 51 marks · MD2 · PDF, 75 KB
- Kinematics with variable acceleration15 questions · 66 marks · MD4 · PDF, 80 KB
- Motion in a vertical circle15 questions · 66 marks · MD4, MD6 · PDF, 80 KB
MD Circular motion, Optional application 1, mechanics, on the specification map
ME Centres of mass and moments91 questions6 topics
- Centre of mass of a discrete distribution15 questions · 59 marks · ME1 · PDF, 56 KB
- Centres of mass of plane figures and frameworks15 questions · 58 marks · ME2, ME6 · PDF, 59 KB
- Centres of mass by integration15 questions · 72 marks · ME3, ME4 · PDF, 57 KB
- Equilibrium, suspension, toppling and sliding15 questions · 57 marks · ME5, ME6 · PDF, 59 KB
- Statics of a particle15 questions · 68 marks · ME6 · PDF, 77 KB
- Moments16 questions · 69 marks · ME6 · PDF, 83 KB
ME Centres of mass and moments, Optional application 1, mechanics, on the specification map
Optional application 2, statistics
SA Discrete random variables and expectation77 questions5 topics
- The binomial distribution15 questions · 52 marks · SA1, SA2, SA6 · PDF, 54 KB
- Discrete random variables and expectation15 questions · 57 marks · SA1, SA2, SA3, SA4 and 2 more · PDF, 76 KB
- Measures of location and spread16 questions · 59 marks · SA3 · PDF, 82 KB
- Goodness-of-fit tests16 questions · 67 marks · SA6 · PDF, 85 KB
- Summing series and the method of differences15 questions · 67 marks · SA7 · PDF, 77 KB
SB Poisson distribution45 questions3 topics
- The Poisson distribution15 questions · 65 marks · SB1, SB2, SB3, SB4 · PDF, 77 KB
- Discrete random variables and expectation15 questions · 57 marks · SB3 · PDF, 76 KB
- Hypothesis tests for Poisson and geometric models15 questions · 58 marks · SB5 · PDF, 81 KB
SB Poisson distribution, Optional application 2, statistics, on the specification map
SC Type I and Type II errors61 questions4 topics
- Hypothesis testing with the binomial16 questions · 67 marks · SC1 · PDF, 61 KB
- Hypothesis testing: correlation and the normal15 questions · 61 marks · SC1 · PDF, 82 KB
- Hypothesis tests for Poisson and geometric models15 questions · 58 marks · SC1 · PDF, 81 KB
- Type I and Type II errors, test size and power15 questions · 59 marks · SC1, SC2 · PDF, 79 KB
SC Type I and Type II errors, Optional application 2, statistics, on the specification map
SD Continuous random variables75 questions5 topics
- Discrete random variables and expectation15 questions · 57 marks · SD1, SD5 · PDF, 76 KB
- Continuous random variables: density and distribution functions15 questions · 61 marks · SD1, SD2, SD3, SD6 · PDF, 78 KB
- Mean, variance and skewness of continuous variables15 questions · 63 marks · SD3, SD4, SD5 · PDF, 78 KB
- The continuous uniform distribution15 questions · 67 marks · SD7 · PDF, 56 KB
- Combinations of normal random variables15 questions · 68 marks · SD8 · PDF, 80 KB
SD Continuous random variables, Optional application 2, statistics, on the specification map
SE Chi squared tests for association32 questions2 topics
- Contingency tables16 questions · 62 marks · SE1, SE2, SE3, SE4 and 1 more · PDF, 83 KB
- Goodness-of-fit tests16 questions · 67 marks · SE2, SE3, SE5 · PDF, 85 KB
SE Chi squared tests for association, Optional application 2, statistics, on the specification map
SF Exponential distribution60 questions4 topics
- The Poisson distribution15 questions · 65 marks · SF1, SF4 · PDF, 77 KB
- Continuous random variables: density and distribution functions15 questions · 61 marks · SF1, SF2, SF3, SF4 · PDF, 78 KB
- Reduction formulae15 questions · 69 marks · SF3 · PDF, 55 KB
- Mean, variance and skewness of continuous variables15 questions · 63 marks · SF3 · PDF, 78 KB
SF Exponential distribution, Optional application 2, statistics, on the specification map
SG Inference: one sample t-distribution15 questions1 topic
SH Confidence intervals30 questions2 topics
- Estimators, standard error and confidence intervals15 questions · 57 marks · SH1, SH2, SH3 · PDF, 79 KB
- Confidence intervals and tests with the t-distribution15 questions · 66 marks · SH2, SH3, SH4 · PDF, 80 KB
SH Confidence intervals, Optional application 2, statistics, on the specification map
Optional application 3, discrete mathematics
DA Graphs108 questions7 topics
- Graphs: order, Eulerian paths and planarity15 questions · 57 marks · DA1, DA2, DA3, DA4 and 3 more · PDF, 57 KB
- Minimum spanning trees: Prim and Kruskal16 questions · 60 marks · DA1, DA5, DA6 · PDF, 67 KB
- Route inspection15 questions · 66 marks · DA1, DA2 · PDF, 57 KB
- The travelling salesman problem15 questions · 71 marks · DA2 · PDF, 57 KB
- Shortest paths: Dijkstra and Floyd16 questions · 76 marks · DA5 · PDF, 62 KB
- Critical path analysis16 questions · 66 marks · DA6 · PDF, 59 KB
- Subgroups, Lagrange's theorem and isomorphism15 questions · 60 marks · DA7 · PDF, 55 KB
DA Graphs, Optional application 3, discrete mathematics, on the specification map
DB Networks78 questions5 topics
- Minimum spanning trees: Prim and Kruskal16 questions · 60 marks · DB1, DB2 · PDF, 67 KB
- Shortest paths: Dijkstra and Floyd16 questions · 76 marks · DB1 · PDF, 62 KB
- Route inspection15 questions · 66 marks · DB1, DB3, DB5 · PDF, 57 KB
- Flows in networks: cuts and capacity16 questions · 66 marks · DB1, DB5 · PDF, 64 KB
- The travelling salesman problem15 questions · 71 marks · DB2, DB4, DB5 · PDF, 57 KB
DB Networks, Optional application 3, discrete mathematics, on the specification map
DC Network flows31 questions2 topics
- Flows in networks: cuts and capacity16 questions · 66 marks · DC1, DC2, DC4, DC6 and 1 more · PDF, 64 KB
- Maximum flow and the labelling procedure15 questions · 59 marks · DC1, DC3, DC5, DC6 · PDF, 59 KB
DC Network flows, Optional application 3, discrete mathematics, on the specification map
DD Linear programming31 questions2 topics
- Linear programming: formulation and graphical solution16 questions · 65 marks · DD1, DD2 · PDF, 63 KB
- The Simplex algorithm15 questions · 68 marks · DD3, DD4 · PDF, 58 KB
DD Linear programming, Optional application 3, discrete mathematics, on the specification map
DE Critical path analysis31 questions2 topics
- Critical path analysis16 questions · 66 marks · DE1, DE2, DE3, DE4 · PDF, 59 KB
- Float, Gantt charts and scheduling15 questions · 58 marks · DE3, DE4, DE5, DE6 · PDF, 57 KB
DE Critical path analysis, Optional application 3, discrete mathematics, on the specification map
DF Game theory for zero-sum games61 questions4 topics
- Game theory: play safe and stable solutions15 questions · 65 marks · DF1, DF2, DF3, DF4 · PDF, 58 KB
- Mixed strategies in game theory15 questions · 70 marks · DF2, DF4, DF5, DF6 · PDF, 57 KB
- Linear programming: formulation and graphical solution16 questions · 65 marks · DF6 · PDF, 63 KB
- The Simplex algorithm15 questions · 68 marks · DF6 · PDF, 58 KB
DG Binary operations76 questions5 topics
- Matrix algebra and transformations16 questions · 65 marks · DG1, DG2, DG5 · PDF, 82 KB
- Groups and their axioms15 questions · 62 marks · DG1, DG2, DG3, DG4 and 7 more · PDF, 55 KB
- Modular arithmetic and Fermat's little theorem15 questions · 60 marks · DG1, DG6 · PDF, 74 KB
- Determinants and inverses15 questions · 53 marks · DG6 · PDF, 74 KB
- Subgroups, Lagrange's theorem and isomorphism15 questions · 60 marks · DG7, DG9, DG10, DG12 · PDF, 55 KB
DG Binary operations, Optional application 3, discrete mathematics, on the specification map
A topic is listed under every section its lesson teaches, so some appear more than once. The codes beside each one are the specification references it covers in that section.
All questions, worked solutions and marking guidance are original InkMaths material. They are not copied from awarding-body papers or mark schemes. The codes show how InkMaths allocates the stated total; an awarding body may credit a valid alternative method differently.
The sections and codes are AQA's. Check the current specification when a mark depends on it. The 7367 specification map lists every statement, with the lesson that teaches it.