A-level Maths and Further Maths questions by topic
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2,593 questions worth 10,575 marks: original questions written for this library; none is taken from a past paper. Write your answer on paper before opening the worked solution and marking guidance.
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Practise 2,593 original A-level Maths and Further Maths questions. Answer each question before viewing the worked solution and InkMaths marking guidance. Filter by topic, unit, demand or response type, or build a timed set.
Choose a topic: all 171 topics with questions, grouped into 29 units with a search field over them. Each one opens its questions in full, with a worked answer under every question.
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Progress lives in this browser, on this device, unless you sign in. 2,593 questions worth 10,575 marks. The same questions are in the printable workbooks, with the answers in a separate book.
Every topic with questions
Proof30 questions2 topics
- The structure of proof: deduction and exhaustion15 questions · 54 marks
- Disproof and proof by contradiction15 questions · 51 marks
Algebra and functions121 questions8 topics
- Indices and surds15 questions · 52 marks
- Quadratic functions15 questions · 56 marks
- Simultaneous equations and inequalities15 questions · 60 marks
- Polynomials and the factor theorem15 questions · 56 marks
- Graphs, proportion and transformations16 questions · 64 marks
- Functions, inverses and the modulus15 questions · 52 marks
- Partial fractions15 questions · 60 marks
- Functions in modelling15 questions · 55 marks
Coordinate geometry45 questions3 topics
- Straight lines15 questions · 56 marks
- Circles15 questions · 56 marks
- Parametric equations15 questions · 56 marks
Sequences and series75 questions5 topics
- The binomial expansion15 questions · 55 marks
- The general binomial expansion15 questions · 70 marks
- Sequences and sigma notation15 questions · 57 marks
- Arithmetic series15 questions · 57 marks
- Geometric series15 questions · 59 marks
Trigonometry91 questions6 topics
- Triangles and the sine and cosine rules15 questions · 57 marks
- Trigonometric graphs and equations16 questions · 63 marks
- Radians, arcs and small angles15 questions · 51 marks
- Reciprocal and inverse trigonometric functions15 questions · 56 marks
- Compound angles and the harmonic form15 questions · 62 marks
- Trigonometric modelling15 questions · 57 marks
Exponentials and logarithms46 questions3 topics
- Exponential functions and e15 questions · 52 marks
- Logarithms and their laws15 questions · 53 marks
- Log graphs and exponential models16 questions · 65 marks
Differentiation106 questions7 topics
- The derivative from first principles15 questions · 60 marks
- Differentiating powers of x15 questions · 52 marks
- Tangents, turning points and curve behaviour16 questions · 74 marks
- Differentiating trig, exponentials and logs15 questions · 54 marks
- The product, quotient and chain rules15 questions · 54 marks
- Implicit and parametric differentiation15 questions · 62 marks
- Rates of change and building differential equations15 questions · 59 marks
Integration106 questions7 topics
- Integration as antidifferentiation15 questions · 56 marks
- Definite integrals and areas16 questions · 64 marks
- Integrating standard functions15 questions · 56 marks
- Integration by substitution and by parts15 questions · 64 marks
- Integrating rational functions15 questions · 62 marks
- Areas, parametric curves and the limit of a sum15 questions · 69 marks
- Solving differential equations15 questions · 73 marks
Numerical methods46 questions3 topics
- Locating roots and iteration15 questions · 51 marks
- The Newton-Raphson method15 questions · 57 marks
- The trapezium rule16 questions · 68 marks
Vectors30 questions2 topics
- Vectors in two dimensions15 questions · 56 marks
- Vectors in three dimensions15 questions · 57 marks
Statistics153 questions10 topics
- Sampling and the large data set15 questions · 52 marks
- Measures of location and spread16 questions · 59 marks
- Representing and interpreting data16 questions · 59 marks
- Correlation and regression16 questions · 57 marks
- Probability and Venn diagrams15 questions · 56 marks
- Conditional probability15 questions · 52 marks
- The binomial distribution15 questions · 52 marks
- The normal distribution15 questions · 56 marks
- Hypothesis testing with the binomial15 questions · 61 marks
- Hypothesis testing: correlation and the normal15 questions · 61 marks
Mechanics138 questions9 topics
- Modelling, quantities and units15 questions · 51 marks
- Kinematics with constant acceleration16 questions · 70 marks
- Kinematics with variable acceleration15 questions · 66 marks
- Forces and Newton's laws15 questions · 59 marks
- Connected particles and pulleys15 questions · 64 marks
- Projectiles15 questions · 59 marks
- Friction and inclined planes16 questions · 73 marks
- Statics of a particle15 questions · 68 marks
- Moments16 questions · 69 marks
Further proof30 questions2 topics
- Proof by induction: sums and series15 questions · 64 marks
- Induction: divisibility and matrices15 questions · 71 marks
Complex numbers61 questions4 topics
- Complex arithmetic and the Argand diagram15 questions · 56 marks
- Modulus, argument and loci16 questions · 67 marks
- De Moivre's theorem and trigonometric identities15 questions · 60 marks
- Roots of unity and complex roots15 questions · 69 marks
Matrices46 questions3 topics
- Matrix algebra and transformations16 questions · 65 marks
- Determinants and inverses15 questions · 53 marks
- Systems of equations and invariance15 questions · 64 marks
Further algebra and series45 questions3 topics
- Roots of polynomials15 questions · 68 marks
- Summing series and the method of differences15 questions · 67 marks
- Maclaurin series15 questions · 60 marks
Further vectors30 questions2 topics
- Lines and planes in three dimensions15 questions · 61 marks
- Intersections, angles and distances15 questions · 58 marks
Further calculus46 questions3 topics
- Volumes of revolution16 questions · 65 marks
- Mean values and improper integrals15 questions · 60 marks
- Calculus with inverse trigonometric functions15 questions · 59 marks
Hyperbolic functions30 questions2 topics
- Hyperbolic functions and identities15 questions · 60 marks
- Calculus with hyperbolic functions15 questions · 62 marks
Polar coordinates31 questions2 topics
- Polar curves16 questions · 66 marks
- Areas with polar coordinates15 questions · 65 marks
Differential equations45 questions3 topics
- First order equations and integrating factors15 questions · 68 marks
- Second order equations15 questions · 68 marks
- Modelling with differential equations15 questions · 68 marks
Further Pure 1151 questions10 topics
- The t-formulae15 questions · 61 marks
- Taylor series15 questions · 62 marks
- Limits and L'Hôpital's rule15 questions · 59 marks
- Leibniz's theorem and the Weierstrass substitution15 questions · 60 marks
- Series solutions of differential equations15 questions · 63 marks
- Conic sections15 questions · 60 marks
- Tangents, normals and loci of conics15 questions · 63 marks
- The vector product and the scalar triple product15 questions · 56 marks
- Numerical methods for differential equations16 questions · 62 marks
- Inequalities and inequations15 questions · 61 marks
Further Statistics 1137 questions9 topics
- Discrete random variables and expectation15 questions · 57 marks
- The Poisson distribution15 questions · 65 marks
- Geometric and negative binomial distributions15 questions · 57 marks
- Hypothesis tests for Poisson and geometric models15 questions · 58 marks
- The Central Limit Theorem15 questions · 60 marks
- Goodness-of-fit tests16 questions · 67 marks
- Contingency tables16 questions · 62 marks
- Probability generating functions15 questions · 66 marks
- Type I and Type II errors, test size and power15 questions · 59 marks
Further Pure 2195 questions13 topics
- Groups and their axioms15 questions · 62 marks
- Subgroups, Lagrange's theorem and isomorphism15 questions · 60 marks
- Reduction formulae15 questions · 69 marks
- Arc length and surface area15 questions · 64 marks
- Functions of two variables15 questions · 64 marks
- Eigenvalues and eigenvectors15 questions · 67 marks
- Diagonalisation and the Cayley-Hamilton theorem15 questions · 63 marks
- Further loci and regions in the Argand diagram15 questions · 64 marks
- Transformations of the complex plane15 questions · 66 marks
- The Euclidean algorithm and Bézout's identity15 questions · 62 marks
- Modular arithmetic and Fermat's little theorem15 questions · 60 marks
- Combinatorics15 questions · 56 marks
- Recurrence relations15 questions · 77 marks
Further Statistics 2181 questions12 topics
- Least squares regression and residuals15 questions · 60 marks
- Continuous random variables: density and distribution functions15 questions · 61 marks
- Mean, variance and skewness of continuous variables15 questions · 63 marks
- The continuous uniform distribution15 questions · 67 marks
- Correlation coefficients: product moment and Spearman16 questions · 64 marks
- Testing a correlation coefficient15 questions · 63 marks
- Combinations of normal random variables15 questions · 68 marks
- Estimators, standard error and confidence intervals15 questions · 57 marks
- Comparing two normal means15 questions · 59 marks
- Testing variances: chi-squared and the F-distribution15 questions · 59 marks
- Confidence intervals and tests with the t-distribution15 questions · 66 marks
- Non-parametric tests15 questions · 67 marks
Further Mechanics 1121 questions8 topics
- Momentum and impulse16 questions · 72 marks
- Impulse and momentum as vectors15 questions · 60 marks
- Work, energy and power15 questions · 65 marks
- Hooke's law and elastic strings15 questions · 60 marks
- Elastic potential energy15 questions · 64 marks
- Direct impact and Newton's law of restitution15 questions · 65 marks
- Successive impacts and impacts with a wall15 questions · 64 marks
- Oblique impact and impact with a smooth surface15 questions · 62 marks
Further Mechanics 2151 questions10 topics
- Angular speed and horizontal circular motion15 questions · 69 marks
- Motion in a vertical circle15 questions · 66 marks
- Centre of mass of a discrete distribution15 questions · 59 marks
- Centres of mass of plane figures and frameworks15 questions · 58 marks
- Centres of mass by integration15 questions · 72 marks
- Equilibrium, suspension, toppling and sliding15 questions · 57 marks
- Newton's laws with a variable force15 questions · 65 marks
- Simple harmonic motion16 questions · 78 marks
- Oscillations on strings and springs15 questions · 65 marks
- Further kinematics: acceleration as a function of x, t or v15 questions · 59 marks
Decision Mathematics 1169 questions11 topics
- Algorithms, sorting and bin packing15 questions · 67 marks
- Graphs: order, Eulerian paths and planarity15 questions · 57 marks
- Minimum spanning trees: Prim and Kruskal16 questions · 60 marks
- Shortest paths: Dijkstra and Floyd16 questions · 76 marks
- Route inspection15 questions · 66 marks
- Further packing and the knapsack problem15 questions · 67 marks
- The travelling salesman problem15 questions · 71 marks
- Critical path analysis16 questions · 66 marks
- Float, Gantt charts and scheduling15 questions · 58 marks
- Linear programming: formulation and graphical solution16 questions · 65 marks
- The Simplex algorithm15 questions · 68 marks
Decision Mathematics 2137 questions9 topics
- Transportation problems and the north-west corner method16 questions · 70 marks
- The stepping-stone method15 questions · 70 marks
- Allocation and the Hungarian algorithm15 questions · 65 marks
- Flows in networks: cuts and capacity16 questions · 66 marks
- Maximum flow and the labelling procedure15 questions · 59 marks
- Dynamic programming and Bellman's principle15 questions · 59 marks
- Game theory: play safe and stable solutions15 questions · 65 marks
- Mixed strategies in game theory15 questions · 70 marks
- Decision trees, expected monetary value and utility15 questions · 66 marks