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Common mistakes from examiner reports

Examiner reports say the same things year after year. These guides gather the mistakes that cost marks and the advice examiners give, first for the whole syllabus, then paper by paper, then topic by topic. Each topic guide ends with past paper questions to practise on.

Whole syllabus

What Cambridge examiners keep telling A Level Math students Every exam session, Cambridge publishes a report for teachers on each paper. Read one report and it can feel like a list of small complaints. Read… Accuracy in A Level Math: significant figures, exact answers and rounding If you could win back only one kind of mark across all of Cambridge A Level Math, accuracy would be a strong candidate. Almost every examiner report…

AS and A Level Paper 1: Pure Mathematics 1

Paper 1 (Pure Mathematics 1): what examiners say, session after session Paper 1 is the paper where most students first meet A Level Math, and the examiner reports for it are among the most consistent. The same handful of… Quadratics in A Level Math Paper 1: common mistakes and examiner advice Quadratics sit underneath a large part of Paper 1. They appear as equations, inequalities, completed squares, discriminants, tangents, and as… Functions in A Level Math Paper 1: common mistakes and examiner advice Functions questions in Paper 1 combine algebra with careful language. A student can find an inverse perfectly and still lose a mark for the domain… Function transformations in A Level Math Paper 1: common mistakes and examiner advice Transformation questions look simple, and many students understand the idea. The marks are lost in two places: the order of the transformations, and… Coordinate geometry in A Level Math Paper 1: common mistakes and examiner advice Coordinate geometry should be a reliable source of marks, and the reports often say so. The mistakes are rarely deep. They are slips in gradients… Equation of a circle in A Level Math Paper 1: common mistakes and examiner advice Circle questions in Paper 1 combine coordinate geometry with algebra, and sometimes with calculus or sector areas. Marks are most often lost in… Circular measure in A Level Math Paper 1: common mistakes and examiner advice Circular measure is a short topic with a lot of ways to lose marks. The formulas are few, but the questions usually combine sectors, triangles and… Trigonometry in A Level Math Paper 1: common mistakes and examiner advice Trigonometry in Paper 1 means solving equations in a given range, proving identities, working with graphs and transformations, and using exact… Binomial expansion in A Level Math Paper 1: common mistakes and examiner advice Binomial expansion is one of the more predictable topics in Paper 1, and one of the most carefully marked for slips. The questions are usually short.… Arithmetic and geometric progressions in A Level Math Paper 1: common mistakes and examiner advice Progressions questions are mostly about choosing the right formula, using the right value of n, and interpreting the context. The reports show that… Differentiation in A Level Math Paper 1: common mistakes and examiner advice Differentiation questions in Paper 1 are rarely about the rules themselves. Most students can differentiate a polynomial. Marks are lost in the chain… Integration in A Level Math Paper 1: common mistakes and examiner advice Integration questions in Paper 1 reward careful setting up. The reports show that students usually know that they need to integrate. The marks go…

A Level Paper 3: Pure Mathematics 3

Paper 3 (Pure Mathematics 3): what examiners say, session after session Paper 3 builds on Paper 1 and adds the topics that make A Level Math feel different: complex numbers, differential equations, partial fractions… Logarithmic and exponential functions in A Level Math Paper 3: common mistakes and examiner advice Logarithms and exponentials appear in Paper 3 as equations, as straight-line graph questions, as inequalities and as the setting for calculus. The… Trigonometry in A Level Math Paper 3: common mistakes and examiner advice Paper 3 trigonometry goes beyond Paper 1: addition and double-angle formulae, the R-formula, proofs of identities, equations in 2θ, and calculus with… Numerical solution of equations in A Level Math Paper 3: common mistakes and examiner advice This topic combines sketching, a change-of-sign test and an iterative formula, and it often starts with a "show that" derivation. The reports show… Polynomials in A Level Math Paper 3: common mistakes and examiner advice Polynomial questions in Paper 3 centre on division, the factor and remainder theorems, finding unknown constants, and solving cubic or quartic… Differentiation in A Level Math Paper 3: common mistakes and examiner advice Paper 3 differentiation covers the product, quotient and chain rules, parametric and implicit differentiation, exponentials, logarithms and… Differential equations in A Level Math Paper 3: common mistakes and examiner advice Differential equation questions in Paper 3 follow a fixed pattern: form or separate the equation, integrate both sides, find the constant, and then… Partial fractions in A Level Math Paper 3: common mistakes and examiner advice Partial fractions rarely stand alone in Paper 3. They are the first part of a question that continues into an integration or a binomial expansion.… Complex numbers in A Level Math Paper 3: common mistakes and examiner advice Complex numbers questions in Paper 3 mix algebra with geometry: arithmetic, roots of equations, polar form, and loci on an Argand diagram. The… Modulus in A Level Math Paper 3: common mistakes and examiner advice Modulus questions in Paper 3 are short and usually come near the start of the paper, so they are marks that students should expect to collect. They… Binomial series in A Level Math Paper 3: common mistakes and examiner advice In Paper 3, the binomial expansion is for negative and fractional powers and is valid only for a certain range of x. It is often combined with… Vectors in A Level Math Paper 3: common mistakes and examiner advice Vectors questions in Paper 3 are about lines and the scalar product: writing the equation of a line, deciding whether two lines meet, finding angles… Integration in A Level Math Paper 3: common mistakes and examiner advice Paper 3 integration asks students to choose a method: substitution, by parts, partial fractions, a trigonometric identity, or a standard form. The…

AS and A Level Paper 4: Mechanics

Paper 4 (Mechanics): what examiners say, session after session The Mechanics paper has the most consistent examiner messages of any A Level Math paper. A handful of reminders appear in report after report, often… Kinematics of motion in a straight line in A Level Math Paper 4 (Mechanics): common mistakes and examiner advice Kinematics is a large topic in the Mechanics paper, and it mixes two toolkits: the constant acceleration equations and calculus. The reports show… Forces and equilibrium in A Level Math Paper 4 (Mechanics): common mistakes and examiner advice This guide covers forces in equilibrium, with and without friction: resolving forces, tensions in strings, inclined planes, limiting friction and the… Newton's laws of motion in A Level Math Paper 4 (Mechanics): common mistakes and examiner advice Newton's second law questions in the Mechanics paper usually involve connected particles, pulleys, slopes, or a car with a trailer. The method is… Energy, work and power in A Level Math Paper 4 (Mechanics): common mistakes and examiner advice Energy questions are a favourite for the longer parts of the Mechanics paper, and they often combine with Newton's laws or kinematics. The reports… Momentum in A Level Math Paper 4 (Mechanics): common mistakes and examiner advice Momentum is a small topic with high-value questions, usually a collision between particles, often combined with motion on a slope or an energy…

AS and A Level Paper 5: Probability and Statistics 1

Paper 5 (Probability & Statistics 1): what examiners say, session after session Statistics 1 is a paper where the method is usually well known and the marks are lost in communication, accuracy and interpretation. The reports… Representation of data in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Representation of data covers histograms, cumulative frequency graphs, box plots, stem-and-leaf diagrams, and the mean, median, quartiles and… Probability in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Probability questions in Statistics 1 are about tree diagrams, conditional probability, independence and the number of ways an event can happen. The… Permutations and combinations in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Counting questions are about arrangements, selections and the number of ways of meeting a condition, and many end in a probability. The reports show… Discrete random variables in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Discrete random variable questions ask for a probability distribution table, followed by E(X) and Var(X). The reports show that students know the… Binomial and geometric distributions in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Binomial and geometric questions look routine, and the method usually is. The reports show that the marks go missing when the wording is turned into… Normal distribution in A Level Math Paper 5 (Statistics 1): common mistakes and examiner advice Normal distribution questions follow a pattern: standardise, find the probability from the tables, and sometimes work backwards from a probability to…

A Level Paper 6: Probability and Statistics 2

Paper 6 (Probability & Statistics 2): what examiners say, session after session Statistics 2 is the paper where the method is usually known and the marks are lost in the details: which distribution to use, the wording of a… Poisson distribution in A Level Math Paper 6 (Statistics 2): common mistakes and examiner advice Poisson questions test the value of λ, the terms in the expression, and the choice of approximation. The reports show a clear pattern: students know… Continuous random variables in A Level Math Paper 6 (Statistics 2): common mistakes and examiner advice Continuous random variable questions are mostly calculus: integrate to find a constant, a probability, the median, the mean and the variance. The… Linear combinations of random variables in A Level Math Paper 6 (Statistics 2): common mistakes and examiner advice Linear combination questions ask for the mean and variance of something like X − 3Y, or of a sum of several independent variables, and then a Normal… Sampling and estimation in A Level Math Paper 6 (Statistics 2): common mistakes and examiner advice This topic covers unbiased estimates, the Central Limit Theorem, confidence intervals, and the reasons a sample may be unsuitable. The reports show… Hypothesis tests in A Level Math Paper 6 (Statistics 2): common mistakes and examiner advice Hypothesis test questions follow a pattern: hypotheses, a test (using a binomial, Poisson or Normal distribution), a comparison, a conclusion, and…

Additional Math 0606 (IGCSE)

Additional Math 0606: what examiners say, session after session Examiner reports for Cambridge Additional Mathematics 0606 repeat the same few messages in almost every session. They apply to every topic and to… Additional Math Paper 1 (non-calculator): what examiners say Since the 2025 syllabus, Paper 1 is a non-calculator paper, and examiners describe it as the paper where algebra, exact values and clear working are… Additional Math Paper 2 (calculator): what examiners say Paper 2 allows a calculator, and the examiner reports return again and again to the way the calculator is used. This guide collects the messages that… Functions in Additional Math 0606: common mistakes and examiner advice Function questions in Additional Math combine several skills: domain and range, inverse and composite functions, and sketching a function with its… Quadratic functions in Additional Math 0606: common mistakes and examiner advice Quadratic questions in Additional Math cover completing the square, the discriminant, and quadratic inequalities. The reports show that students know… Polynomials in Additional Math 0606: common mistakes and examiner advice Polynomial questions use the factor theorem, the remainder theorem, division and sketching. The reports show that most of the marks lost are slips… Modulus in Additional Math 0606: common mistakes and examiner advice Modulus questions in Additional Math cover solving equations and inequalities with a modulus, finding a modulus function from conditions, and drawing… Simultaneous equations in Additional Math 0606: common mistakes and examiner advice Simultaneous equation questions in Additional Math usually have one linear and one non-linear equation, or two equations that can be turned into a… Logarithmic and exponential functions in Additional Math 0606: common mistakes and examiner advice Log and exponential questions in Additional Math cover solving equations, changing base, using the laws of logarithms, and sketching. The reports… Coordinate geometry (straight line and circle) in Additional Math 0606: common mistakes and examiner advice Coordinate geometry questions combine midpoints, gradients, perpendicular lines, distances, areas and, for the circle, the equation of a circle… Linear law in Additional Math 0606: common mistakes and examiner advice Linear law questions ask you to turn a non-linear relationship into a straight line, plot it, and use the gradient and intercept. The reports show… Circular measure in Additional Math 0606: common mistakes and examiner advice Circular measure questions ask for arc lengths, sector and segment areas, and perimeters of shapes built from circles, triangles and rectangles. The… Trigonometry in Additional Math 0606: common mistakes and examiner advice Trigonometry questions in Additional Math include solving equations in a given range, using identities, sketching graphs and their periods, and… Permutations and combinations in Additional Math 0606: common mistakes and examiner advice Counting questions in Additional Math ask for arrangements, selections and the number of ways of meeting a condition. The reports show that the same… Binomial expansion in Additional Math 0606: common mistakes and examiner advice Binomial expansion questions in Additional Math ask for terms of expansions such as (1 + ax)ⁿ or (2x − 3/x)ⁿ, a coefficient or constant term, or… Arithmetic and geometric progressions in Additional Math 0606: common mistakes and examiner advice Progression questions in Additional Math combine the formulae for the nth term and the sum with equations, inequalities, and sometimes logarithms or… Vectors in two dimensions in Additional Math 0606: common mistakes and examiner advice Vector questions in Additional Math cover position vectors, magnitudes, ratios, velocity and motion, and geometry in terms of a and b. The reports… Differentiation in Additional Math 0606: common mistakes and examiner advice Differentiation is the biggest topic in the Additional Math papers. It appears as straightforward derivatives, stationary points, connected rates of… Integration in Additional Math 0606: common mistakes and examiner advice Integration questions in Additional Math include indefinite and definite integrals, finding a curve from its gradient, and areas. The reports show… Kinematics in Additional Math 0606: common mistakes and examiner advice Kinematics in Additional Math is about motion in a straight line using calculus, velocity-time graphs and the relationships between displacement…

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