Exam guide

Paper structure

• All questions are compulsory. There is no choice of questions.
• On average a question part is worth about 3.4 marks. Long multi-step parts of 8–11 marks, often area or binomial questions, appear in most papers.
• Variants: in May/June the variants are 11/12 and 21/22. In Oct/Nov they are 12/13 and 22/23.
• 2025 change: Paper 1 became fully non-calculator and Coordinate geometry of the circle was added. The papers still carry the same marks and time.

Topic weights

Share of all 1,440 sampled marks (Paper 1 + Paper 2, variant 2). "Sessions" = number of the 9 sessions in which the topic earned marks in the sample.

Calculus (differentiation + integration + kinematics) makes up about 28 % of the marks. Calculus plus series plus trigonometry makes up just over half.

Marks per session (both papers, out of 160):

Bankers

These came up in every session in the sample, usually with about the same number of marks each time:

• Binomial expansion (9/9, about 8 marks a session): first few terms, finding unknown constants or n, the term independent of x, and products like (a + x)ⁿ(1 + bx)ᵐ.
• Arithmetic progressions (9/9) and geometric progressions / sum to infinity (9/9 together). These often use log or trig terms, for example terms in lg x, or a GP in sin θ where you must find the θ values that give a sum to infinity.
• Trigonometric equations (9/9, about 7–10 marks): sec, cosec and cot with compound angles like (2x + π/4), in degrees or radians.
• Trig identities / "show that" (9/9, usually 2–5 marks), often followed by "hence solve".
• Permutations and combinations (9/9, about 8 marks): digit or password arrangements with conditions, and committees with "at least" conditions. Since 2025 there are also short ⁿCᵣ algebra questions (solve an equation in n, or prove an identity).
• Circular measure (9/9, 7–9 marks): a radian diagram where you find a perimeter and an area, usually on Paper 1.
• Factor and remainder theorem with a cubic (9/9): find the constants, factorise fully, then solve a related equation (for example in eˣ, u² or sin θ).
• Vectors (9/9): either vector geometry with ratios (find m and n) or position and velocity vectors (show that two objects collide, or never collide).
• Differentiation: tangents and normals (8/9), the chain, product and quotient rules (8/9), and small changes or connected rates of change (6/9).
• Area under a curve or between a curve and a line (7/9, usually 8–11 marks, often the longest question on the paper).
• Functions: domain and range, the inverse function, and sketching y = f(x) with y = f⁻¹(x) (8/9). The function is very often a log, such as 2 ln(3x − 4), or a quadratic with a restricted domain.
• Modulus or cubic sketches and inequalities (9/9).

Rarely tested

• Simultaneous equations as a standalone question (2 of 9 sessions). The skill itself is used all the time inside line-and-curve or coordinate questions.
• Practical maximum/minimum problems (a box, a tank or a solid object): only 2022-ON and 2024-ON in the sample, but worth 6–10 marks when they appear.
• Exact-value triangle work with the sine and cosine rules: only 2022-ON (11 marks).
• Graphs of eˣ and ln x sketched on their own (with an asymptote): 2 sessions.
• Kinematics missed two sampled sessions (2024-MJ and 2025-ON variant 2). Expect it on most papers anyway.
• Quadratic inequalities on their own: 1 session. Completing the square and the discriminant appear more often (4 sessions each).
• Indefinite integration on its own: almost always folded into a bigger question.

Trends

• Paper 1 is now non-calculator (from 2025). Expect exact answers: surds, multiples of π, ln forms and fractions. The topics are the same as before, but you must do the arithmetic and simplify surds by hand.
• Indices and surds no longer appear as standalone questions (0 marks in 2025–2026, against 4–13 marks a session before). The skills are still needed inside other questions, especially on Paper 1.
• Coordinate geometry of the circle is new and is already a regular (8, 4 and 9 marks in the three new-syllabus sessions). Typical tasks: show that a line is a tangent, find the point of contact, find a circle through three points (using perpendicular gradients), and two circles with a common tangent.
• Integration has grown on the new papers. It was 30 marks in 2025-ON, which included an 11-mark "integrate f″(x) twice and find the stationary point" question. Area questions of 10–11 marks appeared in every session from 2025.
• Short ⁿCᵣ algebra questions are new (2025-ON, 2026-MJ). Example tasks: solve an equation involving ⁿCᵣ, or prove an identity.
• Grade thresholds have risen. An A on component 12 needed 48/80 in June 2022 and 61/80 in June 2026. The overall A for option AY (12 + 22) rose from 90/160 to 117/160. Recent papers are not harder. Careless dropped marks now cost more.
• Differentiation's share swings a lot between sessions (9 to 41 marks). Integration and series tend to fill the gap, so revise all three.

Question styles

• Find is by far the most common command (about 200 uses in 18 papers). It is followed by Solve, Show that, Hence and Write down.
• "Exact" appears about 57 times: "give your answer in exact form", "in the form a + b√c", "in terms of π" or "in the form ln p". A decimal answer usually loses the final mark.
• "Hence" means use the previous part. Another method may get no marks or cost a lot of time.
• Sketch … stating the intercepts with the axes: cubics, modulus graphs, log and exponential graphs, f and f⁻¹, and motion graphs. Leaving out the intercepts or the asymptote loses marks.
• Show that questions give you the answer, so every step must be written out.
• Structured multi-part questions build up: find constants → factorise → solve a related equation; or find dy/dx → stationary points → their nature.
• Contexts: particles in a straight line (kinematics), boats or particles with i/j vectors and bearings, codes or passwords, committees, and badges or shaded regions in radians.
• Long single-part questions (7–11 marks) with no help in between, especially areas, binomial expansions and normal/tangent problems. Plan your method before you start writing.

Common mistakes

From the examiner reports for June 2022, Nov 2022 and June 2023.

• Not showing method. This applies to "show that" questions, no-calculator questions, and quadratics or definite integrals worked out on a calculator. Answers with no working can lose all the marks.
• Missing brackets cause sign errors, for example when subtracting an expression or when raising a whole term like (3(2y + 1)) to a power in a GP.
• Sketches without intercepts, or graphs of f and f⁻¹ that do not cross when the question says they meet twice.
• Trig graphs: amplitude and period mixed up, and b in y = a sin bx + c taken from the wrong feature of the graph.
• Modulus equations: keeping only one of the two cases, or giving only one of the two possible cubic functions from a modulus sketch.
• Remainder theorem: not seeing that dividing by x means putting x = 0.
• Logs: adding instead of multiplying when you remove logs from a linear equation; mistakes with the change of base; assuming natural logs when the question uses lg.
• Permutations vs combinations used the wrong way round, and confusing "terms" with "sums" in AP and GP questions.
• Calculus: forgetting the chain-rule factor, for example writing sin 3x → cos 3x instead of 3 cos 3x; integrating trig functions as if differentiating; leaving out +c; poor integral notation.
• Kinematics: using the position vector where the velocity vector is needed, mixing up velocity and position methods, and misreading "at rest".
• Simultaneous equations: forgetting to substitute back to find the second variable, and not rejecting values that are not allowed (for example x = 1 inside a log).

Grade thresholds

Minimum raw marks out of 80 for the sampled components, and out of 160 for the overall option. For May/June the option is AY (components 12 + 22). For Oct/Nov it is also AY (12 + 22).

• An overall A usually needs about 65–75 %, and a C about 25–37 %. The thresholds change a lot from one session to the next, so do not aim for a fixed number.
• Thresholds for the other variant (11/21 or 13/23) are similar.

Revision priorities for Oct/Nov 2026 and 2027

1. Calculus first (about 28 % of the marks). Practise chain, product and quotient rules quickly and accurately, tangents and normals, connected rates and small changes, and stationary points with the second-derivative test. Practise areas between a curve and a line with exact answers: these are 8–11-mark questions. Also practise integrating f″(x) twice to rebuild a curve, and "differentiate, then hence integrate" pairs.
2. Series (about 13 %). Binomial terms including the term independent of x and products of two brackets; AP and GP with log or trig terms; the condition |r| < 1 for a sum to infinity.
3. Trigonometry (about 10 %). Equations in sec, cosec and cot with compound angles in both degrees and radians; identity proofs; reading a, b and c from a graph.
4. Non-calculator fluency for Paper 1. Surds, exact trig values, exact logs, fractions, solving cubics by the factor theorem, and quadratics by hand.
5. The new circle topic. Circle equations by completing the square, tangent checks with the discriminant, the point of contact, and circles through three points.
6. Reliable mid-weight marks. Functions (inverse, domain and range, sketches of f and f⁻¹, composites), radian sectors, vectors (ratio geometry and collision problems), permutations and combinations including ⁿCᵣ algebra, log-linear graphs (find y in terms of x), and modulus equations and inequalities.
7. Lower priority but keep warm. Kinematics graphs, practical max/min (box or tank), quadratic inequalities and completing the square, and simultaneous equations where a line meets a curve.
8. Exam habits. State the intercepts on every sketch, give exact forms when asked, show every step in "show that" and no-calculator work, follow "hence", and check signs and brackets.