Exam guide

1. Paper structure

• Every question is compulsory, and you write your answers on the question paper.
• Each paper has 10–13 questions and 18–29 marked parts. The average part is worth about 3.4 marks.
• Most papers have at least one long question of 8–13 marks. These are usually an area, a binomial expansion or a tangent/normal problem.
• Variants: May/June uses 11/21, 12/22 and 13/23, and so does Oct/Nov. Your time zone decides which variant you sit. Grades are A* to E.
• What changed in 2025: Paper 1 became fully non-calculator, and Coordinate geometry of the circle was added to the syllabus. The time and marks stayed the same.

2. Topic weights

This is the share of the 1,440 sampled marks. "Sessions" counts how many of the 9 sessions had marks for the topic in the sample.

Marks per session (Papers 12 + 22, out of 160). J = May/June, N = Oct/Nov.

Calculus (differentiation, integration and kinematics together) is worth about 28 % of the marks. Add series and trigonometry, and you have just over half the exam.

3. Bankers

These earned marks in every session of the sample, or in almost every one:

• Binomial expansion (9/9, about 8 marks per session). Typical tasks: the first three terms, finding unknown constants or n, the term independent of x, and products of two brackets.
• Arithmetic and geometric progressions (9/9). The terms are often built from logs or trig, for example lg x, lg x⁵, lg x⁹, or a GP in sin θ where you find the angles that give a sum to infinity.
• Trigonometric equations (9/9). These use sec, cosec, cot or tan with compound angles, in degrees or radians, and are often 5–6 marks each.
• Trig identities (9/9): a short "show that", usually followed by "hence solve".
• Circular measure (9/9, 7–9 marks): a radian diagram where you find a perimeter and an area. It is almost always on Paper 1.
• Permutations and combinations (9/9, about 8 marks): digit or password counts with conditions, and committees or teams with "at least" or "must not be separated" conditions.
• Factor and remainder theorems with a cubic (9/9): find the constants, factorise fully, then solve a related equation (in eˣ, u², sin θ and so on).
• Vectors (9/9): either ratio geometry (find m and n), or position and velocity vectors (show that two particles 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 between a curve and a line (7/9, usually 8–11 marks). This is often the biggest single question on the paper.
• Functions (8/9): least value of a for an inverse to exist, range, f⁻¹(x), and sketching f with f⁻¹. The function is often a log, such as 2 ln(3x − 4), or a quadratic on a restricted domain.
• Modulus and cubic graphs and inequalities (9/9): sketch with intercepts, then read off an inequality or a value of k.

4. Rarely tested

• Simultaneous equations as a question of their own (2 of 9 sessions). You still use the skill inside line-and-curve questions all the time.
• Practical maximum and minimum problems (a solid object or an open tank): only in 2022-N and 2024-N, but worth 6–10 marks when they come up.
• Sine and cosine rules with exact values: only 2022-N, but that was a single 11-mark question.
• Sketching eˣ or ln x graphs on their own, with an asymptote: 2 sessions.
• Quadratic inequalities on their own: 1 session. Completing the square and the discriminant appear in 4 sessions each.
• Kinematics was missing from the sampled variant in 2024-J and 2025-N. It is still on most papers, so don't drop it.
• Indefinite integration on its own is rare. It is usually part of a longer question.

5. Trends

• Paper 1 has no calculator at all from 2025. The topics are the same, but answers are exact: surds, multiples of π, ln forms and fractions. The 2025 examiner report praises candidates who simplify numbers early, for example by dividing out common factors, instead of multiplying out large numbers.
• Circle geometry is new and already regular: 8, 4 and 9 marks in the three new-syllabus sessions. The tasks so far: show that a line is a tangent (with the discriminant), find the point of contact, find a circle through three points (with right-angle gradients), and a common chord of two circles (9 marks in 2026-J).
• Indices and surds have disappeared as stand-alone questions since 2025 (before that, 4–13 marks per session). You still need the skills, especially on the non-calculator paper.
• Integration has grown. Area questions of 10–11 marks appeared in every session from 2025. 2025-N had an 11-mark question that rebuilt a curve from its gradient information. "Differentiate, then hence integrate" pairs are common.
• Short ⁿCᵣ algebra (solve an equation in n, or prove an identity) is new: it appeared in all three sessions from 2025.
• The share of Functions is rising (about 5 % in 2022–23, about 7 % in 2025–26), and so is the share of modulus and cubic graphs.
• Differentiation swings a lot (9 to 41 marks per session), and integration and series fill the gap. Revise all three.
• Grade thresholds have risen. The overall A for 12 + 22 went from 90/160 (June 2022) to 115–117/160 (June 2025 and June 2026). The papers have not become easier, so careless lost marks now cost you more.

6. Question styles

• Find is by far the most common command (about 200 times in 18 papers). Then come Solve (about 40), Show that (about 30), Hence (about 27) and Write down (about 19).
• Exact answers are asked for about 57 times, as "exact value", "in exact form", "in the form a + b√c", "in terms of π" or "in the form ln p". A rounded decimal normally loses the last mark.
• Sketch / draw … stating the intercepts (about 27 times): cubics, modulus graphs, trig graphs, log and exponential graphs, f with f⁻¹, and displacement, velocity and acceleration graphs.
• "Hence" means you must use the previous part. A different method may score nothing.
• "Show that" gives you the answer, so every step has to be on the page.
• Linked chains of parts: constants → factors → a related equation; dy/dx → stationary points → their nature; f → range → f⁻¹ → sketch.
• Typical contexts: a particle moving in a straight line, boats or particles with i/j vectors, passwords and digit codes, teams and committees, and badges or shaded regions in radians.
• Long questions with no hints (7–11 marks in one part): area, binomial and normal-line problems. Plan the route before you start writing.

7. Common mistakes

From the examiner reports for June 2022, Nov 2022, June 2023 and June 2025 (papers 12 and 22):

• Missing working. This covers no-calculator questions, quadratics or integrals solved on a calculator, and "show that" steps that are skipped. Wrong answers with no method shown get no marks.
• Not simplifying on the non-calculator paper (June 2025). Candidates multiplied out large numbers, then could not take square roots or finish a GP. Cancel common factors first.
• Rejecting a valid root. Examples: throwing away a negative solution when using a substitution, or discarding the negative value of r in a sum to infinity. A rejected answer cannot score, so check before you cross it out.
• Sketches with missing details: no intercepts, decimals where exact intercepts were asked for, curves bending the wrong way, curves with no asymptote, or f and f⁻¹ graphs that do not meet when the question says they do.
• Trig graphs: working out b (the period) wrongly from the diagram, and forgetting values such as cos π = −1.
• Notation: confusing p′(−1) with p(−1); writing ambiguous products such as sec²x e⁴ˣ; using dy/dx when the variables are S and r.
• Log laws misused, for example treating log(x − y) as a quotient of logs, or getting the change of base wrong.
• Remainder theorem: not seeing that "divided by x" means substituting x = 0.
• Calculus slips: a missing chain-rule factor, differentiating a function that was already the gradient (June 2025), and making simple derivatives harder by not simplifying first.
• Circle questions (June 2025): rearranging the circle equation and getting stuck, when the quick route was to substitute the line and use the discriminant.
• Brackets and signs, especially when subtracting expressions or raising a whole term to a power in a GP.
• Untidy work, such as writing over pencil in pen. This leads to miscopied numbers.

8. Grade thresholds

These are minimum raw marks. The components are out of 80. The option is 12 + 22 (option AY up to 2025), out of 160.

• An overall A has needed between 90 and 126 out of 160 (56–79 %); since 2023 it has been 103–126 (64–79 %). An A* needs 118–143 (74–89 %). A C ranges widely, from 34 to 59 out of 160.
• Thresholds for the 11/21 and 13/23 routes are close to these but not the same. For example, in June 2026 the A for 11 + 21 was 122/160.

9. Revision priorities for Oct/Nov 2026 and 2027

1. Calculus (about 28 %). Be quick and accurate with the chain, product and quotient rules (including ln, eˣ and trig). Practise tangents and normals with exact coordinates, small changes and connected rates, and stationary points with the second-derivative test. Then do area between a curve and a line with exact answers, rebuilding a curve from its gradient, and "differentiate, then hence integrate".
2. Series (about 13 %). Binomial terms, including the term independent of x and products of two brackets. APs and GPs with log or trig terms, and the condition |r| < 1 for a sum to infinity.
3. Trigonometry (about 10 %). Equations in sec, cosec and cot with compound angles, in degrees and in radians. Identity proofs. Finding a, b and c from a graph, plus amplitude and period.
4. Non-calculator skill for Paper 1. Practise surds, exact trig values, ln forms, fractions, cubics by the factor theorem and quadratics by hand. Simplify early. Do at least a few full Paper 1s from 2025–2026 without a calculator.
5. The circle topic. Completing the square for the centre and radius, tangent tests with the discriminant, the point of contact, circles through three points, and common chords.
6. Steady mid-weight marks. Functions (domain, range, inverse, composites, f and f⁻¹ sketches), radian sectors, vector ratio and collision problems, permutations and combinations (including ⁿCᵣ algebra), log-linear graphs, and modulus equations and inequalities.
7. Keep these warm. Kinematics graphs, practical max/min, completing the square and quadratic inequalities, and simultaneous line-curve equations.
8. Exam habits. Give intercepts on every sketch, exact forms when asked, and full steps in "show that". Use "hence" when told to. Don't reject roots without a reason, and watch your brackets.

Comparison with O Level Additional Mathematics (4037)

• Same exam papers. In this sample, every 0606 paper (variants 12 and 22, June 2022 to June 2026) is word-for-word the same as the 4037 paper with the same code. The only differences are the cover, the bar codes and the margins. Both syllabuses made the same 2025 changes: a non-calculator Paper 1 and the new circle topic.
• Same grade thresholds for components 12 and 22 and for the 12 + 22 combination in every session from 2022 to 2026.
• Differences:
  • 0606 is an IGCSE, graded A*–E.
  • 0606 has three variants in both series (11/21, 12/22, 13/23). The local 4037 folder has two per series.
  • The local 0606 folder also has the June 2025 examiner report, the first comments on the non-calculator paper. Its advice (simplify early, don't reject valid roots, read circle questions carefully) applies equally to 4037 candidates.
• In practice: 0606 and 4037 past papers are the same practice material. A student preparing for either can use both sets, but the same session's paper will be a repeat, not new practice.