Exam guide

2. Paper structure (checked against the cover pages)

Correction to the brief: old Paper 1 was 2 hours (not 1 h 30) for 80 marks, and old Paper 2 was 2 h 30. The 2026 threshold sheet also lists a Component 50 (90 marks) route. There is no local paper for it, so it is not analysed here.

3. Topic weights

3a. Marks per topic per session (variant 2; P1 + P2)

Number and Algebra together make up about half of all marks (≈ 50 %). This holds in every session.

3b. % share by paper, old format against new format

4. Bankers: subtopics tested in all 9 sessions

These were examined in every session in the sample. Figures are average marks per session (P1 + P2), with where they usually appear.

Near-bankers (8 of 9 sessions): sequences (nth term, pattern problems, 5.3 marks per session), congruence and similarity (proofs with reasons, area and volume scale factors), factorising and expanding, angles in polygons, histograms, length, midpoint and gradient, speed and rates, area and perimeter, ratio, constructions and loci (always P1), and 1 s.f. estimation (always P1).

High weight but not every session: quadratic equations (6.6 marks per session in 7 of 9). These are usually "form an equation and show it simplifies to …, then solve" (6–7 marks), by factorising on P1 or the formula to 2 d.p. on P2. Since 2025 they also include completing the square plus the turning point. Cumulative frequency and box plots average 4.2 marks per session.

Topic-level banker: all 9 topic areas appear in every session.

6. Trends since the 2025 format change

1. Paper 2 is no longer a set of 10 long context questions. It is now 24–25 shorter questions, so far more topics are sampled per paper. Long multi-step contexts are rarer, but 5–6-mark problems remain (trigonometry in a field, composite solids, forming quadratics).
2. Paper 1 grew from 80 to 100 marks in the same 2 hours. The extra marks went to surds and indices (≈ 7 marks per paper in 2025–26, against ≈ 2 before), composite mensuration in terms of π (e.g. hemisphere and cylinder of equal volume, 5–6 marks), quadratic graphs and sketching, and coordinate geometry.
3. Number rises on Paper 2 (19 % → 25 %). Interest, exchange and bounds stay, and exponential growth and decay is new.
4. Transformations & vectors fall on Paper 2 (6.5 % → 3 %), almost entirely because matrices were dropped. Vectors are now mainly on Paper 1.
5. New-style items not seen in 2022–24: completing the square plus turning point, sketching cubic and exponential curves with an asymptote, recurring decimal to fraction, rationalising denominators (P1), exponential growth (P2), and the given formula sheet.
6. Calculator-paper trigonometry is steady (≈ 8–9 % of P2). It is now more often combined with a perpendicular-distance or speed step, worth 5–6 marks.
7. Grade boundaries rose after the change (see §8). A, B and C on the 100-mark papers sit at about 71–78 %, 50–57 % and 30–38 %.

7. Examiner-report findings: common mistakes and hardest areas

Sources: Principal Examiner reports for June 2022, Nov 2022 and June 2023, all old-format components. They are the only reports stored, so findings for 2025+ are inferred.

Areas named as most challenging:

• Vectors. Named in all three reports. Candidates mix vector and number notation, get routes in the wrong order, and misread ratios such as OC : CR (finding 5c or 0.6c instead of 2.5c). "Show that it is a trapezium" or collinear parts are often left blank.
• Standard form problems. Reverse problems where the mantissa must be between 1 and 10 (a = 20 accepted wrongly), and powers with n.
• Ratio combining. Merging two ratios with a common part (red : blue and green : blue) was "very challenging".
• Combined probability without replacement. Candidates do not reduce the denominator, add instead of multiply, or forget to multiply by 2 for "either order".
• Proportionality (two linked relationships), perpendicular lines and bisectors (using an end point instead of the midpoint), graphical inequalities and functions (first step of the inverse, composite notation).
• Set notation. Describing a shaded region, n( ) against listing the elements.
• Geometric proof. Congruence or similarity with reasons. Correct three-letter angle names and correct vocabulary (alternate, vertically opposite) are needed; "Z-angles" and "X-angles" get no credit.
• Bounds. Choosing the right bound combination for a difference or a quotient.
• Histograms. Using frequency instead of frequency density, and estimating a count from part of an interval.

Recurring technical errors:

• Premature rounding on the calculator paper. Keep at least 4 s.f. in the working and give 3 s.f. or the requested accuracy at the end. In "show that" questions, show one more decimal place than asked.
• Ignoring "by drawing a suitable line" or "by drawing a tangent". An algebraic answer scores nothing.
• Confusing significant figures and decimal places. Rounding 63.7 to 64 instead of 60 when estimating to 1 s.f.
• Converting area units with ÷10 instead of ÷100 (mm² to cm²).
• Giving the total amount instead of the interest, and reducing by the percentage when the question asks for the original price.
• Polygon angle-sum errors, and treating a pentagon as if it were regular.
• Sign errors when expanding −(…) and with negatives in general. Squaring a bracket and getting 2 terms instead of 4.
• Not knowing terms: irrational, congruent, mixed number, plane of symmetry, correlation, relative frequency, HCF.

8. Grade thresholds (raw marks)

Component thresholds for the main-sample variant 2 papers (A / B / C / D / E). Components have no A*.

Overall syllabus thresholds for the option matching the sample (components 12 + 22), out of 200:

Other options, for reference: X (11 + 21) in June 2022 was 168 / 137 / 97 / 58. AZ (13 + 23) in June 2025 was 177 / 154 / 110 / 66, and in June 2026 175 / 150 / 109 / 68.

Reading the numbers:

• A* needs about 86–88 % (≈ 171–176 / 200) in every session since 2023. A needs about 71–76 %, B about 52–56 %, and C about 31–39 %.
• In the new format (both papers out of 100), the Paper 2 A boundary has equalled or exceeded Paper 1's: 78 v 72, 71 v 71, 76 v 71. So the calculator paper is not the harder one to score on. Paper 1's C boundary (30–36) shows how hard non-calculator work is for weaker candidates.
• June 2022 boundaries were noticeably lower, probably reflecting post-pandemic grading. Do not use them as a target.

9. Revision priorities for Oct/Nov 2026 or 2027 (current 2025–2027 syllabus)

The order weighs average marks, how often a topic appears, and the difficulty flagged by examiners.

1. Graphs of functions (≈ 9 marks per session). Plot cubic, reciprocal and exponential curves accurately, use a tangent for the gradient, rearrange so a straight line solves a new equation, and sketch with intercepts and asymptotes. Since 2025: completing the square, turning point, and the range of k for which an equation has two solutions.
2. Quadratics from context (≈ 7 marks). Form an expression, show that it simplifies, solve by factorising (P1) or by the formula to 2 d.p. (P2), and reject the invalid root.
3. Mensuration of composite solids and sectors (≈ 12 marks combined). Cone, sphere, hemisphere, frustum, π-form answers on P1, arc length reversed into a cone, and similar solids (area and volume scale factors).
4. Vectors (≈ 7 marks, mainly P1). Ratio on a line, position vectors, prove parallel or collinear. This is examiners' most-flagged weak area, so it offers big gains.
5. Non-calculator number (≈ 10–12 marks on P1). Fractions and mixed numbers, decimals, surds and rationalising, negative and fractional indices, recurring decimals, prime factors / HCF / LCM, 1 s.f. estimation.
6. Money, percentages and growth (≈ 8–10 marks, mainly P2). Simple and compound interest including finding the rate, reverse percentages, exchange rates, and exponential growth and decay (new, already twice in 3 sessions).
7. Trigonometry on P2 (≈ 8 marks). Sine rule, cosine rule, ½ab sin C, a perpendicular distance as a second step, bearings in triangles. Keep 4+ s.f. throughout.
8. Algebraic fractions, functions and indices (≈ 9 marks, mainly P1). Single fraction, simplify by factorising, f⁻¹, composite functions.
9. Coordinate geometry (≈ 9 marks). Gradient, midpoint, length as a surd, perpendicular bisector equation.
10. Statistics (≈ 17 marks across both papers). Histograms with frequency density, grouped mean, cumulative frequency (median, IQR, percentiles, "how many more than"), compare two distributions in context.
11. Probability, sets and Venn diagrams (≈ 10 marks). Without replacement, tree diagrams, 3-set Venn diagrams from clues, set notation for shaded regions.
12. Geometry with reasons (≈ 17 marks). Circle theorems with named reasons, polygon angles, similarity and congruence proofs, constructions and loci with arcs left visible, scale drawings and bearings (P1 every session).
13. Bounds and standard form (≈ 6 marks). Bounds of a speed or difference, standard form arithmetic, population density.
14. Lower priority: direct and inverse proportion (2–4 marks, but done badly), sequences (nth term including quadratic, pattern problems), simultaneous equations, transformations ("describe fully": name plus every parameter).
15. Skip: matrices. Revise them only if working from pre-2025 papers for practice.

Exam habits that are worth marks:

• Show every step in "show that" items.
• Do exactly what "by drawing a line" or "by drawing a tangent" asks.
• Use three-letter angle names and correct reason words.
• Do not round mid-calculation.
• Read what the final answer must be: interest or total, the pattern number or the counters left over.

Limitations:

• Topic tagging is judgement-based, and each part is assigned to one topic only.
• No examiner reports exist for Nov 2023 onwards, including any new-format session.
• The Nov 2022 grade thresholds are missing.
• The 2026 files come from a re-hosting site (each page carries its trace ID); their content matches the Cambridge layout.