The complete 2026 Paper 1 topic review, the remaining concept gaps and a practical route into Paper 2 revision.
Compare the actual 2026 Paper 1 with the last three Paper 2s. Each printed mark is assigned once to its main topic; supporting concepts are not counted twice.
| Topic | 2026 P1 | 2023 P2 | 2024 P2 | 2025 P2 |
|---|---|---|---|---|
| Algebra & formulae | 10 | 4 | 4 | 5 |
| Equations & inequalities | 9 | 8 | 12 | 10 |
| Numbers & indices | 11 | 1 | 4 | 3 |
| Ratio, proportion & scales | 6 | 3 | 2 | 6 |
| Financial arithmetic | 3 | 0 | 0 | 0 |
| Percentages (embedded too)* | 0 | 4 | 2 | 1 |
| Functions & graphs | 3 | 11 | 11 | 7 |
| Rates, speed & travel graphs | 4 | 2 | 2 | 0 |
| Matrices | 0 | 0 | 5 | 3 |
| Sequences & patterns | 0 | 10 | 0 | 0 |
| Sets | 3 | 0 | 0 | 4 |
| Coordinate geometry | 5 | 7 | 9 | 6 |
| Vectors | 1 | 4 | 0 | 0 |
| Pythagoras, trig & bearings | 6 | 0 | 9 | 11 |
| Mensuration | 8 | 13 | 7 | 6 |
| Circle properties | 4 | 4 | 0 | 0 |
| Congruence & similarity | 5 | 0 | 3 | 2 |
| Angles / polygons (primary)* | 0 | 0 | 0 | 6 |
| Construction | 0 | 0 | 0 | 0 |
| Statistics | 8 | 4 | 5 | 5 |
| Probability | 4 | 5 | 4 | 6 |
| Final real-world problem | 0 | 10 | 11 | 9 |
| Total | 90 | 90 | 90 | 90 |
*Percentages appeared in Q17/Q27; angle reasoning supported Q3/Q24. A zero in a primary-topic category does not mean the method was absent. The final real-world question is kept whole in the historical data.
Select a question to see its checked answer and working.
| Question | Concepts tested | Marks | Primary allocation |
|---|---|---|---|
| Q1 | Simplify a linear expression; factorise by grouping | 3 | Algebra & formulae: 3 |
| Q2 | Prime factorisation; symbolic HCF; recover primes; LCM | 5 | Numbers & indices: 5 |
| Q3 | Circle angles with reasons: equal radii and centre/circumference | 4 | Circle properties: 4 |
| Q4 | Show an algebraic fraction has a constant value | 2 | Algebra & formulae: 2 |
| Q5 | Find two added integers using median and range | 2 | Statistics: 2 |
| Q6 | Equal-distance journey: total time, average speed, unit conversion | 4 | Rates, speed & travel graphs: 4 |
| Q7 | Find the obtuse angle from its sine | 1 | Pythagoras, trig & bearings: 1 |
| Q8 | Venn counts, compound set notation and a restricted-population probability | 4 | Sets: 3 Probability: 1 |
| Q9 | Write and calculate in standard form with an unknown exponent | 3 | Numbers & indices: 3 |
| Q10 | Grouped mean and effect of adding a value to a class | 2 | Statistics: 2 |
| Q11 | Combine two ratios and use a known difference | 3 | Ratio, proportion & scales: 3 |
| Q12 | Compare two box plots using median and spread in context | 3 | Statistics: 3 |
| Q13 | Solve a compound inequality and list all integer solutions | 3 | Equations & inequalities: 3 |
| Q14 | Vector translation; line equation; distance between coordinates | 6 | Vectors: 1 Coordinate geometry: 5 |
| Q15 | Solve two simultaneous linear equations algebraically | 3 | Equations & inequalities: 3 |
| Q16 | Add algebraic fractions with a squared linear denominator | 2 | Algebra & formulae: 2 |
| Q17 | Remove a percentage conversion fee and find the exchange rate | 3 | Financial arithmetic: 3 |
| Q18 | Annulus area from a chord tangent to the inner circle | 2 | Mensuration: 2 |
| Q19 | Complement probability; exactly two red counters in three draws | 3 | Probability: 3 |
| Q20 | Reverse bearing and two right-triangle distances | 5 | Pythagoras, trig & bearings: 5 |
| Q21 | Factorise and cancel a rational expression using square identities | 3 | Algebra & formulae: 3 |
| Q22 | Solve a fractional equation whose quadratic terms cancel | 3 | Equations & inequalities: 3 |
| Q23 | Simplify an expression with a negative fractional outer index | 3 | Numbers & indices: 3 |
| Q24 | Prove triangles similar, then find the height of the middle post | 5 | Congruence & similarity: 5 |
| Q25 | Find a major-sector radius, then the volume of its folded cone | 6 | Mensuration: 6 |
| Q26 | Transform data to achieve a new mean and standard deviation | 1 | Statistics: 1 |
| Q27 | Square-root proportion and percentage increase | 3 | Ratio, proportion & scales: 3 |
| Q28 | Recover quadratic coefficients from the minimum point | 3 | Functions & graphs: 3 |
Read this at the level of a skill. For example, quadratic factorisation was tested; solving a genuine quadratic was not.
Observed in P1
Q2, Q9, Q23: prime powers, HCF/LCM, standard form, negative/fractional indices.
Not explicitly tested
Standalone estimation/rounding explanations, number classification, square/cube multipliers. Ordinary numerical calculation remains embedded.
Observed in P1
Q11 linked ratios; Q27 direct square-root proportion.
Not explicitly tested
Map distance/area scales and inverse proportion.
Observed in P1
Q17 reverse percentage; Q27 percentage increase.
Not explicitly tested
Successive changes and other percentage comparisons. Do not call percentages absent because their marks sit under finance/proportion.
Observed in P1
Q6 total-time model, average speed and km/h to m/s.
Not explicitly tested
Distance-time/speed-time interpretation, gradients, areas and more extended journeys.
Observed in P1
Q1, Q4, Q16, Q21 manipulation and factorisation; Q6(a)(i) forms a time expression.
Not explicitly tested
Sequences/nth term; explicit change of subject; longer formula modelling. Quadratic factorisation WAS tested.
Observed in P1
Q28 minimum point to coefficients; Q14(b) uses a straight-line equation.
Not explicitly tested
Plotting curves, tangent gradients, line-curve intersections, graphical solutions/inequalities and exponential functions.
Observed in P1
Q13 compound inequality; Q15 simultaneous linear equations; Q22 fractional-to-linear; Q8(a) forms a linear equation.
Not explicitly tested
Solving a genuine quadratic, quadratic formula, equations from extended area/time models, and graphical solving.
Observed in P1
Q8 Venn counts, union/intersection/complement notation.
Not explicitly tested
Subset notation and Venn shading were not explicitly required. Sets overall were tested.
Observed in P1
No explicit question.
Not explicitly tested
All matrix skills: dimensions, scalar operations, addition/product and interpreting entries in context.
Observed in P1
Triangle/parallel-line angle reasoning supports Q3 and Q24.
Not explicitly tested
Polygon angle sums, regular polygons, quadrilateral/symmetry classification and geometrical constructions.
Observed in P1
Q24 similarity proof and corresponding lengths.
Not explicitly tested
Congruence tests/proofs; area and volume scale factors; enlargement/scale drawings; compass bisectors.
Observed in P1
Q3 equal radii and centre/circumference angles; Q18 tangent-radius/chord geometry.
Not explicitly tested
Same-segment/opposite-segment reasoning and equal tangents were not explicitly demanded. Circle properties are not an absent topic.
Observed in P1
Q7 obtuse sine; Q20 bearings/right-angle trig; Pythagoras supports Q14(c), Q18 and Q25(b).
Not explicitly tested
Sine/cosine rules, triangle area using sine, elevation/depression and 3D trigonometry.
Observed in P1
Q18 annulus area; Q25 major arc, cone net and cone volume.
Not explicitly tested
Composite-solid surface area/volume, cylinders/prisms/pyramids/spheres, fluid transfer, sector/segment area and explicit radian conversion.
Observed in P1
Q14(b),(c): gradient, equation of a line and distance.
Not explicitly tested
Extended coordinate geometry with intersections, parallel lines, shape constraints and ratios.
Observed in P1
Only Q14(a), 1 primary mark: add a column vector to a point.
Not explicitly tested
Vectors in a/b form, position-vector routes, segment ratios, parallelism/collinearity proofs and vector geometry.
Observed in P1
Q5 median/range; Q10 grouped mean; Q12 box-plot comparison; Q26 transformation of mean/SD.
Not explicitly tested
Cumulative frequency/percentiles, histograms, stem-leaf/dot plots, numerical SD, sampling and misleading displays. SD itself WAS tested.
Observed in P1
Q8(c) restricted sample space; Q19 complement and three draws without replacement.
Not explicitly tested
Other independent/dependent-event settings and diagrams; probability is already substantially represented, not a fresh gap.
Only the quadratic vertex relationship appeared. Recent P2 graph allocations were 11, 11 and 7 marks.
Practise: Plot a curve; draw a tangent; calculate gradient with units; use a suitable straight line to solve a related equation; recognise exponential functions.
Past-year references: 2023 P2 Q4; 2024 P2 Q4; 2025 P2 Q5(b),(c)
Textbook sections and readiness checks →Q22 becomes linear. Quadratic factorisation and vertex form do not cover solving a quadratic.
Practise: Form an equation from area or journey times; clear fractions; solve by factorisation/formula; reject invalid roots with a reason.
Past-year references: 2024 P2 Q6(a)-(c); 2025 P2 Q8(a)(i),(ii); 2023 P2 Q2(d)
Textbook sections and readiness checks →Completely absent in P1; present in P2 in 2024 and 2025. This supports priority, not a guarantee.
Practise: Choose row/column order; check compatible dimensions; multiply quantities by prices/weights; interpret an entry.
Past-year references: 2024 P2 Q2(a); 2025 P2 Q3(d)
Textbook sections and readiness checks →P1 used obtuse sine and right-angle bearings, with no sine/cosine-rule calculation.
Practise: Use sine/cosine rules and 1/2 ab sin C; connect a plan to an elevation triangle; keep full intermediate precision.
Past-year references: 2024 P2 Q5; 2025 P2 Q6(a)
Textbook sections and readiness checks →The final real-world question is specified in the 2026 syllabus. Its context cannot be predicted from P1.
Practise: Select data, convert units, model time/cost/quantity, compare choices, state assumptions and justify a final decision.
Past-year references: 2023 P2 Q9; 2024 P2 Q9; 2025 P2 Q9
Textbook sections and readiness checks →P1 allocated only 1 direct vector mark. Advanced vector methods remain untested; recent P2 allocation is variable.
Practise: Build vectors by routes, apply section ratios, show scalar multiples for collinearity/parallelism; link areas when appropriate.
Past-year references: 2023 P2 Q6(a); 2023 P1 Q27 and 2024 P1 Q27(a),(b) as cross-paper drills
Textbook sections and readiness checks →P1 had 8 statistics marks, but no cumulative-frequency graph or numerical SD calculation.
Practise: Read percentiles, convert percentages to counts, estimate grouped mean/SD, explain midpoint estimates and data limitations.
Past-year references: 2025 P2 Q2(a)(i); 2024 P2 Q7(a),(b)(i)
Textbook sections and readiness checks →P1 tested a cone net and volume, but not composite exposed surfaces or similar-solid scaling.
Practise: Count only exposed surfaces; conserve volume; connect radii/heights; use squared and cubed scale factors; revise radians/segments.
Past-year references: 2023 P2 Q3; 2025 P2 Q6(b); 2024 P2 Q8(a)(ii),(b)
Textbook sections and readiness checks →Absence alone is weak evidence. P2 sequences occurred in 2023, but not 2024-25; construction had 0 primary marks in these three P2s.
Practise: Do a short nth-term/proof drill, compass construction, polygon angles, map scales and interest calculation. Do not replace the core practice above.
Past-year references: 2023 P2 Q8; 2025 P1 Q7; 2024 P1 Q6; 2024 P1 Q16 (last three are cross-paper drills)
Textbook sections and readiness checks →The comparison uses the original preserved ChatGPT specimen. A close method match means a similar solving process, not an identical question or a predicted score.
Inequalities, box plots, rational-expression factorisation and the quadratic minimum.
Useful shared methods, with different demands, structures or untested subparts.
These totalled 25 of the original specimen’s 90 marks.
| Our P1 Q | Result / actual question | What matched or differed |
|---|---|---|
| 1 | Partial Actual: Q2 | Prime factorisation matched; HCF/LCM and recovering primes replaced the predicted perfect-cube task. |
| 2 | Partial Actual: Q9(a) | Standard-form writing matched. The measured-area upper-bound task did not appear. |
| 3 | Partial Actual: Q27 | Square-root proportional reasoning matched broadly; actual was direct proportion and a percentage increase, not inverse proportion. |
| 4 | Partial Actual: Q17, Q27 | Percentage multipliers were useful. Actual used a conversion fee and a proportion change, not successive price changes. |
| 5 | Partial Actual: Q1(a), Q21 | Expansion skills were useful. There was no explicit make-a-variable-the-subject task. |
| 6 | Close method Actual: Q13 | Compound inequality, negative coefficient and integer endpoints: a close method match. |
| 7 | Partial Actual: Q8 | Union, intersection and complement notation matched; actual also required Venn counts and a restricted population. |
| 8 | Not seen Actual: None | No matrices question in actual P1. |
| 9 | Close method Actual: Q12 | Compare box plots using the median and IQR in context: a close method match. |
| 10 | Partial Actual: Q3, Q18 | Circle properties were relevant, but actual used centre/circumference angles and chord geometry instead of the same angle chain. |
| 11 | Partial Actual: Q24 | Similarity appeared as a triangle proof and linked lengths. Similar-solid area/volume scaling did not appear. |
| 12 | Partial Actual: Q14(b) | Gradient and line equation were relevant; no perpendicular-bisector equation was required. |
| 13 | Close method Actual: Q21 | Factorise a rational expression and cancel common factors. Actual added a difference of squares in the numerator. |
| 14 | Close method Actual: Q28 | The vertex-form/minimum-point relationship matched; actual asked for coefficients in the reverse direction. |
| 15 | Not seen Actual: None | No compound-interest question in actual P1; currency exchange is a different financial method. |
| 16 | Not seen Actual: None | No speed-time graph. Actual Q6 was an average-speed word problem, so only the broader topic overlapped. |
| 17 | Not seen Actual: None | No sequence or nth-term question in actual P1. |
| 18 | Not seen Actual: None | No regular-polygon angle question in actual P1. |
| 19 | Partial Actual: Q20 | Reverse bearing matched. Actual distances used right-angle trig, not the cosine rule. |
| 20 | Partial Actual: Q25(a) | Sector/arc relationships were relevant; actual worked in degrees and then folded the sector into a cone. |
| 21 | Partial Actual: Q14(a),(c) | Coordinate-vector and distance skills overlapped; no section-ratio point was required. |
| 22 | Partial Actual: Q19(b) | Without-replacement and exactly-one-type methods were useful; actual selected three counters and required exactly two red. |
| 23 | Partial Actual: Q10(a), Q26 | Mean and transformation ideas were relevant; actual required grouped reasoning and both scaling and translation. |
| 24 | Not seen Actual: None | No ruler-and-compass construction question in actual P1. |
| 25 | Partial Actual: Q22 | Clearing fractions matched, but the actual equation reduced to linear. The predicted quadratic-solving step was absent. |
| 26 | Not seen Actual: None | No curve-line intersections or graphical inequality in actual P1. |
Grouped-mean reasoning (Q10), the tangent-chord annulus (Q18), crossed-post similarity (Q24) and folding a sector into a cone (Q25). The actual P1 had 28 questions; our specimen had 26.
Brief Claude comparison: its P1 Q10 matched simultaneous equations (actual Q15); Q19 matched right-angle bearings (actual Q20); Q21(c) matched sector radius from arc length (actual Q25(a)); and Q26 matched vertex form (actual Q28). Its matrices, construction and cumulative-frequency questions were not seen in actual P1. This is not a full Claude accuracy score.
Historical marks and past-year references come from the previously audited 2023-25 topic ledger and practice guide. Supporting methods are tagged separately from primary marks.