What comes up in Leaving Cert Higher Level Maths
We read every question of every Higher Level Maths paper from 2017 to 2026 and noted the topics each one needs. Here is the full list, paper by paper and question by question, so you can see exactly where each topic has come up, and so teachers can check the counts printed in our Exam Ready workbooks.
How we count. A topic counts for a question when at least one of its parts can't be answered without it. One question often needs two or three topics.
Every question printed. We count all the questions on the paper, including the ones students could choose to skip.
The years. There were no written exams in 2020: grades were calculated instead. The 2021 and 2022 papers had extra choice because of the pandemic.
A guide, not a prediction. The papers are set fresh each year. Use this to plan revision, not to skip topics.
Higher Level Paper 1: questions per topic
Each number is how many of that year's questions needed the topic. 87 questions in all.
| 2017 | 2018 | 2019 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 | Total | |
|---|---|---|---|---|---|---|---|---|---|---|
| Algebra & number | 2 | 2 | 5 | 4 | 4 | 7 | 4 | 6 | 7 | 41 |
| Differentiation | 3 | 3 | 3 | 5 | 4 | 4 | 7 | 4 | 4 | 37 |
| Functions & graphs | 4 | 3 | 3 | 3 | 2 | 3 | 3 | 3 | 2 | 26 |
| Sequences & series | 2 | 3 | 1 | 3 | 2 | 3 | 1 | 2 | 3 | 20 |
| Logs & exponentials | 3 | 2 | 1 | 3 | 3 | 2 | 2 | 2 | 2 | 20 |
| Integration | 2 | 2 | 1 | 2 | 2 | 3 | 3 | 2 | 2 | 19 |
| Complex numbers | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 9 |
| Financial maths | 1 | – | – | – | – | 1 | 1 | 1 | 1 | 5 |
| Proof by induction | – | 1 | 1 | 1 | – | – | – | 1 | 1 | 5 |
Higher Level Paper 1, question by question
2026 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Surd equation; rearranging a reciprocal formula; quadratic factor of cubic | Algebra & number a, b, c |
| 2 | A | Recurring decimal as geometric series; monthly rate and loan repayment | Sequences & series aFinancial maths b |
| 3 | A | Product rule with cosine; integrate second derivative to recover function | Differentiation aIntegration b |
| 4 | A | Conjugate arithmetic; De Moivre power; product in polar form | Complex numbers a, b, c |
| 5 | A | Numbers as powers of 4; number-set Venn diagram; exponential equation | Algebra & number a, bLogs & exponentials c |
| 6 | A | Induction factorial inequality; factorial equation; geometric sequence conditions | Proof by induction aAlgebra & number bSequences & series c |
| 7 | B | Cubic tank volume: rates, decreasing interval, related rates, domain | Differentiation b, c, d, eAlgebra & number cFunctions & graphs f |
| 8 | B | Piano frequency exponential: evaluate, solve, derivative estimate; simultaneous equations | Logs & exponentials a, b, cDifferentiation d, eAlgebra & number f |
| 9 | B | Swimming shuttle pattern: terms and quadratic total; rep formulas equation | Sequences & series a, b, c, d, eAlgebra & number f, g |
| 10 | B | Graph translations; periodic function, integral, derivative graph; functional equation | Functions & graphs a, b, f(ii)Integration c, eDifferentiation dAlgebra & number f(i) |
2025 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Modulus inequality; expanding surd expressions; cubic with given factor | Algebra & number a, b, c |
| 2 | A | Tangent to curve with sine; piecewise graph slope, composite, inverse | Differentiation a, b(i)Functions & graphs b(ii), b(iii) |
| 3 | A | Chain rule; no turning points of rational function; exponential integral | Differentiation a, bIntegration cLogs & exponentials c |
| 4 | A | Complex division; De Moivre double-angle proof; sixth roots | Complex numbers a, b, c |
| 5 | A | Completing the square; laws of logs; linear-quadratic simultaneous equations | Algebra & number a, cLogs & exponentials b |
| 6 | A | Binomial expansion terms; quadratic with exactly one root | Algebra & number a, b |
| 7 | B | Spider web: arithmetic sequence and series, quadratic; geometric series | Sequences & series a, bAlgebra & number a(v) |
| 8 | B | Discounts and exchange rate; kayak-run route time minimisationNote: c-e are distance-time with Pythagoras; T'(x) is given, so calculus is light. | Financial maths a, bAlgebra & number c, d, e(i), e(ii)Differentiation e(ii), e(iii) |
| 9 | B | Fuel use chain-rule rates with ln; piecewise speed graph, average | Differentiation aFunctions & graphs b(i), b(ii)Integration b(iii) |
| 10 | B | Lattice dot patterns; rearranging; limit of proportion; induction proofNote: a-c are a geometric pattern rather than a formal sequence; d(iii) limit tagged Functions. | Sequences & series a, b, c, e(i)Algebra & number d(i), d(ii)Functions & graphs d(iii)Proof by induction e(ii) |
2024 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Surd equation; single algebraic fraction; three simultaneous equations | Algebra & number a, b, c |
| 2 | A | Complex quadratic roots; De Moivre power; Argand plot and angle | Complex numbers a, b, c |
| 3 | A | Integrate cosine; tangent and inflection of cubic; equal slopes graphically | Integration aDifferentiation b, c |
| 4 | A | First principles; quotient rule value; local versus global minimumNote: c is about local minimum on a graph; could also count as Functions. | Differentiation a, b, c |
| 5 | A | Arithmetic and geometric sequence terms; sequence of repeated derivatives | Sequences & series a, b, cDifferentiation c |
| 6 | A | Factor theorem; evaluate exponential, solve log equation, composite function | Algebra & number aLogs & exponentials bFunctions & graphs b(iii) |
| 7 | B | Income tax; mortgage present values; exponential savings rate, average, AER | Financial maths a, b, c(iii)Differentiation c(i)Integration c(ii)Logs & exponentials c(iii) |
| 8 | B | Cubic sales graph; cosine scarf sales model, intersection, first maximumNote: Trigonometric model; no trig topic in list, so tagged Functions & graphs. | Functions & graphs a, b, c, dDifferentiation e |
| 9 | B | Sphere cap volume equation; hemisphere related rates; rearranging cone formula | Algebra & number a, b, c, eDifferentiation d |
| 10 | B | Plant growth derivative, quadratic inequality; logo area; discount optionsNote: d is percentage discounts in algebra, tagged Algebra not Financial. | Differentiation aAlgebra & number b, dIntegration c(i)Functions & graphs c(ii) |
2023 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Modulus equation; rearranging a formula; quadratic factor of a cubic | Algebra & number a, b, c |
| 2 | A | Quadratic from minimum point; limit of a sequence; graph translationsNote: a can be done with calculus or vertex form; b is a sequence limit (could be Functions: limits). | Functions & graphs a, cSequences & series b |
| 3 | A | Root 2 irrational; sum of logs with different bases; meaning of log | Algebra & number aLogs & exponentials b, c |
| 4 | A | Complex root finds constant; square roots by De Moivre; rotations | Complex numbers a, b, c |
| 5 | A | Quotient and product rule derivatives; composite, injective, surjective mappings | Differentiation a, bFunctions & graphs c |
| 6 | A | Line meets parabola; area between them; exponential integral equation | Algebra & number a(i)Integration a(ii), bLogs & exponentials b |
| 7 | B | Cubic speed model: acceleration, maximum, average speed; average-speed zoneNote: f,g are speed-distance-time equations, tagged Algebra. | Differentiation b, c, eIntegration dAlgebra & number f, g |
| 8 | B | Compound interest, present value, equivalent rate, savings series; markupNote: e is an expected-value equation (probability), tagged Algebra; f markup/margin tagged Financial. | Financial maths a, b, c, d, fSequences & series dAlgebra & number e |
| 9 | B | Counting factors of prime powers; graph y=12/x; tangent triangle area | Algebra & number aFunctions & graphs bDifferentiation c |
| 10 | B | Rectangles covering a triangle: area sequence; pyramid volume, related rates | Sequences & series a, b, cAlgebra & number dIntegration e(i)Differentiation e(ii) |
2022 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Quadratic with one root; no real roots; remainder on division | Algebra & number a, b, c |
| 2 | A | Integrate quadratic; areas give three simultaneous equations for coefficients | Integration a, b(i)Algebra & number b(ii) |
| 3 | A | Complex arithmetic, moduli and circle area; De Moivre power | Complex numbers a, b |
| 4 | A | Recursive sequence with indices; arithmetic sequence in e^k | Sequences & series a, b(i)Algebra & number a, b(ii)Logs & exponentials b(ii) |
| 5 | A | Derivative with negative power; cubic roots; where derivative is negative | Differentiation a, b(ii)Algebra & number b(i), b(ii) |
| 6 | A | First principles; rate of change of area; sketch derivative graph | Differentiation a, b, c |
| 7 | B | Heart-rate cubic: derivative meaning, extremes, scaled composite function | Differentiation b, c, d, e, fFunctions & graphs a, g |
| 8 | B | Ferris wheel cosine model: table, graph, period, range, average heightNote: Trigonometric model; no trig topic in list, so tagged Functions & graphs. | Functions & graphs a, b, c, d, eIntegration f |
| 9 | B | Drug decay exponential; repeated doses as geometric series and limit | Logs & exponentials a, bSequences & series c, d, e, f |
| 10 | B | Memory recall log model; derivative meaning, inflection; power law with logs | Logs & exponentials a, b, eDifferentiation c, d |
2021 · Higher Level Paper 1 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Complex division, square root of a complex number, cube roots | Complex numbers a, b, c |
| 2 | A | Modulus equation; cubic with given factor and its roots | Algebra & number a, b |
| 3 | A | Cuboid volume with surds; quadratic leading to exponential equation | Algebra & number a, bLogs & exponentials b(ii) |
| 4 | A | Induction divisibility proof; arithmetic sequence containing 2021 | Proof by induction aSequences & series b |
| 5 | A | Derivative in completed-square form, inequality; tangent to sine curve | Differentiation a, bAlgebra & number a |
| 6 | A | Quadratic derivative from its graph; maximum slope; integrate to cubicNote: a: building the quadratic from its graph could equally be Algebra. | Functions & graphs aDifferentiation bIntegration c |
| 7 | B | Pendulum swings as geometric sequence: terms, sums, infinite angleNote: a(iv): logs are the standard route; trial also works. | Sequences & series a, bLogs & exponentials a(iv) |
| 8 | B | Cubic rollercoaster: table and graph, maximum, inflection, average height | Functions & graphs aDifferentiation bIntegration c |
| 9 | B | Newton cooling exponential model; rate condition; dissolving cube related rates | Logs & exponentials a, b, cDifferentiation c, d |
| 10 | B | Quadratic tank volume calculus; tree growth recurrence with sineNote: b(i),(ii) are sine-function reasoning, tagged Functions. | Algebra & number a(i)Differentiation aFunctions & graphs b(i), b(ii)Sequences & series b(iii), b(iv) |
2019 · Higher Level Paper 1 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Coefficient condition in a product expansion; rational equation | Algebra & number a, b |
| 2 | A | Graph of 3^x against a line; induction inequality 3^n vs 4n+1 | Functions & graphs aProof by induction b |
| 3 | A | Factorise by grouping; solve equation in ln x; derivative value | Algebra & number a, bLogs & exponentials bDifferentiation c |
| 4 | A | Indefinite integral; recover cubic from derivative; find remaining roots | Integration a, b(i)Algebra & number b(ii) |
| 5 | A | Real quadratic with complex root; polar form and square roots | Complex numbers a, b |
| 6 | A | Surd equation; mean equals median of surds; root 2 irrational | Algebra & number a, b |
| 7 | B | Cantor set: removed lengths as geometric series, endpoints, limit | Sequences & series a, b |
| 8 | B | Seasonal cosine revenue model: values, solving, derivative, minimumNote: Trigonometric model; no trig topic in list, so tagged Functions & graphs. | Functions & graphs a, bDifferentiation c, d, e |
| 9 | B | Norman window: perimeter rearranged, linear graph, maximum area | Algebra & number a, c(i)Functions & graphs bDifferentiation c(ii), c(iii) |
2018 · Higher Level Paper 1 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Three simultaneous linear equations; rational inequality | Algebra & number a, b |
| 2 | A | Geometric series terms give a cubic; factor theorem; sum to infinity | Sequences & series a, cAlgebra & number a, b |
| 3 | A | Tangent angle on cos 2x; average value over an interval | Differentiation aIntegration b |
| 4 | A | Induction proof of De Moivre; apply to a power | Proof by induction aComplex numbers a, b |
| 5 | A | Arithmetic table (Sieve of Sundaram) sums and terms; recursive sequence | Sequences & series a, b |
| 6 | A | Intersections of y=x and y=x^3; enclosed area; inverse graph | Functions & graphs a, b(ii)Integration b(i) |
| 7 | B | Typing-speed log model: constant, solving, graphing, maximum difference | Logs & exponentials a, b, cFunctions & graphs c, d, e(i)Differentiation e(ii) |
| 8 | B | Normal curve function: intercept, rectangle area, decreasing, inflectionNote: a,b are only evaluation of the given function. | Functions & graphs a, bDifferentiation c, d |
| 9 | B | Sierpinski triangle: counts, area and perimeter sequences, limitsNote: Logs are the standard route for b(ii), c(i); trial also works. | Sequences & series a, b, c, dLogs & exponentials b(ii), c(i) |
2017 · Higher Level Paper 1 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Quadratic: completed square form, minimum point, discriminant, surd roots | Algebra & number a, cFunctions & graphs b |
| 2 | A | De Moivre power of a complex number; product with modulus-argument form | Complex numbers a, b |
| 3 | A | Quadratic from first principles; chain rule on composite with lnNote: b builds f(g(x)) but the skill tested is the chain rule; not tagged Functions. | Differentiation a, b |
| 4 | A | Exponential decay data as geometric sequence; infinite sum of square perimetersNote: a: logs are the standard route, though trial of terms also works. | Sequences & series a, bLogs & exponentials a |
| 5 | A | Cubic: given root, other roots, turning points, vertical shift condition | Algebra & number aDifferentiation bFunctions & graphs c |
| 6 | A | Sketch e^-x beside e^x; area between the two curvesNote: Exponential graphs/integrals tagged Functions/Integration, not Logs. | Functions & graphs aIntegration b |
| 7 | B | Two exponential population models: constants, equal populations, average, rate | Logs & exponentials a, b, c, d, eIntegration fDifferentiation g |
| 8 | B | Derive loan repayment formula; credit card versus loan comparison | Financial maths a, bSequences & series aLogs & exponentials b(iv) |
| 9 | B | Tidal depth cosine model: graph, constants, solving for given depthNote: Trigonometric model; no trig topic in list, so tagged Functions & graphs. | Functions & graphs a, b, c |
Higher Level Paper 2: questions per topic
Each number is how many of that year's questions needed the topic. 87 questions in all.
| 2017 | 2018 | 2019 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 | Total | |
|---|---|---|---|---|---|---|---|---|---|---|
| Trigonometry | 3 | 2 | 3 | 3 | 3 | 5 | 2 | 3 | 4 | 28 |
| Probability | 3 | 2 | 2 | 3 | 3 | 3 | 4 | 3 | 3 | 26 |
| Statistics | 2 | 2 | 1 | 1 | 3 | 2 | 2 | 2 | 4 | 19 |
| Geometry & constructions | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 3 | 16 |
| Co-ordinate geometry: line | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 12 |
| Co-ordinate geometry: circle | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 12 |
| Area & volume | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 2 | 12 |
Higher Level Paper 2, question by question
2026 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Stem-and-leaf median, range, IQR; pie chart; added data | Statistics a, b, c |
| 2 | A | Margin of error sample size; mean CI and test; p-values | Statistics a, b, c |
| 3 | A | Construct axial symmetry image; cone volume; cuboid inside sphere | Geometry & constructions aArea & volume b, c |
| 4 | A | Perpendicular check; slopes avoiding a segment; perpendicular distance | Co-ordinate geometry: line a, b, c |
| 5 | A | Circle centre and radius; counting circles made from dice | Co-ordinate geometry: circle a, bProbability b(ii), b(iii), b(iv) |
| 6 | A | Exact cos from sin; sketch sin squared graph; prove cos(A-B)Note: c is a trig identity proof, not a geometry theorem | Trigonometry a, b, c |
| 7 | B | Stick triangles: area, cosine and sine rules, limit angle, similar triangles | Trigonometry a, b, cGeometry & constructions d |
| 8 | B | Solar data correlation and best-fit equation; repeat pick; daylight sine modelNote: Line counted for finding the best-fit line equation from two points | Statistics a, bCo-ordinate geometry: line b(iv)Probability cTrigonometry d |
| 9 | B | Belt drive: congruent triangles, tangent lengths, arcs; box volume; trapezoidal ruleNote: b(ii) arc lengths counted as Trig | Geometry & constructions aTrigonometry bArea & volume c, d |
| 10 | B | Spending normal; dice tokens: geometric and binomial; expected value choice | Statistics aProbability b, c |
2025 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Point on line; acute angle between lines; lines from triangle area | Co-ordinate geometry: line a, b, c |
| 2 | A | Circle centre, radius, tangent equation; horizontal tangent condition | Co-ordinate geometry: circle a, b |
| 3 | A | Venn diagram probabilities, addition rule, independence; picking two people | Probability a, b |
| 4 | A | Median and quartiles; effect of outlier; grouped mean unknown frequency | Statistics a, b, c |
| 5 | A | Congruent triangles proof; enlargement scale factor and shaded area | Geometry & constructions a, b |
| 6 | A | Sine equation over extended domain; period and range; cosine rule tan | Trigonometry a, b, c |
| 7 | B | Submarine: scale drawing, composite solid volume, overlapping circles regionNote: a is scale measurement only; c(v) segment area via sectors counted as Trig | Area & volume bCo-ordinate geometry: circle c(i), c(ii)Trigonometry c(iv), c(v) |
| 8 | B | Pyramid roof: Pythagoras, face areas, net construction; elevation problemsNote: a(iii) construction of the net counted as Geometry & constructions | Area & volume a(i), a(ii)Trigonometry a(ii), b, cGeometry & constructions a(iii) |
| 9 | B | Diabetes test tree diagram and Bayes; binomial; counting pairings | Probability a, b, c, d |
| 10 | B | Test scores: empirical rule, normal, CI, z-test, stratified sampling, expectation | Statistics a, b, c, dProbability e |
2024 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Stem-and-leaf mode, range, median; describe change; correlation | Statistics a, b, c |
| 2 | A | Fair game expected value; mutually exclusive, complement, independence | Probability a, b, c, d |
| 3 | A | Parallelogram area; cos 2X equation; ambiguous sine rule case | Trigonometry a, b, c |
| 4 | A | Construct centroid; proof about three parallel lines and transversalsNote: Formal proof of Theorem 11 (three parallel lines cutting equal segments on one transversal cut equal segments on any other) | Geometry & constructions a, b |
| 5 | A | Circle centre and radius; circles touching internally; circle through points | Co-ordinate geometry: circle a, b |
| 6 | A | Dividing a segment; perpendicular distance; picking grid-point pairs | Co-ordinate geometry: line a, bProbability c |
| 7 | B | Hotel guests: normal ages, binomial, Bayes, test on a proportion | Statistics a, dProbability b, c |
| 8 | B | Cylinder net, cylinder in sphere; cones in sphere via similar trianglesNote: c(iv) maximum also needs calculus | Area & volume a, b, c(iv)Geometry & constructions c(i), c(ii), c(iii) |
| 9 | B | Adventure race: circle stream, tangent path, closest road point | Co-ordinate geometry: circle a, bCo-ordinate geometry: line c, d |
| 10 | B | Windscreen wiper sectors, cosine rule; counting traffic-light patterns | Trigonometry a, bProbability c |
2023 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Spinner game: independent outcomes, third success timing, total winnings | Probability a, b, c |
| 2 | A | Prove sin(A+B); exact sin 75; solve sin t = sin 2tNote: a is a trig identity proof, not a geometry theorem | Trigonometry a, b, c |
| 3 | A | Area of triangle from vertices; midpoint and perpendicular bisector | Co-ordinate geometry: line a, b |
| 4 | A | Circle centre and radius; distance from line to centre; equationNote: Line counted for perpendicular-distance formula in a(ii) (not a tangency condition) | Co-ordinate geometry: circle a, bCo-ordinate geometry: line a(ii) |
| 5 | A | Cube colour trials: mean, SD, correlation; painted faces of cuboidNote: b (counting faces of unit cubes in a cuboid) is a judgement call; placed under Area & volume | Statistics aArea & volume b |
| 6 | A | Vertically opposite angles converse; congruent triangles proof; find angle | Geometry & constructions a, b(i)Trigonometry b(ii) |
| 7 | B | Road gradient; hill height with sine rule; lung-volume cosine modelNote: a is Pythagoras only; d and e(ii) are calculus | Trigonometry b, c, e(i), f |
| 8 | B | Word-game scores: normal, mean CI and test, sample size; tree diagram | Statistics a, b, cProbability d |
| 9 | B | Tilings: square and hexagon sides, cosine rule area, circle through tangentsNote: a(ii) hexagon area via (1/2)ab sin C counted as Trig | Trigonometry a(ii), b, c(i)Co-ordinate geometry: circle c(ii) |
| 10 | B | Frustum basin: lengths, surface area, net; counting PIN codesNote: a(iii) sector angle of the net counted as Trig (arcs); similar triangles in cone not counted as Geometry | Area & volume aTrigonometry a(iii)Probability b |
2022 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Two-way table independence; same birthday weekday; class ratio problem | Probability a, b, c |
| 2 | A | Dividing a segment; y-intercept in terms of parameters; angle between lines | Co-ordinate geometry: line a, b, c |
| 3 | A | Find k from radius; slope of tangent; circles touching both axes | Co-ordinate geometry: circle a, b, c |
| 4 | A | Prove tan(A-B) formula; exact tan 15; isosceles triangle sideNote: a(i) is a trig identity proof, not a geometry theorem | Trigonometry a, b |
| 5 | A | Proportion confidence intervals; hypothesis test on a mean spend | Statistics a, b |
| 6 | A | Construct circumcentre; circle angles; circumcentre of obtuse triangle proofNote: c is a proof by contradiction of a non-syllabus result, not a listed theorem | Geometry & constructions a, b, c |
| 7 | B | Candles: cylinder, similar cones, cone net arc, sphere slice, logoNote: c arc length counted as Trig; e allows similar triangles or trig (counted as Geometry) | Area & volume a, b, c, dTrigonometry cGeometry & constructions e |
| 8 | B | Fuel data scatterplot, correlation; median puzzle; expected repair costs | Statistics a, b, cProbability d |
| 9 | B | Fields: area and perimeter by trig; aeroplane sound delay anglesNote: d uses Pythagoras and algebra only | Trigonometry a, b, c |
| 10 | B | Race times normal; first false start; binomial; number sums; z-scores | Statistics a, eProbability b, c, d |
2021 · Higher Level Paper 2 · 10 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Binomial probabilities for left-footed players on a team | Probability a, b, c |
| 2 | A | Point on line, distance to line, dividing a segment, coordinatesNote: c(ii) can also be argued with parallel-line ratio theorem; solved by coordinates | Co-ordinate geometry: line a, b, c |
| 3 | A | Radius from a chord; circles touching externally, collinear centres | Co-ordinate geometry: circle a, b |
| 4 | A | Prove cos 2A identity and apply it; solve a tan equationNote: a(i) is a trig identity proof, not a geometry theorem | Trigonometry a, b |
| 5 | A | Two cones in a sphere: volume comparison; vans speed-time problemNote: b is speed-distance-time arithmetic and fits none of the 7 topics | Area & volume a |
| 6 | A | Proof: similar triangles have proportional sides; parallel lines riderNote: Formal proof of Theorem 13 (similar triangles have proportional sides) | Geometry & constructions a, b |
| 7 | B | Triathlon triangle: speeds, cosine rule, area, altitude, tower heightNote: a, b are speed-distance-time arithmetic | Trigonometry c, d, e, f |
| 8 | B | Exam marks normal; study-time z-test; drawing keys without replacement | Statistics a, bProbability c |
| 9 | B | Aeroplane route by sine rule and fuel; sinusoidal voltage functionNote: b(v) is differentiation (Paper 1) | Trigonometry a, b |
| 10 | B | Blood types: Bernoulli trials, at-least-one; expected costs and premium | Probability a, b, c |
2019 · Higher Level Paper 2 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Selecting students without replacement; combinations of exam questions | Probability a, b |
| 2 | A | Intercept form of a line; intersection in terms of slope | Co-ordinate geometry: line a, b |
| 3 | A | Point on a circle; circle touching both axes and a tangentNote: b uses perpendicular distance for tangency; counted as Circle only | Co-ordinate geometry: circle a, b |
| 4 | A | Derive cos 2A identity; angle between diagonals of a cubeNote: a is a trig identity proof, not a geometry theorem | Trigonometry a, b |
| 5 | A | Construct orthocentre; circle angles with tangent and parallel chord | Geometry & constructions a, b |
| 6 | A | Independent events in a Venn diagram; children selection problem | Probability a, b |
| 7 | B | Trough: segment in radians, area, prism volume; sand timer volumesNote: a(iii) segment area via sector counted as Trig | Trigonometry a(ii), a(iii)Area & volume a(iv), b |
| 8 | B | Car data: proportion CI, normal percentages, p-value interpretation | Statistics a, b |
| 9 | B | Triangle with incircle: cosine/sine rules, area, inradius, pole heightNote: Geometry counted for incircle properties (radius perpendicular to tangent sides, incentre on bisector) | Trigonometry a, b, c, eGeometry & constructions d, e |
2018 · Higher Level Paper 2 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Competition prizes: expected loss; prize increase to break even | Probability a, b |
| 2 | A | Standard normal area; comparing exam z-scores; empirical rule | Statistics a, b |
| 3 | A | Counting six-digit codes; simplifying a factorial expressionNote: b is factorial algebra, counted under Probability (counting) | Probability a, b |
| 4 | A | Solving a cos 2A equation; sin 2A in terms of cos | Trigonometry a, b |
| 5 | A | Parallel lines, closest point; equation of a touching circle | Co-ordinate geometry: line a, bCo-ordinate geometry: circle c |
| 6 | A | Proof: parallel line divides sides in ratio; find a lengthNote: Formal proof of Theorem 12 (line parallel to one side divides the other two in the same ratio) | Geometry & constructions a, b |
| 7 | B | Railing of cylinders and spheres: volumes, heights, gaps, rod lengthNote: Also uses geometric/arithmetic sequences (Paper 1 algebra); c is arithmetic | Area & volume a, b, d |
| 8 | B | Sample means, proportion confidence intervals, standard error; pension fundNote: b(ii) is calculus; c is financial maths (Paper 1) and fits none of the 7 topics | Statistics a, b(i), b(iii) |
| 9 | B | Crank-and-slider: sine rule, periodic function table and graph, cosine rule | Trigonometry a, b, c |
2017 · Higher Level Paper 2 · 9 questions
| Q | Section | What it asks (our summary) | Topics, with the parts that need them |
|---|---|---|---|
| 1 | A | Repeated phone calls: Bernoulli trials, nth success, at-least-once bound | Probability a, b, c, d |
| 2 | A | Speed v fuel data: correlation, best-fit line, slope meaning, costNote: d(i) is speed-time arithmetic only | Statistics a, b, c, d(ii) |
| 3 | A | Triangle with given centroid: find vertices, prove orthocentre by slopesNote: Centroid/orthocentre used by definition only; not counted as Geometry | Co-ordinate geometry: line a, b, c |
| 4 | A | Circle through three points; angle in the inscribed triangleNote: b can be done by cosine rule (counted as Trig) or slopes/angle-at-centre | Co-ordinate geometry: circle aTrigonometry b |
| 5 | A | Rectangle with perpendicular segments: similar triangles, lengths, quadrilateral areaNote: d is plane area by subtraction, not counted as Area & volume | Geometry & constructions a, b, c, d |
| 6 | A | Distance to horizon from cliff; circumference of latitude circleNote: a uses tangent perpendicular to radius + Pythagoras; b uses cos 53 degrees | Geometry & constructions aTrigonometry b |
| 7 | B | Cones in cylinder vs sphere volumes; water surfaces; CavalieriNote: Pythagoras/similar triangles inside the solids not counted as Geometry | Area & volume a, b, c |
| 8 | B | Weights: normal distribution and mean test; rain-traffic tree diagram | Statistics aProbability b |
| 9 | B | Tree across river: elevation angles, distances, chance it reaches bankNote: f is geometric probability (angle fraction of 360 degrees) | Trigonometry a, b, c, d, e, fProbability f |
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