The Most-Tested Topics in A-Level Maths (CIE 9709)

Name: The Most-Tested Topics in A-Level Maths (CIE 9709)
Creator: OwlsPrep

A topic-by-topic breakdown of every 9709 past paper, 2016–2025.

3,254questions analysed

401past papers

2016–2025years covered

6papers (P1–S2)

Most-tested 9709 topics by how often they appear — The topics most likely to appear, ranked by how often they show up across 9709 papers (2016–2025).

Pure Mathematics 1 (Paper 1)

64 papers analysed · top 15 of 42 topics

#	Topic	Appears in	Questions	Avg marks
1	Solving trig equations	98%	71	6.6
2	Inverse functions	95%	61	8.6
3	Binomial expansion (positive integer index)	95%	61	4.8
4	Indefinite integration	89%	59	7.4
5	Sector area	88%	56	7.2
6	Stationary points (max/min)	83%	55	9.4
7	Arithmetic progressions	83%	53	6.8
8	Arc length	77%	50	7.2
9	Tangent and normal lines	75%	54	9.7
10	Composite functions	75%	48	8.2
11	Discriminant and nature of roots	69%	44	6.1
12	Completing the square	59%	39	7.4
13	Pythagorean trig identity	59%	38	6.8
14	Sum to infinity (geometric)	55%	35	7.3
15	Geometric progressions	55%	35	6.8

Pure Mathematics 2 (Paper 2)

63 papers analysed · top 12 topics

#	Topic	Appears in	Questions	Avg marks
1	Integrals of 1/x, e^x, sin/cos/sec^2 etc	100%	106	8.1
2	Iteration: locating root + applying iterative formula	100%	65	8.3
3	Polynomial division and factor/remainder theorems	98%	66	7.6
4	Modulus function: \|ax+b\| equations and inequalities	97%	61	5.4
5	Product, quotient, and chain rule (extended)	79%	50	7.3
6	Logarithm laws and equations	68%	44	4.9
7	Double angle and R sin(θ+α) form	65%	43	9.2
8	e^x and ln x: properties, equations, modelling	56%	42	7.1
9	sec, cosec, cot — graphs and identities	49%	31	7.3
10	Compound angle formulae sin(A±B), cos(A±B), tan(A±B)	32%	20	7.4
11	Reduce y=ax^n or y=Ab^x to linear log form	29%	18	5.1
12	Derivatives of e^x, ln x, sin x, cos x, tan x	24%	16	7.3

Pure Mathematics 3 (Paper 3)

63 papers analysed · top 15 of 22 topics

#	Topic	Appears in	Questions	Avg marks
1	First-order ODE by separation of variables	92%	58	8.3
2	Iterative formula x_{n+1}=F(x_n) (fixed-point iteration)	90%	57	8
3	Partial fractions (linear, repeated linear, quadratic)	84%	53	9.5
4	Solving trig equations using compound/double-angle identities	83%	56	6.5
5	Complex numbers: Cartesian form, conjugate, arithmetic	78%	50	8.2
6	Loci of complex numbers on the Argand diagram	73%	46	7.9
7	Vector equation of a line; intersection; angle	70%	44	9.8
8	Integration by parts	63%	40	7.9
9	Binomial expansion for any rational n; range of validity	63%	40	7.6
10	Modulus, argument, polar form	54%	35	8.1
11	Scalar product; angle between vectors; perpendicular	49%	31	9.5
12	Integration by substitution (definite + indefinite)	48%	31	9
13	Equation of a plane; line-plane intersection; angle	40%	25	10
14	Integration using partial fractions	38%	24	9.9
15	Implicit differentiation	38%	24	7.5

Mechanics (Paper 4)

64 papers analysed · top 15 of 19 topics

#	Topic	Appears in	Questions	Avg marks
1	Connected particles	97%	66	9
2	SUVAT equations (constant acceleration)	92%	95	7.7
3	Power	92%	63	7.3
4	Kinematics with variable acceleration (calculus: v=ds/dt, a=dv/dt, s=integral v dt)	91%	58	9.1
5	Equilibrium of a particle	77%	51	6
6	Friction	75%	57	8.5
7	Conservation of energy	73%	56	7.4
8	Velocity-time graphs	59%	41	8.1
9	Inclined planes	52%	42	7.7
10	Conservation of momentum	52%	33	7.2
11	Newton's second law (F=ma)	41%	31	7.1
12	Resolving forces	38%	24	6.2
13	Kinetic energy	22%	14	6.9
14	Work done by a force	20%	13	6.2
15	Gravitational potential energy	12%	8	6.4

Probability & Statistics 1 (Paper 5)

64 papers analysed · top 15 of 29 topics

#	Topic	Appears in	Questions	Avg marks
1	Binomial distribution	98%	73	8.1
2	Arrangements with restrictions	98%	64	9
3	Computing normal probabilities	98%	63	8.7
4	Inverse normal (find x given p)	97%	63	8.5
5	Probability distribution table	88%	57	6.9
6	Conditional probability	86%	58	7.3
7	Selections	80%	51	9.1
8	Normal approximation to binomial	70%	45	8.8
9	Mean	66%	45	6.7
10	Quartiles and interquartile range	62%	40	8.2
11	Variance Var(X)	56%	36	6.8
12	Geometric distribution	52%	33	7.3
13	Variance and standard deviation	48%	32	6.8
14	Tree diagrams	47%	30	6.7
15	Permutations (nPr)	45%	29	9.1

Probability & Statistics 2 (Paper 6)

62 papers analysed · top 12 topics

#	Topic	Appears in	Questions	Avg marks
1	Type I / Type II errors; significance level; p-value	100%	63	9.3
2	Linear combinations of random variables	98%	63	7.5
3	Continuous random variables: PDF, CDF; verifying validity	97%	60	8.8
4	E(X), Var(X), median, mode for continuous RVs	95%	59	8.8
5	Poisson distribution: probability, mean, variance	94%	80	8.4
6	Hypothesis test for population mean using normal distribution	92%	57	8.4
7	Sampling distribution of sample mean; CLT applications	87%	81	6.3
8	Confidence intervals for population mean (known/unknown variance)	68%	43	6
9	Hypothesis test for a binomial proportion	55%	34	7.4
10	Poisson as approximation to binomial (large n, small p)	55%	34	6.6
11	Confidence interval for a population proportion	45%	28	5.4
12	Hypothesis test for Poisson mean (one-tailed)	42%	26	9.7

How this was measured

Based on OwlsPrep's database of official CIE 9709 past papers (2016–2025), every question tagged to its syllabus topic and marks. “Appears in X% of papers” = the share of that paper's variants (across all sessions and years) containing at least one question on the topic. Pure 2 and Pure 3 share most topics; each is measured against its own papers. Figures are aggregate statistics computed from question metadata — no exam questions or mark schemes are reproduced.

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