A-Level Mathematics Syllabus — 2026/27 Evergreen Guide for Integrated-Programme (IP) Students

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13 Jul 2025, 00:00 Z

TL;DR
The 9758 H2 Mathematics syllabus is assessed by two three-hour papers of 100 marks each.
Paper 1 + Paper 2 together span 11 pure-math themes plus five probability-and-statistics themes.
IP students meet many of the "new" ideas—binomial summations, vectors, derivatives from first principles—in Years 3-4; the A-Level course extends those foundations into proof-level rigour, multistep modelling and formal hypothesis testing.

1 | Assessment Snapshot

Paper	Duration / Marks	Weight	Item blend
Paper 1	3 h / 100 marks	50 %	Pure Maths only
Paper 2	3 h / 100 marks	50 %	Pure Maths + Probability & Statistics

There is no separate statistics paper under the latest 9758 spec; every candidate sits exactly two papers.

Each paper contains 10-12 questions; half are short (4-6 mark) tasks, the rest long (10-12 mark) modelling questions that intertwine multiple syllabus strands.

2 | Topic Map

2.1 Pure Mathematics (≈ 70 % of marks)

Strand	What you must know	IP bridge
Functions	domain, range, modulus, composite & inverse, asymptote behaviour	Y3 graph-sketch & surd work
Equations & Inequalities	simultaneous linear-quadratic systems, sign diagrams	Y2 quadratic sketch
Sequences & Series	sigma notation, AP/GP sums, binomial & Maclaurin to \(n \le 3\)	Y3 binomial (a+b)^n
Vectors	\(\mathbb{R}^3\) scalar & vector products, lines, planes, shortest distance	Y3/Y4 2-D vectors
Complex Numbers	Argand diagram, polar form \(r \cis \theta\), De Moivre, loci	Only touched in IP RA/Olympiad
Calculus	product, quotient, chain, implicit, parametric; techniques of integration; differential equations	Y4 derivatives & simple integrals
Applications of Integration	area, volume of revolution, mean/variance of continuous r.v.	Links to Stats Paper 2

2.2 Probability & Statistics (≈ 30 % of marks)

Strand	Key targets	IP bridge
Probability	permutations, combinations, conditional, Bayes, expectation	Y2 basic probability
Random Variables	discrete & continuous pdf/cdf, mean & variance proofs
Distributions	Binomial, Poisson, Normal; continuity correction
Sampling & Estimation	unbiased estimator, confidence intervals	Statistics WA tasks
Hypothesis Testing	one-/two-tailed \(z, t\) tests, paired data, goodness-of-fit \(\chi^2\)	Appears first in Y4 IP

3 | Micro-Skills Examiners Reward

Exact-value finesse — express \(\pu{\sin 75 ^\circ}\) via compound-angle identities, not decimals.
Vector sign discipline — state direction vectors as column notation, normal vectors as row.
Diagram-first modelling — annotate parameters before launching algebra.
Inference vocabulary — sentences such as "Reject \(H_0\) at the 5 % level because \(p = 0.013 < 0.05\)" earn communication marks.
Error-prop check — quote final answers to 3 s.f. unless the question demands exact form.

4 | Worked Illustrations

4.1 Pure: Vector-Plane Intersection

Find the point where the line
\[ \mathbf{r} = \begin{pmatrix} 2\\1\\-3 \end{pmatrix} + \lambda \begin{pmatrix} 1\\-2\\4 \end{pmatrix} \]
meets the plane \[2x - y + z = 11.\]

Substitute, solve \(2 (2 + \lambda) - (1 - 2 \lambda) + (-3 + 4 \lambda) = 11 \Rightarrow \lambda = 3\).
Hence intersection \(= (5, -5, 9)\).

4.2 Statistics: Two-Tailed Mean Test

A process is claimed to have mean weight \(50 \space \text{g}\) with \(\sigma=2 \space \text{g}\).
Sample \(n=36\) gives \(\bar{x}=49.2\).
Test at \(5\%\).

\[ z = \frac{49.2-50}{2/\sqrt{36}} = -2.4, \quad p = 0.0164 < 0.05 \Rightarrow \text{reject} \space H_0. \]

5 | Year-by-Year IP Alignment

IP Year	Typical new math item that feeds A-Level	Suggested revision cue
Y3	Binomial coefficients, (\Sigma)-notation	Derive \(\dbinom{5}{k}\) row of Pascal's triangle
Y4	Chain rule, parametric differentiation	Prove \(\dfrac{\mathrm{d}}{\mathrm{d}x}(e^{2x}) = 2e^{2x}\) from first principles
JC 1 Term 1	Vector plane geometry	Sketch two skew lines & label shortest distance
JC 1 Term 2	Hypothesis testing	Summarise four outcomes: reject/accept vs true/false \(H_0\)
JC 2	Maclaurin expansion to \(x^3\)	Show \(\ln(1+x)=x-\dfrac{x^2}{2}+\dfrac{x^3}{3}+O(x^4)\)