MF27 Formula List

Every H2 Maths (9758) paper comes with the official formula booklet, List MF27 — the replacement for the older MF26 from the 2025 A-Levels onwards. Most marks lost around the booklet come from two mistakes: hunting for a formula that was never in it, or memorising pages of results that are printed for you. This guide sets out exactly what MF27 gives an H2 student — and what it does not.

MF27 vs MF26: what changed in 2025

If you sit the A-Levels in 2025 or later, you get MF27. It is a slimmed-down MF26:

• The title changed from “List of Formulae and Statistical Tables” (MF26) to “List of Formulae and Results” (MF27) — because the statistical tables (the normal $\Phi(z)$ table, $t$-distribution and $\chi^2$ critical values) were removed. Your graphing calculator does all of that in 9758 anyway.
• The four factor formulae (sum-to-product identities like $\sin P + \sin Q$) were removed. Compound-angle and double-angle formulae are still given.
• The pooled two-sample variance formula was removed (it was never needed for H2).

Everything else an H2 student uses is the same in both booklets — so if your school notes reference MF26, the formula content below is unchanged; just don’t expect the statistical tables or factor formulae in your exam copy.

What the booklet gives you

These are the parts of MF27 H2 students actually use. Get familiar with where each one sits before prelims — exam time spent searching is time lost.

Pure Mathematics

• Maclaurin series: the general expansion, plus the five standard series — $(1+x)^n$ for rational $n$, $e^x$, $\sin x$, $\cos x$ and $\ln(1+x)$ — each with its validity range printed. Questions about range of validity are answerable straight off the booklet.
• Binomial expansion of $(a+b)^n$ for positive integer $n$.
• Partial fractions decomposition templates for the three standard denominator types.
• Trigonometry: compound-angle formulae ($\sin(A \pm B)$ etc.) and double-angle formulae, including all three forms of $\cos 2A$.
• Derivatives — only five: $\sin^{-1}x$, $\cos^{-1}x$, $\tan^{-1}x$, $\operatorname{cosec} x$ and $\sec x$.
• Integrals — eight standard forms, including $\frac{1}{x^2+a^2} \to \frac{1}{a}\tan^{-1}\frac{x}{a}$ and $\frac{1}{\sqrt{a^2-x^2}} \to \sin^{-1}\frac{x}{a}$, the two logarithmic forms for $\frac{1}{x^2-a^2}$ and $\frac{1}{a^2-x^2}$, and the four trigonometric integrals $\tan x$, $\cot x$, $\operatorname{cosec} x$, $\sec x$.
• Vectors — just two entries: the ratio theorem, and the component recipe for the vector (cross) product. Nothing else.

Probability and Statistics

• The binomial distribution row: the probability function, mean $np$ and variance $np(1-p)$.
• The unbiased estimate of population variance, in both equivalent forms: $s^2 = \frac{1}{n-1}\sum (x-\bar{x})^2 = \frac{1}{n-1}\left(\sum x^2 - \frac{(\sum x)^2}{n}\right).$
• The product moment correlation coefficient $r$ and the gradient $b$ of the least-squares regression line of $y$ on $x$.

What you must memorise

None of the following is in MF27 (nor was it in MF26). This is the list to drill.

Sequences and series — everything. The $n$th term and sum of an arithmetic progression, $S_n = \frac{n}{2}(2a + (n-1)d)$; the geometric progression sum $S_n = \frac{a(1-r^n)}{1-r}$ and sum to infinity $S_\infty = \frac{a}{1-r}$ with the convergence condition $|r|<1$. The booklet’s silence on AP and GP formulas surprises almost every JC1 student.

Trigonometry — the Pythagorean identities ($\sin^2 A + \cos^2 A = 1$ and friends) and the R-formula ($a\cos\theta + b\sin\theta = R\cos(\theta - \alpha)$), which 9758 treats as assumed knowledge from O-Level Additional Maths. The small-angle approximations $\sin x \approx x$, $\cos x \approx 1 - \frac{x^2}{2}$, $\tan x \approx x$ should also be known cold.

Calculus — derivatives of $\tan x$, $\cot x$, $e^x$ and $\ln x$ (the booklet only gives the five listed above); integration by parts; the patterns $\int \frac{f'(x)}{f(x)}\,dx = \ln|f(x)| + c$; and the area and volume results $A = \int y\,dx$, $V = \pi \int y^2\,dx$.

Vectors — nearly the whole topic: $\mathbf{a}\cdot\mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta$, $|\mathbf{a}\times\mathbf{b}| = |\mathbf{a}||\mathbf{b}|\sin\theta$, the area of a triangle $\frac{1}{2}|\mathbf{a}\times\mathbf{b}|$, equations of lines and planes, projections, and every distance formula.

Complex numbers — nothing is given. Conjugate properties and the conjugate root theorem are all memory work — see the complex numbers guide.

Statistics — the probability laws (including conditional probability $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$); $E(X)$ and $\operatorname{Var}(X) = E(X^2) - [E(X)]^2$ for discrete random variables; the algebra $\operatorname{Var}(aX \pm bY) = a^2\operatorname{Var}(X) + b^2\operatorname{Var}(Y)$ for independent variables; standardisation $Z = \frac{X-\mu}{\sigma}$ for the normal distribution; the sample-mean results $\bar{X} \sim N\!\left(\mu, \frac{\sigma^2}{n}\right)$ and the Central Limit Theorem; and the form of the $z$-test statistic for hypothesis testing.

Three things people wrongly think you must memorise

Tuition notes often get these wrong — all three are printed in MF27:

1. The binomial mean $np$ and variance $np(1-p)$.
2. The unbiased variance estimate $s^2$ — both algebraic forms.
3. The PMCC $r$ and the regression gradient $b$.

Parts of the booklet you can ignore

MF27 also serves H1, H3 and Further Maths, so an H2 student can skip: the Poisson and geometric rows of the distributions table (Poisson is not in 9758 at all), the exponential distribution, the entire numerical methods block (trapezium rule, Simpson’s rule, Newton-Raphson), the arc-length and surface-of-revolution results, the “functions of two variables” entry, the Mathematical Results page (AM-GM, Cauchy-Schwarz) and the Wilcoxon table — none of it is H2 material.

Using the booklet well

Print the current MF27 from the SEAB website and use it for every timed practice from now until A-Levels. The aim is that by prelims you never search the booklet — you already know whether a result is inside (and where), or in your head.