Edexcel A-level Maths formula booklet

In every Edexcel maths exam you get Pearson's Mathematical Formulae and Statistical Tables booklet. Most lost marks around it come from not knowing what's in it: students either hunt for a formula that isn't there, or memorise ones that are. This page lists both.

Open the official booklet on Pearson's site

Checked against the current booklet by an Edexcel tutor. The same booklet is used for AS (8MA0), which uses only the AS parts.

Given in the booklet

Pure

• Arithmetic series: $S_n = \tfrac{n}{2}(a+l) = \tfrac{n}{2}[2a+(n-1)d]$
• Geometric series: $S_n = \dfrac{a(1-r^n)}{1-r}$ and $S_\infty = \dfrac{a}{1-r}$ for $|r|<1$
• Binomial series, both forms: $(a+b)^n$ with $\binom{n}{r}$, and $(1+x)^n$ for $|x|<1$, $n \in \mathbb{Q}$
• Logarithms: $\log_a x = \dfrac{\log_b x}{\log_b a}$ and $a^x = e^{x\ln a}$
• Addition formulae: $\sin(A \pm B)$, $\cos(A \pm B)$, $\tan(A \pm B)$
• Sum-to-product (factor) formulae, e.g. $\sin A + \sin B = 2\sin\tfrac{A+B}{2}\cos\tfrac{A-B}{2}$
• Small angles: $\sin\theta \approx \theta$, $\cos\theta \approx 1-\tfrac{\theta^2}{2}$, $\tan\theta \approx \theta$
• Derivatives of $\tan kx$, $\sec x$, $\cot x$, $\cosec x$, and the quotient rule
• Integrals of $\sec^2 kx$, $\tan x$, $\cot x$, $\cosec x$, $\sec x$, and integration by parts
• Trapezium rule and the Newton–Raphson iteration

Statistics

• $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ and $P(A \cap B) = P(A)\,P(B \mid A)$
• Standard deviation: $\sqrt{\dfrac{\sum (x-\bar{x})^2}{n}} = \sqrt{\dfrac{\sum x^2}{n} - \bar{x}^2}$
• Discrete distributions: $E(X) = \sum x\,P(X=x)$ and $\mathrm{Var}(X)$
• Binomial $B(n,p)$: mean $np$, variance $np(1-p)$
• Tables: cumulative binomial, percentage points of the normal distribution, critical values of the product-moment correlation coefficient

Mechanics

• Constant acceleration: $v = u + at$, $s = ut + \tfrac{1}{2}at^2$, $s = \tfrac{1}{2}(u+v)t$, $v^2 = u^2 + 2as$, $s = vt - \tfrac{1}{2}at^2$
• The same in vector form: $\mathbf{v} = \mathbf{u} + \mathbf{a}t$, $\mathbf{r} = \mathbf{u}t + \tfrac{1}{2}\mathbf{a}t^2$

Not in the booklet: learn these

Pure

• $\sin^2 x + \cos^2 x \equiv 1$, $\tan x \equiv \dfrac{\sin x}{\cos x}$, $1 + \tan^2 x \equiv \sec^2 x$, $1 + \cot^2 x \equiv \cosec^2 x$
• Double-angle formulae: $\sin 2A$, $\cos 2A$ (all three forms), $\tan 2A$
• Exact values of sin, cos and tan at $0, \tfrac{\pi}{6}, \tfrac{\pi}{4}, \tfrac{\pi}{3}, \tfrac{\pi}{2}$
• Sine rule, cosine rule and area $= \tfrac{1}{2}ab\sin C$
• Arc length $r\theta$ and sector area $\tfrac{1}{2}r^2\theta$
• Chain rule and product rule
• Derivatives of $x^n$, $e^{kx}$, $\ln x$, $\sin kx$, $\cos kx$, and the corresponding integrals
• Laws of logarithms and indices
• Discriminant $b^2 - 4ac$ and completing the square
• Distance, midpoint and the equation of a circle $(x-a)^2+(y-b)^2=r^2$
• Vector magnitude and the distance between two points
• Factor theorem and the shape of standard graphs and their transformations

Statistics

• Normal distribution: how to standardise with $Z = \dfrac{X-\mu}{\sigma}$ (the table is given, the method is not)
• Hypothesis-test method: hypotheses, test statistic, critical region, conclusion in context
• Interquartile range, outlier rules ($Q_1 - 1.5\,\mathrm{IQR}$ and $Q_3 + 1.5\,\mathrm{IQR}$) and histogram frequency density
• Large data set facts: locations, variables, the 1987 and 2015 periods

Mechanics

• Newton's second law $F = ma$, weight $= mg$, and resolving in two perpendicular directions
• Friction: $F \le \mu R$, with $F = \mu R$ when limiting
• Moments: force × perpendicular distance, and the conditions for equilibrium
• Projectile set-up: resolving the initial velocity, and that the horizontal velocity is constant
• Variable acceleration: differentiate displacement for velocity, integrate acceleration for velocity

Test yourself

Tap a formula to see whether it's given or must be learned. Work through the deck until you get them all.