A Level Mathematics A (H240) - Formulae Booklet - Key Mathematics Formulae

Sep 14, 2026

A Level Mathematics A (H240) Formulae Booklet compiles core mathematical formulae across major syllabus areas. It covers arithmetic, geometric, and binomial series, key differentiation rules including first principles, integration results, and integration by parts, as well as small-angle approximations and standard trigonometric identities. The booklet also includes numerical methods such as the trapezium rule and Newton-Raphson iteration, probability tools like standard deviation, distributions, hypothesis testing, and normal distribution percentage points, plus kinematics in one and two dimensions.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Formulae

Series and Calculus

Trigonometry and Approximations

Numerical Methods

Probability and Statistics

Kinematics

A Level Mathematics A (H240) Formulae Booklet Formulae A Level Mathematics A (H240) Arithmetic series Sn = 12n^a +lh = 12n"2a + ^n-1hd, Geometric series S = a^1-rnh n 1-r S3 = ~~ ~~1-a~~ ~~r~~ ~~ for r 1 1 Binomial series ^a +bhn = an + nC 1 an-1b+ nC2 an-2b 2 +f+ nCr an-rbr +f+bn ^n ! Nh J N where nCr = n Cr = nr = r!~~^~~nn-!~~ ~~r~~h~~! ^1+xhn = 1 + nx + n~~^~~n2-!~~ ~~1~~h~~x2 + f + n~~^~~n-1~~h ~~!~~^~~n-r+1~~h~~xr + f ^x 1 1, n ! Rh Differentiation f^xh f l^xh | tankx | k sec2kx | | --- | --- | | secx | secx tanx | | cotx | 2 -cosec x | | cosecx | -cosecx cotx | Quotient rule y = uv , dy~~d~~x = v ~~ d~~u~~d~~x v-2u ~~ dd~~vx Differentiation from first principles f l^xh = f~~^~~x~~ ~~+~~ ~~~~ ~~-f~~^~~x~~h~~ Integration ~~ ~~ffl~~^~~x~~h^~~x~~h~~ dx = ln f^xh + c ;f l^xhaf^xhkn dx = n~~ ~~~~ ~~1~~ ~~ af^xhkn +1 + c Integration by parts ; u ~~ d~~v~~d~~x dx = uv- ;v ~~ d~~u~~d~~x dx Small angle approximations sin i . i , cosi . 1-12 i 2 , tani . i where i is measured in radians Trigonometric identities sin^A!Bh = sinAcosB! cosA sinBcos^A!Bh = cosA cosB"sinAsinB tan^A!Bh = ~~ ~~1tAan!tanBAtanB~~ ~~ aA!B ! ^k+ 12hrk Numerical methods Trapezium rule: yaby dx . 12h"^y0 +ynh +2^y 1 +y2 +f+yn-1h,, where h = b-n~~ ~~a The Newton-Raphson iteration for solving f^xh = 0: xn +1 = xn-f~~f^~~xl~~^~~xn~~h~~n~~h~~ Probability P ^A,Bh = P ^Ah +P^Bh-P^A+Bh P ^A+Bh = P ^AhP ^B Ah = P ^BhP ^A Bh or P ^A Bh = P~~ ^~~AP~~^~~+B~~h~~ Standard deviation /^x-x-h2 = / x2-x-2 or / f ^x-x-h2 = / fx2-x-2 n n / f / f The binomial distribution J N If X + B^n, ph then P ^X = xh = nxpx ^1-phn-x , mean of Xis np, variance of Xis np ^1-ph Hypothesis test for the mean of a normal distribution If X + N^n, v2h then X~~ ~~ + N n, ~~ v~~n2 and Xv-nn + N^0, 1h Percentage points of the normal distribution If Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives the value of z such that P ^Z G zh = p . | p | 0.75 0.90 0.95 | 0.975 0.99 0.995 | 0.9975 0.999 0.9995 | | --- | --- | --- | --- | | z | 0.674 1.282 1.645 | 1.960 2.326 2.576 | 2.807 3.090 3.291 | Kinematics Motion in a straight line v = u + at s = ut + 12 at2 s = 12^u + vhtv2 = u 2 +2as 1 2 s = vt-2 at Motion in two dimensions v = u + at s = ut + 12 at2 s = 12^u +vht 1 2 s = vt-2 at

FAQs

What topics of calculus are included in the formula booklet?

It provides differentiation, differentiation from first principles, integration, and integration by parts, along with key rules such as the quotient rule.

Which numerical methods are listed?

It includes the trapezium rule and the Newton-Raphson iteration for solving equations of the form f(x)=0.

What kinematics formulae are provided?

It lists motion in a straight line and motion in two dimensions, including relations between velocity, displacement, acceleration, and time.

Sep 14, 2026

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