Home › Formula sheets › Formulas to memorise Edexcel A Level Maths formulas not in the formula booklet (9MA0)
The exam gives you a formula booklet, but it leaves these 22 out. Learn them by heart. Each has a short worked example: tap “Worked example” to open it.
Checked line by line against Pearson's booklet, AS and A Level Mathematics sections. Checked against Pearson's formulae booklet (PDF) (Issue 1, July 2017) on 5 October 2026. This list is for Edexcel. AQA and OCR print slightly different booklets: our one-page formula sheet shows which board prints what.
Algebra, sequences and logs
Quadratic formula and discriminant
\(\displaystyle x\)\(\displaystyle {}=\frac{-b\pm\sqrt{b^2-4ac}}{2a};\) \(\displaystyle b^2-4ac>0\text{ two roots},\ \)\(\displaystyle {}=0\text{ one},\ <0\text{ none}\)
Use it for: Solving quadratics that do not factorise, and "for what \(k\)" root questions.
Worked example
Find the exact roots of \(3x^2-7x+1=0\).
\(b^2-4ac=49-12=37>0\): two real roots \(x=\frac{7\pm\sqrt{37}}6\) Answer: \(x=\frac{7\pm\sqrt{37}}6\)
nth terms of arithmetic and geometric sequences
\(\displaystyle u_n=a+(n-1)d,\) \(\displaystyle u_n=ar^{n-1}\)
Use it for: Finding a term, or setting up equations from two terms (the booklet gives only the sums).
Worked example
An arithmetic sequence has \(a=7\), \(d=4\). A geometric sequence has \(a=3\), \(r=2\). Find the 20th term of the first and the 8th term of the second.
\(u_{20}=7+19\times4=83\) \(u_8=3\times2^7=384\) Answer: 83 and 384
Laws of logarithms
\(\displaystyle \log_axy=\log_ax+\log_ay,\) \(\displaystyle \log_a\frac xy\)\(\displaystyle {}=\log_ax-\log_ay,\) \(\displaystyle \log_ax^k=k\log_ax\)
Use it for: Solving log equations and linearising data.
Worked example
Solve \(\log_2x+\log_2(x-2)=3\).
\(\log_2\big(x(x-2)\big)\)\({}=3\)\({}\Rightarrow x^2-2x\)\({}=8\) \((x-4)(x+2)=0\); reject \(x=-2\) (log of a negative) Answer: \(x=4\)
Equation of a circle
\(\displaystyle (x-a)^2+(y-b)^2=r^2\) \(\displaystyle \text{centre }(a,b),\ \text{radius }r\)
Use it for: Circle geometry: centres, radii, tangents and intersections.
Worked example
Complete the square to find where the circle \(x^2-10x+y^2+2y-23=0\) is centred, and how big its radius is.
\(x^2-10x=(x-5)^2-25\) and \(y^2+2y=(y+1)^2-1\) \((x-5)^2+(y+1)^2\)\({}=25+1+23\)\({}=49\) Answer: Centre \((5,-1)\), radius 7
Trigonometry
Sine rule
\(\displaystyle \frac a{\sin A}\)\(\displaystyle {}=\frac b{\sin B}\)\(\displaystyle {}=\frac c{\sin C}\)
Use it for: A side and its opposite angle are known.
Worked example
In triangle \(ABC\), \(A=40^\circ\), \(B=65^\circ\) and \(a=7\) cm. Find \(b\).
\(b\)\({}=\frac{7\sin65^\circ}{\sin40^\circ}\) Answer: \(b\approx9.87\) cm
Cosine rule
\(\displaystyle a^2=b^2+c^2-2bc\cos A\)
Use it for: Two sides and the angle between them, or three sides.
Not in the 9MA0 booklet (the IAL booklet does print it).
Worked example
Two sides of a triangle are 5 cm and 7 cm with an angle of \(60^\circ\) between them. Find the third side.
\(a^2\)\({}=25+49-2(5)(7)\cos60^\circ\)\({}=39\) Answer: \(\sqrt{39}\approx6.24\) cm
Area of a triangle
\(\displaystyle \text{Area}\)\(\displaystyle {}=\tfrac12ab\sin C\)
Use it for: Two sides and the included angle.
Worked example
Two sides of a triangle are 8 cm and 5 cm, and the angle between them is \(150^\circ\). Work out its area.
\(\tfrac12\times8\times5\times\sin150^\circ\)\({}=20\times\tfrac12\) Answer: 10 cm²
Arc length and sector area (radians)
\(\displaystyle s=r\theta,\) \(\displaystyle A=\tfrac12r^2\theta\)
Use it for: Any circle-sector question with the angle in radians.
Worked example
A sector has radius 6 cm and angle 1.2 radians. Find its arc length and area.
\(s=6\times1.2=7.2\) \(A\)\({}=\tfrac12\times36\times1.2\)\({}=21.6\) Answer: Arc 7.2 cm, area 21.6 cm²
Double-angle formulae
\(\displaystyle \sin2A=2\sin A\cos A,\) \(\displaystyle \cos2A\)\(\displaystyle {}=2\cos^2A-1\)\(\displaystyle {}=1-2\sin^2A,\) \(\displaystyle \tan2A\)\(\displaystyle {}=\frac{2\tan A}{1-\tan^2A}\)
Use it for: Equations with \(2x\) and \(x\) together, and integrating \(\sin^2x\).
The 9MA0 booklet prints the compound-angle formulae; derive the double-angle ones by putting B = A, or learn them.
Worked example
\(x\) is acute and \(\cos x=\frac13\). Find the exact values of \(\cos2x\) and \(\sin2x\).
\(\cos2x\)\({}=2\big(\tfrac13\big)^2-1\)\({}=-\tfrac79\) \(\sin x\)\({}=\sqrt{1-\tfrac19}\)\({}=\tfrac{2\sqrt2}3\) \(\sin2x\)\({}=2\times\tfrac{2\sqrt2}3\times\tfrac13\)\({}=\tfrac{4\sqrt2}9\) Answer: \(\cos2x=-\frac79\), \(\sin2x=\frac{4\sqrt2}9\)
Pythagorean identities with sec and cosec
\(\displaystyle \sec^2\theta\)\(\displaystyle {}=1+\tan^2\theta,\) \(\displaystyle \operatorname{cosec}^2\theta\)\(\displaystyle {}=1+\cot^2\theta\)
Use it for: Equations mixing \(\tan^2\) and \(\sec\), or \(\cot^2\) and \(\operatorname{cosec}\).
Worked example
Solve \(2\tan^2\theta-\sec\theta\)\({}=1\) for \(0^\circ<\theta<360^\circ\).
\(2(\sec^2\theta-1)-\sec\theta-1\)\({}=0\)\({}\Rightarrow2\sec^2\theta-\sec\theta-3\)\({}=0\) \((2\sec\theta-3)(\sec\theta+1)\)\({}=0\) \(\cos\theta=\frac23\) or \(\cos\theta=-1\) Answer: \(\theta\)\({}=48.2^\circ,\ 180^\circ,\ 311.8^\circ\)
Harmonic form (R-form)
\(\displaystyle a\sin\theta+b\cos\theta=R\sin(\theta+\alpha),\) \(\displaystyle R=\sqrt{a^2+b^2},\) \(\displaystyle \tan\alpha=\frac ba\)
Use it for: Maximum and minimum values, and solving \(a\sin\theta+b\cos\theta=c\).
Worked example
Write \(3\sin\theta+4\cos\theta\) as \(R\sin(\theta+\alpha)\) and state its maximum value.
\(R=\sqrt{9+16}=5\) \(\tan\alpha\)\({}=\frac43\)\({}\Rightarrow\alpha\)\({}\approx53.1^\circ\) Answer: \(5\sin(\theta+53.1^\circ)\); maximum 5
Calculus
Standard derivatives
\(\displaystyle \frac{d}{dx}e^{kx}=ke^{kx},\) \(\displaystyle \frac{d}{dx}\ln x\)\(\displaystyle {}=\frac1x,\) \(\displaystyle \frac{d}{dx}\sin kx=k\cos kx,\) \(\displaystyle \frac{d}{dx}\cos kx\)\(\displaystyle {}=-k\sin kx\)
Use it for: Every calculus question with exponentials, logs or trig.
Worked example
Differentiate \(y=e^{3x}+\ln(2x)-4\sin\frac x2\).
\(\frac{d}{dx}e^{3x}\)\({}=3e^{3x}\) \(\ln(2x)=\ln2+\ln x\), derivative \(\frac1x\) \(\frac{d}{dx}\big(-4\sin\frac x2\big)\)\({}=-2\cos\frac x2\) Answer: \(\frac{dy}{dx}\)\({}=3e^{3x}+\frac1x-2\cos\frac x2\)
Product rule and chain rule
\(\displaystyle \frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx},\) \(\displaystyle \frac{dy}{dx}\)\(\displaystyle {}=\frac{dy}{du}\times\frac{du}{dx}\)
Use it for: Differentiating products and functions of functions (the booklet gives only the quotient rule).
The 9MA0 booklet prints the quotient rule only.
Worked example
Differentiate \(y=x^2(2x-1)^3\) and factorise your answer.
\(u=x^2\), \(v=(2x-1)^3\), \(v'=3(2x-1)^2\times2\) \(\frac{dy}{dx}\)\({}=2x(2x-1)^3+6x^2(2x-1)^2\) \(=2x(2x-1)^2\big((2x-1)+3x\big)\) Answer: \(2x(2x-1)^2(5x-1)\)
Standard integrals
\(\displaystyle \int e^{kx}dx\)\(\displaystyle {}=\tfrac1ke^{kx}+c,\) \(\displaystyle \int\tfrac1x\,dx\)\(\displaystyle {}=\ln|x|+c,\) \(\displaystyle \int\cos kx\,dx\)\(\displaystyle {}=\tfrac1k\sin kx+c,\) \(\displaystyle \int\sin kx\,dx\)\(\displaystyle {}=-\tfrac1k\cos kx+c\)
Use it for: Reversing the standard derivatives.
The 9MA0 booklet prints the harder trig integrals (sec², tan, cot, cosec, sec), not these.
Worked example
Find \(\int\big(e^{2x}+\frac1x+\cos3x\big)\,dx\).
Integrate term by term, dividing by the coefficient of \(x\) inside. Answer: \(\frac12e^{2x}+\ln|x|+\frac13\sin3x+c\)
Integrating f'(x)/f(x)
\(\displaystyle \int\frac{f'(x)}{f(x)}\,dx\)\(\displaystyle {}=\ln|f(x)|+C\)
Use it for: Any fraction whose top is (a multiple of) the derivative of the bottom.
Worked example
Find \(\int_0^2\frac{2x}{x^2+5}\,dx\).
The top is the derivative of \(x^2+5\). \(\big[\ln(x^2+5)\big]_0^2\)\({}=\ln9-\ln5\) Answer: \(\ln\frac95\)
Integrating sin² and cos²
\(\displaystyle \sin^2x\)\(\displaystyle {}=\tfrac12(1-\cos2x),\) \(\displaystyle \cos^2x\)\(\displaystyle {}=\tfrac12(1+\cos2x)\)
Use it for: Integrating even powers of sin and cos.
Worked example
Find \(\int_0^{\frac\pi2}\sin^2x\,dx\).
\(\int_0^{\frac\pi2}\tfrac12(1-\cos2x)\,dx\) \(=\big[\tfrac x2-\tfrac{\sin2x}4\big]_0^{\frac\pi2}\)\({}=\tfrac\pi4\) Answer: \(\frac\pi4\)
Statistics
Standardising a normal variable
\(\displaystyle X\)\(\displaystyle {}\sim N(\mu,\sigma^2)\ \)\(\displaystyle {}\Rightarrow\ Z\)\(\displaystyle {}=\frac{X-\mu}\sigma\)\(\displaystyle {}\sim N(0,1)\)
Use it for: Using the normal tables, and finding an unknown mean or standard deviation.
The 9MA0 booklet gives the version for a sample mean, not this one.
Worked example
\(X\sim N(50,\,4^2)\). Find \(P(X>56)\).
\(z=\frac{56-50}4=1.5\) \(P(Z>1.5)\)\({}=1-\Phi(1.5)\)\({}=1-0.9332\) Answer: \(0.0668\)
Coding
\(\displaystyle y\)\(\displaystyle {}=\frac{x-a}b\ \)\(\displaystyle {}\Rightarrow\ \bar x=a+b\bar y,\) \(\displaystyle \sigma_x=|b|\,\sigma_y\)
Use it for: Getting back to the original data from coded summaries.
Worked example
Data are coded with \(y=\frac{x-100}5\). The coded mean is 2.4 and the coded standard deviation is 1.2. Find the mean and standard deviation of \(x\).
\(\bar x=100+5\times2.4=112\) \(\sigma_x=5\times1.2=6\) Answer: Mean 112, standard deviation 6
Mechanics
Newton's second law, weight and friction
\(\displaystyle F=ma,\) \(\displaystyle W=mg,\) \(\displaystyle F\le\mu R\ \ (\text{limiting: }F\)\(\displaystyle {}=\mu R)\)
Use it for: Every dynamics question.
Worked example
A 4 kg box on a rough horizontal floor (\(\mu=0.5\)) is pulled by a horizontal force of 30 N. Take \(g=9.8\) m s⁻². Find its acceleration.
\(R=4g=39.2\) N, so friction \(=0.5\times39.2=19.6\) N \(30-19.6=4a\) Answer: \(a=2.6\) m s⁻²
Variable acceleration
\(\displaystyle v=\frac{ds}{dt},\) \(\displaystyle a=\frac{dv}{dt},\) \(\displaystyle s=\int v\,dt,\) \(\displaystyle v=\int a\,dt\)
Use it for: Motion when the acceleration is not constant (suvat does not apply).
Worked example
\(v=3t^2-12t+9\). Find when the particle is at rest and its displacement from \(t=0\) to \(t=1\).
\(3(t-1)(t-3)\)\({}=0\)\({}\Rightarrow t\)\({}=1,\ 3\) \(\int_0^1(3t^2-12t+9)\,dt\)\({}=1-6+9\)\({}=4\) Answer: At rest at \(t=1\) and \(t=3\); displacement 4 m
Projectile motion
\(\displaystyle x=(U\cos\alpha)t,\) \(\displaystyle y\)\(\displaystyle {}=(U\sin\alpha)t-\tfrac12gt^2\)
Use it for: Time of flight, range and greatest height.
Worked example
A ball is projected from level ground at 20 m s⁻¹ at \(30^\circ\) to the horizontal (\(g=9.8\)). Find the time of flight and the range.
\(y=0\): \(10t-4.9t^2\)\({}=0\)\({}\Rightarrow t\)\({}=\frac{10}{4.9}\)\({}\approx2.04\) s Range \(=20\cos30^\circ\times\frac{10}{4.9}\)\({}\approx35.3\) m Answer: 2.04 s, 35.3 m
Moments
\(\displaystyle \text{moment}=F\times d_\perp;\) \(\displaystyle \text{equilibrium: }\textstyle\sum F\)\(\displaystyle {}=0,\ \sum M\)\(\displaystyle {}=0\)
Use it for: Rods on supports, ladders and tipping questions.
Worked example
A uniform 4 m rod of mass 10 kg rests on supports at its ends \(A\) and \(B\). A 20 kg child sits 1 m from \(A\). Find the reactions (\(g=9.8\)).
Moments about \(A\): \(4R_B\)\({}=10g\times2+20g\times1\)\({}=40g\)\({}\Rightarrow R_B\)\({}=10g\)\({}=98\) N Resolve: \(R_A=30g-10g=196\) N Answer: \(R_A=196\) N, \(R_B=98\) N
Questions
Which Edexcel A Level Maths 9MA0 formulas are not in the formula booklet? The ones to learn by heart are: Quadratic formula and discriminant; nth terms of arithmetic and geometric sequences; Laws of logarithms; Equation of a circle; Sine rule; Cosine rule; Area of a triangle; Arc length and sector area (radians); Double-angle formulae; Pythagorean identities with sec and cosec; Harmonic form (R-form); Standard derivatives; Product rule and chain rule; Standard integrals; Integrating f'(x)/f(x); Integrating sin² and cos²; Standardising a normal variable; Coding; Newton's second law, weight and friction; Variable acceleration; Projectile motion; Moments. Each one is on this page with a worked example.
Do I get a formula booklet in the exam? Yes. Pearson's formulae booklet is provided in every Edexcel A Level Mathematics paper. It does not print everything: the results on this page are for you to learn.
What is the best way to memorise them? Cover the formula, write it from memory, then try the worked example without looking. Come back to the ones you missed the next day. Our flashcards do the spacing for you.
Is this page a copy of the official booklet? No. We link to the official Pearson Edexcel Mathematical Formulae and Statistical Tables (8MA0/9MA0); we do not reproduce it. This page lists only what the booklet leaves out, in our own words, with our own examples.
Our own list, wording and examples, written and checked by A Level Math Revision. Not produced or endorsed by Pearson Edexcel, AQA or OCR.