Edexcel IGCSE Maths 4MA1 formulas you must learn

Q: Which Edexcel IGCSE Maths 4MA1 formulas are not in the formula booklet?

The ones to learn by heart are: Laws of indices; Compound interest and growth; Reverse percentages; Upper and lower bounds; Speed, distance and time; nth term of a linear sequence; Gradient and equation of a line; Perpendicular gradients; Differentiation and turning points; Pythagoras' theorem; Right-angled trigonometry; Area and circumference of a circle; Arc length and sector area (degrees); Volume of a pyramid; Similar shapes: area and volume; Frequency density. Each one is on this page with a worked example.

Q: Do I get a formula booklet in the exam?

Yes, a short one. The 4MA1 Higher papers print a formulae page. Most formulas, including Pythagoras, SOHCAHTOA and the area of a circle, are not on it.

Q: 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.

Q: Is this page a copy of the official booklet?

No. We link to the official Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier formulae sheet; we do not reproduce it. This page lists only what the booklet leaves out, in our own words, with our own examples.

The exam gives you a formulae sheet, but it leaves these 16 out. Learn them by heart. Each has a short worked example: tap “Worked example” to open it.

Checked against the Higher tier formulae sheet in Appendix 5 of Pearson's 4MA1 specification. The same sheet is printed in the Higher papers. Checked against Pearson's 4MA1 specification (PDF, Appendix 5) (specification Appendix 5) on 5 October 2026.

Test yourself with flashcards One-page formula sheet

Number

Laws of indices

$\displaystyle a^ma^n=a^{m+n},$ $\displaystyle \frac{a^m}{a^n}=a^{m-n},$ $\displaystyle (a^m)^n=a^{mn},$ $\displaystyle a^{-n}=\frac1{a^n},$ $\displaystyle a^{\frac mn}=\left(\sqrt[n]a\right)^m$

Use it for: Simplifying powers and roots without a calculator, and as the first step of many log and calculus questions.

Worked example

Work out $8^{\frac23}\times4^{-\frac12}$ without a calculator.

$8^{\frac23}=\left(\sqrt[3]8\right)^2=2^2=4$
$4^{-\frac12}$${}=\frac1{\sqrt4}$${}=\frac12$
$4\times\frac12=2$

Answer: $2$

Compound interest and growth

$\displaystyle \text{amount}=P\Big(1+\frac r{100}\Big)^n$ $\displaystyle \Big(\text{decay: }1-\frac r{100}\Big)$

Use it for: Savings, depreciation and population questions.

Worked example

\$2500 is invested at 3.2% compound interest per year. Find its value after 5 years.

Multiplier $1.032$
$2500\times1.032^5$

Answer: \$2926.43

Reverse percentages

$\displaystyle \text{original}$$\displaystyle {}=\frac{\text{new value}}{\text{multiplier}}$

Use it for: Finding the price before a rise or a discount.

Worked example

After a 15% reduction a jacket costs \$68. Find the original price.

Multiplier $0.85$
$68\div0.85=80$

Answer: \$80

Upper and lower bounds

$\displaystyle x\text{ to the nearest }u:$ \(\displaystyle x-\tfrac u2\le\text{value}

Use it for: Rounding and accuracy questions.

Worked example

A square has side 7.4 cm to 1 decimal place. Find the bounds of its perimeter.

Side: $7.35\le s<7.45$
Perimeter $=4s$: $4\times7.35=29.4$, $4\times7.45=29.8$

Answer: $29.4\le P<29.8$ cm

Speed, distance and time

$\displaystyle \text{speed}$$\displaystyle {}=\frac{\text{distance}}{\text{time}}$

Use it for: Travel graphs and average speed.

Worked example

A cyclist rides 54 km in 4 hours 30 minutes. Find the average speed.

$4\text{ h }30\text{ min}$${}=4.5$ h
$54\div4.5=12$

Answer: 12 km/h

Algebra and graphs

nth term of a linear sequence

$\displaystyle u_n=a+(n-1)d$ $\displaystyle (\text{or }dn+(a-d))$

Use it for: Finding a rule and a term of a sequence.

The sheet gives the sum of an arithmetic series, not its nth term.

Worked example

Find the $n$th term of 5, 9, 13, 17, … and the 50th term.

$d=4$: $u_n=5+4(n-1)=4n+1$
$u_{50}=201$

Answer: $4n+1$; 201

Gradient and equation of a line

$\displaystyle m$$\displaystyle {}=\frac{y_2-y_1}{x_2-x_1},$ $\displaystyle y=mx+c$

Use it for: Straight-line graphs.

Worked example

A straight line passes through $(-2,1)$ and $(4,19)$. Write its equation in the form $y=mx+c$.

$m=\frac{19-1}{4+2}=3$
$1=3(-2)+c\Rightarrow c=7$

Answer: $y=3x+7$

Perpendicular gradients

$\displaystyle m_1m_2=-1$ $\displaystyle \Big(m_2$$\displaystyle {}=-\frac1{m_1}\Big)$

Use it for: Finding a perpendicular line, a normal, or a perpendicular bisector.

Worked example

Line $L$ passes through $(2,1)$ and meets $y=3x-4$ at right angles. Give the equation of $L$.

The given gradient is $3$, so the perpendicular gradient is $-\frac13$.
$y-1=-\frac13(x-2)$
$y=-\frac13x+\frac53$

Answer: $y=-\frac13x+\frac53$ (or $x+3y-5=0$)

Differentiation and turning points

$\displaystyle y=ax^n$$\displaystyle {}\Rightarrow\frac{dy}{dx}=nax^{n-1};$ $\displaystyle \text{turning points where }\frac{dy}{dx}$$\displaystyle {}=0$

Use it for: Gradients of curves and finding maximum and minimum points.

Worked example

Find the turning points of $y=x^3-6x^2+5$.

$\frac{dy}{dx}$${}=3x^2-12x$${}=3x(x-4)$${}=0$${}\Rightarrow x$${}=0,\ 4$
$y(0)=5$, $y(4)=64-96+5=-27$
The cubic is positive-led, so $(0,5)$ is the maximum.

Answer: Maximum $(0,5)$, minimum $(4,-27)$

Shape and space

Pythagoras' theorem

$\displaystyle a^2+b^2=c^2$ $\displaystyle (c\text{ the hypotenuse})$

Use it for: Any right-angled triangle, in 2D or 3D.

Worked example

A rope 8.5 m long runs in a straight line from the top of a vertical pole to a peg 4 m from its base. How tall is the pole?

$h^2$${}=8.5^2-4^2$${}=72.25-16$${}=56.25$
$h=\sqrt{56.25}$

Answer: 7.5 m

Right-angled trigonometry

$\displaystyle \sin\theta$$\displaystyle {}=\frac{\text{opp}}{\text{hyp}},$ $\displaystyle \cos\theta$$\displaystyle {}=\frac{\text{adj}}{\text{hyp}},$ $\displaystyle \tan\theta$$\displaystyle {}=\frac{\text{opp}}{\text{adj}}$

Use it for: Sides and angles in right-angled triangles, bearings, and elevation.

Worked example

A ramp makes an angle of $38^\circ$ with level ground and its sloping surface is 13 m long. How high does it rise?

The slope is the hypotenuse; the rise is opposite the $38^\circ$ angle.
$\text{rise}$${}=13\sin38^\circ$

Answer: 8.00 m (3 s.f.)

Area and circumference of a circle

$\displaystyle A=\pi r^2,$ $\displaystyle C=2\pi r=\pi d$

Use it for: Circles, sectors, cylinders and compound shapes.

Not on the 4MA1 Higher sheet: you need these for sectors, cylinders and cones too.

Worked example

A circle has diameter 10 cm. Find its area and circumference in terms of $\pi$.

$r=5$: $A=25\pi$
$C=10\pi$

Answer: $25\pi\approx78.5$ cm², $10\pi\approx31.4$ cm

Arc length and sector area (degrees)

$\displaystyle \text{arc}$$\displaystyle {}=\frac\theta{360}\times2\pi r,$ $\displaystyle \text{sector}$$\displaystyle {}=\frac\theta{360}\times\pi r^2$

Use it for: Sectors with the angle in degrees.

Worked example

A slice of pizza is a sector of radius 12 cm with angle $75^\circ$. Find the length of its curved edge and its area, in terms of $\pi$.

Arc $=\frac{75}{360}\times24\pi$${}=5\pi$
Area $=\frac{75}{360}\times144\pi$${}=30\pi$

Answer: Arc $5\pi\approx15.7$ cm, area $30\pi\approx94.2$ cm²

Volume of a pyramid

$\displaystyle V$$\displaystyle {}=\tfrac13\times\text{base area}\times\text{height}$

Use it for: Pyramids and cones (only the cone is on the 4MA1 Higher sheet).

The 4MA1 Higher sheet gives the cone, sphere, prism and cylinder, but not the pyramid.

Worked example

A pyramid stands on a 5 cm by 8 cm rectangle and is 9 cm tall. Work out its volume.

Base area $=40$
$\tfrac13\times40\times9$

Answer: 120 cm³

Similar shapes: area and volume

$\displaystyle \text{length ratio }k\ $$\displaystyle {}\Rightarrow\ \text{area ratio }k^2,$ $\displaystyle \text{volume ratio }k^3$

Use it for: Scaling areas and volumes of similar shapes and solids.

Worked example

Two similar solids have heights 2 cm and 3 cm. The smaller has volume 160 cm³. Find the volume of the larger.

$k=\frac32$, so the volume ratio is $\frac{27}8$
$160\times\frac{27}8=540$

Answer: 540 cm³

Statistics

Frequency density

$\displaystyle \text{frequency density}$$\displaystyle {}=\frac{\text{frequency}}{\text{class width}}$

Use it for: Drawing and reading histograms.

Worked example

The class \(20

Class width $=15$
$24\div15=1.6$

Answer: Frequency density 1.6

Keep going

Questions

Which Edexcel IGCSE Maths 4MA1 formulas are not in the formula booklet?

The ones to learn by heart are: Laws of indices; Compound interest and growth; Reverse percentages; Upper and lower bounds; Speed, distance and time; nth term of a linear sequence; Gradient and equation of a line; Perpendicular gradients; Differentiation and turning points; Pythagoras' theorem; Right-angled trigonometry; Area and circumference of a circle; Arc length and sector area (degrees); Volume of a pyramid; Similar shapes: area and volume; Frequency density. Each one is on this page with a worked example.

Do I get a formula booklet in the exam?

Yes, a short one. The 4MA1 Higher papers print a formulae page. Most formulas, including Pythagoras, SOHCAHTOA and the area of a circle, are not on it.

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 International GCSE Mathematics A (4MA1) Higher tier formulae sheet; 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 IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.