Edexcel IGCSE foundation Maths formula sheet (4ma1)

Official formula sheet

Download the official Edexcel IGCSE Foundation formulae sheet (PDF)

What the formula sheet gives you

The Edexcel IGCSE Foundation formula sheet is included in your exam paper. It contains a small number of formulae — far fewer than students often expect. Knowing exactly what is provided stops you wasting time memorising something that is already in the paper, and it helps you spot which topic a question is about as soon as you see it.

Area of trapezium

Area = ½(a + b)h, where a and b are the parallel sides and h is the perpendicular height between them. This appears on questions showing a four-sided shape with one pair of parallel sides. Identify the two parallel sides before substituting.

Volume of prism

Volume = area of cross section × length. A prism is any 3D shape with the same cross-section all the way through. Find the area of the face shown, then multiply by the depth. The cross-section could be a triangle, trapezium, L-shape or any other polygon.

Volume of cylinder

Volume = πr²h. A cylinder is a circular prism, so this follows directly from the prism rule. r is the radius of the circular face and h is the height (or length) of the cylinder.

Curved surface area of cylinder

Curved surface area = 2πrh. This covers only the curved side, not the circular ends. To find the total surface area of a closed cylinder you need to add 2πr² for the two circular faces — but you need to remember that part yourself.

Formulas you must memorise

Everything below is needed for the Foundation exam and is not on the formula sheet. These must be committed to memory.

Area and perimeter

Area of rectangle = length × width

Area of triangle = ½ × base × height

Area of circle = πr²

Circumference of circle = 2πr (equivalently πd)

A common mistake is confusing area (πr²) with circumference (2πr). Area always involves r squared; circumference is linear in r.

Pythagoras' theorem

a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). Use this to find a missing side in a right-angled triangle when two sides are known.

Trigonometry (SOHCAHTOA)

For right-angled triangles: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent. Label the triangle before choosing which ratio to use. Always check your calculator is in degree mode.

Speed, density and pressure

Speed = distance ÷ time

Density = mass ÷ volume

Pressure = force ÷ area

All three follow the same triangle structure. Covering the quantity you want gives the calculation needed.

Percentage

Percentage change = (change ÷ original) × 100

Simple interest = (P × R × T) ÷ 100, where P is the principal, R is the annual rate and T is the time in years.

Compound interest: Amount = P × (1 + r/100)ⁿ, where n is the number of years. This formula is not given; it must be memorised.

Sequences and graphs

nth term of an arithmetic sequence = a + (n − 1)d, where a is the first term and d is the common difference.

Equation of a straight line: y = mx + c, where m is the gradient and c is the y-intercept.

Gradient = (y₂ − y₁) ÷ (x₂ − x₁)

Ratio and proportion

For direct proportion: y = kx. For inverse proportion: y = k/x. The value of k must be found using a given pair of values before the formula can be applied to find unknowns.

How to use this formula sheet in revision

The most useful revision habit is to practise retrieving formulas without looking. Cover this page, write out every formula from memory, then check. Repeat the ones you missed in a separate session. Doing this three or four times across the weeks before the exam is more effective than reading through a list the night before.

When you use a formula in a past paper question, write the formula out fully before substituting values. This makes your method clear, earns method marks even if your final answer is wrong, and forces you to slow down at the step where most errors happen.