Memorise, Derive or Look Up: GCSE and IGCSE Formulae

What the paper hands you, and it is not what parents remember

Exam boards first provided formulae sheets in 2022 as a pandemic adaptation, and everybody expected them to be withdrawn. They were not. Ofqual's decision requires exam boards to keep providing support materials setting out the relevant formulae for GCSE mathematics from 2028 onwards, for the lifetime of the current qualifications, including resits. The sheet is no longer a concession — it is part of the assessment.

But the sheets are short, and they differ by board and by tier. This is what the Pearson Edexcel 2026 Higher tier exam aid actually contains, taken from the published document rather than from a revision guide.

• Area of a trapezium, and volume of a prism
• Circumference and area of a circle
• The quadratic formula
• Pythagoras' theorem, the sine rule, the cosine rule, and area of a triangle = ½ab sin C
• Compound interest
• P(A or B) and P(A and B)

Two Edexcel details most students do not know

The Foundation sheet is not the Higher sheet with things removed at random. It drops the quadratic formula, the sine and cosine rules and the conditional probability rule, and it adds the sine, cosine and tangent ratios written out explicitly — which the Higher sheet assumes you know.

The second detail is more useful still. Pearson states that the curved surface area of a cone, the surface area and volume of a sphere and the volume of a cone have always been given in the body of a question where needed, and that the volume of a pyramid is now given the same way. Those five never required memorising on Edexcel at all, and a great deal of revision time has gone into them anyway.

Cambridge prints almost the opposite list

On Cambridge IGCSE Mathematics 0580, a List of formulas appears on page 2 of every question paper. The Core list, on Papers 1 and 3, gives the area of a triangle, the area and circumference of a circle, the curved surface area of a cylinder and of a cone, the surface area of a sphere, and the volumes of a prism, a pyramid, a cylinder, a cone and a sphere. Eleven formulas. The Extended list, on Papers 2 and 4, adds four more: the quadratic formula, the sine rule, the cosine rule and area = ½ab sin C.

What Cambridge does not print is striking if you have arrived from an English GCSE. The syllabus states that for the perimeter and area of a rectangle, triangle, parallelogram and trapezium, 'except for area of a triangle, formulas are not given'. Arc length and sector area are not on the list either — candidates are expected to work them out as fractions of the circumference and area of a circle. Neither Pythagoras' theorem nor compound interest appears anywhere on it.

So a student moving from Edexcel to Cambridge loses the trapezium, Pythagoras and compound interest and gains every solid. Moving the other way, the reverse. Revising from a generic online formula list gets both of them wrong.

The list that is on neither sheet

This is the short list worth learning cold, because no board prints it and it appears constantly. It is written for GCSE and IGCSE Mathematics; Additional and Further Mathematics have a longer one.

• Exact values of sin, cos and tan at 0°, 30°, 45°, 60° and 90°
• Arc length and sector area as fractions of a full circle
• y = mx + c, and gradient as change in y over change in x
• Index laws, including negative and fractional indices
• Speed, density and pressure as the three compound measures
• The difference of two squares, and the expansion of (a + b)²
• Angle facts: angles in polygons, angles in parallel lines, and the circle theorems as statements
• The rules for manipulating surds and standard form

Three worth deriving even though they are printed

A sheet tells you what a formula is. It never tells you that this is the question it belongs to. The commonest formula error at Higher tier is not misremembering the cosine rule — it is using the sine rule where the cosine rule was needed, which no sheet in the world prevents. Deriving a formula once is how selection becomes automatic.

• The area of a trapezium, as the average of the two parallel sides times the height. Derive it once from two triangles and you will never apply it to a shape that is not a trapezium.
• The quadratic formula, from completing the square. A student who has done this once treats completing the square, the formula and the discriminant as one object rather than three unrelated techniques.
• The cosine rule, as Pythagoras with a correction term. Noticing that a² = b² + c² − 2bc cos A collapses to Pythagoras when A is 90° makes the sign obvious and makes 'two sides and the angle between them' an automatic trigger.

What we do in the first sessions

The first thing we do with a new GCSE or IGCSE student is print the formulae sheet for their board and tier and read it with them. Most have never seen it outside an exam hall, which is a remarkable thing to be true of a document that will be on the desk in front of them for three papers.

We mark it up together: what is here, what is not, and which of the missing ones they already know. Then it sits beside every piece of homework for the rest of the course. A sheet you have used forty times is a tool; a sheet you meet for the first time in May is one more thing to search while the clock runs.