Edexcel GCSE Maths Formulae: What You Must Memorise vs What's on the Formula Sheet

Every Edexcel GCSE Maths exam paper comes with a formula sheet printed at the front. Students often assume this means they do not need to learn any formulae. That assumption is dangerous. The sheet contains only a handful of results. The vast majority of formulae you need must be recalled from memory, and if you cannot recall them, you cannot answer the question.

This guide covers every formula relevant to Edexcel GCSE Mathematics (1MA1) across all three papers. Section 1 lists the formulae that appear on the provided sheet. Section 2 lists everything you must memorise. Section 3 gives exam technique advice for formula-based questions. Formulae marked (Higher) apply only to the Higher tier.

For broader exam strategy, see our Edexcel GCSE Maths exam technique guide. For advice on how mark schemes reward working, see how Edexcel mark schemes work.

Section 1: Formulae on the Formula Sheet

These formulae are printed on the front of every exam paper. You do not need to memorise them, but you absolutely need to know what they mean, when to apply them, and how to substitute values correctly. Having a formula in front of you is worthless if you cannot recognise which question requires it.

Area of a Trapezium

A = 1/2 (a + b) h

• a and b are the lengths of the two parallel sides
• h is the perpendicular height (not a slanted side)

Use this whenever a shape has exactly one pair of parallel sides of different lengths.

Example: A trapezium has parallel sides of 6 cm and 10 cm, and a perpendicular height of 4 cm. A = 1/2 (6 + 10) x 4 = 1/2 x 16 x 4 = 32 cm squared.

Volume of a Prism

V = area of cross-section x length

A prism is any 3D shape with a uniform cross-section. Triangular prisms, pentagonal prisms, and L-shaped prisms all use this formula.

Example: A triangular prism has a cross-section that is a triangle with base 5 cm and height 3 cm. The prism is 12 cm long. Cross-section area = 1/2 x 5 x 3 = 7.5 cm squared. V = 7.5 x 12 = 90 cm cubed.

The Quadratic Formula (Higher)

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

Use this to solve any quadratic equation ax^2 + bx + c = 0, particularly when the equation does not factorise neatly.

Example: Solve 2x^2 + 5x - 3 = 0. Here a = 2, b = 5, c = -3. Discriminant: b^2 - 4ac = 25 - 4(2)(-3) = 25 + 24 = 49. x = (-5 +/- 7) / 4. So x = 2/4 = 0.5 or x = -12/4 = -3.

The Sine Rule (Higher)

a / sin A = b / sin B = c / sin C

Use this in any non-right-angled triangle when you know a side and its opposite angle, plus one other side or angle.

Example: In triangle ABC, angle A = 40 degrees, angle B = 75 degrees, and side a = 8 cm. Find side b. 8 / sin 40 = b / sin 75. b = 8 x sin 75 / sin 40 = 8 x 0.9659 / 0.6428 = 12.02 cm (2 d.p.).

The Cosine Rule (Higher)

a^2 = b^2 + c^2 - 2bc cos A

Use this in a non-right-angled triangle when you know two sides and the included angle (SAS), or all three sides (SSS) and need to find an angle.

Example: In triangle PQR, PQ = 7 cm, PR = 9 cm, and angle P = 60 degrees. Find QR. QR^2 = 7^2 + 9^2 - 2(7)(9) cos 60 = 49 + 81 - 126 x 0.5 = 67. QR = sqrt(67) = 8.19 cm (2 d.p.).

Area of a Triangle Using Sine (Higher)

A = 1/2 ab sin C

Use this when you know two sides and the included angle of any triangle.

Example: A triangle has sides 10 cm and 14 cm with an included angle of 30 degrees. A = 1/2 x 10 x 14 x sin 30 = 1/2 x 10 x 14 x 0.5 = 35 cm squared.

Section 2: Formulae You Must Memorise

These formulae are NOT on the formula sheet. If you do not have them committed to memory before you sit down in the exam hall, you cannot answer the questions that require them. There is no way around this.

Number

Percentage Change

Percentage change = (change / original) x 100

Example: A price rises from 40 pounds to 46 pounds. Change = 6. Percentage change = (6 / 40) x 100 = 15%.

Simple Interest

Interest = (principal x rate x time) / 100

Example: 500 pounds at 4% per year for 3 years. Interest = (500 x 4 x 3) / 100 = 60 pounds.

Compound Interest and Growth

Amount = principal x (1 + rate/100)^n

Use this for compound interest, population growth, or repeated percentage increase. For depreciation or decrease, use (1 - rate/100)^n.

Example: A savings account has 2000 pounds at 3% compound interest per year for 5 years. Amount = 2000 x (1.03)^5 = 2000 x 1.15927... = 2318.55 pounds (to the nearest penny).

Speed, Distance and Time

Speed = distance / time

Rearranges to: distance = speed x time, and time = distance / speed.

Example: A car travels 150 miles in 2.5 hours. Speed = 150 / 2.5 = 60 mph.

Density, Mass and Volume

Density = mass / volume

Example: A block has a mass of 240 g and a volume of 80 cm cubed. Density = 240 / 80 = 3 g/cm cubed.

Pressure, Force and Area

Pressure = force / area

Example: A force of 600 N acts on an area of 0.5 m squared. Pressure = 600 / 0.5 = 1200 Pa.

Algebra

nth Term of a Linear Sequence

nth term = dn + (a - d)

• d is the common difference
• a is the first term

This is equivalent to a + (n - 1)d, but the form dn + (a - d) makes it easier to write as an expression in n.

Example: The sequence 5, 8, 11, 14, ... has d = 3 and a = 5. nth term = 3n + (5 - 3) = 3n + 2.

Quadratic Factorising

For x^2 + bx + c = 0, find two numbers that multiply to give c and add to give b. Then write (x + p)(x + q) = 0.

Example: x^2 + 5x + 6 = 0. The numbers 2 and 3 multiply to 6 and add to 5. So (x + 2)(x + 3) = 0, giving x = -2 or x = -3.

Difference of Two Squares

a^2 - b^2 = (a + b)(a - b)

Example: Factorise x^2 - 49. This is x^2 - 7^2 = (x + 7)(x - 7).

Simultaneous Equations

For a pair of linear equations, eliminate one variable by making its coefficients equal, then add or subtract. No single formula exists, but the method must be memorised.

Example: 2x + y = 7 and 3x - y = 8. Adding the two equations: 5x = 15, so x = 3. Substituting: 2(3) + y = 7, so y = 1.

Geometry

Area of a Rectangle

A = length x width

Example: A rectangle measures 8 cm by 5 cm. A = 8 x 5 = 40 cm squared.

Area of a Triangle

A = 1/2 x base x height

The height must be perpendicular to the base.

Example: Base = 12 cm, perpendicular height = 7 cm. A = 1/2 x 12 x 7 = 42 cm squared.

Area of a Parallelogram

A = base x perpendicular height

Example: Base = 9 cm, perpendicular height = 4 cm. A = 9 x 4 = 36 cm squared.

Area of a Circle

A = pi r^2

Example: A circle has radius 6 cm. A = pi x 6^2 = 36 pi = 113.1 cm squared (1 d.p.).

Circumference of a Circle

C = 2 pi r (equivalently, C = pi d)

Example: A circle has diameter 10 cm. C = pi x 10 = 31.4 cm (1 d.p.).

Pythagoras' Theorem

a^2 + b^2 = c^2

• c is the hypotenuse (the longest side, opposite the right angle)

Example: A right-angled triangle has shorter sides 5 cm and 12 cm. c^2 = 25 + 144 = 169. c = 13 cm.

Trigonometric Ratios -- SOH CAH TOA

sin x = opposite / hypotenuse cos x = adjacent / hypotenuse tan x = opposite / adjacent

Example: In a right-angled triangle, the side opposite the angle is 4 cm and the hypotenuse is 10 cm. sin x = 4 / 10 = 0.4. x = sin^(-1)(0.4) = 23.6 degrees (1 d.p.).

Volume of a Cuboid

V = length x width x height

Example: A cuboid measures 4 cm by 3 cm by 10 cm. V = 4 x 3 x 10 = 120 cm cubed.

Volume of a Cylinder

V = pi r^2 h

Example: A cylinder has radius 5 cm and height 8 cm. V = pi x 25 x 8 = 200 pi = 628.3 cm cubed (1 d.p.).

Volume of a Cone (Higher)

V = 1/3 pi r^2 h

Example: A cone has radius 3 cm and height 7 cm. V = 1/3 x pi x 9 x 7 = 21 pi = 65.97 cm cubed (2 d.p.).

Volume of a Sphere (Higher)

V = 4/3 pi r^3

Example: A sphere has radius 4 cm. V = 4/3 x pi x 64 = 256/3 pi = 268.1 cm cubed (1 d.p.).

Surface Area of a Cylinder

SA = 2 pi r^2 + 2 pi r h

The first term gives the two circular ends; the second gives the curved surface.

Example: A cylinder has radius 3 cm and height 10 cm. SA = 2 pi (9) + 2 pi (3)(10) = 18 pi + 60 pi = 78 pi = 245.0 cm squared (1 d.p.).

Surface Area of a Sphere (Higher)

SA = 4 pi r^2

Example: A sphere has radius 5 cm. SA = 4 x pi x 25 = 100 pi = 314.2 cm squared (1 d.p.).

Interior and Exterior Angles of Regular Polygons

Exterior angle = 360 / n Interior angle = 180 - (360 / n)

• n is the number of sides

Example: A regular pentagon has 5 sides. Exterior angle = 360 / 5 = 72 degrees. Interior angle = 180 - 72 = 108 degrees.

Probability

Probability of an Event

P(event) = number of favourable outcomes / total number of outcomes

Example: A bag contains 3 red and 7 blue counters. P(red) = 3 / 10 = 0.3.

Complementary Events

P(not A) = 1 - P(A)

Example: If P(rain) = 0.35, then P(no rain) = 1 - 0.35 = 0.65.

Statistics

Mean

Mean = sum of all values / number of values

Example: The values are 4, 7, 9, 12, 8. Mean = (4 + 7 + 9 + 12 + 8) / 5 = 40 / 5 = 8.

Section 3: Exam Tips for Formula Questions

Show Every Step of Your Working

Edexcel awards method marks for each correct step in a calculation, even if your final answer is wrong. If a question is worth 3 marks, there are typically 2 method marks and 1 accuracy mark. Writing down the formula, substituting values, and then calculating earns you those method marks.

Always follow this pattern:

1. Write the formula. This earns the first method mark in many cases.
2. Substitute the values. Show the numbers going into the formula.
3. Calculate and state the answer with correct units.

If you skip straight to an answer and that answer is wrong, you score zero. If you write the formula and substitute correctly but make an arithmetic slip, you still pick up 2 out of 3 marks.

Common Formula Mistakes

Confusing radius and diameter. If a question gives you a diameter of 10 cm, the radius is 5 cm. Substituting 10 into a formula that requires the radius is one of the most common errors in the exam.

Forgetting to square or cube. In A = pi r^2, the radius must be squared before multiplying by pi. Calculate r^2 first, then multiply. The same applies to V = 4/3 pi r^3. Students who write pi x r x 2 instead of pi x r^2 lose all marks.

Using the wrong triangle formula. A = 1/2 x base x height requires the perpendicular height, not a slanted side. If you are given a slanted side but not the perpendicular height, you may need Pythagoras' theorem first.

Mixing up the sine and cosine rules. The sine rule needs a known side-angle pair. The cosine rule needs SAS (two sides and the included angle) or SSS (all three sides). Drawing a quick sketch and labelling the known values will help you decide which rule applies.

Dropping the negative in the quadratic formula. When b is positive, -b is negative. When c is negative, -4ac becomes positive. Write each substitution out carefully and use brackets.

Unit Conversions to Know

Many formula questions require you to work in consistent units. The most common conversions are:

• 1 km = 1000 m
• 1 m = 100 cm
• 1 cm = 10 mm
• 1 hour = 60 minutes = 3600 seconds
• 1 kg = 1000 g
• 1 litre = 1000 ml = 1000 cm cubed

If a question gives speed in km/h but distance in metres, convert before substituting. Examiners deliberately mix units to test whether you are paying attention.

Use the Formula Sheet Strategically

At the start of each paper, spend 30 seconds reviewing the formula sheet. Remind yourself what is there so that you do not waste time trying to recall something that is already printed for you. Equally, this reminds you that everything not on the sheet must come from memory.

If you are unsure whether a formula is on the sheet, check before writing anything down. It is faster to look at the front of the paper than to reconstruct a formula from a half-remembered version.

What to Do Next

Knowing the formulae is only the first step. You need to practise applying them under timed conditions using past papers. For a full revision plan, see our Edexcel GCSE Maths revision guide. For detailed advice on structuring your answers across all three papers, read our Edexcel GCSE Maths exam technique guide. And for more on understanding how examiners award marks, see how Edexcel mark schemes work.

You can also explore all of our Edexcel subject resources for more exam-focused guides.