GCSE Maths Formula Sheet: Essential Formulas for Your Exam

GCSE maths can feel overwhelming when you’re trying to remember dozens of formulas for topics ranging from algebra to geometry. The relief? Your exam provides a formula sheet with many of the equations you’ll need. The catch? Not every formula is on that sheet, and knowing which ones you must memorise can make the difference between a grade 7 and a grade 9.

Here’s your complete guide to the GCSE maths formula sheet – what’s on it, what’s not, and how to use it effectively.

What is the GCSE Maths Formula Sheet?

The GCSE maths formula sheet is a single page provided in both your Foundation and Higher tier maths papers. It contains approximately 15-20 formulas covering geometry, algebra, and some statistical concepts.

All major exam boards (AQA, Edexcel, OCR) provide this sheet, though the exact layout differs slightly. The formulas themselves are largely the same across boards.

Which Formulas Are Included on the Sheet?

The formula sheet typically includes:

Geometry and Mensuration

Circumference of a circle: C = πd or C = 2πr
Area of a circle: A = πr²
Curved surface area of a cylinder: A = 2πrh
Volume of a cylinder: V = πr²h
Volume of a prism: V = area of cross-section × length
Volume of a cone: V = ⅓πr²h
Curved surface area of a cone: A = πrl (where l is slant height)
Volume of a sphere: V = ⁴⁄₃πr³
Surface area of a sphere: A = 4πr²
Pythagoras’ theorem: a² + b² = c²

Trigonometry

Sine rule: a/sin A = b/sin B = c/sin C
Cosine rule: a² = b² + c² - 2bc cos A
Area of a triangle: Area = ½ab sin C

Quadratic Formula

Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

Some exam boards also include:

Compound interest formula: Total = P(1 + r/100)ⁿ
Simple interest formula: Interest = (P × r × t) / 100

The exact formulas may vary slightly by board and tier (Foundation vs Higher), so always check your specific exam board’s specimen papers.

Formulas You MUST Memorise (Not on the Sheet)

These essential formulas do NOT appear on the formula sheet, so you must commit them to memory:

Basic Operations

Fractions: Adding, subtracting, multiplying, dividing fractions
Percentages: Finding percentages, percentage increase/decrease
Ratio: Dividing amounts in given ratios

Algebra

Expanding brackets: (a + b)(c + d) = ac + ad + bc + bd
Factorising: Reversing expansion
Difference of two squares: a² - b² = (a + b)(a - b)
Rearranging formulas: Making a different letter the subject

Geometry Basics

Area of a rectangle: A = length × width
Area of a triangle: A = ½ × base × height (the basic version, not the sine version)
Area of a trapezium: A = ½(a + b)h
Area of a parallelogram: A = base × height
Perimeter: Sum of all sides

Speed, Distance, Time

Speed: speed = distance ÷ time
Distance: distance = speed × time
Time: time = distance ÷ speed

Density

Density: density = mass ÷ volume

Probability

Probability: P(event) = number of favourable outcomes ÷ total number of outcomes
Combined events: P(A and B) = P(A) × P(B) (for independent events)

Statistics

Mean: mean = sum of values ÷ number of values
Range: range = highest value - lowest value
Median: the middle value when data is ordered
Mode: the most frequent value

These formulas form the foundation of GCSE maths. If you don’t know them instantly, you’ll struggle.

How Formulas Differ by Topic

Algebra

Algebra relies heavily on methods rather than formulas. You need to know:

How to solve linear equations (e.g., 3x + 5 = 14)
How to solve simultaneous equations (elimination or substitution)
How to complete the square
How to factorise quadratics

The quadratic formula IS on the sheet, but you still need to know how to substitute values correctly and simplify surds.

Geometry and Measures

Most geometry formulas for circles, cones, spheres, and cylinders ARE on the formula sheet. However, basic area formulas (rectangle, triangle, trapezium, parallelogram) are NOT.

You also need to know:

How to convert between units (cm to m, mm to cm, etc.)
How to calculate perimeters
Angle rules (angles in parallel lines, angles in polygons, circle theorems)

Ratio and Proportion

Ratio questions don’t require formula memorisation as much as they require method understanding:

How to simplify ratios
How to divide amounts in a given ratio
How to scale recipes or maps using ratios
Direct and inverse proportion

Statistics and Probability

You must memorise how to calculate:

Mean (sum ÷ count)
Median (middle value)
Mode (most frequent)
Range (max - min)

The formula sheet doesn’t include these because they’re considered fundamental.

Trigonometry

Basic SOHCAHTOA is NOT on the formula sheet. You must know:

sin θ = opposite ÷ hypotenuse
cos θ = adjacent ÷ hypotenuse
tan θ = opposite ÷ adjacent

The sine rule and cosine rule ARE on the sheet, as these are more complex.

How to Use the Formula Sheet Effectively in Your Exam

1. Familiarise Yourself Beforehand

Download the formula sheet from your exam board’s website (search “AQA GCSE maths formula sheet” or similar). Keep it on your desk during revision. Use it when doing past papers so you get comfortable finding formulas quickly.

2. Don’t Rely on It for Everything

Just because a formula is on the sheet doesn’t mean you should look it up every time. Memorise formulas you use frequently (like area of a circle or Pythagoras) so you can work faster. Save the formula sheet for occasional use.

3. Know When You Need It

If a question mentions:

Circles, cones, spheres → check the sheet for volume/surface area formulas
Non-right-angled triangles → check for sine rule or cosine rule
Quadratic equations that won’t factorise → use the quadratic formula

If a question asks for:

Area of a rectangle, triangle, trapezium → recall from memory (NOT on the sheet)
Speed, distance, time → recall from memory
Mean, median, mode → recall from memory

4. Check Your Substitution

The formula sheet gives you the formula, but you still need to substitute values correctly. Common mistakes include:

Using diameter instead of radius (or vice versa)
Forgetting to square the radius in area/volume calculations
Using degrees when your calculator is in radians (or vice versa) for trigonometry

Always write out the formula, substitute values clearly, then calculate. This makes it easier to spot errors.

Common Mistakes Students Make with Formulas

Mistake 1: Looking for formulas that aren’t there

Students waste time searching the formula sheet for area of a rectangle or the formula for mean. These are considered too basic to include. Know what’s NOT on the sheet.

Mistake 2: Using the wrong formula

Confusing circumference with area, or using the wrong volume formula, costs easy marks. Read the question carefully – does it ask for surface area or volume? Perimeter or area?

Mistake 3: Not showing working

Even if you use the formula sheet, you must show your working. Write the formula, substitute numbers, then calculate. You can still earn method marks if your final answer is wrong.

Mistake 4: Forgetting units

If the question gives measurements in centimetres but asks for volume in cubic metres, you must convert. Always check units in the question and the required answer.

Mistake 5: Misreading the formula

The quadratic formula has ± in it. Students often forget to calculate both solutions (+ and -). The sine rule can be written upside down (sin A / a = sin B / b). Make sure you understand how to read and apply each formula.

Memory Techniques for GCSE Maths Formulas

Since many essential formulas aren’t on the sheet, you need effective memorisation strategies:

1. Create a Formula Flashcard Set

Write each formula on one side of a card, with an example question on the back. Test yourself daily. Focus on formulas you struggle to recall.

2. Use Mnemonics

SOHCAHTOA for trigonometry (sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent)
BIDMAS/BODMAS for order of operations (Brackets, Indices/Orders, Division/Multiplication, Addition/Subtraction)
Distance = Speed × Time can be remembered with a triangle diagram (DST)

3. Practise Application, Not Just Memorisation

Memorising formulas in isolation doesn’t work. Do past paper questions that require each formula. The more you use a formula in context, the better you’ll remember it.

4. Group Formulas by Topic

Don’t try to memorise 50 random formulas. Group them:

Geometry (areas, perimeters)
Algebra (quadratic formula, rearranging)
Statistics (mean, median, mode)
Trigonometry (SOHCAHTOA, sine/cosine rules)

This makes recall easier during exams when you know which topic a question relates to.

How to Revise Formulas for Foundation vs Higher Tier

Foundation Tier:

Focus on basic area formulas (rectangle, triangle, trapezium)
Memorise SOHCAHTOA for right-angled triangles
Know how to use Pythagoras’ theorem
Understand simple probability and statistics (mean, median, mode)

The formula sheet will cover most geometry volume formulas you need.

Higher Tier:

Everything from Foundation tier, plus:
Sine and cosine rules for non-right-angled triangles
Quadratic formula (though it’s on the sheet, memorise it anyway for speed)
Completing the square method
Circle theorems
More complex probability (tree diagrams, conditional probability)

Higher tier questions assume faster formula recall because they’re testing problem-solving, not just calculation.

How UpGrades Helps with GCSE Maths Formulas

Knowing formulas is only the first step. You also need to:

Recognise which formula applies to a given question
Substitute values correctly
Rearrange formulas when needed
Work under time pressure

UpGrades provides targeted practice questions that test your ability to select and apply the right formula for each scenario. With instant feedback, you’ll quickly learn:

Which formulas you’re confident with
Which formulas you’re misapplying
Where your calculation errors occur

The adaptive system ensures you spend time practising the areas you find hardest, building both speed and accuracy before exam day. Combine smart formula revision with UpGrades’ exam-style practice, and you’ll walk into your GCSE maths exam fully prepared.

Final Checklist for GCSE Maths Formula Success

Download and familiarise yourself with your exam board’s formula sheet
Memorise all formulas NOT on the sheet (area of rectangle, triangle, trapezium; speed/distance/time; mean/median/mode)
Practise using the formula sheet during timed past papers
Create a one-page summary of formulas you must memorise
Test yourself on formula application, not just recall
Check units carefully in every question
Always show your working, even when using the formula sheet

The GCSE maths formula sheet is a helpful resource, but it’s not a crutch. Master the fundamentals that aren’t on the sheet, know when to reference what is on the sheet, and you’ll be ready to tackle any question your exam throws at you.