GCSE Maths Formulas to Memorise for Higher and Foundation

Walking into your GCSE maths exam without knowing your formulas is like trying to build a flat-pack wardrobe without the instructions. While exam boards like AQA, Edexcel, and OCR have provided formula sheets in recent years, you cannot rely on them forever, and knowing them by heart saves precious time during the paper.

Mathematical fluency comes from being able to recall a formula instantly so you can focus on the actual problem-solving. This guide covers the essential formulas for both Foundation and Higher tiers, along with practical ways to make them stick.

Area and Perimeter Formulas

You are expected to know the area formulas for all basic 2D shapes. These often appear in the first half of the paper and are essential for more complex geometry questions later on.

The Basics

• Rectangle: Area = length × width
• Triangle: Area = 0.5 × base × height
• Parallelogram: Area = base × perpendicular height
• Trapezium: Area = 0.5(a + b)h (where a and b are the parallel sides)

Circles

Circles are a frequent source of lost marks. Remember that the radius is half the diameter.

• Circumference: C = πd or C = 2πr
• Area of a Circle: A = πr²

Study Tip: To remember which is which, look at the units. Area is always measured in units squared (like cm²), and the formula for area includes the radius squared (r²).

Algebra and Graphs

Algebra makes up a huge percentage of the GCSE maths marks. If you are sitting the Higher tier, the quadratic formula is a non-negotiable.

Linear Graphs

The equation of a straight line is y = mx + c.

• m is the gradient (change in y / change in x).
• c is the y-intercept (where the line crosses the vertical axis).

The Quadratic Formula (Higher Tier Only)

When a quadratic equation is in the form ax² + bx + c = 0, you find x using: x = [-b ± √(b² - 4ac)] / 2a

Worked Example: Solve 2x² + 7x + 3 = 0

1. Identify a=2, b=7, c=3.
2. Substitute: x = [-7 ± √(7² - 4(2)(3))] / (2 * 2)
3. Simplify: x = [-7 ± √(49 - 24)] / 4
4. x = [-7 ± √25] / 4
5. x = (-7 + 5)/4 = -0.5 OR x = (-7 - 5)/4 = -3

Pythagoras and Trigonometry

These formulas are used to find missing sides and angles in triangles. You should include these in your GCSE revision plan as they appear in both calculator and non-calculator papers.

Pythagoras' Theorem

For a right-angled triangle: a² + b² = c² Remember that 'c' must always be the longest side (the hypotenuse).

Trigonometry (SOH CAH TOA)

• Sin(θ) = Opposite / Hypotenuse
• Cos(θ) = Adjacent / Hypotenuse
• Tan(θ) = Opposite / Adjacent

For Higher tier students, you also need the Sine and Cosine rules for non-right-angled triangles:

• Sine Rule: a/sinA = b/sinB = c/sinC
• Cosine Rule: a² = b² + c² - 2bc cosA
• Area of any Triangle: 1/2 ab sinC

Compound Measures

Compound measures are used in real-world contexts and are standard marks in The Complete GCSE Revision Guide. Use the triangle method to rearrange these easily.

• Speed: Speed = Distance / Time
• Density: Density = Mass / Volume
• Pressure: Pressure = Force / Area

Worked Example: A car travels 150 miles in 3 hours. What is its average speed? Speed = 150 / 3 = 50 mph. If the question asks for the answer in metres per second, you must convert the units before or after the calculation.

Statistics and Probability

While often seen as easier, these formulas are easy to mix up under exam pressure.

• Mean: Total sum of data / Number of values
• Probability of an event: Number of successful outcomes / Total number of possible outcomes
• Relative Frequency: Number of times an event occurs / Total number of trials

How to Memorise These Formulas Effectively

Reading a list of formulas is the least effective way to learn them. Instead, use active recall methods found in popular revision tips.

Use Flashcards

Put the name of the formula on one side (e.g., "Area of a Trapezium") and the formula on the other. Use a digital tool or physical cards to test yourself daily. You can create a free deck to track which ones you keep getting wrong.

The 'Brain Dump' Method

At the start of every practice paper or study session, take a blank piece of paper and write down every formula you can remember. Check against a master list and highlight the ones you missed. Do this every day for a week, and you will find you rarely forget them.

Apply Them Immediately

Do not just learn the formula in isolation. As soon as you learn the Sine Rule, complete five different practice questions that require it. This builds the connection in your brain between the visual shape of a triangle and the formula required to solve it. Using study guides that offer tiered practice questions can help bridge this gap.

Summary for Exam Day

Check your specific exam board (AQA, Edexcel, or OCR) to see if they are providing a formula sheet for your specific exam year. Even if they are, memorising the basics like speed, area, and Pythagoras will give you more time to tackle the difficult multi-step problems at the end of the paper. Just like memorising GCSE Chemistry Equations, being prepared for maths is about repetition and practice.