Formulas are at the heart of GCSE Maths. They give you the tools to solve a wide range of problems, from calculating areas and volumes to working out probabilities or solving quadratic equations. While some formulas are provided on the exam paper, many are not — students are expected to memorise them and know when to apply them.
For many learners, this is a challenge. Forgetting even one key formula can make an otherwise straightforward question feel impossible. The good news is that with steady practice, formulas can become second nature. In this blog, we look at the most important formulas you must know for GCSE Maths, explain what they are used for, and share tips on how to memorise them effectively.
1. Why Formulas Matter in GCSE Maths
Formulas are the backbone of GCSE Maths. They allow you to solve problems efficiently and accurately, from finding the area of a shape to calculating the solution of a quadratic equation. In the exam, some formulas are provided on a formula sheet, but many are not. Students are expected to memorise and apply them without prompts.
This means that knowing the formulas is not just about learning by heart, but also about practising when and how to use them. For example, remembering Pythagoras’ theorem is one step, but recognising when a question actually requires it is just as important.
A strong grasp of formulas helps in two ways. First, it saves time during the exam because you can go straight to the method. Second, it boosts confidence, since you know you have the tools to tackle a wide range of problems. Forgetting a formula, on the other hand, can make even a simple question feel impossible.
👉 On our site, you can find a complete GCSE Maths Formula Sheet along with a Formula Practice Room designed to help you test your knowledge and memorise everything you need.
2. Pythagoras’ Theorem
Pythagoras’ theorem is one of the most fundamental formulas in GCSE Maths. It applies to right-angled triangles and links the lengths of the sides:
$$a^2 + b^2 = c^2$$
where a and b are the shorter sides and c is the hypotenuse. This formula is used to:
- Find the length of a missing side when the other two are known.
- Prove that a triangle is right-angled.
- Solve real-life problems involving distance.
Example: $$c = \sqrt{3^2 + 4^2} = \sqrt{25} = 5 \; cm$$
3. Trigonometric Ratios (sine, cosine, tangent)
The three main ratios link the angles and sides of right-angled triangles:
$$\sin \theta = \tfrac{\text{opposite}}{\text{hypotenuse}}, \quad \cos \theta = \tfrac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan \theta = \tfrac{\text{opposite}}{\text{adjacent}}$$
These allow you to find missing sides or angles. A common memory aid is SOHCAHTOA.
4. The Quadratic Formula
Quadratic equations of the form $$ax^2 + bx + c = 0$$ can always be solved using:
$$x = \tfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Example: For $$2x^2 + 3x - 2 = 0$$:
$$x = \tfrac{-3 \pm \sqrt{3^2 - 4(2)(-2)}}{2(2)} = \tfrac{-3 \pm \sqrt{25}}{4} = \tfrac{-3 \pm 5}{4}$$
So $$x = \tfrac{1}{2} \; \text{or} \; -2$$.
5. Area Formulas
- Triangle: $$\tfrac{1}{2} \times \text{base} \times \text{height}$$
- Parallelogram: $$\text{base} \times \text{height}$$
- Trapezium: $$\tfrac{1}{2} (a+b)h$$
- Circle: $$\pi r^2$$
6. Volume Formulas
- Prism: $$\text{area of cross-section} \times \text{length}$$
- Cylinder: $$\pi r^2 h$$
- Sphere: $$\tfrac{4}{3}\pi r^3$$
- Cone: $$\tfrac{1}{3}\pi r^2 h$$
- Pyramid: $$\tfrac{1}{3} \times \text{base area} \times h$$
7. Surface Area Formulas
- Cuboid: $$2lw + 2lh + 2wh$$
- Cylinder: $$2\pi r^2 + 2\pi rh$$
- Sphere: $$4\pi r^2$$
- Cone: $$\pi r^2 + \pi rl$$
8. Circle Theorems
Key theorems include:
- Angle in a semicircle = 90°
- Angle at centre = 2 × angle at circumference
- Angles in the same segment are equal
- Opposite angles in a cyclic quadrilateral = 180°
- Tangent ⟂ radius at point of contact
- Alternate segment theorem
9. Probability and Statistics Formulas
- $$P(\text{not A}) = 1 - P(A)$$
- Relative frequency: $$P(\text{event}) = \tfrac{\text{successful outcomes}}{\text{total trials}}$$
- Mean = $$\tfrac{\Sigma fx}{\Sigma f}$$
- $$P(A \text{ and } B) = P(A) \times P(B)$$ (independent events)
- $$P(A \text{ or } B) = P(A) + P(B)$$ (mutually exclusive)
10. Tips for Memorising and Practising Formulas
- Write formulas out repeatedly.
- Use flashcards to test recall.
- Apply formulas in practice questions regularly.
👉 On our site, you can find a complete GCSE Maths Formula Sheet along with a Formula Practice Room where you can test your knowledge interactively.
Conclusion
GCSE Maths is much easier to tackle when you have a strong memory for the essential formulas. Whether it is Pythagoras’ theorem, trigonometric ratios, the quadratic formula, or the rules for probability, each one is a building block that unlocks a set of exam questions.
Success comes not just from memorising the formulas, but from practising how and when to use them. By writing them out, testing yourself, and applying them in real exam-style problems, you can build the confidence to recall them under pressure.
👉 On our site, you will find a complete GCSE Maths Formula Sheet and a dedicated Formula Practice Room to help you strengthen your memory and apply these formulas until they become second nature.