As the GCSE Mathematics exam approaches, having a strong command of key formulas can make a huge difference to your performance. Many exam questions are built around a few core mathematical principles that come up again and again across both Foundation and Higher tiers. Memorising these and practising how to apply them can help you solve problems more quickly and confidently in the exam.
✅ 7 Essential GCSE Maths Formulas to Know by Heart
1️⃣ Area of a Circle
A = πr²
(Where A is the area and r is the radius)
2️⃣ Circumference of a Circle
C = 2πr or πd
(Where C is circumference, r is radius, d is diameter)
3️⃣ Pythagoras’ Theorem
a² + b² = c²
(Used in right-angled triangles to find the missing side)
4️⃣ Quadratic Formula
x = (-b ± √(b² – 4ac)) / 2a
(Used to find the roots of a quadratic equation ax² + bx + c = 0)
5️⃣ Trigonometric Ratios
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
(Used in right-angled triangle problems involving angles and lengths)
6️⃣ Area of a Trapezium
A = ½(a + b)h
(Where a and b are the parallel sides and h is the height)
7️⃣ Simple Interest Formula
I = (P × R × T) / 100
(Where I is interest, P is principal, R is rate, T is time)
These formulas cover several key topics — algebra, geometry, and trigonometry — and often appear in both calculator and non-calculator papers. The examiner may not always give these formulas on the formula sheet, so it’s best to memorise them early and practise using them in different types of questions.
How to Prepare for the GCSE Maths Exam
1. Revise Every Formula with Examples
Don’t just memorise formulas — practise applying them to real questions. For example, use the circle area formula to find missing radius or solve problems where both area and circumference are involved.
2. Make a Formula Sheet for Daily Revision
Write all key formulas on one sheet and keep it handy for daily review. Repetition is key to long-term memory.
3. Practise Past Papers Under Timed Conditions
The more you practise under exam timing, the better your pacing becomes. Try to complete at least one past paper every week before the exam.
4. Focus on High-Frequency Topics
Spend extra time on algebra, geometry, ratio, and trigonometry — these areas carry a large number of marks in the final paper.
5. Check Common Mistakes
Many students lose marks for rounding errors, missing units, or skipping steps. Always double-check your answers carefully.
6. Show Full Working in Every Question
Even if your final answer is wrong, you can still earn method marks for showing your calculation steps clearly.
7. Stay Calm and Confident
Before the exam, take short breaks, review key formulas, and enter the paper with a clear mind. Confidence built through consistent practice leads to success.
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