Essential GCSE Maths Formulas and Concepts
Geometry fundamentals form the backbone of so many maths problems you'll face. In circles, remember that the diameter is twice the radius, and a chord is any line segment connecting two points on the circle. For triangles, the angles always add up to 180°, whilst quadrilaterals total 360°.
Trigonometry becomes much easier when you master SOH CAH TOA for right-angled triangles. Use SIN = opposite/hypotenuse, COS = adjacent/hypotenuse, and TAN = opposite/adjacent. For any triangle, the sine rule (a/sinA = b/sinB = c/sinC) and cosine rule (a² = b² + c² - 2bc×cosA) are your go-to tools.
Probability follows simple rules that you can rely on. For independent events, P(A and B) = P(A) × P(B), whilst P(A or B) = P(A) + P(B). When dealing with "at least" problems, use 1 - P(the opposite outcome) to save time.
Top Tip: The Pythagorean theorem appears everywhere in GCSE maths, so make sure you can apply it quickly and confidently.
Data handling requires you to understand the difference between mean (total ÷ number of items), median (middle value), and mode (most common). For cumulative frequency graphs, find the median at the halfway point and quartiles at ¼ and ¾ positions.
Percentage calculations are straightforward once you know the formulas. Percentage change = (change/original) × 100, whilst compound interest uses N = N₀ⁿ. These formulas will appear in multiple exam questions, so practise them until they're second nature.