GCSE Maths Formulas You Must Know Before the Exam

 To succeed in your GCSE Maths exam, you must memorise and understand key formulas. Some formulas are provided in the exam formula sheet, but others must be learned. Below is a list of the most important GCSE Maths formulas, grouped by topic.

1. Number & Algebra Formulas

Fractions, Decimals & Percentages

  • Percentage Change: Percentage Change=New Value−Original ValueOriginal Value×100\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100

  • Compound Interest: A=P(1+r100)tA = P \left(1 + \frac{r}{100} \right)^t where:

    • AA = final amount

    • PP = principal (starting amount)

    • rr = interest rate (%)

    • tt = time (years)

Algebraic Expansions

  • Quadratic Expansion: (a+b)(a−b)=a2−b2(a + b)(a - b) = a^2 - b^2

  • Factorising the Difference of Squares: a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)

Solving Quadratics

2. Ratio, Proportion & Probability

Direct and Inverse Proportion

  • Direct Proportion: y=kxy = kx

  • Inverse Proportion: y=kxy = \frac{k}{x} where kk is the constant of proportionality.

Probability

  • Probability of an Event: P(A)=Number of successful outcomesTotal number of outcomesP(A) = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}}

  • Expected Frequency: Expected Frequency=Probability×Number of Trials\text{Expected Frequency} = \text{Probability} \times \text{Number of Trials}

3. Geometry & Measures

Perimeter, Area & Volume

  • Area of a Triangle: A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

  • Area of a Parallelogram: A=base×heightA = \text{base} \times \text{height}

  • Area of a Trapezium: A=12×(a+b)×hA = \frac{1}{2} \times (a + b) \times h

  • Circumference of a Circle: C=2πrorC=πdC = 2\pi r \quad \text{or} \quad C = \pi d

  • Area of a Circle: A=πr2A = \pi r^2

  • Volume of a Cylinder: V=πr2hV = \pi r^2 h

  • Volume of a Sphere: V=43πr3V = \frac{4}{3} \pi r^3

  • Volume of a Cone: V=13πr2hV = \frac{1}{3} \pi r^2 h

Pythagoras’ Theorem

  • For a right-angled triangle: a2+b2=c2a^2 + b^2 = c^2 where cc is the hypotenuse.

Trigonometry (Right-Angled Triangles)

  • SOH CAH TOA: sin⁡θ=oppositehypotenuse\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} cos⁡θ=adjacenthypotenuse\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} tan⁡θ=oppositeadjacent\tan \theta = \frac{\text{opposite}}{\text{adjacent}} 

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Sine and Cosine Rules (Non-Right-Angled Triangles)

  • Sine Rule: asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

  • Cosine Rule: c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab \cos C

  • Area of a Triangle Using Sine: A=12absin⁡CA = \frac{1}{2} ab \sin C

4. Coordinate Geometry

Straight Line Equation

  • Gradient Formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

  • Equation of a Straight Line: y=mx+cy = mx + c where:

    • mm = gradient

    • cc = y-intercept

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5. Statistics & Probability

Mean, Median & Mode

  • Mean (Average): Mean=Sum of all valuesNumber of values\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}

  • Median: The middle value when data is arranged in order.

  • Mode: The most frequently occurring value.

Probability Rules

  • Addition Rule for Probability (Mutually Exclusive Events): P(A or B)=P(A)+P(B)P(A \text{ or } B) = P(A) + P(B)

  • Multiplication Rule for Probability (Independent Events): P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)

6. Speed, Distance & Time

  • Speed Formula: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

  • Density Formula: Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}

  • Pressure Formula: Pressure=ForceArea\text{Pressure} = \frac{\text{Force}}{\text{Area}}

Tips for Remembering and Using GCSE Maths Formulas

  • Practice using formulas in past paper questions.

  • Write them out regularly to help memorisation.

  • Understand when and how to use them, rather than just memorising.

  • Use flashcards for quick recall before the exam.

  • Make a formula sheet with the ones you must learn and review it often.

By mastering these formulas, you will have a strong foundation for your GCSE Maths exam.  Enrol now for affordable Online Tutoring UK

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