Maths formulae for revision

Algebra

• Quadratic roots: x = (−b ± √(b² − 4ac))/(2a), for ax² + bx + c = 0 and a ≠ 0. Real roots require b² − 4ac ≥ 0.
• Arithmetic nth term: a + (n − 1)d. With a = 5 and d = 3, the tenth term is 32.
• Gradient: (y₂ − y₁)/(x₂ − x₁), provided x₂ ≠ x₁. A vertical line has no finite gradient.

Geometry and measure

• Right triangle: a² + b² = c², where c is the hypotenuse. Legs 9 and 12 give c = 15.
• Circle area: πr²; circumference: 2πr. A radius of 3 gives area 9π and circumference 6π.
• Triangle area: ½bh, with perpendicular height h. Alternatively ½ab sin C uses the angle included between sides a and b.
• Prism volume: cross-sectional area × perpendicular length. An area of 12 cm² and length of 5 cm give 60 cm³.

Statistics and probability

• Mean from a frequency table: Σfx/Σf. For grouped intervals, using midpoints gives an estimate, not usually an exact mean.
• Frequency density = frequency/class width. A frequency of 24 over width 8 gives density 3.
• P(A and B) = P(A)P(B|A). For independent events, P(B|A) = P(B).
• P(not A) = 1 − P(A). A success probability of 0.7 gives failure probability 0.3.

Check before substituting

Use consistent units, identify which angle or length each symbol represents and retain exact or unrounded values until the final step. Squared and cubed units should match areas and volumes. If a result violates a condition, such as a shorter side exceeding the hypotenuse, revisit the substitution.

Find the specification, question papers and mark schemes on Pearson

Related resources

• The quadratic formula
• Right-angled trigonometry
• Histograms
• Edexcel IGCSE Maths revision