GCSE Maths Formulas: Year 9-11
Number
Percentage Change: ((New Value - Original Value) / Original Value) * 100%
Compound Interest: A = P(1 + r/n)^(nt) where A=amount, P=principal, r=rate, n=compounding
periods per year, t=time in years
Compound Depreciation: A = P(1 - r/n)^(nt)
Ratio: For a ratio a:b, the total parts are a+b. A quantity is divided into shares of a/(a+b) and
b/(a+b).
Algebra
Quadratic Formula: For ax^2 + bx + c = 0, x = [-b ± sqrt(b^2 - 4ac)] / 2a
Difference of Two Squares: a^2 - b^2 = (a - b)(a + b)
Completing the Square: x^2 + bx = (x + b/2)^2 - (b/2)^2
Linear Sequences: nth term = a + (n-1)d where a=first term, d=common difference
Geometry
Area of a Triangle: 1/2 * base * height
Area of a Parallelogram: base * height
Area of a Trapezium: 1/2 * (a + b) * height (where a and b are parallel sides)
Circumference of a Circle: C = 2 * pi * r or C = pi * d
Area of a Circle: A = pi * r^2
Volume of a Cuboid: length * width * height
Volume of a Cylinder: pi * r^2 * height
Surface Area of a Cuboid: 2(lw + lh + wh)
Pythagoras' Theorem: a^2 + b^2 = c^2 (for a right-angled triangle, where c is the hypotenuse)
Trigonometric Ratios: - sin(theta) = Opposite / Hypotenuse - cos(theta) = Adjacent /
Hypotenuse - tan(theta) = Opposite / Adjacent
Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
Cosine Rule: c^2 = a^2 + b^2 - 2ab cos(C)
Statistics and Probability
Mean: Sum of values / Number of values
Median: Middle value when data is ordered
Mode: Most frequent value
Range: Highest value - Lowest value
Probability: Number of favourable outcomes / Total number of possible outcomes
Other Useful Formulas
Speed, Distance, Time: Speed = Distance / Time
Number
Percentage Change: ((New Value - Original Value) / Original Value) * 100%
Compound Interest: A = P(1 + r/n)^(nt) where A=amount, P=principal, r=rate, n=compounding
periods per year, t=time in years
Compound Depreciation: A = P(1 - r/n)^(nt)
Ratio: For a ratio a:b, the total parts are a+b. A quantity is divided into shares of a/(a+b) and
b/(a+b).
Algebra
Quadratic Formula: For ax^2 + bx + c = 0, x = [-b ± sqrt(b^2 - 4ac)] / 2a
Difference of Two Squares: a^2 - b^2 = (a - b)(a + b)
Completing the Square: x^2 + bx = (x + b/2)^2 - (b/2)^2
Linear Sequences: nth term = a + (n-1)d where a=first term, d=common difference
Geometry
Area of a Triangle: 1/2 * base * height
Area of a Parallelogram: base * height
Area of a Trapezium: 1/2 * (a + b) * height (where a and b are parallel sides)
Circumference of a Circle: C = 2 * pi * r or C = pi * d
Area of a Circle: A = pi * r^2
Volume of a Cuboid: length * width * height
Volume of a Cylinder: pi * r^2 * height
Surface Area of a Cuboid: 2(lw + lh + wh)
Pythagoras' Theorem: a^2 + b^2 = c^2 (for a right-angled triangle, where c is the hypotenuse)
Trigonometric Ratios: - sin(theta) = Opposite / Hypotenuse - cos(theta) = Adjacent /
Hypotenuse - tan(theta) = Opposite / Adjacent
Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
Cosine Rule: c^2 = a^2 + b^2 - 2ab cos(C)
Statistics and Probability
Mean: Sum of values / Number of values
Median: Middle value when data is ordered
Mode: Most frequent value
Range: Highest value - Lowest value
Probability: Number of favourable outcomes / Total number of possible outcomes
Other Useful Formulas
Speed, Distance, Time: Speed = Distance / Time
