AQA GCSE Maths Foundation Cheat Sheet 2026

ExpertMinds Editorial·3 March 2026·8 min read

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Foundation tier covers grades 1–5. The highest grade available is 5 (a "strong pass"). If you are targeting grade 5, you need to be solid on all Foundation content and comfortable with the harder Foundation questions. This reference covers every topic area and the formulas given in the exam versus those you must memorise.

Key fact:AQA GCSE Maths: 3 papers — Paper 1 (non-calculator, 80 marks, 90 min) + Papers 2 & 3 (calculator, 80 marks each, 90 min each). Total: 240 marks. The formula sheet is NOT provided — you must memorise all formulas.

Formulas You Must Memorise

Formula	Used for
Area of triangle = ½ × base × height	Any triangle
Area of trapezium = ½(a + b)h	Trapezium (a and b are parallel sides)
Area of circle = πr²	Circle (r = radius)
Circumference = πd = 2πr	Circle perimeter
Volume of cuboid = l × w × h	Box/rectangular prism
Volume of prism = area of cross-section × length	Any prism (cylinder, triangular prism)
Pythagoras: a² + b² = c²	Right-angled triangles only; c is the hypotenuse
Speed = Distance ÷ Time	Compound measure — rearrange triangle: SDT
Density = Mass ÷ Volume	Compound measure — rearrange triangle: DMV
Pressure = Force ÷ Area	Compound measure

Number — Key Rules

Topic	Rule / method	Common mistake
Fractions — multiply	Multiply numerators; multiply denominators	Trying to find common denominator (not needed)
Fractions — divide	Keep, Change, Flip — multiply by reciprocal	Flipping the wrong fraction
Fractions — add/subtract	Find LCM; convert to equivalent fractions	Adding numerators AND denominators
Percentage increase	Multiply by (1 + %/100). e.g. +15% → × 1.15	Adding % directly without converting
Percentage decrease	Multiply by (1 − %/100). e.g. −20% → × 0.8	Forgetting to subtract from 1
Reverse percentage	Divide by the multiplier. e.g. after +25%, divide by 1.25	Subtracting % from the result
Standard form	a × 10ⁿ where 1 ≤ a < 10	Value of a not in range; wrong power of 10
Ratio — share	Find total parts; divide amount; multiply per part	Not adding ratio parts first

Algebra — Key Rules

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Questions graded, hints, and explained.

Topic	Method
Expand single bracket	Multiply everything inside by the term outside
Expand double brackets (FOIL)	First, Outside, Inside, Last — then simplify like terms
Factorise — common factor	Find HCF of all terms; place outside bracket
Solve linear equation	Do the same to both sides; isolate x
Solve linear inequality	Same as equation — but flip the sign if dividing by negative
nth term of arithmetic sequence	aₙ = a + (n−1)d where a = first term, d = common difference
Substitution	Replace letters with numbers; follow BIDMAS
Rearrange a formula	Treat as an equation — isolate the target variable

Tip:BIDMAS order: Brackets → Indices → Division/Multiplication (left to right) → Addition/Subtraction (left to right). Division and multiplication have equal priority — work left to right. Same for addition and subtraction.

Practice GCSE Maths questions

Formulas are only useful when you know which one to apply. Practice exam-style questions to build the judgment.

Geometry — Key Facts

Topic	Rule
Angles in a triangle	Sum = 180°
Angles in a quadrilateral	Sum = 360°
Angles on a straight line	Sum = 180°
Angles around a point	Sum = 360°
Corresponding angles (parallel lines)	Equal (F-angles)
Alternate angles (parallel lines)	Equal (Z-angles)
Co-interior / allied angles (parallel lines)	Sum = 180° (C-angles)
Interior angles of regular n-gon	(n−2) × 180° ÷ n
Exterior angles of any polygon	Sum = 360°
Pythagoras	a² + b² = c² — right-angled triangles only; c is always the hypotenuse

Statistics & Probability

Topic	Rule / formula
Mean	Sum of all values ÷ number of values
Median	Middle value when ordered (or mean of middle two)
Mode	Most frequently occurring value
Range	Largest − Smallest
Probability (basic)	P(event) = favourable outcomes ÷ total outcomes; always between 0 and 1
Mutually exclusive events	P(A or B) = P(A) + P(B)
Independent events	P(A and B) = P(A) × P(B)
Relative frequency	Experimental probability = frequency ÷ total trials
Scatter graphs	Positive/negative/no correlation; line of best fit through mean point

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