Percentage Change
Use for percentage increase, decrease, profit, loss, error.
% change = (change / original) × 100% Cambridge O Level 4024
🧮 O Level Mathematics Formula Sheet 2026
All key formulas for Cambridge O Level Mathematics (4024) — number, algebra, geometry, mensuration, trigonometry, statistics and probability.
Algebra Geometry Trigonometry Statistics Mensuration
Our formula sheets are free to download — save this one as PDF for offline revision.
Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
Every O Level Maths Formula You Need
Cambridge O Level Mathematics (4024) has two papers. Paper 1 is non-calculator — number, algebra and geometry. Paper 2 allows a calculator and includes trigonometry, statistics, vectors and matrices. This sheet covers all formulas from both papers.
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Geometry and mensuration formulas
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Statistics, probability and graphs
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Trigonometry: right-angled and non-right
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Algebra: sequences, quadratics, functions
Number
Compound Interest
A = final amount, P = principal, r = rate per period (%), n = number of periods.
A = P(1 + r/100)ⁿ Simple Interest
I = interest (same currency as P), P = principal, R = rate (%), T = time (years).
I = PRT/100 Speed
Units: m/s, km/h. Convert: 1 m/s = 3.6 km/h.
Speed = Distance / Time Density
Units: g/cm³ or kg/m³.
Density = Mass / Volume Exchange Rate
Multiply or divide carefully. If £1 = 250 PKR, then PKR → £: divide by 250; £ → PKR: multiply by 250.
Algebra
Quadratic Formula
For ax² + bx + c = 0. Discriminant = b² − 4ac: positive → 2 roots; zero → 1 root; negative → no real roots.
x = (−b ± √(b² − 4ac)) / 2a Difference of Two Squares
a² − b² = (a + b)(a − b) Laws of Indices
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁰ = 1
a⁻ⁿ = 1/aⁿ
a^(1/n) = ⁿ√a
nth Term of Arithmetic Sequence
a = first term, d = common difference.
Tₙ = a + (n − 1)d Sum of Arithmetic Series
S = n/2 × (2a + (n−1)d) = n/2 × (first + last) nth Term of Geometric Sequence
a = first term, r = common ratio.
Tₙ = arⁿ⁻¹ Geometry and Mensuration
Area Formulas
Rectangle: A = l × w
Triangle: A = ½bh
Trapezium: A = ½(a + b)h
Circle: A = πr²
Sector: A = (θ/360) × πr²
Perimeter / Circumference
Circle: C = 2πr = πd
Arc length: l = (θ/360) × 2πr
Volume Formulas
Cuboid: V = lwh
Cylinder: V = πr²h
Cone: V = ⅓πr²h
Sphere: V = 4/3 πr³
Pyramid: V = ⅓ × base area × h
Surface Area
Cylinder (total): 2πrh + 2πr²
Sphere: 4πr²
Cone (curved): πrl where l = slant height
Pythagoras' Theorem
c = hypotenuse (longest side). Use to find any side of a right-angled triangle.
a² + b² = c² Angle Sum Rules
Triangle: angles sum to 180°
Quadrilateral: angles sum to 360°
Polygon interior angles sum: (n − 2) × 180°
Each interior angle of regular polygon: (n − 2) × 180° / n
Trigonometry
Right-Angled Trigonometry (SOH CAH TOA)
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Sine Rule
Use when: two angles + one side known, or two sides + non-included angle.
a/sin A = b/sin B = c/sin C Cosine Rule
Use when: three sides known, or two sides + included angle.
a² = b² + c² − 2bc cos A
cos A = (b² + c² − a²) / 2bc
Area of Triangle (non-right)
a and b are two sides, C is the included angle.
Area = ½ab sin C Statistics and Probability
Mean
For grouped data: x = midpoint of each class, f = frequency.
Mean = Σ(f × x) / Σf Probability
P(A') = 1 − P(A). P(A and B) = P(A) × P(B) if independent.
P(event) = number of favourable outcomes / total outcomes Combined Events
P(A or B) = P(A) + P(B) − P(A and B)
P(A and B) = P(A) × P(B|A)
Gradient of a Line
Use any two points on the line. Gradient of perpendicular line = −1/m.
m = (y₂ − y₁) / (x₂ − x₁) Equation of a Line
m = gradient, c = y-intercept.
y = mx + c How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Show all working — method marks matter
In Paper 2, method marks are available even if your final answer is wrong. Never skip steps.
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Learn which formula to use when
Sine rule: two angles + one side, or two sides + non-included angle. Cosine rule: two sides + included angle, or three sides.
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Paper 1 is non-calculator
All Paper 1 answers should be exact (fractions, surds). Check if the question asks for an estimate or exact value.
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Statistics: mean from grouped data
Use midpoints of each class interval, multiply by frequency, sum, then divide by total frequency.
Formula Sheet FAQ
Quick answers about this free PDF and how to use it for exam revision and active recall.
Is the Cambridge O Level Mathematics Formula Sheet 2026 free to download as a PDF?
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
What Mathematics topics and equations does this formula sheet cover?
This page groups key Mathematics formulas in one place for revision. Complete formula reference for Cambridge O Level Mathematics (4024). All key formulas for number, algebra, geometry, trigonometry, statistics and probability with O Level exam technique tips. Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
Who is this formula sheet for (Secondary)?
It is written for students preparing for assessments at Secondary in Mathematics, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
Where can I get more help with Mathematics revision?
Explore Tutopiya’s study tools, past paper finder, and revision checklists linked from our tools hub, or book a trial lesson with a subject specialist for personalised support alongside this formula reference.
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This formula sheet aligns with Cambridge O Level Mathematics (4024) syllabus content.
Note: Cambridge O Level Mathematics (4024) differs slightly from Cambridge IGCSE (0580) in syllabus coverage. Always use official 4024 past papers for exam practice.