📐 IGCSE Maths Formula Sheet 2026

Complete Cambridge IGCSE Mathematics (0580/0607/0980) Formula Reference Guide

Cambridge IGCSE Extended Papers Free Download

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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.

Essential IGCSE Mathematics Formulas

Master your IGCSE Mathematics exams with our comprehensive formula sheet covering all essential formulas for Cambridge IGCSE (0580/0607/0980) Extended papers. This reference guide includes area, volume, trigonometry, algebra, and more.

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Cambridge IGCSE™ Mathematics (0580, 0607, and 0980)

List of formulas for Extended papers

Area and Circumference

Area, A, of triangle, base b, height h.

A = (1/2)bh

Area, A, of circle of radius r.

A = πr²

Circumference, C, of circle of radius r.

C = 2πr

Surface Area

Curved surface area, A, of cylinder of radius r, height h.

A = 2πrh

Curved surface area, A, of cone of radius r, sloping edge l.

A = πrl

Surface area, A, of sphere of radius r.

A = 4πr²

Volume

Volume, V, of prism, cross-sectional area A, length l.

V = Al

Volume, V, of pyramid, base area A, height h.

V = (1/3)Ah

Volume, V, of cylinder of radius r, height h.

V = πr²h

Volume, V, of cone of radius r, height h.

V = (1/3)πr²h

Volume, V, of sphere of radius r.

V = (4/3)πr³

Quadratic Equation

For the equation ax² + bx + c = 0, where a ≠ 0.

x = (-b ± √(b² - 4ac)) / 2a

Triangle Formulas

For the triangle shown,

Sine Rule:

a / sin A = b / sin B = c / sin C

Cosine Rule:

a² = b² + c² - 2bc cos A

Area of triangle:

Area = (1/2)ab sin C

Geometric Formulas

Rectangle - length l, width w

Area = lw, Perimeter = 2(l + w)

Square - side s

Area = s², Perimeter = 4s

Parallelogram - base b, height h

Area = bh, Perimeter = 2(a + b)

Rhombus - side s, height h

Area = sh = (1/2)d₁d₂, Perimeter = 4s

Trapezium - parallel sides a,b, height h

Area = (1/2)(a + b)h

Sector of Circle - radius r, angle θ (degrees)

Area = (θ/360) × πr², Arc length = (θ/360) × 2πr

Segment of Circle - radius r, angle θ

Area = (1/2)r²(θ - sin θ) where θ is in radians

3D Geometric Formulas

Cuboid - length l, width w, height h

Volume = lwh, Surface Area = 2(lw + lh + wh)

Cube - side s

Volume = s³, Surface Area = 6s²

Triangular Prism - base area A, length l

Volume = Al, Surface Area = 2A + perimeter × l

Square-based Pyramid - base side s, height h

Volume = (1/3)s²h, Surface Area = s² + 2sl

Triangular Pyramid - base area A, height h

Volume = (1/3)Ah

Hemisphere - radius r

Volume = (2/3)πr³, Surface Area = 3πr²

Angle Theorems in Geometry

Angles on a straight line

Sum = 180°

Angles around a point

Sum = 360°

Vertically opposite angles

Are equal

Angles in a triangle

Sum = 180°

Angles in a quadrilateral

Sum = 360°

Exterior angle of triangle

= Sum of opposite interior angles

Angles in a polygon (n sides)

Sum = (n - 2) × 180°

Interior angle of regular polygon

= (n - 2) × 180° / n

Exterior angle of regular polygon

= 360° / n

Corresponding angles (parallel lines)

Are equal

Alternate angles (parallel lines)

Are equal

Co-interior angles (parallel lines)

Sum = 180°

Angle at center of circle

= 2 × angle at circumference

Angles in same segment

Are equal

Angle in semicircle

= 90°

Opposite angles in cyclic quadrilateral

Sum = 180°

Exterior angle of cyclic quadrilateral

= Opposite interior angle

Tangent perpendicular to radius

Angle = 90°

Angle between tangent and chord

= Angle in alternate segment

Additional Essential Formulas

Pythagoras' Theorem (for right-angled triangles):

a² + b² = c²

Distance between two points (x₁, y₁) and (x₂, y₂):

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint of line segment:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Gradient of line:

m = (y₂ - y₁)/(x₂ - x₁)

Equation of straight line:

y = mx + c

Arithmetic sequence nth term:

aₙ = a₁ + (n-1)d

Geometric sequence nth term:

aₙ = a₁ × r^(n-1)

Sum of arithmetic sequence:

Sₙ = n/2[2a₁ + (n-1)d]

Sum of geometric sequence:

Sₙ = a₁(1 - rⁿ)/(1 - r)

📚 How to Use This Formula Sheet

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Practice Regularly

Use these formulas in practice problems to build muscle memory and confidence for your exams.

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Understand, Don't Memorize

Learn the logic behind each formula rather than just memorizing. This helps in problem-solving.

⏰

Time Management

Know which formulas to apply quickly during exams. Practice identifying formula patterns in questions.

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Review Consistently

Regular revision of formulas ensures they stay fresh in your memory when you need them most.

Formula sheet FAQ

Quick answers about this free PDF, how to use it for exam revision, and how it relates to your official syllabus.

Is the IGCSE Maths 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 IGCSE Mathematics formula sheet 2026. Essential formulas for Cambridge IGCSE (0580/0607/0980) Extended papers - area, volume, trigonometry, algebra, and more. Free downloadable reference guide. 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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