Free Formula Sheet
Cambridge IGCSE Maths Formula Sheet
Every formula printed in the Cambridge IGCSE Mathematics (0580) exam, plus every formula your child must learn by heart, with diagrams. Read it here or download the PDF.
At a Glance
Cambridge IGCSE Mathematics
A list of formulas is printed in every paper, but some formulas must be learnt. This page shows exactly what is on it, and the formulas that are not given, which students most often forget.
Core11 formulas given · 15 to learn
Extended15 formulas given · 27 to learn
Formula Sheet
Cambridge IGCSE Maths Formulas
Choose your child's tier: Foundation (the easier papers) or Higher (the harder papers). Not sure which? Ask their maths teacher, or look at the front of a mock exam paper.
1Given in Your Exam
These 11 formulas are printed on the list of formulas in every Cambridge IGCSE Core paper. Learn when and how to use each one.
Area of a Triangle
A = 12 × base × height
The height is perpendicular to the baseArea of a Circle
A = πr2
r is the radiusCircumference of a Circle
C = 2πr = πd
r is the radius, d is the diameterCurved Surface Area of a Cylinder
A = 2πrh
r is the radius, h is the heightCurved Surface Area of a Cone
A = πrl
l is the slant heightSurface Area of a Sphere
A = 4πr2
r is the radiusVolume of a Prism
V = area of cross-section × length
Works for any prism, including a cylinderVolume of a Pyramid
V = 13 × base area × h
h is the perpendicular heightVolume of a Cylinder
V = πr2h
r is the radius, h is the heightVolume of a Cone
V = 13πr2h
h is the perpendicular heightVolume of a Sphere
V = 43πr3
r is the radius2Learn These by Heart
These are not given in the exam. Students lose marks on them every year.
Shape and Space
Area of a Rectangle
A = length × width
Area of a Parallelogram
A = base × perpendicular height
Area of a Trapezium
A = 12(a + b)h
a and b are the parallel sides, h is the perpendicular heightArc Length and Sector Area
Arc = θ360 × 2πr
Sector = θ360 × πr2
θ is the angle at the centreSector = θ360 × πr2
Angles in Polygons
Interior angles add to (n − 2) × 180°
Exterior angles add to 360°
n is the number of sides; a triangle is 180°, a quadrilateral 360°Exterior angles add to 360°
Trigonometry
Pythagoras' Theorem
a2 + b2 = c2
In a right-angled triangle, c is the hypotenuseTrigonometric Ratios
sin A = ac
cos A = bc
tan A = ab
SOH CAH TOA: a is opposite A, b is adjacent to A, c is the hypotenusecos A = bc
tan A = ab
Number and Measures
Speed, Distance and Time
Speed = DistanceTime
Cover the one you want in the trianglePercentage Change
% change = changeoriginal × 100
Use the original amount, not the new oneSimple Interest
Interest = P × r100 × n
P is the amount, r is the % rate, n is the number of yearsCompound Interest
Total = P(1 + r100)n
P is the amount invested, r is the % rate per period, n is the number of periodsAlgebra
Straight-Line Graphs
y = mx + c
m = y2 − y1x2 − x1
m is the gradient, c is the y-interceptm = y2 − y1x2 − x1
Laws of Indices
am × an = am+n
am ÷ an = am−n
(am)n = amn
a0 = 1
a−n = 1an
am ÷ an = am−n
(am)n = amn
a0 = 1
a−n = 1an
Statistics and Probability
Mean
Mean = total of the valuesnumber of values
From a table: Σfx ÷ Σf (Σ means "add up")Probability Basics
P(not A) = 1 − P(A)
Expected number = P(A) × number of trials
Expected number = P(A) × number of trials
1Given in Your Exam
These 15 formulas are printed on the list of formulas in every Cambridge IGCSE Extended paper. Learn when and how to use each one.
Area of a Triangle
A = 12 × base × height
The height is perpendicular to the baseArea of a Circle
A = πr2
r is the radiusCircumference of a Circle
C = 2πr = πd
r is the radius, d is the diameterCurved Surface Area of a Cylinder
A = 2πrh
r is the radius, h is the heightCurved Surface Area of a Cone
A = πrl
l is the slant heightSurface Area of a Sphere
A = 4πr2
r is the radiusVolume of a Prism
V = area of cross-section × length
Works for any prism, including a cylinderVolume of a Pyramid
V = 13 × base area × h
h is the perpendicular heightVolume of a Cylinder
V = πr2h
r is the radius, h is the heightVolume of a Cone
V = 13πr2h
h is the perpendicular heightVolume of a Sphere
V = 43πr3
r is the radiusThe Quadratic Formula
x = −b ± √b2 − 4ac2a
Solves ax2 + bx + c = 0, where a ≠ 0The Sine Rule
asin A = bsin B = csin C
Side a is opposite angle A, and so onThe Cosine Rule
a2 = b2 + c2 − 2bc cos A
Use when you know two sides and the angle between them, or all three sidesArea of Any Triangle
A = 12ab sin C
C is the angle between sides a and b2Learn These by Heart
These are not given in the exam. Students lose marks on them every year.
Shape and Space
Area of a Rectangle
A = length × width
Area of a Parallelogram
A = base × perpendicular height
Area of a Trapezium
A = 12(a + b)h
a and b are the parallel sides, h is the perpendicular heightArc Length and Sector Area
Arc = θ360 × 2πr
Sector = θ360 × πr2
θ is the angle at the centreSector = θ360 × πr2
Angles in Polygons
Interior angles add to (n − 2) × 180°
Exterior angles add to 360°
n is the number of sides; a triangle is 180°, a quadrilateral 360°Exterior angles add to 360°
Similar Shapes
Lengths × k
Areas × k2
Volumes × k3
k is the length scale factorAreas × k2
Volumes × k3
Trigonometry
Pythagoras' Theorem
a2 + b2 = c2
In a right-angled triangle, c is the hypotenuseTrigonometric Ratios
sin A = ac
cos A = bc
tan A = ab
SOH CAH TOA: a is opposite A, b is adjacent to A, c is the hypotenusecos A = bc
tan A = ab
Exact Trigonometric Values
| 0° | 30° | 45° | 60° | 90° | |
|---|---|---|---|---|---|
| sin | 0 | 12 | √22 | √32 | 1 |
| cos | 1 | √32 | √22 | 12 | 0 |
| tan | 0 | √33 | 1 | √3 | – |
Number and Measures
Speed, Distance and Time
Speed = DistanceTime
Cover the one you want in the trianglePercentage Change
% change = changeoriginal × 100
Use the original amount, not the new oneReverse Percentages
Original = new amountmultiplier
For a 20% increase the multiplier is 1.2; for a 20% decrease it is 0.8Compound Interest
Total = P(1 + r100)n
P is the amount invested, r is the % rate per period, n is the number of periodsSurds
√a × √b = √ab
√a√b = √ab
Rationalise by multiplying top and bottom by the surd√a√b = √ab
Algebra
Straight-Line Graphs
y = mx + c
m = y2 − y1x2 − x1
m is the gradient, c is the y-interceptm = y2 − y1x2 − x1
Perpendicular Gradients
m1 × m2 = −1
Perpendicular gradients are negative reciprocalsMidpoint and Length of a Line
Midpoint = (x1 + x22, y1 + y22)
Length = √(x2 − x1)2 + (y2 − y1)2
Length = √(x2 − x1)2 + (y2 − y1)2
Laws of Indices
am × an = am+n
am ÷ an = am−n
(am)n = amn
a0 = 1
a−n = 1an
am ÷ an = am−n
(am)n = amn
a0 = 1
a−n = 1an
Fractional Indices
a1/n = n√a
am/n = (n√a)m
am/n = (n√a)m
Completing the Square
x2 + bx = (x + b2)2 − (b2)2
The turning point of y = (x + p)² + q is (−p, q)Direct and Inverse Proportion
y ∝ x → y = kx
y ∝ 1x → y = kx
Find k first using the values you are giveny ∝ 1x → y = kx
Differentiation
If y = axn then dydx = anxn−1
At a turning point dydx = 0Vectors, Statistics and Probability
Magnitude of a Vector
|(xy)| = √x2 + y2
The length of the vector, using PythagorasMean
Mean = total of the valuesnumber of values
From a table: Σfx ÷ Σf (Σ means "add up")Probability Basics
P(not A) = 1 − P(A)
Expected number = P(A) × number of trials
Expected number = P(A) × number of trials
Interquartile Range
IQR = upper quartile − lower quartile
Histograms
Frequency density = frequencyclass width
Frequency = area of the barDifferent Exam Board?
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