Free Formula Sheet
Edexcel IGCSE Maths Formula Sheet
Every formula printed in the Pearson Edexcel International GCSE Mathematics A (4MA1) exam, plus every formula your child must learn by heart, with diagrams. Read it here or download the PDF.
At a Glance
Pearson Edexcel International GCSE Mathematics A
A formulae sheet is printed in every paper. This page shows exactly what is on it, and the formulas that are not given, which students most often forget.
Foundation4 formulas given · 20 to learn
Higher13 formulas given · 29 to learn
Formula Sheet
Edexcel 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 4 formulas are printed on the formulae sheet in every Edexcel IGCSE Foundation paper. Learn when and how to use each one.
Area of a Trapezium
A = 12(a + b)h
a and b are the parallel sides, h is the perpendicular heightVolume of a Prism
V = area of cross-section × length
Works for any prism, including a cylinderVolume of a Cylinder
V = πr2h
r is the radius, h is the heightCurved Surface Area of a Cylinder
A = 2πrh
r is the radius, h is the height2Learn 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 Triangle
A = 12 × base × height
The height is perpendicular to the baseArea of a Parallelogram
A = base × perpendicular height
Circumference of a Circle
C = 2πr = πd
r is the radius, d is the diameterArea of a Circle
A = πr2
r is the radiusArc 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 triangleDensity and Pressure
Density = MassVolume
Pressure = ForceArea
Check the units match before you calculatePressure = ForceArea
Percentage 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 periodsAlgebra
Straight-Line Graphs
y = mx + c
m = y2 − y1x2 − x1
m is the gradient, c is the y-interceptm = y2 − y1x2 − x1
nth Term of a Linear Sequence
nth term = dn + (first term − d)
d is the common differenceLaws 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
Independent Events
P(A and B) = P(A) × P(B)
Only when one event does not affect the other1Given in Your Exam
These 13 formulas are printed on the formulae sheet in every Edexcel IGCSE Higher paper. Learn when and how to use each one.
Sum of an Arithmetic Series
Sn = n2[2a + (n − 1)d]
a is the first term, d is the common differenceArea of a Trapezium
A = 12(a + b)h
a and b are the parallel sides, h is the perpendicular heightThe 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 bVolume of a Cone
V = 13πr2h
h is the perpendicular heightCurved Surface Area of a Cone
A = πrl
l is the slant heightVolume of a Prism
V = area of cross-section × length
Works for any prism, including a cylinderVolume of a Cylinder
V = πr2h
r is the radius, h is the heightCurved Surface Area of a Cylinder
A = 2πrh
r is the radius, h is the heightVolume of a Sphere
V = 43πr3
r is the radiusSurface Area of a Sphere
A = 4πr2
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 Triangle
A = 12 × base × height
The height is perpendicular to the baseArea of a Parallelogram
A = base × perpendicular height
Circumference of a Circle
C = 2πr = πd
r is the radius, d is the diameterArea of a Circle
A = πr2
r is the radiusArc 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
Number and Measures
Speed, Distance and Time
Speed = DistanceTime
Cover the one you want in the triangleDensity and Pressure
Density = MassVolume
Pressure = ForceArea
Check the units match before you calculatePressure = ForceArea
Percentage 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 reciprocalsnth Term of an Arithmetic Sequence
nth term = a + (n − 1)d
a is the first term, d is the common differenceLaws 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 = 0Statistics 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
Independent Events
P(A and B) = P(A) × P(B)
Only when one event does not affect the otherInterquartile Range
IQR = upper quartile − lower quartile
Histograms
Frequency density = frequencyclass width
Frequency = area of the barDifferent Exam Board?
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