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IGCSE Maths Formula Sheet
Levels & boards: IGCSE Mathematics (Years 10-11) Cambridge International 0580; Pearson Edexcel International GCSE Maths. Independent revision, not a permitted exam-booklet substitute.
Search this IGCSE Maths formula resource by topic, save useful equations and reveal original worked examples. Number, algebra, geometry, mensuration, trigonometry, statistics and probability are organised into individual cards with notation, conditions and common mistakes.
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32 formulas
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Percentage of a quantity
part = percentage / 100 * whole
Notation / units: All quantities must share compatible units.
Use when: Use when the whole and the percentage are known.
Worked example and common mistake
18% of 250 = 0.18 * 250 = 45.
Watch out: 18% is 0.18, not 18.
Percentage change
change % = (new – original) / original * 100
Notation / units: Percentage; original must be non-zero.
Use when: Use the starting value as the denominator.
Worked example and common mistake
From 80 to 100: 20/80 * 100 = 25% increase.
Watch out: Dividing by the new value answers a different question.
Compound growth
final = initial * (1 + r/100)^n
Notation / units: r is the percentage rate per period; n is the number of periods.
Use when: Assumes the same growth rate each period.
Worked example and common mistake
200 at 5% for two periods = 200 * 1.05^2 = 220.50.
Watch out: Use 0.95 for 5% decay, not 1.05.
Reverse percentage
original = final / multiplier
Notation / units: Use matching money or measurement units.
Use when: Find the original before a percentage change.
Worked example and common mistake
An item costs 96 after a 20% increase: 96/1.2 = 80.
Watch out: Subtracting 20% of the final price does not reverse an increase.
Simple interest
I = P * r * t / 100
Notation / units: P principal; r annual percent; t years.
Use when: Interest is calculated on the original principal only.
Worked example and common mistake
P=500, r=4, t=3 gives I=60; total=560.
Watch out: Do not compound a simple-interest question.
Speed-distance-time
speed = distance / time
Notation / units: For m and s the answer is m/s.
Use when: This is average speed over the interval.
Worked example and common mistake
150 km in 2.5 hours gives 60 km/h.
Watch out: Convert minutes to hours before using kilometres per hour.
Density
density = mass / volume
Notation / units: kg/m^3 or consistent alternatives.
Use when: Mass and volume must describe the same material sample.
Worked example and common mistake
600 g / 200 cm^3 = 3 g/cm^3.
Watch out: Do not mix grams with a volume in m^3 without conversion.
Direct proportion
y = k*x
Notation / units: k is the constant of proportionality.
Use when: The ratio y/x is fixed when x is non-zero.
Worked example and common mistake
If y=12 when x=3, k=4; when x=5, y=20.
Watch out: A straight line not through the origin is not direct proportion.
Inverse proportion
y = k/x
Notation / units: x must be non-zero.
Use when: The product xy is fixed.
Worked example and common mistake
If y=8 at x=3, k=24; at x=6, y=4.
Watch out: Doubling x halves y only for inverse first-power proportion.
Quadratic formula
x = (-b +/- sqrt(b^2 – 4*a*c)) / (2*a)
Notation / units: a must be non-zero.
Use when: Solves ax^2+bx+c=0; negative discriminant has no real roots.
Worked example and common mistake
x^2-5x+6=0 gives (5 +/- 1)/2, so x=2 or 3.
Watch out: Apply the denominator 2a to the entire numerator.
Difference of two squares
a^2 – b^2 = (a-b)*(a+b)
Notation / units: Algebraic identity.
Use when: Useful for factorising a difference, not a sum, of squares.
Worked example and common mistake
x^2-16=(x-4)(x+4).
Watch out: x^2+16 does not factor this way over real numbers.
Arithmetic sequence
u_n = a + (n-1)*d
Notation / units: a first term; d common difference.
Use when: The difference between successive terms is constant.
Worked example and common mistake
3,7,11,… has u_n=3+4(n-1); u_10=39.
Watch out: The first term has n=1, not n=0.
Straight-line gradient
m = (y2-y1)/(x2-x1)
Notation / units: Vertical change per horizontal unit.
Use when: Requires different x-coordinates.
Worked example and common mistake
Through (1,3) and (5,11): m=8/4=2.
Watch out: Keep the point order the same in numerator and denominator.
Straight-line equation
y = m*x + c
Notation / units: m gradient; c y-intercept.
Use when: A non-vertical straight line.
Worked example and common mistake
m=3 through (2,7): 7=6+c, so y=3x+1.
Watch out: The y-intercept is not normally the x-intercept.
Midpoint
M = ((x1+x2)/2, (y1+y2)/2)
Notation / units: Coordinate units.
Use when: Average corresponding coordinates.
Worked example and common mistake
Midpoint of (2,4) and (8,10) is (5,7).
Watch out: Do not average an x-coordinate with a y-coordinate.
Distance between points
d = sqrt((x2-x1)^2 + (y2-y1)^2)
Notation / units: Same coordinate scale on both axes.
Use when: Euclidean distance on a flat coordinate plane.
Worked example and common mistake
Between (1,2) and (4,6): sqrt(9+16)=5.
Watch out: Square both coordinate differences before adding.
Triangle area
A = b*h/2
Notation / units: Square units; h perpendicular to base b.
Use when: Use the perpendicular height.
Worked example and common mistake
Base 12 cm, height 7 cm: A=42 cm^2.
Watch out: The sloping side is not necessarily the height.
Trapezium area
A = (a+b)*h/2
Notation / units: a and b parallel sides; h perpendicular separation.
Use when: Parallel sides must be identified correctly.
Worked example and common mistake
Parallel sides 6 and 10, height 4: A=32 square units.
Watch out: Do not use both sloping sides as a and b.
Circle area and circumference
A = pi*r^2; C = 2*pi*r
Notation / units: r radius; area in square units.
Use when: Diameter d=2r.
Worked example and common mistake
r=3 cm gives A=9pi cm^2 and C=6pi cm.
Watch out: Using the diameter as r makes the area four times too large.
Arc length
L = theta/360 * 2*pi*r
Notation / units: theta in degrees; L length.
Use when: For a sector with central angle theta.
Worked example and common mistake
r=6, theta=60 gives L=2pi.
Watch out: The denominator 360 applies to degrees, not radians.
Sector area
A = theta/360 * pi*r^2
Notation / units: theta in degrees; area in square units.
Use when: The angle must be at the centre.
Worked example and common mistake
r=6, theta=60 gives A=6pi.
Watch out: Arc length and sector area use different full-circle formulas.
Prism volume
V = cross-section area * length
Notation / units: Cubic units.
Use when: Cross-section remains constant along the length.
Worked example and common mistake
A=12 cm^2, length=5 cm: V=60 cm^3.
Watch out: Use the prism length, not a sloping face measurement.
Cylinder volume
V = pi*r^2*h
Notation / units: r radius; h perpendicular height.
Use when: A circular prism.
Worked example and common mistake
r=2 cm, h=7 cm: V=28pi cm^3.
Watch out: A radius squared is needed, not just the radius.
Cone volume
V = pi*r^2*h/3
Notation / units: h perpendicular height; cubic units.
Use when: Right circular cone.
Worked example and common mistake
r=3, h=4 gives V=12pi.
Watch out: Slant height belongs in a surface-area formula, not this volume.
Sphere volume
V = 4*pi*r^3/3
Notation / units: Cubic units.
Use when: Sphere radius r.
Worked example and common mistake
r=3 gives V=36pi.
Watch out: Volume grows with r cubed, not r squared.
Pythagoras theorem
c^2 = a^2 + b^2
Notation / units: c is the hypotenuse.
Use when: Right-angled triangles only.
Worked example and common mistake
Legs 5 and 12 give c=sqrt(169)=13.
Watch out: Do not use the longest side as a leg in the equation.
SOHCAHTOA
sin(theta)=opposite/hypotenuse; cos(theta)=adjacent/hypotenuse; tan(theta)=opposite/adjacent
Notation / units: Sides relative to the chosen angle.
Use when: Right-angled triangle; check degree/radian mode.
Worked example and common mistake
Opposite 3, hypotenuse 5 gives theta=asin(0.6), about 36.87 degrees.
Watch out: The opposite side changes when the reference angle changes.
Sine rule
a/sin(A) = b/sin(B) = c/sin(C)
Notation / units: Match each side to its opposite angle.
Use when: Any triangle; an ambiguous sine case can give two solutions.
Worked example and common mistake
A=30, B=45, a=10 gives b=10*sin45/sin30, about 14.14.
Watch out: Pairing a with the wrong angle gives a plausible but wrong result.
Cosine rule
c^2 = a^2+b^2-2*a*b*cos(C)
Notation / units: C is the included angle between a and b.
Use when: Any triangle.
Worked example and common mistake
a=3, b=4, C=60 gives c=sqrt(13).
Watch out: Use the angle opposite c, not an arbitrary angle.
Mean from frequencies
mean = sum(f*x)/sum(f)
Notation / units: f frequency; x value or class midpoint.
Use when: Midpoints give an estimate for grouped data.
Worked example and common mistake
Values 2,4 with frequencies 3,2: mean=(6+8)/5=2.8.
Watch out: Divide by total frequency, not the number of rows.
Probability complement
P(not A) = 1 – P(A)
Notation / units: Probability between 0 and 1.
Use when: A and not A partition the sample space.
Worked example and common mistake
If P(rain)=0.3 then P(no rain)=0.7.
Watch out: A probability cannot be 1.7 or a negative number.
Independent events
P(A and B) = P(A)*P(B)
Notation / units: Probabilities.
Use when: Use only when events are independent.
Worked example and common mistake
Two fair coin heads: 1/2 * 1/2 = 1/4.
Watch out: Without-replacement events are usually dependent.
How to use the IGCSE Maths Formula Sheet
- Choose a topic or enter a formula name, symbol or unit in the search field.
- Open the worked example and check the conditions before substituting values.
- Save difficult formulas for a focused list, test recall, then print or export that list.
A worked example
For a right triangle with opposite side 3 and adjacent side 4, tan(theta) = 3/4. Use inverse tangent in degree mode to obtain approximately 36.87 degrees. Using tan(3/4) instead finds a different quantity.
What to check before using your result
- Cambridge 0580 and Pearson 4MA1 have different specifications and tier arrangements. These shared Maths relationships do not imply that every listed equation is required at every tier.
- Use consistent units before substitution; a correct formula with incompatible units still gives a wrong result.
- A saved formula is a revision prompt, not evidence that you can apply it to an unfamiliar problem.
Make your next practice session count
Use this result as a starting point, not a label for your ability. Record one error, explain its cause and complete a similar question without the worked answer. Then try a different example to check that you understood the method rather than remembered a number.
For exam-style application, choose the correct board and component in the MYT past-paper directory. For guided explanations, explore subject-specific online tutoring or request a free 30-minute demo.
Questions about this tool
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Cover the equation, define each quantity, state a condition and solve one new example. Then change a quantity and predict how the answer should change before calculating.
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Reference sources and scope
- Cambridge IGCSE Mathematics 0580 – syllabus and updates
- Pearson Edexcel International GCSE Mathematics A
MYT provides independent learning resources, not official exam-board certification or school-entry decisions. Formula explanations, diagnostic questions and study plans here are original study aids. Check your current syllabus and official examination instructions before relying on a resource for an assessment.