Cambridge IGCSE Mathematics 0580

0580 formula sheet

Every Cambridge IGCSE Mathematics 0580 paper prints a list of formulas on page 2 — 11 on the Core papers (1 and 3), 15 on the Extended papers (2 and 4). Both lists give the area and circumference of a circle and the surface area and volume of cylinders, cones, spheres, prisms and pyramids. Extended adds the quadratic formula, the sine rule, the cosine rule and ½ab sin C.

What neither list gives you: the area of a trapezium or parallelogram, arc length and sector area, Pythagoras, SOHCAHTOA, compound interest and the straight-line formulas. Those you have to know. This page covers the syllabus for exams in 2025, 2026 and 2027.

Updated 28 September 2026

The formulas printed on the paper

Rows marked Extended appear only on Papers 2 and 4. Everything else is on all four papers.

Algebra

Quadratic formulaExtended

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

for ax² + bx + c = 0

Trigonometry

Sine ruleExtended	$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Cosine ruleExtended	$a^{2} = b^{2} + c^{2} - 2 b c \cos A$
Area of a triangleExtended	$Area = \frac{1}{2} a b \sin C$

Mensuration

Area of triangle	$A = \frac{1}{2} b h$	base b, height h
Circumference of circle	$C = 2 π r$
Area of circle	$A = π r^{2}$
Curved surface of cylinder	$A = 2 π r h$
Volume of cylinder	$V = π r^{2} h$
Curved surface of cone	$A = π r l$
Volume of cone	$V = \frac{1}{3} π r^{2} h$
Surface area of sphere	$A = 4 π r^{2}$
Volume of sphere	$V = \frac{4}{3} π r^{3}$
Volume of prism	$V = A l$	cross-sectional area A, length l
Volume of pyramid	$V = \frac{1}{3} \times base area \times height$

Not given: the formulas you must memorise

The syllabus is explicit on area: apart from the triangle, the formulas for rectangles, parallelograms and trapeziums are not given. Arc length and sector area are tested as fractions of the circle, so they are not printed either. The full list of what you need but will not be handed:

Area of a rectangle	$A = l w$
Area of a parallelogram	$A = b h$	perpendicular height
Area of a trapezium	$A = \frac{1}{2} (a + b) h$	a, b the parallel sides
Arc length	$\frac{θ}{360} \times 2 π r$	θ in degrees
Sector area	$\frac{θ}{360} \times π r^{2}$	θ in degrees
Pythagoras	$a^{2} + b^{2} = c^{2}$	c the hypotenuse
Right-angled trigonometry	$\sin θ = \frac{opp}{hyp}, \cos θ = \frac{adj}{hyp}, \tan θ = \frac{opp}{adj}$
Straight line	$y = m x + c$	gradient m, y-intercept c
Gradient	$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Midpoint	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$
Length of a line segment	$\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
Compound interest	$P {(1 + \frac{r}{100})}^{n}$	r% per period, n periods
Percentage change	$\frac{change}{original} \times 100$
Speed	$speed = \frac{distance}{time}$
Interior angles of a polygon	$(n - 2) \times 180^{\circ}$	n sides
Mean from a frequency table	$\overset{ˉ}{x} = \frac{\sum f x}{\sum f}$	midpoints for grouped data

Using the list in the exam

Given is not the same as easy. The volume formulas are printed, yet surface area and volume is still one of the heaviest topics on the paper — the marks are in choosing the right shape and the right radius, not in the formula.
Sine or cosine rule? The list gives both but not when to use which: the cosine rule when you have two sides and the angle between them (or all three sides), the sine rule when you have a side and its opposite angle.
Slant height, not height. The curved surface of a cone uses l, the sloping edge; the volume uses h, the perpendicular height. Swapping them is the classic error.
Answers in terms of π mean exactly that: leave π in and do not round.
The quadratic formula is on the Extended list, but a question that says “factorise” or “complete the square” wants that method, not the formula.

Common questions

Is there a formula sheet in IGCSE Maths 0580?

Yes. Under the 2025–2027 syllabus every 0580 paper prints a list of formulas on page 2 — a Core list on Papers 1 and 3, and a longer Extended list on Papers 2 and 4.

Is the quadratic formula given in IGCSE 0580?

On the Extended papers (2 and 4), yes. It is not on the Core list.

Are the sine and cosine rules given?

Yes, on the Extended papers, along with the area of a triangle as ½ab sin C. Core candidates are not examined on them.

Is the area of a trapezium given?

No. The syllabus states that, except for the area of a triangle, area formulas are not given — so the trapezium, parallelogram and rectangle must be memorised.

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