Cambridge IGCSE Mathematics (0580) New syllabus 2025-2027

Cambridge IGCSE Mathematics (0580) New syllabus

Syllabus Cambridge IGCSE™ Mathematics 0580
Use this syllabus for exams in 2025, 2026 and 2027.
Exams are available in the June and November series.
Exams are also available in the March series in India.

C1.1 Types of number

Identify and use:

natural numbers
integers (positive, zero and negative)
prime numbers
square numbers
cube numbers
common factors
common multiples
rational and irrational numbers
reciprocals.

Example tasks include

convert between numbers and words,
- e.g. six billion is 6 000 000 000
- 10 007 is ten thousand and seven
express 72 as a product of its prime factors
find the highest common factor (HCF) of two numbers
find the lowest common multiple (LCM) of two numbers.

C1.2 Sets

Understand and use set language, notation and Venn diagrams to describe sets.

Notes and examples

Venn diagrams are limited to two sets.
The following set notation will be used:
• n(A) Number of elements in set A
• A′ Complement of set A
• Universal set
• A ∪ B Union of A and B
• A ∩ B Intersection of A and B.
Example definition of sets:
A = {x: x is a natural number}
B = {a, b, c, …}
C = {x: a ⩽ x ⩽ b}.

C1.3 Powers and roots

Calculate with the following:

squares
square roots
cubes
cube roots
other powers and roots of numbers.

Notes and examples

Includes recall of squares and their corresponding
roots from 1 to 15, and recall of cubes and their
corresponding roots of 1, 2, 3, 4, 5 and 10, e.g.:

Write down the value of $\sqrt{169}$.
Work out $ 5^2 \times \sqrt[3]{8}$

C1.4 Fractions, decimals and percentages

Use the language and notation of the following in appropriate contexts:

proper fractions
improper fractions
mixed numbers
decimals
percentages.

Recognise equivalence and convert between these forms.

Notes and examples

Candidates are expected to be able to write fractions in their simplest form.
Candidates are not expected to use recurring decimal notation.
Candidates are not expected to demonstrate the conversion of a recurring decimal to a fraction and vice versa

C1.5 Ordering

Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽ .

C1.6 The four operations

Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets.

Notes and examples

Includes:

negative numbers
improper fractions
mixed numbers
practical situations, e.g. temperature changes.

C1.7 Indices I

Understand and use indices (positive, zero and negative integers).
Understand and use the rules of indices.

Notes and examples

e.g. find the value of $7^{-2}$.
e.g. find the value of $2^{-3} \times 2^4,\left(2^3\right)^2, 2^3 \div 2^4$.

C1.8 Standard form

Use the standard form A × 10ⁿ where n is a positive or negative integer and 1 ⩽ A < 10.
Convert numbers into and out of standard form.
Calculate with values in standard form.

Notes and examples

Core candidates are expected to calculate with standard form only on Paper 3.

C1.9 Estimation

Round values to a specified degree of accuracy.
Make estimates for calculations involving numbers, quantities and measurements.
Round answers to a reasonable degree of accuracy in the context of a given problem.

Notes and examples

Includes decimal places and significant figures.
e.g. write 5764 correct to the nearest thousand.
e.g. by writing each number correct to 1 significant
figure, estimate the value of $\frac{41.3}{9.79\times 0.765}$

C1.10 Limits of accuracy

Give upper and lower bounds for data rounded to a specified accuracy.

Notes and examples

e.g. write down the upper bound of a length measured correct to the nearest metre.
Candidates are not expected to find the bounds of the results of calculations which have used data rounded to a specified accuracy.

C1.11 Ratio and proportion

Understand and use ratio and proportion to:

give ratios in their simplest form
divide a quantity in a given ratio
use proportional reasoning and ratios in context.

Notes and examples

e.g. 20:30:40 in its simplest form is 2:3:4.
e.g. adapt recipes; use map scales; determine best value.

C1.12 Rates

Use common measures of rate.
Apply other measures of rate.
Solve problems involving average speed.

Notes and examples

e.g. calculate with:

hourly rates of pay
exchange rates between currencies
flow rates

fuel consumption. e.g. calculate with:

pressure
density
population density.

Required formulas will be given in the question. Knowledge of speed/distance/time formula is required.
e.g. A cyclist travels 45km in 3 hours 45 minutes.
What is their average speed?
Notation used will be, e.g. m/s (metres per second), g/cm³ (grams per cubic centimetre)

C1.13 Percentages

Calculate a given percentage of a quantity.
Express one quantity as a percentage of another.
Calculate percentage increase or decrease.
Calculate with simple and compound interest

Notes and examples

C1.14 Using a calculator

Use a calculator efficiently.
Enter values appropriately on a calculator.
Interpret the calculator display appropriately

Notes and examples

C1.15 Time

Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
Calculate times in terms of the 24-hour and 12-hour clock.
Read clocks and timetables

Notes and examples

C1.16 Money

Calculate with money.
Convert from one currency to another.

C3.1 Coordinates

Use and interpret Cartesian coordinates in two dimensions.

Notes and example

C3.2 Drawing linear graphs

Draw straight-line graphs for linear equations.

Notes and examples

C3.3 Gradient of linear graphs

Find the gradient of a straight line

Notes and examples

C3.5 Equations of linear graphs

Interpret and obtain the equation of a straight-line graph in the form y = mx + cNotes and examples

C3.6 Parallel lines

Find the gradient and equation of a straight line parallel to a given line.

Notes and examples

C4.1 Geometrical terms

Use and interpret the following geometrical terms:

point
vertex
line
parallel
perpendicular
bearing
right angle
acute, obtuse and reflex angles
interior and exterior angles
similar
congruent
scale factor.

Use and interpret the vocabulary of:

triangles
special quadrilaterals
polygons
nets
simple solids.

Use and interpret the vocabulary of a circle

Notes and example

C4.2 Geometrical constructions

Measure and draw lines and angles.
Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only.
Draw, use and interpret nets

Notes and examples

C4.3 Scale drawings

Draw and interpret scale drawings.
Use and interpret three-figure bearings

Notes and examples

C4.4 Similarity

Calculate lengths of similar shapes.

Notes and examples

C4.5 Symmetry

Recognise line symmetry and order of rotational symmetry in two dimensions.

Notes and examples

C4.6 Angles

Calculate unknown angles and give simple explanations using the following geomatrical properties:

sum of angles at a point $=360^{\circ}$
sum of angles at a point on a straight line $=180^{\circ}$
vertically opposite angles are equal
angle sum of a triangle $=180^{\circ}$ and angle sum of a quadriateral $=360^{\circ}$.

Calculate unknown angles and give geometric explanations for angles formed within parallel lines:

corresponding angles are equal
alternate angles are equal
co-interior angles sum to $180^{\circ}$ (supplementary).

Know and use angle properties of regular polygons.

Notes and examples

C4.7 Circle theorems

Calculate unknown angles and give explanations using the following geometrical properties of circles:

angle in a semicircle = 90°
angle between tangent and radius = 90°

Notes and examples

C5.1 Units of measure

Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units.

Notes and examples

C5.2 Area and perimeter

Carry out calculations involving the perimeter and area of a rectangle, triangle, paralelogram and trapezium.

Notes and examples

C5.3 Circles, arcs and sectors

Carry out calculations involving the circumference and area of a circle.
Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle, where the sector angle is a factor of $360^{\circ}$.

Notes and examples

C5.4 Surface area and volume

Carry out calculations and solve problems involving the surface area and volume of a:

cuboid
prism
cylinder
sphere
pyramid
cone.

Notes and examples

C5.5 Compound shapes and parts of shapes

Carry out calculations and solve problems involving perimeters and areas of:
• compound shapes
• parts of shapes.
Carry out calculations and solve problems involving surface areas and volumes of:
• compound solids
• parts of solids.

C6.1 Pythagoras’ theorem

Know and use Pythagoras’ theorem.

Notes and examples

C6.2 Right-angled triangles

Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle.
Solve problems in two dimensions using Pythagoras’ theorem and trigonometry.

Notes and examples

C7.1 Transformations

Recognise, describe and draw the following transformations:

Reflection of a shape in a vertical or horizontal line.
Rotation of a shape about the origin, vertices or midpoints of edges of the shape, through multiples of 90°.
Enlargement of a shape from a centre by a scale factor.
Translation of a shape by a vector $\binom{x}{y}$

Notes and examples

C8.1 Introduction to probability

Understand and use the probability scale from 0 to 1.
Calculate the probability of a single event.
Understand that the probability of an event not occurring $=1-$ the probability of the event occurring.

Notes and examples

C8.2 Relative and expected frequencies

Understand relative frequency as an estimate of probability.
Calculate expected frequencies.

Notes and examples

C8.3 Probability of combined events

Calculate the probability of combined events using, where appropriate:

sample space diagrams
Venn diagrams
tree diagrams.

Notes and examples

C9.1 Classifying statistical data

Classify and tabulate statistical data.

Notes and examples

C9.2 Interpreting statistical data

Read, interpret and draw inferences from tables and statistical diagrams.
Compare sets of data using tables, graphs and statistical measures.
Appreciate restrictions on drawing conclusions from given data.

Notes and examples

C9.3 Averages and range

Calculate the mean, median, mode and range for individual data and distinguish between the purposes for which these are used.

Notes and examples

C9.4 Statistical charts and diagrams

Draw and interpret:

(a) bar charts
(b) pie charts
(c) pictograms
(d) stem-and-leaf diagrams
(e) simple frequency distributions.

Notes and examples

C9.5 Scatter diagrams

Draw and interpret scatter diagrams.
Understand what is meant by positive, negative and zero correlation.
Draw by eye, interpret and use a straight line of best fit.