## 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.

### Core subject content - Number

#### 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 × 10
^{n}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/cm^{3} (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.

### Core subject content - Coordinate geometry

#### 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

### Core subject content - Geometry

#### 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**

### Core subject content - Mensuration

#### 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.

### Core subject content - Trigonometry

#### 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

### Core subject content - Transformations and vectors

#### 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

### Core subject content - Probability

#### 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**

### Core subject content - Statistics

#### 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.