IGCSE Mathematics 0580 Paper 31, Oct/Nov 2025

Measure the length of line $AB$ in centimetres.

Draw a line that is perpendicular to the line $AB$.

$\sqrt{1.96}$

${17}^3$

$-0.8\times -1.2$

Write these numbers in order, starting with the smallest. $$\frac{11}{19}58\mathrm{\%}\frac{27}{47}0.574$$

the mode

the range.

Zia takes a green ball

Zia takes a yellow ball

Zia does not take a blue ball.

$8x=32$

$6x-3=12$

Represent the inequality $-4⩽x<2$ on the number line.

Write down the mathematical name for this type of angle.

$ABC$ is a triangle. Lily says $x$ is 34. Give a geometrical reason why Lily is not correct.

$ABCD$ is a quadrilateral. $DCE$ is a straight line. Calculate the value of $x$.

Naz pays $76.25 per day to hire a car. He hires this car for 7 days. He also pays $146 for fuel. Calculate the total amount Naz pays.

Li pays $1400 to hire a car. $364 of this is insurance. Calculate the insurance as a percentage of the $1400.

Show that 75 students choose the museum.

45 students choose the art gallery and 120 students choose the sports stadium. Complete the pie chart to show this information.

The surface area of a solid cube is $121.5{\text{ cm}}^2$. Calculate the length of the side of the cube.

The area of the trapezium is $106.25{\text{ cm}}^2$. Calculate the height of the trapezium.

Convert $106.25{\text{ cm}}^2$ into ${\text{m}}^2$.

Describe fully the single transformation that maps shape $A$ onto shape $B$.

On the grid, draw the image of shape $A$ after a translation by the vector $\left(\begin{array}{c}6\\ 7\end{array}\right)$.

Between which two times did Bob stop for a rest? Explain how you know. ................ and ................ because .....................................................................................................

Calculate Bob's average speed, in km/h, for the whole journey.

The $n$th term of a sequence is $n^2-4$. Find the first 3 terms of this sequence.

These are the first four terms of a different sequence. $$52-1-4$$ Find the $n$th term.

Work out the size of one interior angle of a regular 8-sided polygon.

$A$, $B$ and $C$ lie on the circumference of the circle, centre $O$. $AB$ is a diameter. $DBE$ is a tangent to the circle at $B$. Find the value of $x$. Give a geometrical reason for your answer. ................ because ......................................................................................................................

A train to town $P$ leaves a station every 20 minutes. A train to town $Q$ leaves the same station every 35 minutes. Both trains leave at 0930. Find the next time both trains leave together.

The distance, $d\text{ km}$, between town $P$ and town $Q$ is 97 km, correct to the nearest kilometre. Complete the statement about the value of $d$. ................... $⩽d<$ ...................