IGCSE Mathematics 0580 Paper 23, May/June 2026

Write $30 as a percentage of $120.

The table shows information about the favourite drink of each of 60 students.

Write down the inequality shown by the number line.

These are the wages of 8 office workers. $$\mathrm{\$}220\mathrm{\$}210\mathrm{\$}850\mathrm{\$}265\mathrm{\$}245\mathrm{\$}230\mathrm{\$}245\mathrm{\$}235$$

Reem has a six-sided spinner numbered 1 to 6. Reem spins the spinner 50 times. Her results are shown in the table.

A red light flashes every 20 minutes. A blue light flashes every 35 minutes. The two lights flash together at 1000. Find the next time that the two lights flash together.

The diagram shows the position of two towns, $A$ and $B$. The scale is $1\text{ cm}$ represents $2\text{ km}$.

The line $L$ is shown on the grid.

The position vector of $A$ is $\left(\begin{array}{c}4\\ -1\end{array}\right)$ and $\overrightarrow{AB}=\left(\begin{array}{c}-7\\ 5\end{array}\right)$. Find the position vector of $B$.

The interior angle of a regular polygon is ${135}^{\circ }$. Find the number of sides of this regular polygon.

$A$, $B$ and $C$ are points on a circle with centre $O$. $AOC$ is a straight line and $M$ is the midpoint of $AB$. $AB=6\text{ cm}$ and $OM=4\text{ cm}$.

A sphere has volume $36\pi {\text{ cm}}^3$. Find the radius of the sphere.

The diagram shows a cyclic quadrilateral $ABCD$. Find

$y$ is inversely proportional to $x$. When $y=5$, $x=20$. Find $y$ when $x=4$.

The diagram shows a rectangle. The shaded area is $30{\text{ cm}}^2$.

Find the exact value of $x$. Give your answer in the form $a\sqrt{b}$.

The two cylinders, $A$ and $B$, are mathematically similar. The surface area of $A$ is $80{\text{ cm}}^2$ and the surface area of $B$ is $180{\text{ cm}}^2$. The height of $A$ is $h\text{ cm}$ and the height of $B$ is $12\text{ cm}$. Find the value of $h$.

A minor sector of a circle of radius $6\text{ cm}$ has sector angle ${50}^{\circ }$. Find the area of the major sector. Give your answer in terms of $\pi$ in its simplest form.

Write as a single fraction in its simplest form. $$\frac{x-2}{x+3}+\frac{x+3}{x-2}$$

$x$ is an integer. $$\mathcal{E}=\{x:1⩽x⩽12\}$$ $$A=\{x:x\text{ is a square number}\}$$ $$B=\{x:4⩽x⩽8\}$$ $$C=\{x:x\text{ is a factor of }12\}$$

Juan has a bag containing 2 red counters, 3 green counters and 5 blue counters. Juan picks two counters from the bag at random, without replacement. Find the probability that the two counters are different colours.

In the diagram, $O$ is the origin, $\overrightarrow{OR}=\mathbf{r}$ and $\overrightarrow{OS}=\mathbf{s}$. $P$ is a point on $RS$ and $RP:PS=2:5$. Find the position vector of $P$. Give your answer, in terms of $\mathbf{r}$ and $\mathbf{s}$, in its simplest form.