IGCSE Mathematics 0580 Paper 12, May/June 2023

Shade two squares so that the diagram has rotational symmetry of order 4.

Kai and Ava each have a piece of wood 57 cm long.

In the diagram, $ABC$ is a triangle and $ACD$ is a straight line. Find the value of $x$ and the value of $y$. $x=\dots$ $y=\dots$

Find the temperature that is $8{}^{\circ }\mathrm{C}$ colder than $-5{}^{\circ }\mathrm{C}$.

There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers.

On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8

The scale drawing shows the positions of town $A$ and town $B$. Measure the bearing of town $B$ from town $A$.

The diagram shows a right-angled triangular prism. On the $1{\text{ cm}}^2$ grid, complete the net of this prism. One face has been drawn for you.

The distance from town $A$ to town $B$ on a map is $3.5\text{ cm}$. The scale on the map is $1:250000$. Find the actual distance, in kilometres, from town $A$ to town $B$.

A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Complete the table.

$\mathcal{E}=\{x:1⩽x⩽20\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of }5\}$

Without using a calculator, work out $\frac{4}{7}÷1\frac{5}{21}$. You must show all your working and give your answer as a fraction in its simplest form.

$F$ is the point $(1,-4)$, $\overrightarrow{FG}=\left(\begin{array}{c}8\\ -3\end{array}\right)$ and $\overrightarrow{GH}=\left(\begin{array}{c}-12\\ 35\end{array}\right)$. Find

$x$ is an integer where $x⩾-3$ and $x<3$. Write down all the possible values of $x$.

Find the size of an interior angle of a regular 15-sided polygon.

Simplify. $$18x^{12}÷3x^3$$

Buses at a station go to the port or to the town. Buses leave every 28 minutes for the port. Buses leave every 48 minutes for the town. At 10 18 a bus for the port and a bus for the town leave the station together. Find the next time when a bus for the port and a bus for the town leave the station together.

Triangle $ABC$ is similar to triangle $PQR$. Calculate $QR$.