IGCSE Mathematics 0580 Paper 33, May/June 2025

a multiple of 12

a square number

a cube number.

Write down the time Tim leaves work.

Tim stops on the way home. Find how far Tim travels before he stops.

Find how long Tim stops for.

Find the value of $x$. Give a geometrical reason for your answer.

Find the value of $y$. Give a geometrical reason for your answer.

Expand and simplify. $$5(x-2)+3(x-7)$$

Factorise. $$4a^2+16a$$

In week 1 there were 200 customers in total. Complete the bar chart.

Write down the mode for week 2.

Find the mean number of customers for the 5 days in week 2.

Calculate the percentage increase in the profit from May to June.

The shop gives $\frac{2}{5}$ of the profit from May to a charity. Find the amount the shop gives to the charity.

The shop spends 38% of the profit from June on a fridge. Find the amount the shop spends on the fridge.

Work out the cost of hiring 2 road bikes for 3 days.

The cost, $M$, of hiring a mountain bike for $d$ days can be written as $M=35d+5$. Write a formula for the cost, $E$, of hiring an electric bike for $d$ days.

The cost of hiring an electric bike for 6 days is the same as the cost of hiring a mountain bike for $d$ days. Find the value of $d$.

Work out the actual distance between $S$ and $P$.

Measure the bearing of $S$ from $P$.

$E$ is 20 km from $P$ on a bearing of 070°. On the scale drawing, mark the position of $E$.

Sue describes the single transformation that maps shape $A$ onto shape $B$ as a translation by the vector $\left(\begin{array}{c}7\\ 1\end{array}\right)$. Explain why Sue is incorrect.

On the grid, draw the image of shape $A$ after a rotation of 90° anticlockwise about (0, 0).

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

Points $C$ and $D$ lie on the circle. Write down the mathematical name for the line $CD$.

The diagram shows a circle with centre $O$. Points $K$, $L$ and $M$ lie on the circumference of the circle. Draw triangle $KLM$ so that angle $KLM={90}^{\circ }$.

Complete the table of values for $y=\frac{20}{x}$.

On the grid, draw the graph of $y=\frac{20}{x}$ for $1⩽x⩽5$.

Use your graph to solve the equation $\frac{20}{x}=8$.

Complete the table.

Rinesh spins the spinner another 1500 times. Calculate the expected number of times the spinner lands on 2.

These are the distances above the surface of the Earth of five satellites, $A$, $B$, $C$, $D$ and $E$. Each distance is in kilometres.

Write these distances in order, starting with the shortest.

The radius of Earth is 6370 km. Satellite $A$ is $k$ times further from the centre of Earth than satellite $D$. Show that $k=6.11$ correct to 2 decimal places.

A satellite travels at a speed of 27 000 km/h. Find the distance the satellite travels in 95 minutes.

A different satellite travels at a speed of 25 200 km/h. Convert this speed into m/s.

Find the radius of the cylinder.

The cylinder is made from gold. The density of the gold is $19.3{\text{ g/cm}}^3$. Calculate the mass of the cylinder. $$[\text{Density}=\frac{\text{mass}}{\text{volume}}]$$