IGCSE Mathematics 0580 Paper 13, May/June 2024

Write the number two million two thousand and two in figures.

Put one pair of brackets into this calculation to make it correct. $$5+4\times 3+9=53$$

Simplify. $$7x-8y-x-y$$

Write these numbers in order, starting with the smallest. $$0.4542\mathrm{\%}\frac{4}{11}\frac{2}{5}$$

The base of a cuboid measures $10\text{ cm}$ by $7\text{ cm}$. The volume of the cuboid is $280{\text{ cm}}^3$. Calculate the height of the cuboid.

In a city, the probability that it will rain today is 0.15. Find the probability that it will not rain today in this city.

One day the temperature in Tokyo is $-5^{\circ }\text{C}$ and the temperature in Manila is ${18}^{\circ }\text{C}$.

The diagram shows an isosceles triangle. Find the value of $x$.

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

Factorise completely. $$4x^{2}y-5x{y}^2$$

The scale of a map is $1:40000$. On the map the distance between two villages is $37\text{ cm}$. Calculate the actual distance between the two villages. Give your answer in kilometres.

Without using a calculator, work out $\frac{3}{7}-\frac{1}{14}$. You must show all your working and give your answer as a fraction in its simplest form.

The price of a game increases from $\mathrm{\$}48$ to $\mathrm{\$}56.40$. Calculate the percentage increase in the price.

The diagram shows a right-angled triangle. Calculate $AB$.

The length, $s$ metres, of a ship is $83\text{ m}$, correct to the nearest metre. Complete this statement about the value of $s$.

Solve the simultaneous equations. $$5t-2w=19$$ $$3t+2w=5$$

The diagram shows the positions of three towns $A$, $B$ and $C$. Angle $ABC={103}^{\circ }$. The bearing of town $B$ from town $A$ is ${048}^{\circ }$. Town $C$ is due east of town $A$. Find the bearing of town $C$ from town $B$.

The diagram shows a spherical tank with radius $0.5\text{ m}$ and a cylindrical jug with diameter $24\text{ cm}$ and height $32\text{ cm}$. The tank is full of water. Calculate how many times the jug can be completely filled with water from the tank. [The volume, $V$, of a sphere with radius $r$ is $\frac{4}{3}\pi r^3$.]