IGCSE Mathematics 0580 Paper 12, May/June 2024

Write the number 31 072 000 in words.

Find the value of the reciprocal of 0.4 .

Write these numbers in order, starting with the smallest. $$\frac{6}{7}8.6\times {10}^{-1}\frac{11}{13}86.5\mathrm{\%}$$

The temperature at midnight is $-4{}^{\circ }\mathrm{C}$. The temperature at noon is $25{}^{\circ }\mathrm{C}$. Work out the difference between these two temperatures.

A gardener charges $6.55 for each hour he works plus a fixed charge of $15.50 . Calculate the total amount he charges when he works for 4 hours.

Jonah has $750. He spends $\frac{1}{4}$ of this money on travel, and some of this money on food. He now has $437.50 . Work out the fraction of the $750 he spends on food.

A delivery driver records the number of pizzas she delivers each month for one year. $$\begin{array}{cccccc}48& 44& 39& 28& 57& 22\\ 36& 41& 54& 57& 49& 52\end{array}$$

$$\mathbf{a}=\left(\begin{array}{c}5\\ -7\end{array}\right)\mathbf{b}=\left(\begin{array}{c}6\\ -7\end{array}\right)$$ Work out $\mathbf{a}-\mathbf{b}$.

These are the first four terms of a sequence. $$2317115$$

Write 0.04628 correct to 2 significant figures.

On the Venn diagram, shade the region $A\cup B$.

Factorise completely. $$20x-90x^2$$

Describe the type of correlation between the speed of runners and the time taken to complete a race.

A circle has an area of $36\pi {\text{ cm}}^2$.

Write 174 000 in standard form.

The diagram shows a right-angled triangle. Calculate the value of $x$.

Without using a calculator, work out $2\frac{1}{4}÷1\frac{7}{8}$. You must show all your working and give your answer as a mixed number in its simplest form.

Expand and simplify. $$(x-4)(x-7)$$

$$5^7÷5^x=5^3$$ Find the value of $x$.

The length, $l$ metres, of a piece of material is $4.5\text{ m}$, correct to the nearest $10\text{ cm}$. Complete this statement about the value of $l$.

$$\mathcal{E}=\{x:x\text{ is a natural number less than }12\}$$ $$S=\{1,4,7,10\}$$ $$T=\{1,3,5,7,9,11\}$$ Complete the Venn diagram.

In a class of 30 students, 13 travel to school by bus. There are 570 students in the school. Find the expected number of students in the school who travel by bus.

The diagram shows a flagpole, $BD$, held by two ropes, $AD$ and $CD$. $ABC$ is a straight line and angle $ABD={90}^{\circ }$. $AD=21.2\text{ m}$, $AB=16.5\text{ m}$ and angle $BCD={48}^{\circ }$.