IGCSE Mathematics 0580 Paper 43, May/June 2025

Find the median of these numbers. 5 11 11 13 17 21

In triangle $ABC$, $AC=21\text{ m}$ and $BC=15.9\text{ m}$. Using a ruler and compasses only, complete the scale drawing of the triangle. Use a scale of $1\text{ cm}$ to represent $3\text{ m}$. The side $AB$ is drawn for you.

$\frac{2}{5}\sqrt{15}23\sqrt{144}-20.8$ From this list, write down

The diagram shows a pentagon made from two congruent trapeziums. The area of the pentagon is $130.2{\text{ cm}}^2$. Calculate the value of $x$.

One titanium atom has a mass of $7.95\times {10}^{-23}\text{ grams}$. Calculate the number of titanium atoms in $1\text{ kg}$ of titanium. Give your answer in standard form.

$\mathcal{E}=\{x:x\text{ is an integer and }1⩽x⩽12\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of }3\}$

Factorise.

Expand and simplify.

The table shows three sequences. Complete the table.

$\sqrt{\frac{{10}^{400}}{{10}^{220}\times {10}^{80}}}={10}^k$ Find the value of $k$.

Line $L$ has the equation $y=2(x-5)$.

Jess invests $\mathrm{\$}1400$ in an account. The account pays compound interest at a rate of $r\mathrm{\%}$ per year. At the end of 4 years the value of her investment is $\mathrm{\$}1523.15$. Find the value of $r$.

$m$ is inversely proportional to the square root of $(t+2)$. $m=0.5$ when $t=23$. Find $m$ when $t=98$.

By shading the unwanted regions of the grid, draw and label the region $R$ which satisfies these three inequalities. $$y<3x⩽2y<x+3$$

In the Venn diagram, shade the region $(A\cup B)\cap C^{\mathrm{\prime }}$.

The diagram shows a solid cuboid with sides of length $4.5\text{ cm}$, $8\text{ cm}$ and $13.2\text{ cm}$.

The table shows some information about the heights of 200 plants.

Stephan has two bags, $A$ and $B$, each containing red sweets and yellow sweets only. He picks two sweets at random, one from bag $A$ and the other from bag $B$. The probability that Stephan picks a red sweet from bag $A$ is $\frac{3}{5}$. The probability that Stephan picks a red sweet from bag $A$ and a red sweet from bag $B$ is $\frac{2}{15}$.

The diagram shows an equilateral triangle $ABC$ with all sides of length $12\text{ cm}$. $ANP$ is a sector of a circle, centre $A$. $N$ lies on $AC$ such that $AN:NC=2:1$. $P$ lies on $AB$ such that $AP:PB=2:1$. Calculate the area of the shaded region.

A metal cube has mass $14.2\text{ g}$, correct to 1 decimal place.

The diagram shows a frustum made by removing a small cone from a large cone. The height of the small cone is $7.5\text{ cm}$. The height of the frustum is $4.5\text{ cm}$. The radius of the large cone is $4.2\text{ cm}$. Work out the volume of the frustum.

The histogram shows information about the distance some people travel to work.

The diagram shows a quadrilateral $OXPY$ with diagonals meeting at $T$. $\overrightarrow{OX}=3\mathbf{a}$ and $\overrightarrow{OY}=12\mathbf{b}$.