IGCSE Mathematics 0580 Paper 42, May/June 2026

Triangle $ABC$ is isosceles with $AB=AC$. Find the value of $x$.

A librarian records the number of books borrowed by each of 40 students. The frequency table shows the results.

In triangle $ABC$, $AC=10\text{ cm}$ and $BC=8.5\text{ cm}$. Using a ruler and compasses only, construct triangle $ABC$. The line $AB$ has been drawn for you.

A television costs $\mathrm{\$}1260$. Liesl pays a deposit of $35\mathrm{\%}$ of the cost of the television. She then pays monthly payments of $\mathrm{\$}45.50$ for the remaining cost of the television. Find the number of monthly payments that Liesl pays.

$P$ is the point $(-3,5)$ and $\overrightarrow{PQ}$ is $\left(\begin{array}{c}8\\ -3\end{array}\right)$. Find the coordinates of the point $Q$.

A semicircle has a diameter of $15.8\text{ cm}$. Calculate the perimeter of the semicircle.

The table shows some values, correct to 1 decimal place, for $y=x^3-2x^2-2$.

Solve the equation. $$\frac{w+8}{4}=\frac{2w-3}{3}$$

Yasmin collects coins. $10\mathrm{\%}$ of her coins are gold. $25\mathrm{\%}$ of the remaining coins are silver. The other 54 coins are copper.

Calculate $XY$.

A scientist records the mass of a radioactive substance at the same time each day. On 10 January, the scientist records a mass of 150 grams. Each day, the mass of the substance decreases by $5\mathrm{\%}$. Find the date on which the scientist first records a mass of less than 96 grams.

$y$ is inversely proportional to $x$. When $x=6$, $y=10.5$. Find $y$ when $x=9$.

$\cos x=0.41$ Find the reflex angle $x$.

Write $\frac{8}{x+2}+\frac{3}{x-4}$ as a single fraction in its simplest form.

$ABCDE$ is a square-based pyramid. $EC$ and $BD$ intersect at $F$. $AF$ is perpendicular to the base $BCDE$. $BC=16.5\text{ cm}$ and $AF=28\text{ cm}$.

$\mathrm{f}(x)=20-3x\mathrm{g}(x)=\frac{64}{2^x}\mathrm{h}(x)=7+2x$

In this question, all lengths are in centimetres.

The time spent in a shop by each of 40 customers is recorded. The table shows the results.

The diagram shows a field $ABCD$ with a straight footpath from $A$ to $C$.

The volume of a solid metal cuboid is $22{\text{ cm}}^3$, correct to the nearest ${\text{cm}}^3$. The mass of the metal cuboid is 140 grams, correct to the nearest 10 grams. Calculate the lower bound of the density of the metal. [$\text{Density}=\text{mass}÷\text{volume}$]

Write $\frac{8x^2+24x}{2x^2-18}$ as a single fraction in its simplest form.