IGCSE Mathematics 0580 Paper 21, May/June 2026

Complete the statement with the correct month. Hannah spends more time running in ................................ than in any of the other months.

In May, Hannah spends 9 more hours swimming than she spends cycling. Find the number of hours Hannah spends swimming in July.

Find the coordinates of the midpoint of $PQ$.

Find the vector $\overrightarrow{QP}$.

The graph of $y=x^2+ax+b$ passes through the points $P$ and $Q$. This graph also passes through the point $(-2,c)$. Find the value of $c$.

$24192=2^7\times 3^3\times 7$ $245000=2^3\times 5^4\times 7^2$ Find the highest common factor (HCF) of $24192$ and $245000$.

A number, $k$, is written as a product of its prime factors. $$k=2^3\times 3^4\times 5\times c^2$$ where $c$ is a prime number greater than 5. Write the number $20k^2$ as a product of its prime factors. Give your answer in terms of $c$ in its simplest form.

$A$, $B$ and $C$ are linear sequences. The table gives some information about these sequences.

For these sequences, $C_n=A_n+B_n$. Work out $A_n$, the $n\text{th}$ term of sequence $A$.

These are the first five terms of another sequence. $$\frac{1}{2}1248$$ Find the next term in this sequence.

Find the $n\text{th}$ term of this sequence.

Work out. $$0.9\dot{2}\dot{4}-0.2\dot{1}\dot{3}$$ Give your answer as a decimal correct to 5 decimal places.

Write $0.6\dot{7}$ as a fraction.

Find an estimate for the median

Find an estimate for the interquartile range.

Use the cumulative frequency diagram to complete this frequency table.

On the grid, draw the image of shape $A$ after a reflection in the line $x=1$.

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

Calculate the volume of the cuboid.

Calculate the surface area of the cuboid.

Calculate $CE$.

The angle between $CE$ and the base $CDHG$ is $x^{\circ }$. Find the value of $\sin x^{\circ }$.

Find the coordinates of the turning points of the graph of $y=x^3-6x^2+7$.

By drawing a suitable sketch, determine whether each turning point is a maximum or a minimum.

Find $\overrightarrow{BC}$. Give your answer in terms of $\mathbf{m}$ and $\mathbf{n}$ in its simplest form.

Find $\overrightarrow{PQ}$. Give your answer in terms of $\mathbf{m}$ and $\mathbf{n}$ in its simplest form.

$\overrightarrow{CD}=3\mathbf{n}$ Show that $P$, $Q$ and $D$ lie on a straight line.

Expand and simplify. $$(5+\sqrt{2})(3-\sqrt{8})$$

$$\sqrt{2\frac{9}{20}}+\frac{6}{\sqrt{5}}=k\sqrt{5}$$ Find the value of $k$.