IGCSE Mathematics 0580 Paper 22, May/June 2025

Shade one more small square so that the diagram has one line of symmetry.

Shade one more small square so that the diagram has rotational symmetry of order 2.

Find the actual distance between village $P$ and village $Q$.

Measure the bearing of village $Q$ from village $P$.

Find the probability that she picks an odd number.

Samira repeats this 35 times. Calculate the number of times Samira is expected to pick an odd number.

Translate triangle $T$ by the vector $\left(\begin{array}{c}0\\ -2\end{array}\right)$.

Describe fully the single transformation that maps triangle $T$ onto triangle $U$.

$8x+7=39$

$2(5y-1)=24$

Find the next term of this sequence.

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

$\overrightarrow{AC}=2\overrightarrow{AB}$ Find the coordinates of the point $C$.

The length of $AB$ is $k\sqrt{5}$. Find the value of $k$.

$P$ is a point on $AB$. $$AP:PB=1:3$$ Find the position vector of $P$.

Write 0.007 08 in standard form.

Work out $(3.8\times {10}^{22})+(3.8\times {10}^{23})$. Give your answer in standard form.

100 students solve a puzzle. The table shows information about the time taken by each student to solve the puzzle.

Work out an estimate of the mean.

Complete the histogram to show the information in the table.

80 adults solve the same puzzle as the students. The cumulative frequency table shows information about the time taken by each adult to solve the puzzle.

On the grid, draw a cumulative frequency diagram.

Use your cumulative frequency diagram to find an estimate for the median

Use your cumulative frequency diagram to find an estimate for the lower quartile.

Write down the coordinates of the point where the graph crosses the $x$-axis.

Write down the equation of each asymptote.

By drawing a suitable straight line on the grid, solve $\frac{2}{x}-x-1=0$.

${125}^{\frac{2}{3}}$

$4^{-\frac{5}{2}}$.

$\frac{9}{\sqrt{3}}$ Rationalise the denominator. Give your answer in its simplest form.

$(5-\sqrt{2})(1+3\sqrt{2})=c+k\sqrt{2}$ Find the value of $c$ and the value of $k$.

$\frac{5a}{6}\times \frac{3b}{a}$

$\frac{p}{2}+\frac{3t}{4}$

$\frac{2}{x-2}-\frac{3}{x+1}$

When $x=9$, $y=2$. Find the value of $y$ when $x=36$.

When $x$ is increased by a factor of 4, the value of $y$ changes by a factor of $p$. Find the value of $p$.

Find the $x$-coordinate of $A$ and the $x$-coordinate of $B$. Give your answers as exact values.

Differentiate $3x-x^3$.

Find the coordinates of $P$ and $Q$.

Write down the exact value of $\tan {60}^{\circ }$.

Solve $2\sin x-1=0$ for $0^{\circ }⩽x⩽{360}^{\circ }$.