IGCSE Mathematics 0580 Paper 22, May/June 2026

Another car has a fuel consumption of 6.2 litres/100km and CO2 emissions of 162g/km. Plot a point on the scatter diagram to show this information.

What type of correlation does the scatter diagram show?

Draw a line of best fit on the scatter diagram.

Paulo’s car has CO2 emissions of 140 g/km. Use your line of best fit to estimate the fuel consumption of his car.

Find the total area of the net.

Find the volume of the open box.

On the grid, draw the image of shape $A$ after a translation by the vector $\left(\begin{array}{c}-2\\ 5\end{array}\right)$.

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

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

Find the value of $E$ when $c=\sqrt{18}$ and $d=2$.

Rearrange the formula to write $c$ in terms of $E$ and $d$.

Write 63 as a product of its prime factors.

Find the lowest common multiple (LCM) of 63 and 42.

Find the highest common factor (HCF) of $63a^5{c}^2$ and $42a^2{c}^5$.

On the grid, draw these four straight lines. $x=8$ $y=2$ $x+y=8$ $2y-x=4$

Region $R$ satisfies these four inequalities. $x⩽8$ $y⩾2$ $x+y⩾8$ $2y-x⩽4$ By shading the unwanted regions of the grid, find and label the region $R$.

The $n$th term of a sequence is given by $n^2-3$. Write down the first three terms of this sequence.

These are the first four terms of another sequence. 4 12 36 108 Find the $n$th term of this sequence.

Expand and simplify. $(4-\sqrt{7})(3+2\sqrt{7})$

Rationalise the denominator and simplify. $\frac{2}{3-\sqrt{5}}$

Marwa picks one of the tiles at random. She replaces the tile and then picks a second tile at random. Find the probability that the two tiles have the same even number.

From the 10 numbered tiles, Marwa now picks three tiles at random without replacement. Find the probability that the sum of the numbers on the three tiles is 11.

Write $x^2+8x-7$ in the form $(x+a{)}^2+b$ where $a$ and $b$ are integers.

Write down the coordinates of the turning point of the curve $y=x^2+8x-7$.

Find, in terms of $\mathbf{a}$ and $\mathbf{c}$, in its simplest form $\overrightarrow{AP}$

Find, in terms of $\mathbf{a}$ and $\mathbf{c}$, in its simplest form $\overrightarrow{OP}$.

$Q$ is a point on $AB$ and $\overrightarrow{AQ}=\frac{1}{4}\mathbf{c}$. Show that $O$, $P$ and $Q$ lie in a straight line.

Find the gradient of the tangent to the curve at $x=2$.

Line $L$ intersects the curve at $x=2$. Line $L$ is perpendicular to the tangent to the curve at $x=2$. Find the equation of line $L$.