IGCSE Mathematics 0580 Paper 23, Oct/Nov 2025

The diagram shows an isosceles triangle. Find the value of $x$.

Find the largest odd number that is a common factor of 90 and 120.

The diagram shows a net for a dice. The dice has six faces numbered 1 to 6. The sum of each pair of opposite faces on the dice is 7. Write the missing numbers on the net.

A rectangle measures $5\text{ cm}$ by $19\text{ cm}$. Two of these rectangles are joined to make a shape. Work out the perimeter of the shape.

The diagram shows a rectangle $ABCD$. $EFG$ is an equilateral triangle that touches the rectangle at $F$ and $G$. Find the value of $x$ and the value of $y$.

The scatter diagram shows the value, in thousands of dollars, of ten paintings in 2005 and the value of the same paintings in 2025.

$\overrightarrow{DE}=\left(\begin{array}{c}3\\ -4\end{array}\right)$

$n^{15}÷n^x=n^5$ Find the value of $x$.

The diagram shows a right-angled triangle $ABC$.

Sarah rolls a fair 6-sided dice twice. Find the probability she rolls a number greater than 4 both times.

$A$, $B$, $C$ and $D$ are points on the circumference of a circle with centre $O$. $ED$ and $EB$ are tangents to the circle. $AC$ is parallel to $EB$. Angle $AOD={44}^{\circ }$. Find the value of $x$.

The minimum point on a quadratic curve is $(-3,-5)$.

Factorise.

The table shows three sequences. Complete the table to show the $n\text{th}$ term of each sequence.

Shade the region in each Venn diagram.

The diagram shows a circle, centre $O$, radius $12\text{ cm}$.

Work out $0.11\dot{4}+0.\dot{2}$. Give your answer as a fraction.

The diagram shows a cyclic quadrilateral. The ratio $p:m=2:3$. Find the value of $y$.

The equation of line $L$ is $y=-\frac{1}{2}x+7$. Find an equation of the line perpendicular to line $L$ that passes through the point $(3,5)$. Give your answer in the form $y=mx+c$.

Work out the area of triangle $ABC$.

Mahir picks one number at random from the numbers 5, 10 and 15. He then picks one number at random from the numbers 4, 5 and 6. He adds the two numbers. The sample space diagram shows some of the possible outcomes.

Write as a single fraction in its simplest form.

Solve the simultaneous equations. $y=x^2-8x+22$ $y+2=3x$

Simplify. $\frac{2x^2-11x-21}{x^2-49}$

In this question all measurements are in centimetres. Solid $A$ is made from a cylinder and a hemisphere, both of radius $2R$. The cylinder has height $5R$. Solid $B$ is a cone of radius $R$ and sloping edge $x$. The total surface area of solid $A$ is equal to the total surface area of solid $B$. Find $R$ in terms of $x$.