IGCSE Mathematics 0580 Paper 42, May/June 2025

A quadrilateral has these properties • the diagonals are the only lines of symmetry • it has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral.

The diagram shows the net of a solid. Write down the mathematical name of this solid.

Mass of box $A$ : Mass of box $B=4:7$ The mass of box $B$ is $2.4\text{ kg}$ more than the mass of box $A$. Calculate the mass of box $A$ and the mass of box $B$.

$ABCD$ is a trapezium. Work out the area of the trapezium.

Scott changes $\mathrm{\$}300$ into pounds (£). The exchange rate is £$1=\mathrm{\$}1.20$. Calculate the amount Scott receives.

A solid wooden cone has base radius $4\text{ cm}$ and height $12\text{ cm}$. The density of the wood is $0.74{\text{ g/cm}}^3$. Calculate the mass of the cone. [$\text{Density}=\text{Mass}÷\text{Volume}$]

$y=mx+c$ Rearrange the formula to make $m$ the subject.

Calculate. $$\frac{{2.1}^2-1.9}{0.5}$$

Solve the simultaneous equations. You must show all your working. $$2w-3y=11$$ $$3w+y=11$$

A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $\mathrm{\$}n$. The cost of a child ticket is $\mathrm{\$}(n-10)$. The total cost of the tickets is $\mathrm{\$}277.50$. Find the cost of one adult ticket.

In a sale, the original price of a shirt is reduced by 15%. The sale price of the shirt is $\mathrm{\$}23.63$. Find the original price of the shirt.

The length of a rectangle is $16\text{ cm}$, correct to the nearest centimetre. The width of the rectangle is $14\text{ cm}$, correct to the nearest centimetre. Calculate the lower bound of the perimeter of the rectangle.

Triangle $ABC$ and triangle $PQR$ are mathematically similar.

Factorise. $$5x-10-ax+2a$$

The interior angle of a regular polygon is ${172}^{\circ }$. Find the number of sides of this polygon.

On any day, the probability that the weather will be sunny is 0.7.

$A$, $B$, $C$, $D$ and $E$ lie on a circle. Find the values of $x$, $y$ and $z$.

$$\mathrm{f}(x)=x+1\mathrm{g}(x)=5-2x\mathrm{h}(x)=2^x$$

The diagram shows a quadrilateral $ABCD$. $CD=10\text{ m}$ and $DB=12\text{ m}$. Angle $DBA={90}^{\circ }$, angle $CDB={56}^{\circ }$ and angle $ADB={34}^{\circ }$.

Simplify.

$\mathcal{E}=\{\text{number of students in a class}\}$ $G=\{\text{number of students who study geography}\}$ $H=\{\text{number of students who study history}\}$ The Venn diagram shows information about the 33 students in a class.

Simplify. $$\frac{h^2+4h}{h^2-16}$$

Ahmed walks $2\text{ km}$ at a speed of $x\text{ km/h}$. He then walks a further $3\text{ km}$ at a speed of $(x+1)\text{ km/h}$. The total time he takes to walk the $5\text{ km}$ is $1\frac{1}{4}\text{ hours}$.

$P$ is the point $(8,0)$ and $Q$ is the point $(20,6)$. Find the equation of the perpendicular bisector of $PQ$. Give your answer in the form $y=mx+c$.

$$y=a{x}^{11}+3x^b$$ $$\frac{\mathrm{d}y}{\mathrm{d}x}=44x^{10}+18x^c$$ Find the values of $a$, $b$ and $c$.

The diagram shows a cube. Calculate the angle between the diagonal $AP$ and the base $ABCD$.