IGCSE Mathematics 0580 Paper 23, May/June 2024

Write the number two million two thousand and two in figures.

Put one pair of brackets into this calculation to make it correct. $$5-4\times 3-9-2=0$$

Simplify. $$7x-8y-x-y$$

The base of a cuboid measures $10\text{ cm}$ by $7\text{ cm}$. The volume of the cuboid is $280{\text{ cm}}^3$. Calculate the height of the cuboid.

In a city, the probability that it will rain today is $0.15$. Find the probability that it will not rain today in this city.

Factorise completely. $$4x^{2}y-5x{y}^2$$

The scale of a map is $1:40000$. On the map the distance between two villages is $37\text{ cm}$. Calculate the actual distance between the two villages. Give your answer in kilometres.

Without using a calculator, work out $\frac{3}{7}-\frac{1}{14}$. You must show all your working and give your answer as a fraction in its simplest form.

The diagram shows a right-angled triangle. Calculate $AB$.

Find the gradient of the line joining the points $(-2,7)$ and $(3,1)$.

Solve the simultaneous equations. $$\begin{array}{rl}{\displaystyle 5t-2w}& {\displaystyle =19}\\ {\displaystyle 3t+2w}& {\displaystyle =5}\end{array}$$

Simplify.

$P$, $Q$, $R$ and $T$ are points on the circle. $AB$ is a tangent to the circle at $T$. Angle $ATP={50}^{\circ }$, angle $PTR={48}^{\circ }$ and $PQ=QR$.

The time taken for each of 200 students to complete a calculation is measured. The cumulative frequency diagram shows the results. Use the diagram to find an estimate for

$$A=\pi r^2+\pi dh$$ Rearrange the formula to make $h$ the subject.

Work out, giving each answer in standard form.

The diagram shows two sides, $VA$ and $VB$, of a regular polygon. $AVX$ is a straight line. Angle $BVX=y^{\circ }$ and angle $AVB=11.5y^{\circ }$. Find the number of sides of this polygon.

$$\mathrm{f}(x)=3^x+2$$

Write the recurring decimal $0.4\dot{1}$ as a fraction in its simplest form. You must show all your working.

Solve the equation $\tan x+\sqrt{3}=0$ for $0^{\circ }⩽x⩽{360}^{\circ }$.

Simplify. $$\frac{2}{y+1}-\frac{3}{y}$$ Give your answer as a single fraction in its simplest form.

The diagram shows a triangular prism with cross-section triangle $BCV$. Angle $BCV={90}^{\circ }$, $BC=5\text{ cm}$, $CV=4\text{ cm}$ and $AB=15\text{ cm}$. Calculate the angle between $AV$ and the base $ABCD$.

Simplify. $$\frac{pt-p-t+1}{1-t^2}$$

In the diagram, $O$ is the origin. $\overrightarrow{OP}=\mathbf{p}$ and $\overrightarrow{OQ}=\mathbf{q}$. $R$ is the point of intersection of $PQ$ and $OS$, with $PR:RQ=1:2$ and $OR=RS$. Find the position vector of $S$ in terms of $\mathbf{p}$ and $\mathbf{q}$. Give your answer in its simplest form.