IGCSE Mathematics 0580 Paper 22, Oct/Nov 2024

These are the first eight terms of a sequence. $$c-3-9-15-21-27-33k$$ Find the value of $c$ and the value of $k$.

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

$$0.253.142\sqrt{3}-324-0.41.2-\frac{1}{4}$$ Complete each statement with a number from the list. .................................................. is a natural number. .................................................. is an irrational number. .................................................. is the reciprocal of 4.

The scatter diagram shows the number of rooms and the number of people in each of eight buildings.

Convert $7.51{\text{ m}}^2$ into ${\text{cm}}^2$.

The diagram shows a trapezium. The area of the trapezium is $42{\text{ cm}}^2$. Calculate the value of $x$.

Without using a calculator, work out $\frac{2}{7}÷\frac{6}{11}$. You must show all your working and give your answer as a fraction in its simplest form.

The diagram shows a parallelogram. Work out the size of the smallest interior angle of the parallelogram.

Points $A$, $B$, $C$ and $D$ lie on a circle. $ABCD$ is a square with area $72{\text{ cm}}^2$. Calculate the area of the circle. Give your answer as a multiple of $\pi$.

Calculate $\sqrt[3]{1+10.9\times {0.4}^2}$.

Factorise fully.

$y$ is directly proportional to the square root of $x+1$. $y=10.5$ when $x=8$. Find $y$ when $x=1.56$.

The region $R$ satisfies these inequalities. $$-3<y⩽2y⩽x-1$$ By drawing suitable straight lines and shading unwanted regions, find and label the region $R$.

The diagram shows the speed–time graph for 17 seconds of a car journey.

At the start of an experiment there are $40000$ bacteria. The number of bacteria increases at a rate of $15\mathrm{\%}$ per hour. Calculate the number of bacteria after 3 hours.

75 people are asked if they have a car, $C$, and if they have a job, $J$. The Venn diagram shows the results. A person is chosen at random from those who have a car. Find the probability that this person also has a job.

$A$, $B$ and $C$ are points on the circumference of a circle with centre $O$. $DA$ and $DC$ are tangents to the circle. Angle $ABC={64}^{\circ }$. Work out the value of $x$.

A solid is made from a cylinder and a hemisphere, both of radius $4.3\text{ cm}$. The cylinder has length $11.9\text{ cm}$.

Find an expression for the $n\text{th}$ term of this sequence. $$\frac{1}{7},1,7,49,343,2401,\dots$$

Expand and simplify. $$(x+3)(x+5)(2x+1)$$

$A$ is the point $(17,9)$ and $B$ is the point $(23,39)$. Find the equation of the perpendicular bisector of line $AB$. Give your answer in the form $y=mx+c$.

The small box is mathematically similar to the large box. The volume of the large box is $72.8\mathrm{\%}$ greater than the volume of the small box. The small box has length $3.5\text{ cm}$ and the large box has length $x\text{ cm}$. Calculate the value of $x$.