IGCSE Mathematics 0580 Paper 22, May/June 2023

Find the temperature that is $8^{\circ }\mathrm{C}$ colder than $-5{}^{\circ }\mathrm{C}$.

There are two prime numbers in this list. 27 47 57 61 75 93 Work out the sum of these two prime numbers.

On ten days, Stefan records the number of minutes he has to wait for a train. 1 3 12 5 4 23 5 24 11 8

The distance from town $A$ to town $B$ on a map is $3.5\mathrm{c}\mathrm{m}$. The scale on the map is $1:250000$. Find the actual distance, in kilometres, from town $A$ to town $B$.

A spinner is spun. The possible outcomes are A, B, C or D. The probability of spinning A, C or D is shown in the table. Letter on spinner | A | B | C | D Probability | 0.2 | | 0.05 | 0.35 Complete the table.

$\mathcal{E}=\{x:1⩽x⩽20\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of }5\}$

Without using a calculator, work out $\frac{4}{7}÷1\frac{5}{21}$. You must show all your working and give your answer as a fraction in its simplest form.

Solve.

$F$ is the point $(1,-4)$, $\overrightarrow{FG}=\left(\begin{array}{c}8\\ -3\end{array}\right)$ and $\overrightarrow{GH}=\left(\begin{array}{c}-12\\ 35\end{array}\right)$. Find

The diagram shows a shape, $ABCD$, formed by the sectors of two circles with the same centre $O$. Both sector angles are ${140}^{\circ }$, $OC=3.2\mathrm{c}\mathrm{m}$ and $CB=2.6\mathrm{c}\mathrm{m}$. The area of the shape is $k\pi {\mathrm{c}\mathrm{m}}^2$. Find the value of $k$.

One solution of the equation $a{x}^2+b=181$ is $x=8$. $a$ and $b$ are both positive integers greater than 1.

$A$, $B$, $C$ and $D$ are points on a circle. $AB$ is parallel to $DC$ and angle $ACD={32}^{\circ }$. Chords $AC$ and $DB$ intersect at $E$. Find the value of $x$.

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

$C$ is the point $(5,-1)$ and $D$ is the point $(13,15)$.

Write $0.6\dot{2}\dot{1}$ as a fraction in its simplest form. You must show all your working.

The diagram shows a triangle with an acute angle marked $x^{\circ }$. The area of the triangle is $2143{\mathrm{c}\mathrm{m}}^2$. Work out the value of $x$.

Make $x$ the subject of the formula. $$c=\frac{3x}{2x-5}$$

$m$ is inversely proportional to the square of $(t+2)$. $m=0.64$ when $t=3$. Find $m$ when $t=8$.

In the Venn diagram, shade the region $A\cap B^{\mathrm{\prime }}\cap C$.

Solve the equation $5\sin x=-3$ for $0^{\circ }⩽x⩽{360}^{\circ }$.

Write as a single fraction in its simplest form. $$\frac{5}{3x+2}+\frac{4}{2x-1}$$

Bag $A$ and bag $B$ each contain red sweets and yellow sweets. Anna picks a sweet at random from bag $A$. Ben picks a sweet at random from bag $B$. The probability that Anna picks a red sweet is $\frac{2}{5}$. The probability Anna and Ben both pick a yellow sweet is $\frac{1}{10}$. Find the probability that Anna and Ben both pick a red sweet.