IGCSE Mathematics 0580 Paper 23, Oct/Nov 2024

61 62 63 64 65 66 67 68 69 From the list of numbers, write down

A train journey starts at 23 30 and finishes at 07 15 the next day. Find the time taken for this journey.

Simplify. $$3p-t-p-4t$$

The scale drawing shows the positions of town $K$ and town $L$. The scale is $1\text{ cm}$ represents $10\text{ km}$.

Each student in a class of 20 students records the number of coins in their pockets. The table shows the results.

The diagram shows three lines meeting at a point. Find the value of $w$.

Solve the equation. $$7-h=3-5h$$

Sacha buys $b$ books and $m$ magazines. The cost of each book is $\mathrm{\$}12$ and the cost of each magazine is $\mathrm{\$}5$. Write an expression, in terms of $b$ and $m$, for the total cost of the books and the magazines.

Find the size of an interior angle of a regular 15-sided polygon.

Without using a calculator, work out $2\frac{1}{4}-1\frac{11}{12}$. You must show all your working and give your answer as a fraction in its simplest form.

Solve the simultaneous equations. $$\begin{array}{rl}{\displaystyle 3p-2q}& {\displaystyle =7}\\ {\displaystyle p+2q}& {\displaystyle =1}\end{array}$$

$$V=\sqrt[3]{\frac{x}{y}}$$ Rearrange the formula to write $x$ in terms of $V$ and $y$.

Find the $n$th term of each sequence.

The box-and-whisker diagram shows information about the heights of some plants.

Calculate the shortest distance from $C$ to $AB$.

Simplify.

Two mathematically similar solids have volumes $81{\text{ cm}}^3$ and $24{\text{ cm}}^3$. The height of the smaller solid is $4.8\text{ cm}$. Calculate the height of the larger solid.

$y$ is inversely proportional to $\sqrt{x+2}$. When $x=2$, $y=3$. Find $y$ in terms of $x$.

Solve the equation $\tan x+2=0$ for $0^{\circ }⩽x⩽{360}^{\circ }$.

The Venn diagram shows the number of elements in each region.

The diagram shows a cuboid with a diagonal $PB$. Calculate the angle between the diagonal $PB$ and the base $ABCD$.

Write $x^2+8x-7$ in the form $(x+a{)}^2+b$.

A rectangle has an area of $150{\text{ m}}^2$, correct to the nearest square metre. The length of the rectangle is $22\text{ m}$, correct to the nearest metre. Calculate the upper bound of the width of the rectangle.

Simplify. $$\frac{3x-2-3xy+2y}{1-y^2}$$

In the diagram, $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=\mathbf{b}$. $AK:KB=2:1$. $OK=KC$. Find $\overrightarrow{AC}$ in terms of $\mathbf{a}$ and $\mathbf{b}$. Give your answer in its simplest form.