IGCSE Mathematics 0580 Paper 32, May/June 2024

6 7 10 12 18 32 49 63 From this list of numbers, write down a factor of 21

a square number

a prime number.

Find the value of the cube root of 1728

$2^5$

$5^0$

${36}^{\frac{1}{2}}$

Put one pair of brackets into this calculation to make it correct. $$3\times 2-6-2÷2=4$$

Find the lowest common multiple (LCM) of 30 and 68.

Simplify. $5a-6a+3a$

$6x^2-6x-4x^2-x$

Find the value of $c^2+d^2$ when $c=7$ and $d=-5$.

The time, $T$ minutes, to cook a chicken with a mass of $m\text{ kg}$ is $T=35m+20$. Make $m$ the subject of the formula.

Find the mass of a chicken that takes 83 minutes to cook.

Solve these simultaneous equations. You must show all your working. $$5x-6y=24$$ $$15x+8y=33$$

Write down the mathematical name of quadrilateral $A$.

Find the area of quadrilateral $A$.

Measure the perimeter of quadrilateral $A$.

Describe fully the single transformation that maps quadrilateral $A$ onto quadrilateral $B$

quadrilateral $A$ onto quadrilateral $C$

quadrilateral $A$ onto quadrilateral $D$.

On the grid, enlarge quadrilateral $A$ by scale factor 2, centre $(-3,-3)$.

Anton records the number of pets owned by each of 50 families. The table shows some of his results.

There are twice as many families with 4 pets than with 5 pets. Complete the table.

Complete the bar chart.

Write down the mode.

Calculate the mean.

80 of the pets owned by the families are cats, rabbits or hamsters. The table shows the number of each pet.

Complete the table.

Complete the pie chart.

One of the pets is chosen at random. Find the probability that a rabbit is chosen.

The diagram shows a pair of parallel lines and a straight line. Write down the mathematical name for the type of angle marked ${125}^{\circ }$.

Give the geometrical reason why the value of $x$ is 125.

The diagram shows three straight lines. Find the value of $y$. Write down the geometrical properties needed to find the value of $y$.

The diagram shows a circle, centre $O$, with diameter $AOB$. The line $CDE$ touches the circle at $D$ and angle $DOB={74}^{\circ }$. Write down the mathematical name of the line $CDE$.

Work out angle $ODB$.

Work out angle $BDE$. Give a geometrical reason for your answer.

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

Complete the table of values for $y=-x^2+8x+1$.

On the grid, draw the graph of $y=-x^2+8x+1$ for $0⩽x⩽8$.

Write down the equation of the line of symmetry of the graph.

A straight line has a gradient of $\frac{1}{2}$ and passes through the point $(2,7)$. On the grid, draw this line for $0⩽x⩽8$.

Write down the equation of this line in the form $y=mx+c$.

Write down the coordinates of the points where this line intersects the graph of $y=-x^2+8x+1$.

Work out the area of the gardens and the area of the playground.

The park area of $4620{\text{ m}}^2$ is made up of paths and grassland. $18\mathrm{\%}$ of the park area is paths. Show that the grassland area is $3788.4{\text{ m}}^2$.

Seed for the grassland is sold in bags. The seed in one bag covers an area of $280{\text{ m}}^2$. The bags cost $\mathrm{\$}72$ each for the first 5 bags and then $\mathrm{\$}58$ each for any extra bags. Calculate the cost of the seed needed to cover the grassland.

The owners of the land buy new equipment for the playground. They borrow $\mathrm{\$}8500$ for 4 years at a rate of $6.5$ per year compound interest. Calculate the amount they repay at the end of the 4 years. Give your answer correct to the nearest dollar.

The caf\'{e} in the park sells water in bottles $A$, $B$ and $C$. Work out which bottle is the best value. You must show all your working.

Show that $EF=1.9\text{ m}$.

Work out $AF$.

Calculate the area of the floor.

A cupboard in the room is in the shape of a cuboid. The area of the base of the cupboard is $1.2{\text{ m}}^2$ and the height of the cupboard is $2.3\text{ m}$. Calculate the volume of the cupboard. Give the units of your answer.

Jo buys 275 floor tiles which cost $\mathrm{\$}1.64$ each. Calculate the total cost of the floor tiles.

Jo builds a patio in the shape of a semicircle with radius $2.3\text{ m}$. Calculate the area of the patio.

Sara rides her bicycle at a speed of 420 metres per minute. Work out her speed in kilometres per hour.

Jan cycles a distance of $51\text{ km}$. She starts at 1155. She has a rest stop for 25 minutes. She finishes at 1441. Calculate her average speed, in km/h, for the time she is cycling.