IGCSE Mathematics 0580 Paper 31, Oct/Nov 2024

Write the number six million and thirty in figures.

Write 7.896 correct to 2 decimal places.

8 24 25 36 39 41 48 From this list of numbers, write down a multiple of 16

From this list of numbers, write down a factor of 24

From this list of numbers, write down a cube number

From this list of numbers, write down a prime number.

Put one pair of brackets into this calculation to make it correct. $$10-12÷4+2=8$$

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of $$\frac{596\times 0.047}{\sqrt{8.65}}\mathrm{.}$$ You must show all your working.

Calculate $(8\times {10}^6)\times (3\times {10}^{-2})$. Give your answer in standard form.

$$216=2^3\times 3^3$$ Write 2160 as a product of its prime factors.

In the diagram, $BCG$ is a triangle. $ABCD$ and $EF$ are parallel lines. Find the value of $x$. Give a geometrical reason for your answer. $x=\text{................}$ because ........................................................................................................

Find the value of $y$. Give a geometrical reason for your answer. $y=\text{................}$ because ........................................................................................................ .............................................................................................................................................

Find the value of $z$.

$R$, $S$ and $T$ are points on a circle, centre $O$. Line $XY$ touches the circle at $T$. Write down the mathematical name for the line $XY$.

Write down the mathematical name for the line $SR$.

Toby thinks shape $RST$ is a right-angled triangle. Give a geometrical reason why Toby is incorrect.

The bar chart shows the percentage of people in each age group who use a bicycle. Write down the percentage of people aged 60 to 69 who use a bicycle.

980 people in the survey are in the 30–39 age group. Work out how many of these people use a bicycle.

Jack makes 18 cycling trips in one year. Each cycling trip lasts 23 minutes. Find the total time Jack spends cycling in this year. Give your answer in hours and minutes.

The table shows where 240 people cycle the most. Complete the table.

Complete the pie chart to show this information.

A bicycle costs $720. Carlo pays one-fifth of the cost as a deposit. He pays the rest of the money in equal monthly payments of $16. Work out how many monthly payments Carlo makes.

A parallelogram $ABCD$ has sides $8\text{ cm}$ and $6\text{ cm}$. Lines $AB$ and $BC$ have been drawn. By constructing triangle $ACD$, complete the parallelogram. Use a ruler and compasses only and leave in your construction arcs.

Describe fully the single transformation that maps shape $A$ onto shape $B$.

On the grid, draw the image of shape $A$ after a rotation, ${90}^{\circ }$ anticlockwise, centre $(5,1)$.

'The scatter diagram shows positive correlation.' Is this statement true or false? Give a reason for your answer. ................ because ............................................................................................................... .............................................................................................................................................

On one journey, the cost per kilometre travelled was much more expensive than on all of the other journeys. Draw a ring around this point on the scatter diagram.

Draw a line of best fit on the scatter diagram.

Another journey is $8\text{ km}$ long. Use your line of best fit to find an estimate for the cost of this journey.

Arit, Luke and Marie share the cost of a taxi journey. The cost is $26.40 . Calculate how much Arit pays if they share the cost equally.

They decide to share the cost in proportion to the distance they each travel in the taxi. Arit travels $12\text{ km}$, Luke travels $3\text{ km}$ and Marie travels $7.5\text{ km}$. Write the ratio $12:3:7.5$ in its simplest form.

Calculate how much more Arit pays than if they share the cost equally.

Jin invests some money from his taxi company. He invests $18600$ at a rate of $1.7\mathrm{\%}$ per year compound interest. Calculate the value of the investment at the end of 6 years. Give your answer correct to the nearest dollar.

This is a recipe to make ice cream for 6 people. 270 ml cream 270 ml milk 100 g sugar 4 egg yolks Tom makes ice cream for 10 people. Work out how much milk he uses.

The mass of all the ingredients Tom uses is $1100\text{ g}$. After Tom heats the mixture, this mass reduces by $15\mathrm{\%}$. Find the mass of the mixture after heating.

Tom lets the mixture cool to $5^{\circ }\mathrm{C}$. He then puts it into a freezer to cool to $-{18}^{\circ }\mathrm{C}$. Find the difference in these temperatures.

In a factory, a machine fills $25920$ tubs of ice cream in 8 hours. Work out the number of tubs the machine fills in 1 minute.

A pack of ice cream contains 6 tubs. There are 120 packs on a tray. There are 24 trays on a truck. Work out how many tubs of ice cream are on the truck.

Mario sells ice creams in five flavours. The table shows the relative frequency of some of the ice cream flavours Mario sells. Mario sells three times as many chocolate ice creams as banana ice creams. Complete the table.

One week Mario sells 450 ice creams. Find how many strawberry ice creams Mario expects to sell.

The probability that any customer is an adult is 0.7 . Complete the tree diagram.

Find the probability that the first two customers are adults.

Find the perimeter of the triangle.

The diagram shows a shape made from rectangles. Calculate the area of the shape.

The diagram shows a right-angled triangle $ABC$. Calculate the area of the triangle.

Calculate the volume of a sphere with diameter $5.25\text{ cm}$. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$.]

The diagram shows the net of a solid. Write down the mathematical name of the solid.

Find the volume of the solid when $x=4$.

Write down an expression, in terms of $x$, for the volume of the solid.

Find the value of $x$ when the volume of the solid is $360{\text{ cm}}^3$.

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

On the grid, draw the graph of $y=2x^2+x$ for $0⩽x⩽5$.

Use your graph to solve the equation $2x^2+x=30$ for $0⩽x⩽5$.

On the grid, draw a travel graph to show Samir’s whole journey.

Calculate Samir’s average speed for the whole journey.

Solve. $$4x-7=3$$

Simplify. $$(x^6{)}^2$$

Simplify. $$(5x^3{y}^4)\times (2x^2{y}^2)$$

Expand and simplify. $$4a+5-2(a-1)$$

Expand and simplify. $$(d+7)(d-3)$$