IGCSE Mathematics 0580 Paper 33, Oct/Nov 2023

Tom has a restaurant bill. Soup $............. Pasta $ 13.30 Ice cream $ 4.80 Drinks $ 3.81 Total cost $ 25.40 Complete the bill to show the cost of soup.

Find the cost of drinks as a percentage of the total cost.

Work out $\frac{2}{5}$ of $2400.

Decrease $3450 by 18%.

Amelia invests $14000 at a rate of 1.6% per year compound interest. Calculate the value of her investment at the end of 5 years. Give your answer correct to the nearest dollar.

This conversion graph can be used to change between dollars and Swiss francs. Use the graph to change $80 to Swiss francs

108 Swiss francs to dollars.

Explain how you can use the graph to change $360 to Swiss francs.

Bayside, Millwater and Westbridge are towns beside a lake. The scale drawing shows the positions of Bayside ($B$) and Millwater ($M$). The scale is 1 centimetre represents 2 kilometres. Find the actual distance between Bayside and Millwater.

Westbridge ($W$) is $17\text{ km}$ from Bayside on a bearing of ${155}^{\circ }$. On the scale drawing, mark the position of Westbridge.

A boat travels from Bayside to Westbridge. The table gives some information about its journey.

Work out how long the boat takes to travel from Millwater to Westbridge. Give your answer in hours and minutes.

The boat returns directly to Bayside. It takes 1 hour 20 minutes to travel the $17\text{ km}$. Work out the average speed of this journey.

Here are the ticket prices for a boat trip from Bayside to Westbridge. 1 person: $9.80 Group of 6 people: $57.30 Group of 15 people: $138.75 Calculate the cost per person for a group of 15 people.

A group of 24 people buy tickets for the boat trip from Bayside to Westbridge. Calculate the least amount of money the group needs to pay.

Aneel has 80 tea bags, $\frac{1}{2}\text{ kg}$ of sugar and 1 litre of milk. To make a cup of tea he uses: • 1 tea bag • 8 grams of sugar • 40 millilitres of milk. In the morning, Aneel makes 15 cups of tea. Work out the fraction of the tea bags he uses, in its simplest form

the mass of sugar, in grams, he has left.

During the day, Aneel uses all of the milk to make cups of tea. Work out the total number of cups of tea Aneel makes.

Bobby, Carl and Davood share $6875 in the ratio $Bobby:Carl:Davood=6:8:11$. Calculate the amount of money they each receive.

Write $\frac{3^2\times 3^4}{3^6}$ as a power of 3.

Write the value of $2^{-4}$ as a decimal.

Simplify. $(b^5{)}^3$

Simplify. ${\left(\frac{4}{m}\right)}^{-2}$

$30=2\times 3\times 584=2^2\times 3\times 7$ Use this information to find the lowest common multiple (LCM) of 30 and 84.

$$\frac{2}{9}\sqrt{7}\frac{5}{4}\sqrt{16}{2}^3$$ Put a ring around the irrational number in this list.

A company makes glass using silica, soda, lime and magnesia. The table gives information about the proportions used.

Complete the table.

Complete the pie chart to show this information.

The masses of lime and magnesia used are in the ratio $\text{lime}:\text{magnesia}=3:2$. Find the percentage of the total mass of glass that is magnesia.

The company uses $8.25\text{ kg}$ of soda to make some glass. Work out how many kilograms of silica they use.

The company uses the formula $M=2.5\times A\times T$ to find the mass of a sheet of glass. $M$ is the mass in kilograms. $A$ is the area in square metres. $T$ is the thickness in millimetres. Use the formula to calculate the mass of a rectangular sheet of glass that is $1.9\text{ m}$ long, $0.6\text{ m}$ wide and $8\text{ mm}$ thick.

In one year, $130000000$ tonnes of glass were produced worldwide. Write this number in standard form.

The company sets targets to recycle its waste materials. The bar chart shows the target rate and the actual rate for some of its recycling. The target rate for recycling glass was 55%. The actual rate for recycling glass was 70%. Complete the bar chart.

Which materials did the company recycle at more than double their target rate?

Zena records the number of letters she posts on each of 12 days. $$373871065172$$ Write down the mode.

Find the median.

Zena posts 6 parcels. • The lightest parcel has a mass of $4.6\text{ kg}$. • The heaviest parcel has a mass of $6.2\text{ kg}$. • The other 4 parcels have a mean mass of $5.01\text{ kg}$. Calculate the mean mass of the 6 parcels.

Zena pays 105 euros to post a parcel. The exchange rate is $1=0.84\text{ euros}$. Work out the cost in dollars to post the parcel.

The cost to post a box increases from $22.68 to $44. Work out the percentage increase in the cost.

The diagram shows a parcel in the shape of a cuboid. Complete the net of the parcel on the $1{\text{ cm}}^2$ grid. Two faces have been drawn for you.

Find the volume of the parcel.

In the diagram, $PST$ is a straight line. Give the geometrical reason why the lines $PQ$ and $SR$ are parallel.

Write down the mathematical name for the shape $PQRS$.

Find the value of $y$.

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

Describe fully the single transformation that maps triangle $A$ onto triangle $C$.

On the grid, enlarge triangle $A$ by scale factor 3, centre $(4,-5)$.

Complete the table.

Complete this statement. A diagram in this sequence cannot have 51 small squares because ...........................................

An expression for the number of dots in Diagram $n$ is $3n+3$. Which diagram has 249 dots?

Find an expression, in terms of $n$, for the number of lines in Diagram $n$.

Find the number of lines in Diagram 41.

Expand and simplify. $4(x+3)+2(x-1)$

Expand and simplify. $(m-6)(m-4)$

Make $t$ the subject of the formula $p=4t+3$.

In this part, all measurements are in centimetres. The perimeter of this triangle is $49\text{ cm}$. Work out the value of $x$.

The diagram shows a semicircle with diameter $AB$. $O$ is the midpoint of $AB$ and $C$ is a point on the circumference. Calculate the area of triangle $ABC$.

Show that $AB=20.4\text{ cm}$.

Calculate the shaded area.

The diagram shows two right-angled triangles, $PQR$ and $XYZ$. Calculate the difference in the heights $RQ$ and $XY$.

Find the equation of the line of symmetry of the graph.

The point $A$ with coordinates $(6,k)$ lies on the graph. Show that the value of $k$ is 21.

The point $B$ with coordinates $(p,21)$ also lies on the graph. Find the value of $p$.

Write down the $y$-coordinate of the point where the graph crosses the $y$-axis.