Cambridge IGCSE Mathematics 0580 · Extended · Syllabus 2025-2027

Rate Worked ExamplesIGCSE Maths 0580

Exam-style worked examples on speed, density and rates of flow, plus converting between rate units. The average-speed question is included because it is the one most often answered wrongly. Diagram questions cover pressure, filling a cylindrical tank, and reading tap and drain rates from a graph.

This page has 10 exam-style IGCSE Maths 0580 rate worked examples — 1 Core, 7 Extended and 2 Challenge, 3 with diagrams. Each one shows the full method step by step, the final answer in the form a marker expects, and an examiner tip on where marks are commonly lost.

Example 1CoreSpeed[3 marks]

Speed, distance and time

A train travels $240\text{ km}$ in $3$ hours.

(a) Find its average speed. (b) At the same speed, find how long it takes to travel $340\text{ km}$ . Give your answer in hours and minutes.

Example 2ExtendedAverage speed[4 marks]

Average speed over two stages

A cyclist rides $60\text{ km}$ at $30\text{ km/h}$ , then a further $60\text{ km}$ at $60\text{ km/h}$ .

Calculate the average speed for the whole journey.

Example 3ExtendedRate conversion[3 marks]

Converting between rate units

(a) Convert $72\text{ km/h}$ into $\text{m/s}$ . (b) Convert $15\text{ m/s}$ into $\text{km/h}$ .

Example 4ChallengeDensity[5 marks]

Density of an alloy

An alloy is made by combining $400\text{ g}$ of metal A, of density $8\text{ g/cm}^3$ , with $300\text{ g}$ of metal B, of density $3\text{ g/cm}^3$ .

Calculate the density of the alloy, correct to $3$ significant figures.

Example 5ExtendedRate of flow[4 marks]

Rate of flow

A tank holds $540$ litres. A tap fills it at $18$ litres per minute.

(a) Find how long the tap takes to fill the empty tank. (b) A second tap, filling at $12$ litres per minute, is opened at the same time. Find how long the two taps together take to fill the empty tank.

Example 6ExtendedRate in context[4 marks]

Rate in a costing context

A printer produces $45$ pages per minute. Ink costs $0.012 per page.

(a) Find the cost of ink for $1$ hour of continuous printing. (b) The printer runs for $2$ hours $20$ minutes. Find the number of pages printed.

Example 7ExtendedNon-calculator — pressure on different faces[4 marks]

Pressure of a crate on different faces

The diagram shows a crate in the shape of a cuboid measuring $0.5$ m by $0.4$ m by $0.2$ m. The crate has a weight of $480$ N.

$\text{pressure} = \frac{\text{force}}{\text{area}}$

The crate can rest on the ground on any of its faces.

(a) Find the greatest possible pressure the crate can exert on the ground. Give the units of your answer.

(b) Find the least possible pressure.

(c) A second identical crate is placed exactly on top of the first, which rests on its smallest face. Find the pressure on the ground now.

NOT TO SCALE

Example 8ExtendedCalculator — flow rate into a part-filled cylinder[6 marks]

Filling a part-full cylindrical tank

The diagram shows a tank in the shape of a cylinder with radius $0.6$ m and height $1.5$ m. The tank stands on level ground and already contains water to a depth of $0.4$ m.

Water flows into the tank from a pipe at a constant rate of $12$ litres per minute.

(a) Calculate the time it takes to fill the tank completely. Give your answer in hours and minutes, correct to the nearest minute. $[1\text{ m}^3 = 1000\text{ litres}]$

(b) Calculate the rate, in centimetres per minute, at which the water level rises.

NOT TO SCALE

1
(a) Only the empty part needs filling. Its depth is $1.5 - 0.4 = 1.1$ m. Use the volume of a cylinder, $\pi r^2 h$ .
$V = \pi \times 0.6^2 \times 1.1 = 1.24407\ldots\text{ m}^3$
2
Convert to litres so that the units match the flow rate.
$1.24407\ldots \times 1000 = 1244.07\ldots\text{ litres}$
3
Time = volume ÷ rate of flow.
$\frac{1244.07\ldots}{12} = 103.67\ldots\text{ minutes}$
4
Take off $60$ minutes to make $1$ hour and round the remainder to the nearest minute.
$103.67\ldots - 60 = 43.67\ldots \;\Rightarrow\; 1\text{ hour } 44\text{ minutes}$
5
(b) Work in centimetres: $12$ litres $= 12\,000\text{ cm}^3$ and the radius is $60$ cm. Each minute this volume forms a cylindrical layer of water with area $\pi \times 60^2$ .
$\text{rise per minute} = \frac{12\,000}{\pi \times 60^2} = 1.0610\ldots$
6
Round to $3$ significant figures. Check: $110\text{ cm} \div 1.0610\ldots = 103.67\ldots$ minutes, which matches part (a). ✓
$1.06\text{ cm per minute}$

Answer

(a) $1$ hour $44$ minutes (b) $1.06$ cm per minute

Examiner tip

Two common errors are using the full height of $1.5$ m (ignoring the water already there) and mixing units — $\text{m}^3$ divided by litres per minute gives nonsense. Convert $1\text{ m}^3 = 1000$ litres, and $1$ litre $= 1000\text{ cm}^3$ . On a similar flow-rate question, the March 2026 examiner report noted that some candidates rounded the time in minutes too early before converting, which made the final answer inaccurate. Keep full calculator accuracy until the final answer.

Example 9ChallengeRates as gradients of a volume–time graph[7 marks]

Reading tap and drain rates from a graph

A tank contains some water. At time $0$ , tap $A$ is turned on. After $10$ minutes, tap $B$ is also turned on. After $20$ minutes, a drain is opened while both taps stay on. The taps and the drain each work at a constant rate.

The graph shows the volume of water in the tank for the first $30$ minutes.

(a) Find the rate of flow of tap $A$ , in litres per minute.

(b) Find the rate of flow of tap $B$ .

(c) Show that the drain removes water at $50$ litres per minute.

(d) At $30$ minutes, both taps are turned off and the drain stays open. Find the time at which the tank becomes empty, and describe the line you would add to complete the graph.

1
(a) A rate of flow is the gradient of a volume–time graph. From $0$ to $10$ minutes only tap $A$ is on. Read the volumes $40$ litres and $280$ litres.
$\text{rate of } A = \frac{280 - 40}{10} = 24\text{ litres per minute}$
2
(b) From $10$ to $20$ minutes both taps are on, so the gradient is the combined rate.
$\frac{680 - 280}{10} = 40\text{ litres per minute}$
3
Tap $B$ supplies the difference.
$\text{rate of } B = 40 - 24 = 16\text{ litres per minute}$
4
(c) From $20$ to $30$ minutes the volume falls, so the net rate is negative.
$\frac{580 - 680}{10} = -10\text{ litres per minute}$
5
The taps still add $40$ litres per minute, yet the tank loses $10$ litres per minute overall. So the drain removes $40 + 10$ .
$40 - \text{drain} = -10 \;\Rightarrow\; \text{drain} = 50\text{ litres per minute}$
6
(d) With the taps off, only the drain acts on the $580$ litres left.
$\frac{580}{50} = 11.6\text{ minutes} \;\Rightarrow\; 30 + 11.6 = 41.6\text{ minutes}$
7
$0.6$ of a minute is $0.6 \times 60 = 36$ seconds. On the graph, draw a straight line from $(30, 580)$ to $(41.6, 0)$ — its gradient is $-50$ . The time axis would need extending beyond $40$ minutes.

Answer

(a) $24$ litres/min (b) $16$ litres/min (c) $40 - d = -10$ , so $d = 50$ litres/min (d) $41.6$ minutes ( $41$ min $36$ s); a straight line from $(30, 580)$ to $(41.6, 0)$

Examiner tip

In (b), $40$ litres per minute is the rate of both taps together — giving $40$ as tap $B$ 's rate is a common error. In (c), a common slip is to give $10$ as the drain's rate, forgetting that the taps are still running. Read values from the graph with care: $280$ and $680$ lie on minor grid lines, not on the labelled ones.

Example 10ExtendedCalculator — capacity ÷ flow rate, answer in minutes and seconds[3 marks]

Time to drain a cylindrical tank, in minutes and seconds

A water tank is a cylinder with radius $45$ cm. The water in the tank is $80$ cm deep.

The water drains out of the tank at a constant rate of $36$ litres per minute.

Calculate the time it takes for the tank to empty. Give your answer in minutes and seconds, correct to the nearest second. $[1\text{ litre} = 1000\text{ cm}^3]$

These worked examples are written by Tutopiya to cover the same syllabus content as the official Cambridge IGCSE 0580 specification (2025-2027). They are exam-style questions, not reproductions of past paper questions.

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Rate Worked ExamplesIGCSE Maths 0580

Example 1CoreSpeed[3 marks]

Speed, distance and time

A train travels $240\text{ km}$ in $3$ hours.

(a) Find its average speed. (b) At the same speed, find how long it takes to travel $340\text{ km}$ . Give your answer in hours and minutes.

Example 2ExtendedAverage speed[4 marks]

Average speed over two stages

A cyclist rides $60\text{ km}$ at $30\text{ km/h}$ , then a further $60\text{ km}$ at $60\text{ km/h}$ .

Calculate the average speed for the whole journey.

Example 3ExtendedRate conversion[3 marks]

Converting between rate units

(a) Convert $72\text{ km/h}$ into $\text{m/s}$ . (b) Convert $15\text{ m/s}$ into $\text{km/h}$ .

Example 4ChallengeDensity[5 marks]

Density of an alloy

An alloy is made by combining $400\text{ g}$ of metal A, of density $8\text{ g/cm}^3$ , with $300\text{ g}$ of metal B, of density $3\text{ g/cm}^3$ .

Calculate the density of the alloy, correct to $3$ significant figures.

Example 5ExtendedRate of flow[4 marks]

Rate of flow

A tank holds $540$ litres. A tap fills it at $18$ litres per minute.

Example 6ExtendedRate in context[4 marks]

Rate in a costing context

A printer produces $45$ pages per minute. Ink costs $0.012 per page.

(a) Find the cost of ink for $1$ hour of continuous printing. (b) The printer runs for $2$ hours $20$ minutes. Find the number of pages printed.

Example 7ExtendedNon-calculator — pressure on different faces[4 marks]

Pressure of a crate on different faces

The diagram shows a crate in the shape of a cuboid measuring $0.5$ m by $0.4$ m by $0.2$ m. The crate has a weight of $480$ N.

$\text{pressure} = \frac{\text{force}}{\text{area}}$

The crate can rest on the ground on any of its faces.

(a) Find the greatest possible pressure the crate can exert on the ground. Give the units of your answer.

(b) Find the least possible pressure.

(c) A second identical crate is placed exactly on top of the first, which rests on its smallest face. Find the pressure on the ground now.

NOT TO SCALE

Example 8ExtendedCalculator — flow rate into a part-filled cylinder[6 marks]

Filling a part-full cylindrical tank

The diagram shows a tank in the shape of a cylinder with radius $0.6$ m and height $1.5$ m. The tank stands on level ground and already contains water to a depth of $0.4$ m.

Water flows into the tank from a pipe at a constant rate of $12$ litres per minute.

(a) Calculate the time it takes to fill the tank completely. Give your answer in hours and minutes, correct to the nearest minute. $[1\text{ m}^3 = 1000\text{ litres}]$

(b) Calculate the rate, in centimetres per minute, at which the water level rises.

NOT TO SCALE

1
(a) Only the empty part needs filling. Its depth is $1.5 - 0.4 = 1.1$ m. Use the volume of a cylinder, $\pi r^2 h$ .
$V = \pi \times 0.6^2 \times 1.1 = 1.24407\ldots\text{ m}^3$
2
Convert to litres so that the units match the flow rate.
$1.24407\ldots \times 1000 = 1244.07\ldots\text{ litres}$
3
Time = volume ÷ rate of flow.
$\frac{1244.07\ldots}{12} = 103.67\ldots\text{ minutes}$
4
Take off $60$ minutes to make $1$ hour and round the remainder to the nearest minute.
$103.67\ldots - 60 = 43.67\ldots \;\Rightarrow\; 1\text{ hour } 44\text{ minutes}$
5
(b) Work in centimetres: $12$ litres $= 12\,000\text{ cm}^3$ and the radius is $60$ cm. Each minute this volume forms a cylindrical layer of water with area $\pi \times 60^2$ .
$\text{rise per minute} = \frac{12\,000}{\pi \times 60^2} = 1.0610\ldots$
6
Round to $3$ significant figures. Check: $110\text{ cm} \div 1.0610\ldots = 103.67\ldots$ minutes, which matches part (a). ✓
$1.06\text{ cm per minute}$

Answer

(a) $1$ hour $44$ minutes (b) $1.06$ cm per minute

Examiner tip

Example 9ChallengeRates as gradients of a volume–time graph[7 marks]

Reading tap and drain rates from a graph

The graph shows the volume of water in the tank for the first $30$ minutes.

(a) Find the rate of flow of tap $A$ , in litres per minute.

(b) Find the rate of flow of tap $B$ .

(c) Show that the drain removes water at $50$ litres per minute.

(d) At $30$ minutes, both taps are turned off and the drain stays open. Find the time at which the tank becomes empty, and describe the line you would add to complete the graph.

1
(a) A rate of flow is the gradient of a volume–time graph. From $0$ to $10$ minutes only tap $A$ is on. Read the volumes $40$ litres and $280$ litres.
$\text{rate of } A = \frac{280 - 40}{10} = 24\text{ litres per minute}$
2
(b) From $10$ to $20$ minutes both taps are on, so the gradient is the combined rate.
$\frac{680 - 280}{10} = 40\text{ litres per minute}$
3
Tap $B$ supplies the difference.
$\text{rate of } B = 40 - 24 = 16\text{ litres per minute}$
4
(c) From $20$ to $30$ minutes the volume falls, so the net rate is negative.
$\frac{580 - 680}{10} = -10\text{ litres per minute}$
5
The taps still add $40$ litres per minute, yet the tank loses $10$ litres per minute overall. So the drain removes $40 + 10$ .
$40 - \text{drain} = -10 \;\Rightarrow\; \text{drain} = 50\text{ litres per minute}$
6
(d) With the taps off, only the drain acts on the $580$ litres left.
$\frac{580}{50} = 11.6\text{ minutes} \;\Rightarrow\; 30 + 11.6 = 41.6\text{ minutes}$
7
$0.6$ of a minute is $0.6 \times 60 = 36$ seconds. On the graph, draw a straight line from $(30, 580)$ to $(41.6, 0)$ — its gradient is $-50$ . The time axis would need extending beyond $40$ minutes.

Answer

(a) $24$ litres/min (b) $16$ litres/min (c) $40 - d = -10$ , so $d = 50$ litres/min (d) $41.6$ minutes ( $41$ min $36$ s); a straight line from $(30, 580)$ to $(41.6, 0)$

Examiner tip

Example 10ExtendedCalculator — capacity ÷ flow rate, answer in minutes and seconds[3 marks]

Time to drain a cylindrical tank, in minutes and seconds

A water tank is a cylinder with radius $45$ cm. The water in the tank is $80$ cm deep.

The water drains out of the tank at a constant rate of $36$ litres per minute.

Calculate the time it takes for the tank to empty. Give your answer in minutes and seconds, correct to the nearest second. $[1\text{ litre} = 1000\text{ cm}^3]$

Rate Worked ExamplesIGCSE Maths 0580

Speed, distance and time

Average speed over two stages

Converting between rate units

Density of an alloy

Rate of flow

Rate in a costing context

Pressure of a crate on different faces

Filling a part-full cylindrical tank

Reading tap and drain rates from a graph

Time to drain a cylindrical tank, in minutes and seconds

More IGCSE Maths 0580 worked examples

Number

Algebra

Functions

Coordinate Geometry

Geometry

Vectors and Transfomations

Mensuration

Trigonometry

Sets

Probability

Statistics

Calculator Skills

Rate Worked ExamplesIGCSE Maths 0580

Speed, distance and time

Average speed over two stages

Converting between rate units

Density of an alloy

Rate of flow

Rate in a costing context

Pressure of a crate on different faces

Filling a part-full cylindrical tank

Reading tap and drain rates from a graph

Time to drain a cylindrical tank, in minutes and seconds

More IGCSE Maths 0580 worked examples

Number

Algebra

Functions

Coordinate Geometry

Geometry

Vectors and Transfomations

Mensuration

Trigonometry

Sets

Probability

Statistics

Calculator Skills