Real-Life Graphs (Edexcel IGCSE Maths)

Exam Questions

3 hours35 questions
1a
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1 mark

Simon went for a cycle ride.
He left home at 2 pm.

The travel graph represents part of Simon's cycle ride.

q1-easy-2-20-realtiime-graphs-edexcel-gcse-maths

At 3 pm Simon stopped for a rest.

How many minutes did he rest?

1b
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1 mark

How far was Simon from home at 5 pm?

1c
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2 marks

At 5 pm Simon stopped for 30 minutes.
Then he cycled home at a steady speed.
It took him 1 hour 30 minutes to get home.

Complete the travel graph.

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2a
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1 mark

Jane walked from her home to the ice rink.
The travel graph for Jane's journey to the ice rink is shown below.

q2-easy-2-20-realtiime-graphs-edexcel-gcse-maths

On the way to the ice rink Jane stopped at her friend's house.

How far is it from her friend's house to the ice rink?

2b
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2 marks

Jane was at the ice rink for 1 hour 30 minutes.
She then walked home at a steady speed.
Jane took 2 hours to walk home.

Complete the travel graph for this information.

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3a
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2 marks

Here is part of a distance-time graph for a car's journey.

q3-easy-2-20-realtiime-graphs-edexcel-gcse-maths

Between which two times does the car travel at its greatest speed?
Give a reason for your answer.

3b
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1 mark

Work out this greatest speed.

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4a
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2 marks

The graph shows the depth, d cm, of water in a tank after t seconds.

q4-easy-2-20-realtiime-graphs-edexcel-gcse-maths

Find the gradient of this graph.

4b
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1 mark

Explain what this gradient represents.

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5a
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2 marks

The graph shows the volume of liquid (L litres) in a container at time t seconds.

q5-easy-2-20-realtiime-graphs-edexcel-gcse-maths

Find the gradient of the graph.

5b
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1 mark

Explain what this gradient represents.

5c
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1 mark

The graph intersects the volume axis at L space equals space 4

Explain what this intercept represents.

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6
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3 marks

A ship is sailing in a straight line from its home port.

The distance-time graph shows 4 hours of the journey.

q6-paper-1h-nov-2018-aqa-gcse-mathsWork out the speed of the ship during these 4 hours.

..........................mph

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7a
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3 marks

The graph shows the cost of electricity with Company A.

q3-paper6-nov2020-ocr-gcse-maths

Use the information in the graph to estimate the cost of electricity for a customer who uses 450kwH of electricity.

£ ........................................................ 

7b
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3 marks

Company B charges 14.3 pence per kwH of electricity used.

If Company B’s cost of electricity was plotted on the same axes as Company A’s cost of electricity, which line would be steeper?
Explain how you know.


Company ................ would have the steeper line because ......................................................

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8
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3 marks

The graph shows the speed of a cyclist during 20 seconds of a journey.

q8-paper6-nov2018-ocr-gcse-maths

Find the acceleration of the cyclist

(i)
for the first 4 seconds

......................m/s2 [2]

(ii)
between 4 seconds and 14 seconds.

......................m/s2 [1]

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1a
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1 mark

You can use this conversion graph to change between pounds (£) and dollars ($).

q1a-medium-2-20-realtiime-graphs-edexcel-gcse-maths

Use the conversion graph to change £5 to dollars.

1b
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4 marks

Ella has $200 and £800
Her hotel bill is $600

Ella pays the bill with the $200 and some of the pounds.

Use the conversion graph to work out how many pounds she has left.

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2
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4 marks

Debbie drove from Junction 12 to Junction 13 on a motorway.
The travel graph shows Debbie's journey.

q2-medium-2-20-realtiime-graphs-edexcel-gcse-maths

Ian also drove from Junction 12 to Junction 13 on the same motorway.
He drove at an average speed of 66 km/hour.

Who had the faster average speed, Debbie or Ian?
You must explain your answer.

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3a
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3 marks

At 9 am, Bradley began a journey on his bicycle.

From 9 am to 9.36 am, he cycled at an average speed of 15 km/h
From 9.36 am to 10.45 am, he cycled a further 8 km.

Draw a travel graph to show Bradley's journey.


q3-medium-2-20-realtiime-graphs-edexcel-gcse-maths
3b
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2 marks

From 10.45 am to 11 am, Bradley cycled at an average speed of 18 km/h.

Work out the distance Bradley cycled from 10.45 am to 11 am.

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4a
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2 marks

A coach travels from Dronston to Luscoe.
The travel graph for this journey is shown below.

q4-medium-2-20-realtiime-graphs-edexcel-gcse-maths

Work out the average speed of the coach, in kilometres per hour, for the first 10 minutes of the journey.

4b
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3 marks

The coach stops in Luscoe for 15 minutes.
The coach then returns to Dronston at a constant speed of 42 km/h.

Show this information on the travel graph.

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5a
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1 mark

Bill uses his van to deliver parcels.
For each parcel Bill delivers there is a fixed charge plus £1.00 for each mile.

You can use the graph to find the total cost of having a parcel delivered by Bill.

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How much is the fixed charge?

5b
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3 marks

Ed uses a van to deliver parcels.
For each parcel Ed delivers it costs £1.50 for each mile.
There is no fixed charge.

Compare the cost of having a parcel delivered by Bill with the cost of having a parcel delivered by Ed.

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6
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3 marks

Jim buys a plant of height 20 cm.

The graph shows how the height of the plant changes during the next 4 days.

q17-paper-1h-nov-2020-aqa-gcse-maths

Work out a formula forspace h space in terms of n.

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7
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3 marks

Chris visits a library.

He cycles to the library in half an hour at a speed of 12 miles per hour.
He stays at the library for one hour.
He then cycles home.

The sketch graph represents his visit.

q8-paper-3h-nov-2020-aqa-gcse-maths

Work out the speed, in miles per hour, at which Chris cycles home.

..........................mph

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8a
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1 mark

Here is a velocity-time graph of a motorbike for 25 seconds.

q23-paper1h-june2017-aqa-gcse-maths

After how many seconds was the acceleration zero?

...................................seconds

8b
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2 marks

Work out the distance travelled in the last 15 seconds.

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9
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1 mark

Water is poured into a tank.

The graph shows the number of litres of water in the tank.

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How much water is poured into the tank each minute?
Circle your answer.

1.5 litres 15 litres 30 litres 120 litres

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10a
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1 mark

The graph shows the speed of a train during the first 60 seconds of motion.

q14-paper4-june2019-ocr-gcse-maths

What is the speed of the train after 9 seconds?

................................................... m/s

10b
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1 mark

What does the straight line suggest about the speed of the train over the first 15 seconds?

10c
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5 marks

Work out the average speed of the train, in m/ s, during the 60 seconds.

................................................... m/ s

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11
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4 marks

The graph shows the speed of a cyclist during 20 seconds of a journey.

q8-paper6-nov2018-ocr-gcse-maths

Work out the distance travelled by the cyclist during the 20 seconds.

......................... m

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12
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3 marks

The graph shows Mia’s journey from her home to university.

q2-paper5-june2017-ocr-gcse-maths

Calculate Mia’s average speed for the whole journey.

.................................................. km/h

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13a
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2 marks

The graph shows the speed of a tram as it travels from the library to the town hall.

q8-paper6-june2018-ocr-gcse-maths

Calculate the deceleration of the tram as it approaches the town hall.

........................ m/s2 

13b
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3 marks

Calculate the distance travelled by the tram between the library and the town hall.

........................ m

13c
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4 marks

What was the maximum speed of the tram as it travelled between the library and the
town hall?
Give your answer in kilometres per hour.

..................... km/h

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14
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3 marks

The graph shows the speed of a vehicle during the first 40 seconds of motion.

q19a-paper4-nov2020-ocr-gcse-maths

Calculate the distance travelled by the vehicle during the 40 seconds.

...................................................... m

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1a
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3 marks

Here is a speed-time graph for a car journey.
The journey took 100 seconds.

q1-hard-2-20-realtiime-graphs-edexcel-gcse-maths

The car travelled 1.75km in the 100 seconds.

Work out the value of V.

1b
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2 marks

Describe the acceleration of the car for each part of this journey.

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2a
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1 mark

Jalina left her home at 10 00 to cycle to a park.
On her way to the park, she stopped at a friend’s house and then continued her journey to the park.
Here is the distance-time graph for her journey to the park.

q2-paper1h-june2019-edexcel-igcse-maths

On her journey to the park, did Jalina cycle at a faster speed before or after she stopped at her friend’s house?
Give a reason for your answer.

2b
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2 marks

Jalina stayed at the park for 45 minutes.
She then cycled, without stopping, at a constant speed of 16 km/h from the park back to her home.

Show all this information on the distance-time graph.

2c
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3 marks

Work out Jalina’s average cycling speed, in kilometres per hour, for the complete journey to the park and back.
Do not include the times when she was not cycling in your calculation.
Give your answer correct to 1 decimal place.

.........................km/h

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3
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3 marks

A horse runs in a field.

The speed-time graph represents the first 12 seconds of the run.

q28-paper-2h-nov-2020-aqa-gcse-maths

After how many seconds had the horse run a distance of 75 metres?

.........................seconds

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4a
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1 mark

A ball is thrown vertically upwards.

The graph shows the height of the ball above the ground after it is thrown.

q17-paper-2h-june-2018-aqa-gcse-maths

For how many seconds is the ball at a height of more than 2 metres?

............................s

4b
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1 mark

After how many seconds is the ball at instantaneous rest when it is in the air?

..................................s

4c
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2 marks

Work out the average speed of the ball when it is moving downwards.

........................m/s

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5
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3 marks

Beth ran a 200 metre race.

Here is a graph of the first 8 seconds of her race.

She completed the race at a constant speed of 9 m/s

q24-paper2h-nov2017-aqa-gcse-maths

Amy completed the race in 27 seconds.

Did Beth finish before Amy?
You must show your working.

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6a
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3 marks

Lily goes on a car journey.

For the first 30 minutes her average speed is 40 miles per hour.
She then stops for 15 minutes.
She then completes the journey at an average speed of 60 miles per hour.
The total journey time is 1 hour.

Draw a distance-time graph for her journey.

q8a-paper2h-june2017-aqa-gcse-maths

6b
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1 mark

Write down the average speed for the total journey.

................................... mph

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7
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4 marks

Amina and Ben had a cycle race.

Here is Amina’s speed-time graph from the start of the race.

q24-paper3h-specimen2015-aqa-gcse-maths

The distance of the race was 400 metres.

Ben cycled the 400 metres in 64 seconds.

Who won the race?

You must show your working.

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8a
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1 mark

The graph shows the height above ground of a toy rocket for 10 seconds.

q19-paper-2h-nov-2021-aqa-gcse-maths

For how long is the rocket in the air?

Circle your answer.

10 seconds 9 seconds 6 seconds  4 seconds

          

8b
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3 marks

Using the graph, estimate the speed of the rocket after 6 seconds.

State the units of your answer.

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9
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3 marks

The graph shows how much Molly is paid for working for up to 40 hours.
She receives

a basic rate of pay for the first 35 hours worked
a higher rate of pay for the next 5 hours worked.

q12-paper3h-nov2019-aqa-gcse-maths

Work out the difference between the higher rate of pay and the basic rate of pay.
Give your answer in £ per hour.

£.....................................per hour

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10a
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2 marks

Izzy runs an 80-metre race in 14 seconds.

   During the first 6 seconds her speed increases at a constant rate.
   During the last 8 seconds her speed increases at a different constant rate.
   Her speed at 14 seconds is 2 m/s more than her speed at 6 seconds.

Here is a sketch of her speed-time graph.

q28-paper-2h-nov-2018-aqa-gcse-maths

Work out her acceleration during the last 8 seconds.

State the units of your answer.

10b
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4 marks

When Izzy finishes the 80-metre race, her speed is v space straight m divided by straight s

Work out the value of v.

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11a
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1 mark

The graph shows the speed, v metres per second (m/s), of a car at time t seconds.

q15-paper4-june2017-ocr-gcse-maths

Find the speed of the car at t = 7.

.................................................... m/s

11b
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5 marks

It is claimed that the car has accelerated from 0 to 60 miles per hour in the first 10 seconds.

Does the graph support this claim? Show your reasoning.
Use 1 mile = 1.6 kilometres.

11c
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3 marks

Use the graph to estimate the acceleration at t = 7.

...................................................m/s2

11d
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1 mark

Georgina says that the graph shows that the speed of the car will continue to increase after 10 seconds.

Make one comment to show that this statement is incorrect.

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12a
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2 marks

The graph shows information about the speed of a vehicle during the final 50 seconds of a journey.
At the start of the 50 seconds the speed is k metres per second.
The distance travelled during the 50 seconds is 1.35 kilometres.

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Work out the average speed of the vehicle during the 50 seconds.
Give your answer in metres per second.

................... m/s

12b
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5 marks

Work out the value of k.

k = .......................

12c
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3 marks
(i)
Calculate the gradient of the graph in the final 10 seconds of the journey.

[1]

(ii)
Describe what this gradient represents.

[2]

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13a
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3 marks

A toy car is placed on the floor of a sports hall.

It moves in a straight line starting from rest.
It travels with constant acceleration for 4 seconds reaching a velocity of 5 m/s.
It then slows down with constant deceleration of 1 m/s2 for 2 seconds.
It then hits a wall and stops.

Draw a velocity-time graph for the toy car.

q11a-paper5-spec2015-ocr-gcse-maths

13b
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3 marks

Work out the total distance travelled by the toy car.

....................... m

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