Sets

www.Q8Maths.com 1
1) June 2010 V1

12 Q = {2, 4, 6, 8, 10} and R = {5, 10, 15, 20}.

15 ∈ P, n( P) = 1 and P ∩ Q = Ø.

Label each set and complete the Venn diagram to show this information.

[3]

2) June 2010 V2
7
A B

The shaded area in the diagram shows the set ( A ∩ C ) ∩ B'.

Write down the set shown by the shaded area in each diagram below.

A B A B

C C

[2]

www.Q8Maths.com 2
3) June 2010 V3

7 Shade the required regions in the Venn diagrams below.

A B A B

C C

[2]

www.Q8Maths.com 3
4) November 2010 V1
22 In a survey of 60 cars, 25 use diesel, 20 use liquid hydrogen and 22 use electricity.

No cars use all three fuels and 14 cars use both diesel and electricity.

There are 8 cars which use diesel only, 15 cars which use liquid hydrogen only and 6 cars which use
electricity only.

In the Venn diagram below

= {cars in the survey},

D = {cars which use diesel},
L = {cars which use liquid hydrogen},
E = {cars which use electricity}.

D E

8 ........ 6

........

........ ........

15 ........
L

(a) Use the information above to fill in the five missing numbers in the Venn diagram. [4]

(b) Find the number of cars which use diesel but not electricity.

Answer(b) [1]

(c) Find n(D'∩ (E ∪ L)).

Answer(c) [1]

www.Q8Maths.com 4
5) November 2010 V2

2 In a group of 30 students, 18 have visited Australia, 15 have visited Botswana and 5 have not visited
either country.

Work out the number of students who have visited Australia but not Botswana.

Answer [2]

6) November 2010 V3

4 Shade the required region on each Venn diagram.

P Q

A B

A ∩ B' (P ∪ Q) ∩ R'
[2]

www.Q8Maths.com 5
7) November 2010 V3

11 In a group of 24 students, 21 like football and 15 like swimming.

One student does not like football and does not like swimming.
Find the number of students who like both football and swimming.

Answer [2]

8) June 2011 V1

2 Shade the required region on each Venn diagram.

A B A B

A ∪ B' (A ∩ B)'
[2]

www.Q8Maths.com 6
9) June 2011 V1

15 A teacher asks 36 students which musical instruments they play.

P = {students who play the piano}

G = {students who play the guitar}
D = {students who play the drums}

The Venn diagram shows the results.

P G
x 2 8
1
5 4

7
5 D

(a) Find the value of x.

Answer(a) x = [1]

(b) A student is chosen at random.

Find the probability that this student

(i) plays the drums but not the guitar,

Answer(b)(i) [1]

(ii) plays only 2 different instruments.

Answer(b)(ii) [1]

(c) A student is chosen at random from those who play the guitar.

Find the probability that this student plays no other instrument.

Answer(c) [1]

www.Q8Maths.com 7
10) June 2011 V3

3 (a)
A B

Shade the region A ∩ B'. [1]

(b)
A B
7 4 5
3

This Venn diagram shows the number of elements in each region.

Write down the value of n ( A ∪ B' ).

Answer(b) n ( A ∪ B' ) = [1]

www.Q8Maths.com 8
11) November 2011 V3

17
R F

In the Venn diagram, = {students in a survey}, R = {students who like rugby} and
F = {students who like football}.

n( ) = 20 n(R ∪ F) = 17 n( R) = 13 n(F) = 11

(a) Find

(i) n(R ∩ F),

Answer(a)(i) [1]

(ii) n(RV∩ F=).

Answer(a)(ii) [1]

(b) A student who likes rugby is chosen at random.

Find the probability that this student also likes football.

Answer(b) [1]

www.Q8Maths.com 9
12) November 2012 V3

9 Shade the required region in each of the Venn diagrams.

P Q

A B

A' (P ∩ R ) ∪ Q

[2]

13) June 2013 V1

12
2

1 3 5

R F

11 students are asked if they like rugby ( R) and if they like football (F ).
The Venn diagram shows the results.

(a) A student is chosen at random.

What is the probability that the student likes rugby and football?

Answer(a) ............................................... [1]

(b) On the Venn diagram shade the region R' ∩ F' . [1]

www.Q8Maths.com 10
14) June 2013 V2

1 Shade the required region on each Venn diagram.

A B A B

A' ∪ B A' ∩ B'

[2]

www.Q8Maths.com 11
15) June 2013 V3

15
A B

12 – x
13 14

x
20 – x 15 – x

8 y
C

The Venn diagram shows the number of elements in sets A, B and C.

(a) n(A ∪ B ∪ C ) = 74

Find x.

Answer(a) x = ............................................... [2]

(b) n( ) = 100

Find y.

Answer(b) y = ............................................... [1]

(c) Find the value of n((A ∪ B )' ∩ C ).

Answer(c) ............................................... [1]

www.Q8Maths.com 12
16) November 2013 V1

22
R T

15 5 11

19

The Venn diagram shows the number of red cars and the number of two-door cars in a car park.
There is a total of 50 cars in the car park.
R = {red cars} and T = {two-door cars}.

(a) A car is chosen at random.

Write down the probability that

(i) it is red and it is a two-door car,

Answer(a)(i) ............................................... [1]

(ii) it is not red and it is a two-door car.

Answer(a)(ii) ............................................... [1]

(b) A two-door car is chosen at random.

Write down the probability that it is not red.

Answer(b) ............................................... [1]

(c) Two cars are chosen at random.

Find the probability that they are both red.

Answer(c) ............................................... [2]

(d) On the Venn diagram, shade the region R ∪ T '. [1]

www.Q8Maths.com 13
17) June 2014 V3

17 = { x : 1 Y x Y 10, where x is an integer}

A = {square numbers}

B = {1, 2, 3, 4, 5, 6}

(a) Write all the elements of in their correct place in the Venn diagram.

A B

[2]

(b) List the elements of ( A ∪ B )' .

Answer(b) ................................................ [1]

(c) Find n( A ∩ B' ).

Answer(c) ................................................ [1]

www.Q8Maths.com 14
18) November 2014 V2

4 Shade the region required in each Venn diagram.

A B A B

(A ∪ B)' A' ∩ B
[2]

19) November 2014 V3

15 The lights and brakes of 30 bicycles are tested.
The table shows the results.

Lights Brakes

Fail test 3 9
Pass test 27 21

The lights and brakes both failed on one bicycle only.

= {30 bicycles}
Complete the Venn diagrams.

(a)

ts f ail Br akes
Li gh fa i l

.......... .......... .......... ..........

[2]

(b)

ht s pas s Br ak es p
Lig ass

.......... .......... .......... ..........

[2]

www.Q8Maths.com 15
20) June 2015 V2

20 (a) You may use this Venn diagram to help you answer part (a).

 = {x : 1  x  12, x is an integer}
M = {odd numbers}
N = {multiples of 3}


M N

(i) Find n(N).

Answer(a)(i) ................................................ [1]

(ii) Write down the set M N .

Answer(a) (ii) M N = { ............................................... } [1]

(iii) Write down a set P where P 1 M .

Answer(a)(iii) P = { ............................................... } [1]

(b) Shade (A C) B ' in the Venn diagram below.


A B

[1]

www.Q8Maths.com 16
21) June 2015 V3
16 (a) In this part, you may use this Venn diagram to help you answer the questions.

F S

In a class of 30 students, 25 study French ( F), 18 study Spanish ( S ).

One student does not study French or Spanish.

(i) Find the number of students who study French and Spanish.

Answer(a)(i) ................................................ [2]

(ii) One of the 30 students is chosen at random.

Find the probability that this student studies French but not Spanish.

Answer(a)(ii) ................................................ [1]

(iii) A student who does not study Spanish is chosen at random.

Find the probability that this student studies French.

Answer(a)(iii) ................................................ [1]

(b)

P Q

On this Venn diagram, shade the region R (P Q )′. [1]

www.Q8Maths.com 17
22) November 2015 V1

2

A B

In the Venn diagram shade the region A B '. [1]

23) November 2015 V2

6 The Venn diagram shows the number of students who study French ( F), Spanish ( S) and Arabic (A).

F S

7 4 5

1
2 3

8
0
A

(a) Find n( A (F S )).

Answer(a) .................................................. [1]

(b) On the Venn diagram, shade the region F l S. [1]

www.Q8Maths.com 18
24) November 2015 V3

12

P Q

3 5 10

The Venn diagram shows the number of elements in each set.

(a) Find n (P ' Q).

Answer(a) ................................................ [1]

(b) Complete the statement n (..................................) = 17. [1]

25) June 2016 V1

22

A B
3 7 12

The Venn diagram shows the numbers of elements in each region.

(a) Find n(A B l) .

................................................... [1]

(b) An element is chosen at random.

Find the probability that this element is in set B .

................................................... [1]

(c) An element is chosen at random from set A.

Find the probability that this element is also a member of set B .

...................................................

[1]

(d) On the Venn diagram, shade the region (A B ) l. [1]

www.Q8Maths.com 19
26) June 2016 V3

14 (a)  = {x: 2 G x G 16, x is an integer}

M = {even numbers}
P = {prime numbers}

(i) Find n( M ).

..................................................

[1]

(ii) Write down the set ( P , M )′.

(P , M )′ = { ................................................ } [1]

(b) On the Venn diagram, shade A + B ′.


A B

[1]

www.Q8Maths.com 20
27) November 2016 V1

22 (a) n() = 10, n(A ) = 7, n( B) = 6, n (A , B )l = 1.


A B

..................................................

(i) Complete the Venn diagram by writing the number of elements in each subset. [2]

(ii) An element of  is chosen at random.

Find the probability that this element is an element of Al + B .

................................................. [1]

(b) On the Venn diagram below, shade the region C l + Dl.


C D

[1]

www.Q8Maths.com 21
28) November 2016 V2

15


F M
8 2 4
3
1 0
2 2
R ..................................................

The Venn diagram shows the number of people who like films (F), music (M) and reading (R).

(a) Find

(i) n (M) ,

................................................. [1]
(ii) n (R , M ) .

................................................. [1]

(b) A person is chosen at random from the people who like films.

Write down the probability that this person also likes music.

................................................. [1]

(c) On the Venn diagram, shade M l + (F , R) . [1]

www.Q8Maths.com 22
29) November 2016 V3

5
20 (a)  = % 7, 9.3, r, , 2 8 /
9
A = {integers}
B = {irrational numbers}

Write all the elements of  in their correct place on the Venn diagram.
..................................................


A B

.
[2]

(b) Shade the region in each of the Venn diagrams below.


E F


C D

Cl, D E + F l+ G
[2]

www.Q8Maths.com 23
30) June 2018 V2

23 The Venn diagram shows information about the number of elements in sets A, B and .

A B

20 – x x 8–x

(a) n (A , B) = 23

Find the value of x.

x = ................................................ [3]

(b) An element is chosen at random from .

Find the probability that this element is in (A , B)l .

................................................. [2]

www.Q8Maths.com 24
Simple and Compound
Interest

www.Q8Maths.com 1
1) November 2010 V1
9 Johan invested $600 for 3 years at 4% per year compound interest.

Calculate the final amount he had after three years.

Answer $ [3]

www.Q8Maths.com 2
2) November 2010 V3

10 Nikhil invests $200 for 2 years at 4% per year compound interest.

Calculate the exact amount Nikhil has after 2 years.

Answer $ [2]

3) June 2011 V3

9 Eva invests $120 at a rate of 3% per year compound interest.

Calculate the total amount Eva has after 2 years.

Give your answer correct to 2 decimal places.

Answer $ [3]

www.Q8Maths.com 3
4) November 2011 V3

6 Pedro invested $800 at a rate of 5% per year compound interest.

Calculate the total amount he has after 2 years.

Answer $ [2]

5) June 2012 V1
1
10 Shania invests $750 at a rate of 2 2 % per year simple interest.
Calculate the total amount Shania has after 5 years.

Answer $ [3]

www.Q8Maths.com 4
6) June 2012 V3

2 Hans invests $750 for 8 years at a rate of 2% per year simple interest.

Calculate the interest Hans receives.

Answer $ [2]

7) June 2012 V3
11 Boris invests $280 for 2 years at a rate of 3% per year compound interest.

Calculate the interest Boris receives at the end of the 2 years.

Give your answer correct to 2 decimal places.

Answer $ [4]

www.Q8Maths.com 5
8) November 2012 V1

8 Acri invested $500 for 3 years at a rate of 2.8% per year compound interest.

Calculate the final amount he has after 3 years.

Answer $ [3]

9) November 2012 V3

1 Samantha invests $600 at a rate of 2% per year simple interest.

Calculate the interest Samantha earns in 8 years.

Answer $ [2]

www.Q8Maths.com 6
10) June 2013 V1

14 Bruce invested $420 at a rate of 4% per year compound interest.

Calculate the total amount Bruce has after 2 years.

Give your answer correct to 2 decimal places.

Answer $ ...................................... [3]

11) June 2013 V2

13 Carol invests $6250 at a rate of 2% per year compound interest.

Calculate the total amount Carol has after 3 years.

Answer $ ............................................... [3]

www.Q8Maths.com 7
12) November 2013 V1

8 Emily invests $x at a rate of 3% per year simple interest.

After 5 years she has $20.10 interest.

Find the value of x.

Answer x = ............................................... [3]

13) November 2014 V1

7 The population of Dubai at the end of 2012 was 2.1 million.

This was predicted to increase at a rate of 6% each year.

Calculate the predicted population of Dubai at the end of 2015.

Answer .................................... million [3]

www.Q8Maths.com 8
14) November 2014 V2

17 Alex invests $200 for 2 years at a rate of 2% per year simple interest.
Chris invests $200 for 2 years at a rate of 2% per year compound interest.

Calculate how much more interest Chris has than Alex.

Answer $ ................................................. [4]

15) November 2014 V3

10 Maryah borrows $12 000 to start a business.

The loan is for 3 years at a rate of 5% per year compound interest.
The loan has to be paid back at the end of the 3 years.

Calculate the total amount to be paid back.

Answer $ ................................................. [3]

www.Q8Maths.com 9
16) June 2015 V1

16 Georg invests $5000 for 14 years at a rate of 2% per year compound interest.

Calculate the interest he receives.

Give your answer correct to the nearest dollar.

Answer $ ................................................ [4]

17) November 2015 V1

16 Hazel invests $1800 for 7 years at a rate of 1.5% per year compound interest.

Calculate how much interest she will receive after the 7 years.
Give your answer correct to the nearest dollar.

Answer $ ................................................ [4]

www.Q8Maths.com 10
21) June 2017 V3

24 Marcel invests $2500 for 3 years at a rate of 1.6% per year simple interest.
Jacques invests $2000 for 3 years at a rate of x% per year compound interest.
At the end of the 3 years Marcel and Jacques receive the same amount of interest.

Calculate the value of x correct to 3 significant figures.

x = ............................................[5]

www.Q8Maths.com 11
18) November 2015 V2

8 Robert buys a car for $8000.

At the end of each year the value of the car has decreased by 10% of its value at the beginning of that year.

Calculate the value of the car at the end of 7 years.

Answer $ ................................................. [2]

www.Q8Maths.com 12
19) March 2015 V2

12 The population of Olton is decreasing at a rate of 3% per year.

In 2013, the population was 50 000.

Calculate the population after 4 years.

Give your answer correct to the nearest hundred.

Answer ................................................ [3]

www.Q8Maths.com 13
20) June 2016 V2

19 It is estimated that the world’s population is growing at a rate of 1.14% per year.
On January 1st 2014 the population was 7.23 billion.

(a) Find the expected population on January 1st 2020.

........................................billion [2]

(b) Find the year when the population is expected to reach 10 billion.

.................................................. [2]

www.Q8Maths.com 14
21) June 2016 V3

19 At the start of an experiment there are 20 000 bacteria .

The number of bacteria increases at a rate of 30% per hour.

(a) Work out the number of bacteria after 4 hours.

.................................................. [2]

(b) After how many whole hours, from the start of the experiment, will the number of bacteria be greater
than one million?

.........................................
hours [2]

www.Q8Maths.com 15
 Speed, Distance
and Time
Speed, Distance
and Time

www.Q8Maths.com 1
1) June 2010 V1

4 A person in a car, travelling at 108 kilometres per hour, takes 1 second to go past a building on the
side of the road.

Calculate the length of the building in metres.

Answer m [2]

2) June 2010 V1

9 A cyclist left Melbourne on Wednesday 21 May at 09 45 to travel to Sydney.

The journey took 97 hours.

Write down the day, date and time that the cyclist arrived in Sydney.

Answer Day Date Time [3]

www.Q8Maths.com 2
3) June 2010 V3

4 The maximum speed of a car is 252 km/h.

Change this speed into metres per second.

Answer m/s [2]

www.Q8Maths.com 3
4) November 2010 V3

2 A plane took 1 hour and 10 minutes to fly from Riyadh to Jeddah.

The plane arrived in Jeddah at 23 05.
At what time did the plane depart from Riyadh?

Answer [1]

5) November 2010 V3

14 Priyantha completes a 10 km run in 55 minutes 20 seconds.

Calculate Priyantha’s average speed in km/h.

Answer km/h [3]

www.Q8Maths.com 4
6) June 2011 V1

12 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reach Paris.

(a) Calculate the time the next day when the train arrives in Paris.

Answer(a) [1]

(b) The distance from Barcelona to Paris is 827 km.

Calculate the average speed of the train in kilometres per hour.

Answer(b) km/h [3]

www.Q8Maths.com 5
7) June 2011 V2

10 The table shows the opening and closing times of a café.

Mon Tue Wed Thu Fri Sat Sun

Opening time 0600 0600 0600 0600 0600 ( a) 0800

Closing time 2200 2200 2200 2200 2200 2200 1300

(a) The café is open for a total of 100 hours each week.
Work out the opening time on Saturday.

Answer(a) [2]

(b) The owner decides to close the café at a later time on Sunday. This increases the total number
of hours the café is open by 4%.
Work out the new closing time on Sunday.

Answer(b) [1]

www.Q8Maths.com 6
8) November 2011 V2

1 A bus leaves a port every 15 minutes, starting at 09 00.

The last bus leaves at 17 30.

How many times does a bus leave the port during one day?

Answer [2]

9) November 2011 V2
8 A cruise ship travels at 22 knots.

[1 knot is 1.852 kilometres per hour.]

Convert this speed into metres per second.

Answer m/s [3]

www.Q8Maths.com 7
10) November 2012 V2

9 A shop is open during the following hours.

Monday to Friday Saturday Sunday

Opening time 06 45 07 30 08 45

Closing time 17 30 17 30 12 00

(a) Write the closing time on Saturday in the 12-hour clock time.

Answer(a) [1]

(b) Calculate the total number of hours the shop is open in one week.

Answer(b) h [2]

www.Q8Maths.com 8
11) June 2013 V3

3 The time in Lisbon is the same as the time in Funchal.

A plane left Lisbon at 08 30 and arrived in Funchal at 10 20.
It then left Funchal at 12 55 and returned to Lisbon.
The return journey took 15 minutes more.

What time did the plane arrive in Lisbon?

Answer ............................................... [2]

12) November 2013 V1

19 (a) Convert 144 km/h into metres per second.

Answer(a) ........................................ m/s [2]

(b) A train of length 120 m is travelling at 144 km/h.

It passes under a bridge of width 20 m.

Find the time taken for the whole train to pass under the bridge.
Give your answer in seconds.

Answer(b) .............................................

s [2]

www.Q8Maths.com 9
13) November 2013 V3

1 Christa had a music lesson every week for one year.

Each of the 52 lessons lasted for 45 minutes.

Calculate the total time that Christa spent in music lessons.

Give your time in hours.

Answer ............................................ h [2]

www.Q8Maths.com 10
14) June 2014 V1

9 A bus company in Dubai has the following operating times.

Starting Finishing
Day
time time

Saturday 06 00 24 00

Sunday 06 00 24 00

Monday 06 00 24 00

Tuesday 06 00 24 00

Wednesday 06 00 24 00

Thursday 06 00 24 00

Friday 13 00 24 00

(a) Calculate the total number of hours that the bus company operates in one week.

Answer(a) ............................................. h [3]

(b) Write the starting time on Friday in the 12-hour clock.

Answer(b) ................................................ [1]

www.Q8Maths.com 11
15) November 2014 V3

5 A train takes 65 minutes to travel 52 km.

Calculate the average speed of the train in kilometres per hour.

Answer ....................................... km/h [2]

www.Q8Maths.com 12
16) June 2015 V1

13 A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour.

Calculate the time it takes for the car to travel this distance.
Give your answer in seconds.

Answer .............................................. s [3]

17) June 2015 V2

2 A doctor starts work at 20 40 and finishes work at 06 10 the next day.

How long is the doctor at work?

Give your answer in hours and minutes.

Answer ...................... h ...................... min [1]

www.Q8Maths.com 13
18) November 2015 V1

14 A car travels at 56 km/h.

Find the time it takes to travel 300 metres.

Give your answer in seconds correct to the nearest second.

Answer .............................................. s [4]

www.Q8Maths.com 14
19) March 2015 V2

19 Fritz drives a distance of 381 km in 2 hours and 18 minutes.

He then drives 75 km at a constant speed of 30 km/h.

Calculate his average speed for the whole journey.

Answer ....................................... km/h [4]

20) June 2016 V1

1 A train leaves Zurich at 22 40 and arrives in Vienna at 07 32 the next day.

Work out the time taken.

..................... h ..................... min [1]

www.Q8Maths.com 15
21) June 2016 V1

18 A car of length 4.3 m is travelling at 105 km/h.

It passes over a bridge of length 36 m.

Calculate the time, in seconds, it takes to pass over the bridge completely.

................................................ s [3]

22) June 2012 V2

1 The ferry from Helsinki to Travemunde leaves Helsinki at 17 30 on a Tuesday.

The journey takes 28 hours 45 minutes.

Work out the day and time that the ferry arrives in Travemunde.

Answer Day Time [2]

23) June 2016 V1

1 A train leaves Zurich at 22 40 and arrives in Vienna at 07 32 the next day.

Work out the time taken.

..................... h ..................... min [1]

www.Q8Maths.com 16
24) November 2016 V1

20 A train travels for m minutes at a speed of x metres per second.

(a) Find the distance travelled, in kilometres, in terms of m and x.

Give your answer in its simplest form.

.......................................... km [2]

(b) When m = 5, the train travels 10.5 km.

Find the value of x.

x = ................................................ [2]

www.Q8Maths.com 17
25) June 2010 V2

19 The braking distance, d metres, for Alex’s car travelling at v km/h is given by the formula
200d = v(v + 40).
(a) Calculate the missing values in the table.

v
0 20 40 60 80 100 120
(km/h)
d
0 16 48 96
(metres)
[2]

(b) On the grid below, draw the graph of 200d = v(v + 40) for 0 Y v Y 120.
d
100

90

80

70

60
Distance
50
(metres)
40

30

20

10

v
0
10 20 30 40 50 60 70 80 90 100 110 120
Speed (km / h)
[3]
(c) Find the braking distance when the car is travelling at 110 km/h.

Answer(c) m [1]

(d) Find the speed of the car when the braking distance is 80 m.

Answer(d) km/h [1]

www.Q8Maths.com 18
26) November 2016 V3

30

28

26

24

22
D
20

C
18
Distance
(km) 16

B
14

12

10

A
6

0
0 10 20 30 40 50 60 70 80 90
Time (minutes)
The diagram shows the distance-time graph for the first 65 minutes of a bicycle journey.

(a) There are four different parts to the journey labelled A , B, C and D.

Write down the part of the journey with the fastest speed.

................................................. [1]

(b) After the first 65 minutes the bicycle travels at a constant speed of 20 km/h for 15 minutes.
Draw this part of the journey on the diagram. [1]

www.Q8Maths.com 19
27) June 2010 V2
16 The graphs show the speeds of two cyclists, Alonso and Boris.

Alonso accelerated to 10 m/s, travelled at a steady speed and then slowed to a stop.

10

Speed
Alonso
(m / s)

0 10
2 4 6 8 12 14 16
Time (seconds)

Boris accelerated to his maximum speed, v m/s, and then slowed to a stop.

v NOT TO
SCALE

Speed
(m / s)
Boris

0
Time (seconds) 16

Both cyclists travelled the same distance in the 16 seconds.

Calculate the maximum speed for Boris.

Show all your working.

Answer m/s [5]

www.Q8Maths.com 20
28) June 2010 V3

19
v

3
NOT TO
SCALE
Speed
(m / s)

t
0
4 15
Time (seconds)

The diagram shows the speed-time graph for 15 seconds of the journey of a cyclist.

(a) Calculate the acceleration of the cyclist during the first 4 seconds.

Answer(a) m/s 2 [1]

(b) Calculate the average speed for the first 15 seconds.

Answer(b) m/s [3]

www.Q8Maths.com 21
29) November 2010 V1
18
60

50

40
Speed
30
(m / s)

20

10

t
0
5 10 15 20 25 30 35
Time (seconds)

The graph shows the speed of a sports car after t seconds.

It starts from rest and accelerates to its maximum speed in 12 seconds.

(a) (i) Draw a tangent to the graph at t = 7. [1]

(ii) Find the acceleration of the car at t = 7.

Answer(a)(ii) m/s2 [2]

(b) The car travels at its maximum speed for 13 seconds.

Find the distance travelled by the car at its maximum speed.

Answer(b) m [2]

www.Q8Maths.com 22
30) November 2010 V2

21 An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for
9 seconds and then slows to a stop in a further 4 seconds.

The graph shows this information.

14

12

10

Speed 8
(m / s)
6

0
2 4 6 8 10 12 14 16 18 20

Time (seconds)

(a) Calculate its acceleration during the first seven seconds.

Answer(a) m/s2 [1]

(b) Write down its speed 18 seconds after the start.

Answer(b) m/s [1]

(c) Calculate the total distance that the animal travelled.

Answer(c) m [3]

www.Q8Maths.com 23
31) November 2010 V3

21
20

18

16

14

12
Speed
10
(m / s)

0
10 20 30 40
Time (seconds)

The graph shows 40 seconds of a car journey.

The car travelled at a constant speed of 20 m/s, decelerated to 8 m/s then accelerated back to 20 m/s.

Calculate

(a) the deceleration of the car,

Answer(a) m/s2 [1]

(b) the total distance travelled by the car during the 40 seconds.

Answer(b) m [3]

www.Q8Maths.com 24
32) June 2011 V1

19
15

10
Speed
(metres
per second)
5

0
2 4 6 8 10 12 14
Time (minutes)

The diagram shows the speed-time graph of a train journey between two stations.
The train accelerates for two minutes, travels at a constant maximum speed, then slows to a stop.

(a) Write down the number of seconds that the train travels at its constant maximum speed.

Answer(a) s [1]

(b) Calculate the distance between the two stations in metres.

Answer(b) m [3]

(c) Find the acceleration of the train in the first two minutes.
Give your answer in m/s2.

Answer(c) m/s2 [2]

www.Q8Maths.com 25
33) June 2011 V3

22

3 NOT TO
SCALE

Speed
(km / min)

0
4 50 60
Time (min)

A train journey takes one hour.

The diagram shows the speed-time graph for this journey.

(a) Calculate the total distance of the journey.

Give your answer in kilometres.

Answer(a) km [3]

(b) (i) Convert 3 kilometres / minute into metres / second.

Answer(b)(i) m/s [2]

(ii) Calculate the acceleration of the train during the first 4 minutes.

Give your answer in metres / second2.

Answer(b)(ii) m/s2 [2]

www.Q8Maths.com 26
34) November 2011 V1

15 A container ship travelled at 14 km/h for 8 hours and then slowed down to 9 km/h over a period of
30 minutes.

It travelled at this speed for another 4 hours and then slowed to a stop over 30 minutes.

The speed-time graph shows this voyage.

16

14

12

10
Speed
8
(km/ h)
6

0
1 2 3 4 5 6 7 8 9 10 11 12 13
Time (hours)

(a) Calculate the total distance travelled by the ship.

Answer(a) km [4]

(b) Calculate the average speed of the ship for the whole voyage.

Answer(b) km/h [1]

www.Q8Maths.com 27
35) November 2011 V2

12
40

30

Small
car
Speed
20
(m / s)
Large
car

10

0
1 2 3 4 5 6 7 8 9 10
Time (seconds)

A small car accelerates from 0 m/s to 40 m/s in 6 seconds and then travels at this constant speed.
A large car accelerates from 0 m/s to 40 m/s in 10 seconds.

Calculate how much further the small car travels in the first 10 seconds.

Answer m [4]

www.Q8Maths.com 28
36) November 2011 V3

23

40

NOT TO
Speed SCALE
(m / s)

0
5 10 15
Time (minutes)

The diagram shows the speed-time graph for the first 15 minutes of a train journey.
The train accelerates for 5 minutes and then continues at a constant speed of 40 metres/second.

(a) Calculate the acceleration of the train during the first 5 minutes.
Give your answer in m/s2.

Answer(a) m/s2 [2]

(b) Calculate the average speed for the first 15 minutes of the train journey.
Give your answer in m/s.

Answer(b) m/s [3]

www.Q8Maths.com 29
37) June 2012 V1

18
20

15
Speed
(m / s) 10

0
10 20 30 40 50 60 70 80 90 100 110 120
Time (s)

The diagram shows the speed-time graph for the first 120 seconds of a car journey.

(a) Calculate the acceleration of the car during the first 25 seconds.

Answer(a) m/s2 [1]

(b) Calculate the distance travelled by the car in the first 120 seconds.

Answer(b) m [4]

www.Q8Maths.com 30
38) June 2012 V2
10
500

400

300
Speed
(m / min)
200

100

0
10 20 30 40 50 60
Time (min)

The diagram shows the speed-time graph for a boat journey.

(a) Work out the acceleration of the boat in metres / minute 2.

Answer(a) m /min 2 [1]

(b) Calculate the total distance travelled by the boat.

Give your answer in kilometres.

Answer(b) km [2]

www.Q8Maths.com 31
39) June 2012 V3

19
120

100

80
Speed
(km / h) 60

40

20

0
0.5 1 1.5 2 2.5 3 3.5
Time (minutes)

The diagram shows the speed-time graph for part of a car journey.
The speed of the car is shown in kilometres / hour.

Calculate the distance travelled by the car during the 3.5 minutes shown in the diagram.
Give your answer in kilometres.

Answer km [4]

www.Q8Maths.com 32
40) November 2012 V1

15
14

Speed
(metres per
second)

0
20 40 60
Time (seconds)

The diagram shows the speed-time graph of a bus journey between two bus stops.
Hamid runs at a constant speed of 4 m/s along the bus route.
He passes the bus as it leaves the first bus stop.
The bus arrives at the second bus stop after 60 seconds.

How many metres from the bus is Hamid at this time?

Answer m [3]

www.Q8Maths.com 33
41) November 2012 V2
15
25

20

15
Speed
(metres per
second)
10

0
5 10 15 20 25 30 35
Time (seconds)

The diagram shows the speed-time graph for the last 35 seconds of a car journey.

(a) Find the deceleration of the car as it came to a stop.

Answer(a) m/s2 [1]

(b) Calculate the total distance travelled by the car in the 35 seconds.

Answer(b) m [3]

www.Q8Maths.com 34
42) November 2012 V3

19
5

Speed 3
(metres per
second) 2

0
2 4 6 8 10 12 14 16 18
Time (seconds)

The diagram shows the speed-time graph for the last 18 seconds of Roman’s cycle journey.

(a) Calculate the deceleration.

Answer(a) m/s2 [1]

(b) Calculate the total distance Roman travels during the 18 seconds.

Answer(b) m [3]

www.Q8Maths.com 35
43) June 2013 V1

25
28

NOT TO
SCALE
Speed
(m/s)

0
20 30
Time (seconds)

The diagram shows the speed-time graph of a car.

It travels at 28 m/s for 20 seconds and then decelerates until it stops after a further 10 seconds.

(a) Calculate the deceleration of the car.

Answer(a) ...................................... m/s2 [1]

(b) Calculate the distance travelled during the 30 seconds.

Answer(b) ........................................... m [3]

www.Q8Maths.com 36
44) June 2013 V2

16

40

NOT TO
SCALE
Speed
(km/h)

0
3 22 26
Time (minutes)

The diagram shows the speed-time graph of a train journey between two stations.

The train accelerates for 3 minutes, travels at a constant maximum speed of 40 km/h, then takes
4 minutes to slow to a stop.

Calculate the distance in kilometres between the two stations.

Answer ......................................... km [4]

www.Q8Maths.com 37
45) June 2015 V1

10

12

Speed
(metres per
second)

0
0 1 2 3 4 5 6
Time (minutes)

A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.

Calculate the distance, in metres, between the two stations.

Answer ............................................ m [3]

www.Q8Maths.com 38
46) June 2015 V2
23 20
18
16
14
12
Speed
(m/s) 10
8
6
4
2

0
10 20 30 40 50 60 70 80 90 100 110 120
Time (s)

The diagram shows the speed-time graph for 120 seconds of a car journey.

(a) Calculate the deceleration of the car during the first 20 seconds.

Answer(a) ........................................ m/s2 [1]

(b) Calculate the total distance travelled by the car during the 120 seconds.

Answer(b) ............................................ m [3]

(c) Calculate the average speed for this 120 second journey.

Answer(c) ......................................... m/s [1]

www.Q8Maths.com 39
47) June 2015 V3

12
10

NOT TO
SCALE
Speed (m/s)

0 u 3u
Time (seconds)

A car starts from rest and accelerates for u seconds until it reaches a speed of 10 m/s.
The car then travels at 10 m/s for 2u seconds.
The diagram shows the speed-time graph for this journey.

The distance travelled by the car in the first 3u seconds is 125 m.

(a) Find the value of u .

Answer(a) u = ................................................ [3]

(b) Find the acceleration in the first u seconds.

Answer(b) ........................................ m/s 2 [1]

www.Q8Maths.com 40
48) November 2015 V2

20 A car passes through a checkpoint at time t = 0 seconds, travelling at 8 m/s.

It travels at this speed for 10 seconds.
The car then decelerates at a constant rate until it stops when t = 55 seconds.

(a) On the grid, draw the speed-time graph.

10

6
Speed
(m/s)
4

t
0 10 20 30 40 50 60
Time (seconds)
[2]

(b) Calculate the total distance travelled by the car after passing through the checkpoint.

Answer(b) ............................................. m [3]

www.Q8Maths.com 41
49) November 2015 V3

26

45
NOT TO
SCALE
Speed
(km/h)

0
10 20 30
Time (seconds)

The diagram shows the speed-time graph of a car.

The car travels at 45 km/h for 20 seconds.
The car then decelerates for 10 seconds until it stops.

(a) Change 45 km/h into m/s.

Answer(a) ......................................... m/s [2]

(b) Find the deceleration of the car, giving your answer in m/s2.

Answer(b) ........................................ m/s2 [1]

(c) Find the distance travelled by the car during the 30 seconds, giving your answer in metres.

Answer(c) ............................................ m [3]

www.Q8Maths.com 42
50) June 2018 V1

17

20

Speed NOT TO
(m/s) SCALE

0
0 10 100 130
Time (seconds)

The speed time graph shows information about the journey of a tram between two stations.
-

(a) Calculate the distance between the two stations.

.......................................... m [3]

www.Q8Maths.com 43
51) June 2018 V2

17 The diagram shows information about the first 8 seconds of a car journey.

NOT TO
SCALE

Speed
(m/s)

0
0 6 8
Time (seconds)

The car travels with constant acceleration reaching a speed of v m/s after 6 seconds.
The car then travels at a constant speed of v m/s for a further 2 seconds.
The car travels a total distance of 150 metres.

Work out the value of v.

v = .............................................. [3]

www.Q8Maths.com 44
52) November 2020 V2

17

3
Speed
2
(m/s)
1

0
0 10 20 30 40
Time (seconds)

The diagram shows the speed–time graph for the first 40 seconds of a cycle ride.

(a) Find the acceleration between 20 and 40 seconds.

......................................... m/s 2 [1]

(b) Find the total distance travelled.

.............................................. m [3]

www.Q8Maths.com 45