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OCR F NOV 2020 Paper 1

1.
Oxford Cambridge and RSA

F

Tuesday 03 November 2020 – Morning

GCSE (9–1) Mathematics

J560/01 Paper 1 (Foundation Tier)

Time allowed: 1 hour 30 minutes

You can use:

* 8 1 8 1 5 8 6 3 4 5 *

• a scientific or graphical calculator

• geometrical instruments

• tracing paper

* J 5 6 0 0 1 *

Please write clearly in black ink. Do not write in the barcodes.

Centre number Candidate number

First name(s) �

Last name �

INSTRUCTIONS

• Use black ink. You can use an HB pencil, but only for graphs and diagrams.

• Write your answer to each question in the space provided. You can use extra paper if

you need to, but you must clearly show your candidate number, the centre number and

the question numbers.

• Answer all the questions.

• Where appropriate, your answer should be supported with working. Marks might be

given for using a correct method, even if your answer is wrong.

• Use the r button on your calculator or take r to be 3.142 unless the question says

something different.

INFORMATION

• The total mark for this paper is 100.

• The marks for each question are shown in brackets [ ].

• This document has 20 pages.

ADVICE

• Read each question carefully before you start your answer.

© OCR 2020 [601/4606/0] OCR is an exempt Charity

DC (NF/SG) 190040/4 Turn over

F

Tuesday 03 November 2020 – Morning

GCSE (9–1) Mathematics

J560/01 Paper 1 (Foundation Tier)

Time allowed: 1 hour 30 minutes

You can use:

* 8 1 8 1 5 8 6 3 4 5 *

• a scientific or graphical calculator

• geometrical instruments

• tracing paper

* J 5 6 0 0 1 *

Please write clearly in black ink. Do not write in the barcodes.

Centre number Candidate number

First name(s) �

Last name �

INSTRUCTIONS

• Use black ink. You can use an HB pencil, but only for graphs and diagrams.

• Write your answer to each question in the space provided. You can use extra paper if

you need to, but you must clearly show your candidate number, the centre number and

the question numbers.

• Answer all the questions.

• Where appropriate, your answer should be supported with working. Marks might be

given for using a correct method, even if your answer is wrong.

• Use the r button on your calculator or take r to be 3.142 unless the question says

something different.

INFORMATION

• The total mark for this paper is 100.

• The marks for each question are shown in brackets [ ].

• This document has 20 pages.

ADVICE

• Read each question carefully before you start your answer.

© OCR 2020 [601/4606/0] OCR is an exempt Charity

DC (NF/SG) 190040/4 Turn over

2.
2

Answer all the questions.

1 Reece asked some friends what type of programme they watch most on television.

The bar chart shows some of his results.

14

12

10

8

Frequency

6

4

2

0

Comedy Sport Nature Film News Soaps

Type of programme

(a) 10 people answered Film.

Complete the bar chart to show this information. [1]

(b) Complete these sentences.

(i) .................................... was chosen by the most people. [1]

(ii) .................................... people chose News. [1]

(iii) .................................... fewer people chose Nature than Comedy. [1]

© OCR 2020

Answer all the questions.

1 Reece asked some friends what type of programme they watch most on television.

The bar chart shows some of his results.

14

12

10

8

Frequency

6

4

2

0

Comedy Sport Nature Film News Soaps

Type of programme

(a) 10 people answered Film.

Complete the bar chart to show this information. [1]

(b) Complete these sentences.

(i) .................................... was chosen by the most people. [1]

(ii) .................................... people chose News. [1]

(iii) .................................... fewer people chose Nature than Comedy. [1]

© OCR 2020

3.
3

2 (a) Reflect the triangle in the mirror line.

mirror line

[2]

(b) Rotate the triangle 90° clockwise about the point P.

P

[2]

© OCR 2020 Turn over

2 (a) Reflect the triangle in the mirror line.

mirror line

[2]

(b) Rotate the triangle 90° clockwise about the point P.

P

[2]

© OCR 2020 Turn over

4.
4

3 Work out the volume of this cuboid.

5 cm

2 cm

7 cm

.................................................... cm3 [2]

4 (a) Write 2% as a decimal.

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

11

(b) Write as a percentage.

20

(b) ....................................................... % [1]

5 Use one of the symbols 1, = or2 to make each statement true.

2

(a) 0.7 ........................... [1]

3

(b) 27.06 ................... 27.59 [1]

© OCR 2020

3 Work out the volume of this cuboid.

5 cm

2 cm

7 cm

.................................................... cm3 [2]

4 (a) Write 2% as a decimal.

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

11

(b) Write as a percentage.

20

(b) ....................................................... % [1]

5 Use one of the symbols 1, = or2 to make each statement true.

2

(a) 0.7 ........................... [1]

3

(b) 27.06 ................... 27.59 [1]

© OCR 2020

5.
5

6 A bag contains 12 counters.

6 are red, 4 are blue and 2 are yellow.

A counter is taken from the bag at random.

Mark with an arrow ( ) the probability the counter is

(a) red,

0 1

[1]

(b) yellow,

0 1

[1]

(c) green.

0 1

[1]

© OCR 2020 Turn over

6 A bag contains 12 counters.

6 are red, 4 are blue and 2 are yellow.

A counter is taken from the bag at random.

Mark with an arrow ( ) the probability the counter is

(a) red,

0 1

[1]

(b) yellow,

0 1

[1]

(c) green.

0 1

[1]

© OCR 2020 Turn over

6.
6

7 (a) Divide 72 in the ratio 4 : 5.

(a) ........................... : ............................ [2]

(b) In one year, Clara and Dave borrowed books from a library in the ratio 3 : 7.

Dave borrowed 35 books.

Work out the number of books borrowed by Clara.

(b) .......................................................... [2]

8 Yoghurts are packed in trays.

Each tray holds 12 yoghurts.

What is the smallest number of trays needed to pack 460 yoghurts?

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

© OCR 2020

7 (a) Divide 72 in the ratio 4 : 5.

(a) ........................... : ............................ [2]

(b) In one year, Clara and Dave borrowed books from a library in the ratio 3 : 7.

Dave borrowed 35 books.

Work out the number of books borrowed by Clara.

(b) .......................................................... [2]

8 Yoghurts are packed in trays.

Each tray holds 12 yoghurts.

What is the smallest number of trays needed to pack 460 yoghurts?

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

© OCR 2020

7.
7

9 59 families are asked whether they have a cat (C) or a dog (D).

• 26 only have a cat.

• 14 only have a dog.

• 11 have both a cat and a dog.

(a) Show this information on the Venn diagram.

C D

[1]

(b) (i) How many of the families do not have a cat or a dog?

(b)(i) .......................................................... [1]

(ii) Write your answer in the correct place on the Venn diagram. [1]

(c) One of the families is chosen at random.

Write down the probability that they have a dog.

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

© OCR 2020 Turn over

9 59 families are asked whether they have a cat (C) or a dog (D).

• 26 only have a cat.

• 14 only have a dog.

• 11 have both a cat and a dog.

(a) Show this information on the Venn diagram.

C D

[1]

(b) (i) How many of the families do not have a cat or a dog?

(b)(i) .......................................................... [1]

(ii) Write your answer in the correct place on the Venn diagram. [1]

(c) One of the families is chosen at random.

Write down the probability that they have a dog.

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

© OCR 2020 Turn over

8.
8

10 Nadia thinks of a number.

She finds the square root and then divides by 5.

Her answer is 20.

What number is she thinking of?

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

11 The scale on a map is 1 : 50 000.

How many kilometres on the ground are represented by 8 cm on the map?

..................................................... km [3]

© OCR 2020

10 Nadia thinks of a number.

She finds the square root and then divides by 5.

Her answer is 20.

What number is she thinking of?

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

11 The scale on a map is 1 : 50 000.

How many kilometres on the ground are represented by 8 cm on the map?

..................................................... km [3]

© OCR 2020

9.
9

12 (a) A train is travelling with a velocity of 15 m / s.

It then accelerates at 0.5 m / s2 for 6 seconds.

Use the formula v = u + at to calculate the velocity of the train after the 6 seconds.

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

(b) Rearrange the formula v = u + at to make a the subject.

(b) .......................................................... [2]

© OCR 2020 Turn over

12 (a) A train is travelling with a velocity of 15 m / s.

It then accelerates at 0.5 m / s2 for 6 seconds.

Use the formula v = u + at to calculate the velocity of the train after the 6 seconds.

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

(b) Rearrange the formula v = u + at to make a the subject.

(b) .......................................................... [2]

© OCR 2020 Turn over

10.
10

13 Choose a word from this list that best describes each statement.

Identity Expression Formula Term Equation

(a) 8 = n + 2 (a) .......................................................... [1]

(b) 3x + 2y (b) .......................................................... [1]

2 2

(c) (a + b) (a - b) = a - b (c) .......................................................... [1]

14 Harry is paid £8.60 per hour for the first 30 hours he works each week.

1

After 30 hours he is paid 1 times the hourly rate.

2

Last week, Harry worked for 33 hours.

1

He was also paid a bonus of of his earnings for that week.

10

Calculate how much Harry was paid in total last week.

£ ........................................................ [6]

© OCR 2020

13 Choose a word from this list that best describes each statement.

Identity Expression Formula Term Equation

(a) 8 = n + 2 (a) .......................................................... [1]

(b) 3x + 2y (b) .......................................................... [1]

2 2

(c) (a + b) (a - b) = a - b (c) .......................................................... [1]

14 Harry is paid £8.60 per hour for the first 30 hours he works each week.

1

After 30 hours he is paid 1 times the hourly rate.

2

Last week, Harry worked for 33 hours.

1

He was also paid a bonus of of his earnings for that week.

10

Calculate how much Harry was paid in total last week.

£ ........................................................ [6]

© OCR 2020

11.
11

15 (a) Solve.

x

+ 5 = 15

2

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

(b) Factorise.

2

5a - 10a

(b) .......................................................... [2]

(c) Solve by factorising.

2

x + 15x + 56 = 0

(c) x = .................... or x = ..................... [3]

16 The height, h, of a lorry is 4.3 metres, correct to 1 decimal place.

Complete the error interval for the height, h.

....................... G h 1 ........................ [2]

© OCR 2020 Turn over

15 (a) Solve.

x

+ 5 = 15

2

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

(b) Factorise.

2

5a - 10a

(b) .......................................................... [2]

(c) Solve by factorising.

2

x + 15x + 56 = 0

(c) x = .................... or x = ..................... [3]

16 The height, h, of a lorry is 4.3 metres, correct to 1 decimal place.

Complete the error interval for the height, h.

....................... G h 1 ........................ [2]

© OCR 2020 Turn over

12.
12

17 The table below shows the number of barrels of oil produced per day by some countries.

Barrels of oil produced

Country

per day

7

USA 1.17 # 10

6

China 3.98 # 10

5

UK 9.39 # 10

4

Cameroon 9.32 # 10

3

Japan 3.92 # 10

(a) Write the number of barrels of oil produced per day by Cameroon as an ordinary number.

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

(b) How many more barrels of oil per day did China produce than the UK?

Give your answer in standard form, correct to 3 significant figures.

(b) .......................................................... [4]

(c) Jamal says the USA produced approximately three times more barrels of oil than Japan.

Is he correct?

Show how you decide.

Jamal is .......................................... because ...........................................................................

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

© OCR 2020

17 The table below shows the number of barrels of oil produced per day by some countries.

Barrels of oil produced

Country

per day

7

USA 1.17 # 10

6

China 3.98 # 10

5

UK 9.39 # 10

4

Cameroon 9.32 # 10

3

Japan 3.92 # 10

(a) Write the number of barrels of oil produced per day by Cameroon as an ordinary number.

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

(b) How many more barrels of oil per day did China produce than the UK?

Give your answer in standard form, correct to 3 significant figures.

(b) .......................................................... [4]

(c) Jamal says the USA produced approximately three times more barrels of oil than Japan.

Is he correct?

Show how you decide.

Jamal is .......................................... because ...........................................................................

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

© OCR 2020

13.
13

18 A triangle has sides of length 14.1 cm, 14.8 cm and 19.5 cm.

Is this a right-angled triangle?

Show how you decide.

.................... because .......................................................................................................................

.................................................................................................................................................... [4]

19 One morning Kai records the colour of the cars passing his house.

He then works out the relative frequency of each colour.

Some of his results are shown in this table.

Colour Silver Red Green Black Other

Relative

0.16 0.10 0.24 0.32

frequency

The following morning, Kai is going to record the colour of the first 200 cars to pass his house.

Work out an estimate for the total number of cars, coloured silver or red, that he should expect to

see.

.......................................................... [4]

© OCR 2020 Turn over

18 A triangle has sides of length 14.1 cm, 14.8 cm and 19.5 cm.

Is this a right-angled triangle?

Show how you decide.

.................... because .......................................................................................................................

.................................................................................................................................................... [4]

19 One morning Kai records the colour of the cars passing his house.

He then works out the relative frequency of each colour.

Some of his results are shown in this table.

Colour Silver Red Green Black Other

Relative

0.16 0.10 0.24 0.32

frequency

The following morning, Kai is going to record the colour of the first 200 cars to pass his house.

Work out an estimate for the total number of cars, coloured silver or red, that he should expect to

see.

.......................................................... [4]

© OCR 2020 Turn over

14.
14

20 James is taking three examination papers in Spanish.

Here are his first two results.

Paper 1: 43 Paper 2: 38

80 65

Paper 3 is out of 95.

The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

.......................................................... [4]

© OCR 2020

20 James is taking three examination papers in Spanish.

Here are his first two results.

Paper 1: 43 Paper 2: 38

80 65

Paper 3 is out of 95.

The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

.......................................................... [4]

© OCR 2020

15.
15

1

21 Three people take 2 hours to deliver leaflets to 270 houses.

2

Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver

leaflets to 405 houses?

Give your answer in hours and minutes.

................... hours .................... mins [4]

© OCR 2020 Turn over

1

21 Three people take 2 hours to deliver leaflets to 270 houses.

2

Assuming all people deliver leaflets at the same rate, how long will it take five people to deliver

leaflets to 405 houses?

Give your answer in hours and minutes.

................... hours .................... mins [4]

© OCR 2020 Turn over

16.
16

22 This graph shows part of a straight line.

y

8

7

6

5

4

3

2

1

x

-2 -1 0 1 2 3 4

-1

-2

-3

-4

-5

-6

(a) Write down the y-intercept.

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

(b) Show that the gradient of the line is -2. [1]

© OCR 2020

22 This graph shows part of a straight line.

y

8

7

6

5

4

3

2

1

x

-2 -1 0 1 2 3 4

-1

-2

-3

-4

-5

-6

(a) Write down the y-intercept.

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

(b) Show that the gradient of the line is -2. [1]

© OCR 2020

17.
17

(c) Write down the equation of the line.

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

(d) The line continues to the right.

Will this line pass through the point (50, -103)?

Show how you decide.

.......................... because .........................................................................................................

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

© OCR 2020 Turn over

(c) Write down the equation of the line.

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

(d) The line continues to the right.

Will this line pass through the point (50, -103)?

Show how you decide.

.......................... because .........................................................................................................

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

© OCR 2020 Turn over

18.
18

23 ABCD is a quadrilateral.

B

C

A D

(a) Construct the bisector of angle ABC.

Show all your construction lines. [2]

(b) Construct the perpendicular bisector of BC.

Show all your construction lines. [2]

(c) Shade the region which is

• nearer to BC than to AB

and

• nearer to B than to C.

[1]

© OCR 2020

23 ABCD is a quadrilateral.

B

C

A D

(a) Construct the bisector of angle ABC.

Show all your construction lines. [2]

(b) Construct the perpendicular bisector of BC.

Show all your construction lines. [2]

(c) Shade the region which is

• nearer to BC than to AB

and

• nearer to B than to C.

[1]

© OCR 2020

19.
19

24 Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60.

She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her

another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order.

Showing your working in the boxes below may help you present your work.

Expected number of faulty microwaves: Expected costs:

Income from sales: Expected percentage profit:

....................................................... % [6]

Turn over for Question 25

© OCR 2020 Turn over

24 Lily buys and sells microwaves.

She buys each one for £32 and sells it for £60.

She also pays £7 for the delivery of each microwave she sells.

If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her

another £25 for each faulty microwave.

Last month, 6 out of the 80 microwaves Lily sold were faulty.

This month she has orders for 133 microwaves.

Calculate her expected percentage profit on this month’s order.

Showing your working in the boxes below may help you present your work.

Expected number of faulty microwaves: Expected costs:

Income from sales: Expected percentage profit:

....................................................... % [6]

Turn over for Question 25

© OCR 2020 Turn over

20.
20

25 The diagram shows Jane’s lawn.

It is in the shape of a square of side 36 m and three semi-circles.

Not to scale

She is going to spread fertiliser on the lawn at a rate of 30 g per square metre.

The fertiliser is only sold in 10 kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn.

You must show all your working.

£ ........................................................ [6]

END OF QUESTION PAPER

Oxford Cambridge and RSA

Copyright Information

OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders

whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright

Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.

If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible

For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.

OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a

department of the University of Cambridge.

© OCR 2020

25 The diagram shows Jane’s lawn.

It is in the shape of a square of side 36 m and three semi-circles.

Not to scale

She is going to spread fertiliser on the lawn at a rate of 30 g per square metre.

The fertiliser is only sold in 10 kg bags costing £15.80 each.

Calculate the cost of buying the bags of fertiliser for her lawn.

You must show all your working.

£ ........................................................ [6]

END OF QUESTION PAPER

Oxford Cambridge and RSA

Copyright Information

OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders

whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright

Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download from our public website (www.ocr.org.uk) after the live examination series.

If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible

For queries or further information please contact The OCR Copyright Team, The Triangle Building, Shaftesbury Road, Cambridge CB2 8EA.

OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a

department of the University of Cambridge.

© OCR 2020