MrJacksonMaths Foundation Calcultaor Paper J

Name

For Edexcel

GCSE MathematicsPaper 2J (Calculator)

Foundation TierTime: 1 hour and 30 minutes

Materials required

Ruler, protractor, compasses,pen, pencil, eraser.Tracing paper may be used.

Instructions and Information for Candidates

Write your name in the box at the top of the page.Answer all the questions in the spaces provided in this question paper.The marks for each question and for each part of a question are shown in brackets.The total number of marks for this paper is 100. There are 23 questions in this paper.Calculators may be used.If your calculator does not have a π button, take the value of π to be 3.142 unless thequestion instructs otherwise.

Advice to Candidates

Show all stages in any calculation.Work steadily through the paper. Do not spend too long on one question.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

Written by Shaun Armstrong

Only to be copied for use in the purchaser's school or college

EF2J 09 © Churchill Maths Limited

b

h

a

GCSE Mathematics

Formulae: Foundation Tier

Area of a trapezium = 12

(a + b)h

Volume of a prism = area of cross section × length


sectioncross

length

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Q1

Answer ALL TWENTY THREE questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1. The cost, in pounds, of hiring a van is worked out using this formula.

(a) Work out how much it costs to hire the van for 10 days.

£ …………………………(2)

Tim pays £325 for hiring the van.

(b) Work out how many days he hired the van for.

…………………… days(2)

(Total 4 marks)


Cost = 50 × Number of days + 75

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Q2

a b

2. Diagram NOTaccurately drawn

The diagram shows the net of a 3-D shape.

The net is made up of a square and four equilateral triangles.

(a) Write down the name of the 3-D shape that can be formed from this net.

……………………………………(1)

(b) Write down the size of the angle labelled a.°

…………………… (1)

(c) Work out the size of the angle labelled b.

°……………………

(2)

(Total 4 marks)


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Q3

3. (a) Here is a number sequence.

3 14 25 36

(i) Write down the next number in this sequence.

………………………

(ii) Write down the rule for continuing this sequence.

…………………………………………………………………………………

…………………………………………………………………………………(2)

(b) Here are some patterns made with dots.

Pattern number 1 Pattern number 2 Pattern number 3

(i) In the space below, draw Pattern number 4.

(ii) Complete the table showing the number of dots used to make each pattern.

Pattern number 1 2 3 4 5

Number of dots 8

(3)

(Total 5 marks)


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Q4

4. (a)

(i) Write down the order of rotational symmetry of the shape above.

……………………

(ii) Draw all the lines of symmetry on the shape above.(3)

(b)

The diagram shows a prism.The cross-section of the prism is a trapezium.

On the diagram, draw in a plane of symmetry for this prism.(2)

(Total 5 marks)


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Q5

Q6

5. Gilbert designs an experiment to test people's memories.

He will get each person to look at a list of 20 words for one minute.Then he will ask them to write down as many of the words as they can remember and count how many they get correct.He will do this with a large number of people.

Design a suitable data collection sheet that Gilbert could use to record his results.

(Total 2 marks)

6. Darren pays £180 for 20 boxes of decorative candles.Each box contains 6 candles.

He sells the candles for £2.50 each.How much profit does he make when he sells all the candles?

£ ……………………

(Total 3 marks)


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Q7

7. (a) Write down a sensible metric unit you could use for measuring

(i) the weight of a mobile phone,

………………………………

(ii) the length of the river Thames,

………………………………

(iii) the volume of a book.

………………………………(3)

(b) A car is travelling at 75 kilometres per hour.

Calculate the distance it travels in 30 seconds.Give your answer in metres.

………………………… m(3)

(Total 6 marks)


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Q8

8. 400 tickets are sold for a raffle.Of the tickets sold, 200 are red, 150 are blue and 50 are white.

One ticket is picked at random.

(a) What is the probability that the ticket picked is

(i) red,

……………………

(ii) white,

……………………

(iii) not blue.

……………………(3)

Angus decides to run his own raffle.He sells 20 tickets numbered from 1 to 20.

One ticket is picked at random.

(b) What is the probability that the number on the ticket picked has the digit 2 in it.

……………………(2)

(Total 5 marks)


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Q9

9.

Pam pays for 7 children to go to The Play Patch.All of the children have a kid's meal.

(a) Work out how much she pays in total.

£ ………………………(3)

James says

“It would have been cheaper if one more of our friends had come as well.”

(b) Show that James is right and work out how much cheaper it would have been.

£ ………………………(3)

(Total 6 marks)


The Play Patch

Entrance Kid's meal

Individuals £4.50 £1.80

Groups (8 or more) £3.60 each £1.60 each

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Q10

0

Frequency

4

8

12

16

20

24

28

32

0Age in years

10 20 30 40 50 60 70

Company Y

10. The table below shows the ages (A years) of the employees of Company X.

Age (A years) Frequency

20 < A ≤ 30 12

30 < A ≤ 40 16

40 < A ≤ 50 22

50 < A ≤ 60 21

60 < A ≤ 70 14

The frequency diagram below shows the distribution of the ages of the employees of Company Y.

(a) On the same grid, draw a frequency diagram for the ages of the employees of Company X.

(2)

(b) Write down two differences between the distribution of the ages of the employees of Company X and Company Y.

First difference ……………………………………………………………………

………………………………………………………………………………………

Second difference …………………………………………………………………

………………………………………………………………………………………(2)

(Total 4 marks)


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Q11

80 cm40 cm

40 cm


The diagram shows a fish tank.It is in the shape of a square prism.

(a) Work out the volume of the fish tank.

………………………… cm3

(2)

Liam wants to fill the fish tank with water.He uses a bucket with a volume of 25 000 cm3 to get the water.

(b) Work out the least number of times he will need to put water in the bucket.

……………………… times(2)

(Total 4 marks)


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Q12

12. In a competition, 25 people guessed how many golf balls were in a large jar.

Here are their guesses.

82 54 60 67 71 59 90 74 70 75

65 87 67 70 72 58 69 75 51 60

73 77 95 83 65

(a) Draw an ordered stem and leaf diagram to show these guesses.You should include a key.

(3)

(b) Find the median of these guesses.

…………………………(2)

(Total 5 marks)


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Q13

Q14

13. (a) Work out the exact value of 8.32

…………………………(1)

(b) Giving your answers correct to 2 decimal places, work out the value of

(i)6

82

…………………………

(ii)2 15

1.3

…………………………(3)

(Total 4 marks)

14. Margo is going on holiday to Spain.

She changes £350 into Euros (€).The exchange rate is £1 = €1.42

(a) Work out how many Euros Margo gets.

€ …………………………(2)

When Margo returns from holiday, she has €84 left which she changes into pounds.The exchange rate is now £1 = €1.39

(b) Work out how many pounds Margo gets.Give your answer correct to the nearest pound.

£ …………………………(2)

(Total 4 marks)


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Q15

y

1 2 43 5 6–5 x–2–4 –3 –1

P

Q

R–3

1

2

–2

–1

3

O

15.

Triangle PQR is shown on a centimetre square grid.The point P has coordinates (–4, –2)

(a) Write down the coordinates of the point

(i) Q,( …… , …… )

(ii) R.( …… , …… )

(2)

(b) Find the area of the shaded rectangle.

……………………… cm2

(1)

(c) Find the area of triangle PQR.

……………………… cm2

(3)

(Total 6 marks)


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Q16

Q17

16. Alawi is making a cake with two layers.He divides the cake mixture in the ratio 5 : 3

The difference in weight between the two portions is 140 grams.

Work out the weight of cake mixture he will use for the smaller layer.

…………………… g

(Total 3 marks)

17. Basir is multiplying consecutive whole numbers.Here are some of his calculations.

2 × 3 = 6

3 × 4 = 12

6 × 7 = 42

(a) Find two consecutive numbers that multiply to give 90.

………… and …………(1)

Qadi says

“If you find the square root of a number, the whole numbers on either side will multiply to give that number”

(b) Use Qadi's method to find two consecutive numbers that multiply to give 756.

………… and …………(1)

(c) Find an example to show that Qadi's method does not work with any number.

(2)

(Total 4 marks)


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Q18

6 cm

Q19

18. Calculate the area of this circle.

Diagram NOTaccurately drawn

………………………… cm2

(Total 3 marks)

19. Gary's usual route to work is 27.3 km long.

He tries a new route and finds it is 4 12 % shorter.

Work out the length of the new route.Give your answer to an appropriate degree of accuracy.

…………………… km

(Total 3 marks)


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Q20

20. (a) Solve each equation

(i)p2

= 18

p = ……………………

(ii) 3m + 7 = 22

m = ……………………(3)

(b) Simplify

(i) w × 3w

……………………

(ii) 5a + b – 4a + 3b

………………………………(3)

(c) Make r the subject of the formula y = 2r – 4

…………………………(2)

(Total 8 marks)


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Q21

21.

(a) Reflect triangle A in the line y = – x.Label the image B.

(2)

(b) Rotate triangle A a quarter turn clockwise about the point P.Label the image C.

(2)

(Total 4 marks)


1 2 43 5

1

2

4

3

5

6

x

y

–5–6 –4 –3 –2 –1

–2

–1

O

A

P

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Q22

4

y + 2

y

7


The diagram shows a piece of carpet.

All the corners are right angles and the measurements given are in metres.

(a) Find an expression, in terms of y, for the area of the carpet.Give your answer in its simplest form.

……………………… m2

(2)

The area of the carpet is 41 m2.

(b) Work out the value of y.

y = ……………………(2)

(Total 4 marks)


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Q23

23. The table shows information about the percentage increase, I %, in the value of50 rare stamps in the last year.

Percentage increasein value (I %) Frequency

0 ≤ I < 10 28

10 ≤ I < 20 11

20 ≤ I < 30 4

30 ≤ I < 40 6

40 ≤ I < 50 1

Work out an estimate for the mean percentage increase in the value of these stamps.

…………………… %

(Total 4 marks)

TOTAL FOR PAPER: 100 MARKS

END


MrJacksonMaths Foundation Calcultaor Paper J

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