gcse mathematics - life learning · pdf filegcse mathematics paper 2b ... explain how you...

Name

For Edexcel

GCSE MathematicsPaper 2B (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 26 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

EF2B 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 SIX questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1. (a)

The diagram shows a regular polygon with eight sides.

Write down the name of this polygon.

…………………………(1)

(b)

The diagram shows a shape.

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

…………………………

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

(Total 4 marks)


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Q2

Q3

2. (a) Write 32% as a decimal.

……………………(1)

(b) Write 0.03 as a fraction.

……………………(1)

(c) Shade 23 of this shape.

(1)

(Total 3 marks)

3. A bag contains only apple, orange and strawberry flavoured sweets.

A sweet is picked at random from the bag.The table shows the probability of picking an apple or an orange flavoured sweet.

Flavour apple orange strawberry

Probability 0.2 0.35

Work out the probability of picking a strawberry flavoured sweet.

………………………

(Total 2 marks)


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Q4

4. Gail asked each of her friends who their maths teacher is.

Here are her results.

Mr. York Mrs. Day Mrs. Day Ms. Kirk Mrs. Day

Ms. Kirk Mr. Hughes Mrs. Day Mr. York Ms. Kirk

Mr. York Mrs. Day Ms. Kirk Mr. Hughes Ms. Kirk

Mrs. Day Mr. York Mrs. Day

(a) Complete the table to show Gail's results.

Teacher Tally Frequency

Mrs. Day

Mr. Hughes

Ms. Kirk

Mr. York

(3)

(b) Write down the number of Gail's friends who are taught maths by Mr. York.

……………………(1)

Gail decides to represent her results with a pie chart.

(c) Work out the size of the angle at the centre of the sector that represents Mr. York.

°……………………

(2)

(Total 6 marks)


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Q5

5. (a) Here is a list of numbers.

18 31 37 48 53 59 62 69 73 79

From this list, write down

(i) the number closest to 50,

…………………

(ii) the number closest to 25,

…………………

(iii) two numbers that add together to make 100.

…………… and ……………(3)

(b) Here is another list of numbers.

2 15 25 32 36 48 50 69 75 81

Write down all the numbers from this list that are square numbers.

………………………………………(2)

(Total 5 marks)


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Q6

6.

On the circle above, draw and label

(a) a radius,(1)

(b) a chord,(1)

(c) a tangent.(1)

(Total 3 marks)


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Q7

Q8

7. Jez records how many phone calls he makes each day for a week.Here are his results.

6 3 8 7 4 2 3

For this week,

(a) write down the mode of the number of calls he makes,

……………………(1)

(b) write down the range of the number of calls he makes,

……………………(1)

(c) find the median of the number of calls he makes.

……………………(1)

(Total 3 marks)

8. Brian thinks of a number.

He subtracts 5 from the number and then divides the result by 2.

His answer is 19.

What number did Brian first think of?

……………………

(Total 2 marks)


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Q9

9.

The diagram shows a shaded shape on a centimetre square grid.

(a) Find

(i) the perimeter of the shaded shape,

…………………… cm

(ii) the area of the shaded shape.

…………………… cm2

(2)

The shaded shape is the cross-section of a prism of length 5 cm.

(b) Work out the volume of the prism.

…………………… cm3

(2)

(Total 4 marks)


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Q10

Q11

10. Find the value of

(a) 4.52

…………………………(1)

(b)1

23

…………………………(1)

(Total 2 marks)

11. 26% of a farmer's land is used to grow wheat.

(a) Write down the percentage of the farmer's land that is not used to grow wheat.

…………………… %(1)

In 2006 the farmer produced 65 tonnes of wheat.In 2007 he produced 67.6 tonnes of wheat.

(b) Work out the percentage increase in the amount of wheat he produced.

…………………… %(3)

(Total 4 marks)


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Q12

Q13

12. Suggest a sensible metric unit for measuring

(a) the length of a bracelet,

………………………………(1)

(b) the weight of a table,

………………………………(1)

(c) the volume of water that can be carried in a bucket.

………………………………(1)

(Total 3 marks)

13. Dunia recorded the distance, d m, of each jump in a triple jump competition.

This table summarises her results.

Distance (d m) Number of jumps

6 ≤ d < 7 7

7 ≤ d < 8 14

8 ≤ d < 9 11

9 ≤ d < 10 6

10 ≤ d < 11 2

(a) Find the class interval in which the median lies.

………………………………(2)

(b) Explain how you found the class interval in which the median lies.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………(2)

(Total 4 marks)


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Q14

14. (a) Here are the first five terms of a number sequence.

18 23 28 33 38

(i) Write down the next two terms of this sequence.

…………… , ……………

(ii) Describe the rule for continuing this sequence.

…………………………………………………………………………………

…………………………………………………………………………………(3)

(b) Here are some patterns made with sticks.

Pattern 1 Pattern 2 Pattern 3

Find the number of sticks in Pattern 5.

………………………(2)

(Total 5 marks)


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Q15

Q16

15. (a) Solve x5

= 3

x = ……………………(1)

(b) Multiply out y(y – 2)

………………………………(1)

(c) Solve 7z + 3 ≥ 31

………………………………(2)

(Total 4 marks)

16. Neil walks once round a 400 metre running track.He takes 520 steps.

Work out the average length, in centimetres, of one of Neil's steps.Give your answer correct to an appropriate degree of accuracy.

…………………… cm

(Total 4 marks)


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Q17

17. Diagram NOTaccurately drawn

Phil makes a model of a boat using a scale of 1 : 50

Phil's model is 30 cm long.

(a) Work out the length of the boat.Give your answer in metres.

…………………… m(2)

The maximum width of the boat is 4.5 m.

(b) Work out the maximum width of Phil's model.Give your answer in centimetres.

…………………… cm(2)

(Total 4 marks)


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Q18

Fred PatHarry

O

O

O

P

O

O

18. Fred, Harry and Pat go to the canteen to get lunch.

They can choose to have an omelette (O) or a pizza (P).

(a) List all the different combinations that they could choose.Two are done for you.

(2)

Each of these combinations is equally likely.

(b) Write down the probability that

(i) all three of them have an omelette,

…………………………

(ii) exactly one of them has an omelette.

…………………………(2)

(Total 4 marks)


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Q19

Q20

4 cm

7 cm

8 cm

10 cm

6 cm

19. (a) Find the cube root of 21.952

………………………(1)

(b) Work out 3.6− 0.721.4× 0.37

………………………(2)

(Total 3 marks)

20. Calculate the area of each shape.

(a) Diagram NOTaccurately drawn

…………………… cm2

(1)

(b) Diagram NOTaccurately drawn

………………………… cm2

(2)

(Total 3 marks)


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Q21

A C

B

6.8 cm

5.3 cm

103°

A C


The diagram shows a sketch of triangle ABC.

AB = 6.8 cm.AC = 5.3 cm.Angle BAC = 103°.

Make an accurate drawing of triangle ABC.The line AC has been drawn for you.

(Total 2 marks)


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Q22

r

22. (a) Simplify x4 × x4

……………………(1)

(b) Simplify x + y + 3x – 3y

…………………………(2)

(c) Diagram NOTaccurately drawn

The diagram shows a shape made from a trapezium and two semicircles.

The area, A, of the shape is given by the formula

A = r2(8 + π).

Calculate the value of A when r = 3.2 cm.Give your answer correct to the nearest square centimetre.

A = ………………………… cm2

(2)

(Total 5 marks)


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Q23

B

y

E

x

D

C

A F


In the diagram, ABCDE is a regular pentagon and AEF and CDF are straight lines.

(a) Work out the size of angle x.

°…………………

(2)

(b) (i) Work out the size of angle y.

°…………………

(ii) Give reasons for your answer.

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………(3)

(Total 5 marks)


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Q24

1

2

3

4

y

1 2 3 4 x1

2

3

4

z

O AG F

D

C

E

B


The diagram shows a cuboid on a 3-dimensional grid.

The point B has coordinates (4, 0, 2) and the point D has coordinates (0, 2, 0).

(a) Write down the coordinates of the points

(i) A,

( …… , …… , …… )

(ii) G.

( …… , …… , …… )(2)

(b) Draw one plane of symmetry for this cuboid on the diagram.(2)

(Total 4 marks)


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Q25

–6

–4

O

–2

2

4

6

y

1 2 3 4 x–2 –1

25. (a) On the grid, draw the graph of y = x2 – 2x – 5 for values of x from –2 to 4.

(4)

(b) Use your graph to find estimates of the solutions to the equation

x2 – 2x – 5 = 0

x = …………… or x = ……………(2)

(Total 6 marks)


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Q26

26. (a) The number 135 can be written in the form 3x × y, where x and y are prime numbers.

Find the value of x and the value of y.

x = ……………………

y = ……………………(2)

(b) Find the Highest Common Factor (HCF) of 60 and 135.

……………………(2)

(c) Find the Lowest Common Multiple (LCM) of 60 and 135.

……………………(2)

(Total 6 marks)

TOTAL FOR PAPER: 100 MARKS

END


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