Write Down Your Answers in the Spaces Provided

Centre Number / Paper Reference / Surname / Other Names
Candidate Number / Candidate Signature
1387 / For Examiner’s use only
Edexcel GCSE / For Team Leader’s use only
Mathematics A
Paper 5
HIGHER TIER
Specimen Paper
Time: 2 hours / N0000
Materials required for the examination / Items included with these question papers
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser.
Tracing paper may be used. / Formulae sheets
Instructions to Candidates
In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.
Answer all questions in the spaces provided in this book.
Supplementary answer sheets may be used
Information for Candidates
The total mark for this paper is 100.
The marks for the various parts of questions are shown in round brackets: e.g. (2).
Tracing paper may be used.
Calculators must not be used.
This question paper has 20 questions. There are no blank pages.
Advice to Candidates
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
If you cannot answer a question, leave it and attempt the next one.
Return at the end to those you have left out.
N0000
© 2000 Edexcel
This publication may only be reproduced in accordance with Edexcel copyright policy.
Edexcel Foundation is a registered charity. /

Turn over

Answer ALL TWENTY THREE questions.

Write down your answers in the spaces provided.

Do NOT use a calculator. You must write down all stages in your working.

1. The exterior angle of a regular polygon is 30º.

Work out the number of sides in the regular polygon. SSM2d

Grade C

……………………… sides

(Total 2 marks)

2. Here are the equations of 5 straight lines.

They are labelled from A to E.

A

/ y = 2x + 1
B / y = 1 – 2x
C / 2y = x – 1
D / 2x – y = 1
E / x + 2y = 1

(a) Put ticks in the table to show the two lines that are parallel. NA6c

Grade C

(2)

(b) Write down the two lines that are perpendicular to line E NA6c

Grade A

…………………………..

(2)

(Total 4 marks)

3. The mass of an atom of Uranium is kg.

(a) Calculate the mass of 3 000 000 atoms of Uranium. NA3h

Give your answer in standard form. Grade B

………………………………..

(2)

(b) Evaluate NA2b

Grade B

…………………..

(1)

(Total 3 marks)

Two rods are fastened together.

The total length is inches.

The length of rod B is inches.

Find the length of rod A. NA3c

Grade C

……………..…. inches

(Total 3 marks)

5. (a) (i) Express 72 and 96 as products of their prime factors. NA3a

Grade C

72 = ……………………….……..

96 = ……………………….……..

(4)

(ii) Use your answer to (i) to work out the Highest Common Factor of 72 and 96. NA2a

Grade C

…………………

(2)

(b) Change the decimal into a fraction in its lowest terms. NA3c

Grade A

………………….

(3)

(Total 5 marks)

6. Sybil weighed some pieces of cheese

The table gives information about her results.

Weight (w) grams /

Frequency

90 < w ≤ 94 / 1
94 < w ≤ 98 / 2
98 < w ≤ 102 / 6
102 < w ≤ 106 / 1

Work out an estimate of the mean weight. HD4e

Grade C

………………. grams

(Total 4 marks)

7. (a) Simplify

(i)

…………………..

(ii)

…………………..

(2)

(b) Expand and simplify

(i) (2x + 3)(x – 2) NA5b

Grade B

……………………………..

(ii) (3x – 2)²

……………………………

(4)

x² – 3x – 10 = 0 NA5k

Grade B

…………………………………….

(3)

(d) Solve the equation

NA5f

Grade B

h = ………………..

(4)

(Total 13 marks)

Find the size of the largest angle in the pentagon. SSM2d

NA3e

Grade C

……………………………………..

(Total 6 marks)

9. A boy has a pen that is of length 10 cm, measured to the nearest centimetre.

His pen case is of length 10.1 cm, measured to the nearest millimetre.

Explain why it might not be possible for him to fit the pen in the pen case. SSM4a

Grade B

………………………………………………………………………………………………..

(Total 3 marks)

10. There are 12 boys and 15 girls in a class.

In a test the mean mark for the boys was n.

In the same test the mean mark for the girls was m.

Work out an expression for the mean mark of the whole class of 27 students. HD4e

Grade B

………………………………

(Total 3 marks)

11.

(a) Work out the length of AD. SSM2g

Grade B

…………….. cm

(2)

(b) Work out the length of BC. SSM2g

Grade B

………… cm

(2)

(Total 4 marks)

12. A wax statue of a spaceman is on display in a museum..

Wax models are to be sold in the museum shop.

The statue and the wax models are similar.

The height of the statue is 1.8 m

The height of the model is 15 cm.

The area of the flag in the model is 10 cm²

(a) Calculate the area of the statue’s flag. SSM3d

Grade A

………………………. cm²

(3)

The volume of the wax of the original statue is 172.8 litres.

(b) Calculate the volume of wax used to make the model. SSM3d

Give your answer in ml. Grade A

………………………. ml

(2)

(Total 5 marks)

13. K is an integer.

Find the value of K. NA4a

Grade A

K = ………………..

(Total 3 marks)

14. The probability that a team will win a game is always 0.5.

The team plays n games.

The probability that the team will win all of the n games is less than 0.05.

Find the smallest value of n. HD4g

Grade A

……………………

(Total 3 marks)

15. The intensity of light L, measured in lumens, varies inversely as the square of the distance d m from the light.

When the distance is 2 m the light intensity is 250 lumens.

(a) Calculate the value of L when d is 2.5 m. NA5h

Grade A

…………… lumens

(3)

(b) Calculate the value of d when L is 90 lumens. NA5h

Grade A

……………. m

(2)

(Total 5 marks)

16.

ABCD is a parallelogram.

Prove that triangles ABD and BCD are congruent. SSM2e

Grade A

(Total 3 marks)

17. The equation of a curve is

y = f(x)

where f(x) = x² – 10x + 32.

(a) Complete the square for f(x). NA5k

Grade A*

………………………………..

(2)

(b) Hence, sketch the graph of

(i) y = f(x)

(ii) y = f(x + 5) NA6g

Grade A*

(4)

y = f(x) where

f(x) = sin x where 0 ≤ x ≤ 180°

Grade A*

(2)

(Total 8 marks)

18.

OA = a OB = b AC = 2a OD = 3b

Prove that AB is parallel to CD. SSM3f

Grade A*

(Total 3 marks)

19. The diagram represents a right pyramid.

The base is a square of side 2x.

The length of each of the slant edges

is 8√3 cm.

The height of the pyramid is x cm.

Calculate the value of x.

SSM2f

Grade A*

………………….. cm

(Total 6 marks)

20. Solve the equation

NA6e

Grade A*

x = ………………………….

(Total 6 marks)

21. Leon recorded the lengths, in minutes, of the films shown on television in one week.

His results are shown in the histogram.

20 films had length from 60 minutes up to, but not including, 80 minutes.

(a) Use the information in the histogram to complete the table. HD4a

Grade A

Length in minutes (m) / Frequency
60 ≤ m < 80 / 20
80 ≤ m < 90
90 ≤ m < 100
100 ≤ m ≤ 120

(2)

Leon also recorded the lengths, in minutes, of all the films shown on television the following week. His results are given in the table below.

Length in minutes (m) / Frequency / Height
60 ≤ m < 100 / 72 / 36
100 ≤ m < 160 / x

(b) Complete the table giving your answers in terms of x. HD4a

Grade A*

(2)

(Total 4 marks)

TOTAL FOR PAPER: 100 MARKS

Turn over

Centre Number / Paper Reference / Surname / Other Names
Candidate Number / Candidate Signature
1387 / For Examiner’s use only
Edexcel GCSE / For Team Leader’s use only
Mathematics A
Paper 6
HIGHER TIER
Specimen Paper
Time: 2 hours / N0000
Materials required for the examination / Items included with these question papers
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser, calculator.
Tracing paper may be used. / Formulae sheets
Instructions to Candidates
In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.
Answer all questions in the spaces provided in this book.
Supplementary answer sheets may be used
Information for Candidates
The total mark for this paper is 100.
The marks for the various parts of questions are shown in round brackets: e.g. (2).
Tracing paper may be used.
Calculators may be used.
This question paper has 20 questions. There are no blank pages.
Advice to Candidates
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
If you cannot answer a question, leave it and attempt the next one.
Return at the end to those you have left out.
N0000
© 2000 Edexcel
This publication may only be reproduced in accordance with Edexcel copyright policy.
Edexcel Foundation is a registered charity. /

Turn over

Leave

blank

Answer ALL NINETEEN questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1. Calculate

NA3o

Grade C

………………………

(Total 3 marks)

2. Tony carries out a survey about the words in a book.

He chooses a page at random.

He then counts the number of letters in each of the first hundred words on the page.

The table shows Tony’s results.

Number of letters in a word / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Frequency / 6 / 9 / 31 / 24 / 16 / 9 / 4 / 1

The book has 25000 words.

Estimate the number of 5 letter words in the book. HD4b

Grade C

……………………….

(Total 3 marks)

The diagram shows a field which a farmer wants to fence.

The field is in the shape of an isosceles trapezium in which AB is parallel to DC and AD = BC.

AB = 80 m and CD = 60 m.

The distance between the parallel sides is 30 m.

Calculate the length of fencing the farmer will need. SSM2f

Grade C

……………………… m

(Total 5 marks)

4. Wayne shares £360 between his children, Sharon and Liam, in the ratio of their ages.

Sharon is 13 years old and Liam is 7 years old.

(a) Work out how much Sharon receives. NA3f

Grade C

Sharon £ …………

(2)

(b) What percentage of the £360 does Sharon receive? NA3f

Grade C

………………………. %

(2)

(Total 4 marks)

5. (a) Solve the equation Grade C

NA5f

7p + 3 = 3(p –1)

p = …………….

(2)

q is an integer such that 0 < 3q £ 16

(b) List all the possible values of q. Grade C

NA5j

…………………………….

(2)

NA5j

…………….……….

(3)

(Total 7 marks)

6. The Andromeda Galaxy is 21 900 000 000 000 000 000 km from the Earth.

(a) Write 21 900 000 000 000 000 000 in standard form. Grade B

NA3h

………………………

(1)

Light travels km in one year.

(b) Calculate the number of years that light takes to travel from the Andromeda Galaxy to Grade B

Earth. NA3m

Give your answer in standard form correct to 2 significant figures.

………………………

(2)

(Total 3 marks)

A, B and C are points on the circumference of a circle, with centre O.

(i) Find angle AOC. Grade B

SSM2h

……………………….

(ii) Give a reason for your answer.

…………………………………………………………………………………………………...

(Total 2 marks)

8. (a) Expand Grade C

NA5b

………………………..

(2)

(b) Factorise completely Grade B

NA5b

ax + ay – by – bx..

………………………..

(2)

NA5d

………………………..

(2)

(d) Solve the simultaneous equations Grade B

NA5i

x = …………

y = …………

(4)

(Total 10 marks)

On the grid, triangle Q is the image of triangle P after a reflection.

(a) Rotate triangle Q through 90° clockwise about (2, 1). Grade C

Label this image R. SSM3b

(2)

(b) Describe fully the single transformation which maps triangle P onto triangle R. Grade B

SSM3a

…………………………………….………………………………………………………...

(2)

(Total 4 marks)

10. The cumulative frequency graph gives information about the examination marks of a group of students.

(a) How many students were in the group? Grade B

HD5d

…………

(1)

(b) Use the graph to estimate the inter-quartile range. Grade B