Surname Centre No.

Initial(s)

Paper Reference

Candidate No.

5 3 8 4H

1 3H

Signature

Paper Reference(s)

5384H/13H

Examiner’s use only

Edexcel GCSE

Team Leader’s use only

Mathematics (Modular) – 2381 Paper 13 (Non-Calculator)

Higher Tier Unit 3 – Section A Mock Terminal Paper Time: 1 hour 10 minutes Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Items included with question papers Nil

Instructions to Candidates In the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question paper. Answer ALL the questions. Write your answers in the spaces provided in this question paper. You must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit. If you need more space to complete your answer to any question, use additional answer sheets.

Information for Candidates The marks for individual questions and the parts of questions are shown in round brackets: e.g. (2). There are 18 questions in this question paper. The total mark for this paper is 60. There are 16 pages in this question paper. Any blank pages are indicated. Calculators must not be used.

Advice to Candidates Show all stages in any calculations. 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.

This publication may be reproduced only in accordance with Edexcel Limited copyright policy. ©2007 Edexcel Limited. Printer’s Log. No.

N33854A W850/XXXX/57570 2/2

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Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of a prism = area of cross section × length

cross section length

Volume of sphere = 34 πr 3

Volume of cone = 13 πr 2h

Surface area of sphere = 4πr 2

Curved surface area of cone = πrl

r

l

h r

In any triangle ABC

The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a ≠ 0, are given by

C b A

Sine Rule

a B

c

x=

−b ± (b 2 − 4ac ) 2a

a b c = = sin A sin B sin C

Cosine Rule a2 = b2 + c 2– 2bc cos A Area of triangle = 12 ab sin C

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Answer ALL EIGHTEEN questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator for this paper.

1.

(a) Write down the reciprocal of 9 .............................. (1) (b) Work out

3 of 35 7

.............................. (2) (c) Write

3 as a decimal. 8

............................................... (2)

Q1

(Total 5 marks) 2.

Work out

2

1 5 + 3 4 7

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

Q2

(Total 3 marks)

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3

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3.

5x + 2 = 3x − 7

(a) Solve

x = ................... (3) y 3 = 11 4

(b) Solve

y = ................... (2)

Q3

(Total 5 marks) 4. x 4 cm

B

A 6 cm

Diagram NOT accurately drawn

24 cm

Rectangle B is an enlargement of rectangle A. Work out the value of x.

x = ................... cm (Total 2 marks)

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Q4

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5.

Here is part of a travel graph of Jacob’s journey from his house to the library. y 16 Distance in km 12 from Jacob’s house 8

4

O

10

20

30

40

50

60

70

80

x

Time in minutes

(a) How far is Jacob’s house from the library? .............................. km (1) (b) Work out Jacob’s speed for the first 20 minutes of his journey. Give your answer in km/h.

.............................. km/h (2) Jacob spends 30 minutes at the library. He then travels back to his house at a steady speed of 64 km/h. (c) Complete the travel graph. (2)

Q5

(Total 5 marks)

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5

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6.

The diagram shows the position of Blackport and the position of Clancy Bay. N

N Blackport ×

× Clancy Bay

The bearing of a ship from Blackport is 140°. The bearing of the ship from Clancy Bay is 200°. In the space above, draw an accurate diagram to show the position of the ship. Mark this position with a cross ×. Label it P.

Q6

(Total 3 marks) 7.

Make y the subject of the formula 5x + 3y = 7

y = .............................. (Total 2 marks)

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Q7

8.

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An inequality in x is shown on the number line.

−3

−2

−1

0

1

2

3

4

x

(a) Write down the inequality. .................................................... (2) n is an integer such that −3 < n ” 2 (b) List all the possible values of n.

.............................................................................. (2)

Q8

(Total 4 marks) 9.

(a) Simplify 95 × 910 Write your answer as a power of 9

................... (1) (b) Simplify 728 ÷ 77 Write your answer as a power of 7

................... (1)

Q9

(Total 2 marks)

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7

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10. The diagram shows a solid object made from centimetre cubes. Diagram NOT accurately drawn

(a) In the space below, sketch the front elevation of the solid object from the direction marked with the arrow.

(2) (b) In the space below, sketch a plan of the solid object.

(2) (Total 4 marks)

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Q10

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y

11.

5 4 3 2

P

1 –5

–4

–3

–2

–1

O

1

2

3

4

5

x

–1 –2 –3 –4 –5 Triangle P is reflected in the y axis to give triangle Q. Triangle Q is then reflected in the x axis to give triangle R. Describe the single transformation that takes triangle P to triangle R. .............................................................................................................................................. ..............................................................................................................................................

Q11

(Total 3 marks) 12. (i) Factorise

x2 + 8x − 33

.................................................... (ii) Hence solve

x2 + 8x − 33 = 0

x = ................... or x = ...................

Q12

(Total 3 marks)

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9

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13. Diagram NOT accurately drawn O

A

68°

B

A, B and C are points on the circumference of a circle, centre O. AOB is a straight line. Angle BOC = 68°. Find the size of angle BAC. Give a reason for your answer. ................... ° .............................................................................................................................................. ..............................................................................................................................................

Q13

(Total 2 marks) 14. n is an integer. Explain why n3 + n is always even.

Q14 (Total 2 marks) 10

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y

15.

6 5 A

4 3 2 1 –2

B

–1 O

1

2

3

4

5

6

7

x

–1 –2

(a) Work out the gradient of the line AB. .............................. (2) (b) Write down the gradient of a line perpendicular to the line with equation y=−

1 x−3 4

.............................. (1) (c) Write down the equation of the line that is parallel to y = 6x + 1 and passes through the point (0, 5).

.................................................... (2)

Q15

(Total 5 marks)

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11

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16. Find the value of (i)

6−2

................... 2

(ii)

27 3

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

Q16

(Total 3 marks) 17. Rationalise

6 8 2

Give your answer in the form

p 2 + q where p and q are positive integers.

.................................................... (Total 3 marks)

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Q17

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18.

P

A

B

Diagram NOT accurately drawn

C ABC is a right-angled triangle. P is a point on AB such that AP = 4PB. BC = 3PB Angle ACB = 90°. Show that sin B =

k where k is an integer. 5

Write down the value of k.

k = ..............................

Q18

(Total 4 marks) TOTAL FOR PAPER: 60 MARKS END

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