Surname Centre No.

Initial(s)

Paper Reference

5 3 8 4H

Candidate No.

1 4H

Signature

Paper Reference(s)

5384H/14H

Examiner’s use only

Edexcel GCSE

Team Leader’s use only

Mathematics (Modular) – 2381 Paper 14 (Calculator)

Higher Tier Unit 3 Section B Mock Paper Time: 1 hour 10 minutes Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. 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 19 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 may be used. If your calculator does not have a S button, take the value of S to be 3.142 unless the question instructs otherwise.

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.

N33853A W850/R5384H/57570 2/2/2/2

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GCSE Mathematics 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 NINETEEN questions. Write your answers in the spaces provided. You must write down all stages in your working.

1.

B

A Reflect the shaded shape in the line AB.

Q1 (Total 2 marks)

2.

Two girls share £24.80 in the ratio 3: 5 Work out the difference between the larger share and the smaller share.

£ ...........................

Q2

(Total 3 marks)

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3

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3.

5 cm

Diagram NOT accurately drawn

A circle has a radius of 5cm. Work out the area of the circle. Give your answer correct to 1 decimal place. Write down the units in your answer.

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

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

Q3

(Total 3 marks) 4.

A stall sells apples and figs. Apples cost a pence each. Figs cost f pence each. Sanjay buys 5 apples and 2 figs. The total cost is C pence. Write down a formula for C in terms of a and f.

......................................................... (Total 3 marks) 4

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Q4

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5.

Write 20 minutes as a fraction of 2 hours. Write your answer as a fraction in its simplest form.

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

Q5

(Total 2 marks) 6.

P

On the grid, rotate the shaded triangle through 90°, anticlockwise, about the point P.

Q6

(Total 2 marks)

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5

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7.

(a) Simplify

(i) (x4)3

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

(ii) y6 ÷ y2

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

(b) Ruth says that 7x + 2x  5 is an equation. Ruth is wrong. Explain why. ....................................................................................................................................... (1)

Q7

(Total 3 marks) 8. A Diagram NOT accurately drawn

x+7 B

2x − 1

C

ABC is an isosceles triangle with AB = AC. BC = (2x  1) centimetres. AC = (x + 7) centimetres. The perimeter of the triangle is 27 centimetres. Work out the length of BC.

............................ centimetres (Total 4 marks)

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Q8

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9.

Diagram NOT accurately drawn

40°

The exterior angle of a regular polygon is 40q. Work out the number of sides of this regular polygon.

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

Q9

(Total 2 marks)

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7

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y = x2  x + 3

10. (a) Complete the table of values for x

3

y

15

2

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1

0

1

5

2

3

5

9 (2)

y = x2  x + 3

(b) On the grid, draw the graph of

for

3 - x - 3

y 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 −3

−2

−1

0

1

2

3

x

−1 −2 (2) (Total 4 marks) 8

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Q10

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11. The equation 2x3  x = 200 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show ALL your working.

x = ...............................

Q11

(Total 4 marks)

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9

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12. (a) On the diagram, draw the locus of points which are 3 cm from B. (1) (b) On the diagram, draw accurately the locus of points which are the same distance from the line OA and from the line OB. (2)

A

O

B

Q12 (Total 3 marks)

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13. Jean invests £6000 for 3 years at 5% compound interest per annum. Calculate the value of her investment at the end of the 3 years.

Q13

£ .................................. (Total 3 marks) 14. Calculate the value of 8.343 − 2.9 tan 35° 7.1 + 6.25 Write down all the figures on your calculator display.

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

Q14

(Total 2 marks)

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11

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15. The table shows some expressions. the letters a, b and c represent lengths. S, 2 and 3 are numbers that have no dimensions. Tick () the boxes underneath the three expressions which could represent areas.

2b(3a + c)

3Sc

ac 2 b

2a3  b2

3c + 2b

3a2


b2 2a Q15 (Total 3 marks)

16. In a sale, the normal prices are reduced by 20%. In the sale, Hajra pays £27.60 for a skirt.

% 20 ff o

Calculate the normal price of the skirt.

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

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17. To the nearest metre, x = 24 m and y = 6 m. (a) Calculate the upper bound for the value of xy Write down all the numbers shown on your calculator display.

........................................ m (2) (b) Calculate the lower bound for the value of

x y

Write down all the numbers shown on your calculator display.

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

Q17

(Total 4 marks)

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13

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18. D 6.2 cm

O

Diagram NOT accurately drawn E

80°

6.2 cm F

ODEF is a sector of a circle with centre O. OD = OF = 6.2 cm. Angle DOF = 80° Calculate the area of the shaded segment DEF. Give your answer correct to 3 significant figures.

............................. cm2 (Total 5 marks) 14

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Q18

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19. Solve the simultaneous equations y = 11x + 3 y = 4x2

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

Q19

(Total 5 marks) TOTAL FOR PAPER: 60 MARKS END

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