Maths Paper

Topics: University of Cambridge, Decimal, Triangle Pages: 17 (2107 words) Published: August 25, 2013
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

*9202671358*

CAMBRIDGE INTERNATIONAL MATHEMATICS Paper 4 (Extended)

0607/04
October/November 2010 2 hours 15 minutes

Candidates answer on the Question Paper Additional Materials: Geometrical Instruments Graphics Calculator

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. Do not use staples, paper clips, highlighters, glue or correction fluid. You may use a pencil for any diagrams or graphs. DO NOT WRITE IN ANY BARCODES. Answer all the questions. Unless instructed otherwise, give your answers exactly or correct to three significant figures as appropriate. Answers in degrees should be given to one decimal place. For π, use your calculator value. You must show all the relevant working to gain full marks and you will be given marks for correct methods, including sketches, even if your answer is incorrect. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 120. For Examiner's Use

This document consists of 18 printed pages and 2 blank pages. IB10 11_0607_04/3RP © UCLES 2010

[Turn over

2 Formula List For the equation ax + bx + c = 0
2

x=

_ b ± b2 _ 4ac 2a
A = 2πrh A = πrl A = 4πr2 V=

Curved surface area, A, of cylinder of radius r, height h. Curved surface area, A, of cone of radius r, sloping edge l. Curved surface area, A, of sphere of radius r. Volume, V, of pyramid, base area A, height h. Volume, V, of cylinder of radius r, height h. Volume, V, of cone of radius r, height h.

1 3

Ah

V = πr2h V=

1 3 4 3

πr2h

Volume, V, of sphere of radius r.

V=

πr3

A

a b c = = sin A sin B sin C

c

b

a2 = b2 + c2 – 2bc cos A Area =

1 2

bc sin A

B

a

C

© UCLES 2010

0607/04/O/N/10

3 Answer all the questions. 1 A train from Picton to Christchurch leaves Picton at 13 00. The length of the journey is 340 km. (a) The train arrives at Christchurch at 18 21. Show that the average speed is 63.55 km/h, correct to 2 decimal places. For Examiner's Use

[4] (b) One day the weather is bad and the average speed of 63.55 km/h is reduced by 15 %. (i) Calculate the new average speed.

Answer(b)(i) (ii) Calculate the new time of arrival at Christchurch. Give your answer to the nearest minute.

km/h

[2]

Answer(b)(ii)

[3]

© UCLES 2010

0607/04/O/N/10

[Turn over

4 2 (a) (i) Find the value of 27 × 36.
For Examiner's Use

Answer(a)(i) (ii) Write your answer to part (i) in standard form.

[1]

Answer(a)(ii) (b) Find the value of

[1]

1

( 22 )

3

, giving your answer in standard form.

Answer(b) (c) m5 = 2000. Find the value of m.

[2]

Answer(c) (d) 5n = 2000. Find the value of n.

[1]

Answer(d)

[2]

© UCLES 2010

0607/04/O/N/10

5 3 (a) Solve the equation x2 + 2x – 4 = 0. Give your answers correct to 2 decimal places. For Examiner's Use

Answer(a) x = (b) Solve the inequality x2 + 2x – 4 Y 0.

or x =

[3]

Answer(b)

[2]

© UCLES 2010

0607/04/O/N/10

[Turn over

6 4
5 y
For Examiner's Use

0

x 5

(a) On the diagram above, sketch the lines (i) x + y = 5, (ii) y = 1, (iii) y = 2x. (b) Write R in the region where x [ 0, y [ 1, y [ 2x and x + y Y 5. [1] [1] [1] [1]

© UCLES 2010

0607/04/O/N/10

7 5 The numbers of passengers in 72 taxis arriving at a city centre were recorded. The table shows the results. Number of passengers Frequency (a) Find (i) the range, Answer(a)(i) (ii) the mode, Answer(a)(ii) (iii) the median, Answer(a)(iii) (iv) the mean, Answer(a)(iv) (v) the upper quartile. Answer(a)(v) (b) The probability that a taxi, chosen at random, had n passengers is 3 . 8

For Examiner's Use

1 7

2 27

3 19

4 8

5 9

6 2

[1]

[1]

[1]

[1]

[1]

Find the value of n....
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