Pastpaper

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

MATHEMATICS

*058002*
0580/02 0581/02

Paper 2 (Extended)

Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments October/November 2004 Mathematical tables (optional) Tracing paper (optional) 1hour 30 minutes

Candidate NameCentre Number

Candidate Number

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 in the spaces provided on the Question Paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN THE BARCODE. DO NOT WRITE IN THEGREY AREAS BETWEEN THE PAGES.

Answer all questions. If working is needed for any question it must be shown below that question. The number of marks is given in brackets [ ] at the end of each question or part question.
For Examiner's Use

The total number of marks for this paper is 70. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and ifthe answer is not exact, give the answer to three significant figures. Given answers in degrees to one decimal place. For π , use either your calculator value or 3.142. This document consists of 11 printed pages and 1 blank page.
IB04 11_0580_02/5RP © UCLES 2004

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2 1 A pattern of numbers is shown below.
1 1 1 1 1 1 1 6 5 x 4 10 20 3 6 10 x 2 3 4 5 6 1 1 1 1 1 1
For Examiner'sUse

Write down the value of x. Answer [1]

3

2

Calculate ( 3 + 3 3 ) giving your answer correct to 1 decimal place.

Answer

[2]

22
3 From the list of numbers , π , 14 , 16 , 27.4,

65
write down

7
(a) one integer,

13

Answer(a)

[1]

(b) one irrational number. Answer(b) [1]

4

Solve the inequality

5 − 3 x < 17 .

Answer

[2]

© UCLES 20040580/02/O/N/04

3 5 Solve the equation

3x − 2 = 8. 5

For Examiner's Use

Answer x = 6
120

[2]

100

80

Distance from Hilltown (km)

60

40

20

0 08 00

08 30 Time

09 00

09 30

The graph shows the distance, in kilometres, of a train from Hilltown. Find the speed of the train in kilometres per hour at (a) 08 30,

Answer(a) (b) 09 00.

km/h [2]

Answer(b)km/h [1]

© UCLES 2004

0580/02/O/N/04

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4 7 The air resistance (R) to a car is proportional to the square of its speed (v). When R = 1800, v = 30. Calculate R when v = 40.

For Examiner's Use

Answer R =

[3]

8

In 1997 the population of China was 1.24 × 109. In 2002 the population of China was 1.28 × 109. Calculate the percentage increase from 1997 to 2002.

Answer% [2]

9

8, A sequence of numbers is shown above. (a) Find the 10th term of the sequence.

15,

22,

29,

36, ……..

Answer(a) (b) Find the nth term of the sequence.

[1]

Answer(b) (c) Which term of the sequence is equal to 260?

[1]

Answer(c)

[1]

© UCLES 2004

0580/02/O/N/04

5 10 A mountain railway AB is of length 864 m and rises at an angle of 12o to thehorizontal. A train is 586 m above sea level when it is at A. Calculate the height above sea level of the train when it reaches B.
B 864 m 12o NOT TO SCALE A

For Examiner's Use

Answer

m [3]

11

= {40, 41, 42, 43, 44, 45, 46, 47, 48, 49} A = {prime numbers} B = {odd numbers} (a) Place the 10 numbers in the correct places on the Venn diagram.

B A

[2] (b) State the value of n ( B ∩A' ) . Answer(b) [1]

12 Make c the subject of the formula

3c − 5 = b .

Answer c =

[3]

© UCLES 2004

0580/02/O/N/04

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6 13 A square has sides of length d metres. This length is 120 metres, correct to the nearest 10 metres. (a) Complete the statement in the answer space. Answer(a) d< [1]

For Examiner's Use

(b) Calculate the difference between the largest and...