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MATHEMATICS Paper 2 (Extended) Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments

0580/02, 0581/02

May/June 2007 1 hour 30 minutes Mathematical tables (optional) Tracing paper (optional)

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. 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 ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for the paper is 70. For Examiner's Use

This document consists of 12 printed pages.

IB07 06_0580_02/6RP © UCLES 2007

[Turn over

2 1

For Examiner's Use

For the diagram above write down (a) the order of rotational symmetry, Answer(a) (b) the number of lines of symmetry. Answer(b) 2 (a) Use your calculator to work out 1 − (tan 40o )2 . 2(tan 40o )

[1]

[1]

Answer(a) (b) Write your answer to part (a) in standard form. Answer(b) 3 Xsara throws a ball three times at a target. Each time she throws the ball, the probability that she hits the target is 0.2. Calculate the probability that she does not hit the target in any of the three throws.

[1]

[1]

Answer

[2]

© UCLES 2007

0580/02/J/07

3 4 Write the following in order of size, smallest first. cos100° sin100° tan100° For Examiner's Use

Answer 5 A tin of soup has the following information on the label.

<

<

[2]

200 grams of soup contains Protein 4g Carbohydrate 8.7 g Fat 5.8 g

(a) What fraction of the soup is Protein? Give your answer in its simplest form.

Answer(a) (b) What percentage of the soup is Carbohydrate?

[1]

Answer(b) 6 Carmen spends 5 minutes, correct to the nearest minute, preparing one meal. She spends a total time of T minutes preparing 30 meals. Between what limits does T lie?

% [1]

Answer 7 M=

1 1 1 2

T< M3 =

5 8 8 13

[2]

M2 =

2 3

3 5

Find M4.

Answer M4 =

[2]

© UCLES 2007

0580/02/J/07

[Turn over

4 8 On the Venn diagrams shade the regions (a) A′ ∩ C′, A B C

For Examiner's Use

[1] (b) (A ∪ C ) ∩ B.

A B C

[1] 9 Write down (a) an irrational number, Answer(a) (b) a prime number between 60 and 70. Answer(b) 10 Write as a fraction in its simplest form [1] [1]

x −3 + 4 . x −3 4

Answer

[3]

© UCLES 2007

0580/02/J/07

5 11 A =

x 8 2 x

.

For Examiner's Use

(a) Find │A│, the determinant of A, in terms of x.

Answer(a) (b) Find the values of x when │A│= 9.

[1]

Answer(b) x = 12

or x =

[2]

y 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 x

By shading the unwanted parts of the grid above, find and label the region R which satisfies the following three inequalities y 3, y 5x and x + y 6. [3]

13 The quantity y varies as the cube of (x + 2). y = 32 when x = 0. Find y when x = 1.

Answer y =

[3]

© UCLES 2007

0580/02/J/07

[Turn over

6 14

For Examiner's Use

A

NOT TO SCALE

B

70o

C

The diagram shows three touching circles. A is the centre of a circle of radius x centimetres. B and C are the centres of circles of radius 3.8 centimetres. Angle ABC = 70°. Find the value of x.

Answer x = 15 Two unbiased spinners are used in a game. One spinner is numbered from 1 to 6 and the other is numbered...