CIE IGCSE Mathematics Paper 2 June 2003

[Pages:52]Centre Number

Candidate Number Name

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education

MATHEMATICS

0580/02

0581/02

Paper 2

May/June 2003

Candidates answer on the Question Paper. Additional Materials: Electronic calculator

Geometric instruments Mathematical tables (optional) Tracing paper (optional)

1 hour 30 minutes

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 soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question.

If working is needed for any question it must be shown below that question. The total of the marks for this paper is 70. 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 , use either your calculator value or 3.142.

If you have been given a label, look at the details. If any details are incorrect or missing, please fill in your correct details in the space given at the top of this page.

Stick your personal label here, if provided.

For Examiner's Use

MCS-UCB217-S34076/3 ? CIE 2003

This document consists of 12 printed pages.

[Turn over

2

1 Write in order of size, smallest first, 5 , 0.049, 5%. 98

5/98= 0.05I 5% = 0.05

Answer .0.....0..4..9.....`......5..%......`...5../..9..8.......... [2]

For Examiner's

use

2 The graph below can be used to convert between euros (e) and pounds (?).

6

4 Pounds (?)

2

0

2

(a) Change ?5 into euros. (b) Change e90 into pounds.

4

6

Euros (e)

8

10

Answer (a) e ...7....9.................................... [1] Answer (b) ? ..5.6.....5..0................................. [1]

3 The top speed of a car is 54 metres per second.

Change this speed into kilometres per hour.

54 metres per second = 54 x 60 m per minute

=54 x 60 x 60 m per hour =54 x 60 x 60 km per hour

Answer ........................I.9..4...............km h [2]

I00

=I94

2

5

4 a=

and b = .

-3

-1

Find 3a 0 2b.

( ) ( ) 3a = 6 2b = I0 ,

-9

-2

( ) ( ) 3a

-

2b=

6 -I0 -9-(-2)

=

-4 -7

Answer

( -4 ) -7

[2]

0580/2, 0581/2 Jun 2003

3

5 The ratios of teachers : male students : female students in a school are 2 : 17 : 18. The total number of students is 665. Find the number of teachers.

Teachers : male students : female students = 2 : I7 : I8

The number of students is 665 I part is 665 ? (I7 + I8) = I9 Teachers are 2 parts so 2 x I9 = 38

Answer ..................3..8.............................. [2]

For Examiner's

use

6 A rectangular field is 18 metres long and 12 metres wide. Both measurements are correct to the nearest metre. Work out exactly the smallest possible area of the field.

Smallest value of length = I7.5 metres Smallest value of width = II.5 metres

Area = length x width Smallest area = I7.5 x II.5

= 20I.25

Answer....................2..I.0.....2..5.................m2 [2]

7 Solve the inequality

3 ` 2x 0 5 ` 7.

Two inequalities, 3 < 2x-5 and 2x-5 < 7

3 + 5 < 2x

2x < 7 + 5

=>x > 4

=>x < 6

4 < x < 6

Answer .....4............ ` x ` .....6.................. [2]

8 Complete this table of squares and cubes. The numbers are not in sequence.

Number 3

+/..-.....I I ..I4..... .-..7....

Square 9

121

.I.9..6... .4.9.....

Cube 27

+/..-.....I33I

2744

0343

(Required numbers underlined and bold.)

[3]

0580/2, 0581/2 Jun 2003

[Turn over

4

9

y

4

For Examiner's

use

3 B

2 A

1

?3 ?2 ?1 0 ?1

1 2 3 4 5 6x

?2 (a) Find the gradient of the line AB.

gradient = Vertical ? horizontal =?I6 or 0.I6(...) or 0.I7

Answer (a) .......................0.....I.7................. [1]

(b) Calculate the angle that AB makes with the x-axis.

Angle = arc tan(part (a)) = 9.46? or 9.5?

Answer (b) .......................9....5..?................. [2]

10 Work out as a single fraction

2 _I

x - 3

x + 4

2 x-3

-

1 x+4 .

2(x + 4) - I(x - 3) (x - 3)(x + 4)

2x + 8 - x + 3

(x - 3)(x + 4)

__ x + I I____

x + I I

(x - 3)(x + 4)

Answer ....(.x..-...3..).(.x..+...4.).............................. [3]

11 Write each of these four numbers in the correct place in the Venn Diagram below.

2.6,

4 ,

12,

112

17

7

I2

Rational numbers 4

2.6

I7

Integers

( II2 )

7

[4]

0580/2, 0581/2 Jun 2003

5

For

Examiner's

use

12

B

NOT TO

SCALE

2p?

A

q?

O

3p? C

5q? D

E

A, B, C, D and E lie on a circle, centre O. AOC is a diameter. Find the value of

(a) p, (b) q.

Angle ABC = 90?

Hence 2p + 3p = I80-90

5p = 90?

p = I8?

Answer (a) p # ..........I8...?......................... [2]

q + 5q = I80? 6q = I80? q = 30?

Answer (b) q # .........3..0...?........................ [2]

0580/2, 0581/2 Jun 2003

[Turn over

6 13 A doctor's patients are grouped by age, as shown in the table and the histogram below.

Age (x years) Number of patients

0 x ` 10 300

10 x ` 30

30 x ` 60 60 x ` 100

600

I200

880

Required number underlined and bold

For Examiner's

use

Frequency density

0

20

40

60

80

Age in years

(a) Complete the following:

1 cm2 represents .................I.0..0...... patients.

(b) Use the histogram to fill in the blank in the table.

(c) Draw the missing two rectangles to complete the histogram.

100

[1] [1] [2]

5 4 2 1 -4

14 (a) Multiply

.

-3 -2 0 3 6

( ) 5x2 + 4x0 5xI + 4x3 5x-4 + 4x6 -3x2 + -2x0 -3xI + -2x3 -3x-4 + -2x6

Answer (a)

( ) I0 I7 4

-6 -9 0

[2]

54

(b) Find the inverse of

. -3 -2

The determinant is 5 x (-2) - (-3) x 4 = -I0-(-I2)

( ) I -2 -4

Answer (b) 2 3 5

[2]

= 2

0580/2, 0581/2 Jun 2003

7

15 In 1950, the population of Switzerland was 4 714 900. In 2000, the population was 7 087 000.

(a) Work out the percentage increase in the population from 1950 to 2000.

Population increase = 7 087 000 - 4 7I4 900 = 2 372 I00

Percentage increase = 2 372 I00 x I00

4 7I4 900 = 50.3%

Answer (a)..............................5..0.....3..... % [2]

(b) (i) Write the 1950 population correct to 3 significant figures.

4 7I4 900 = 4 7I0 000 or 4.7I x I06

Answer (b)(i) ...........4....7..I0.....0..0..0............... [1]

(ii) Write the 2000 population in standard form.

Answer (b)(ii) ....7....0..8..7....x....I.0..6.................. [1]

For Examiner's

use

16

NOT TO

B

SCALE

80 m

A

18?

D C

The diagram shows the start of a roller-coaster ride at a fairground. A car rises from A to B along a straight track.

(a) AB # 80 metres and angle BAC # 18?. Calculate the vertical height of B above A.

Sin I8? = BC/80

=>BC = 80 sin I8?

= 24.7m

Answer (a)......................2..4.....7............. m [2]

(b) The car runs down the slope from B to D, a distance of s metres. Use the formula s # t(p ! qt) to find the value of s, given that p # 4, t # 3 and q # 3.8.

s = t( p + qt) s = 3( 4 + 3.8 x 3)

s = 3 x 15.4 s = 46.2

Answer (b) s # ..............4..6....2................... [2]

0580/2, 0581/2 Jun 2003

[Turn over

8 17 (a) y

6 5 4 3 2 1

For Examiner's

use

0

1 2 3 4 5 6x

Draw the shear of the shaded square with the x-axis invariant and the point (0, 2) mapping onto the point (3, 2).

[2]

(b) y 6

5

4

3

2

1

0

1 2 3 4 5 6x

(i) Draw the one-way stretch of the shaded square with the x-axis invariant and the point (0, 2) mapping onto the point (0, 6).

[2]

(ii) Write down the matrix of this stretch.

The

unit

vector

(

I 0

)

stays

as

(

I 0

)

and

the

unit

vector

0

(I )

becomes

(

0 3

)

( ) I 0

Answer (b)(ii) 0 3

[1]

0580/2, 0581/2 Jun 2003

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