Candidate Centre Number Number

Candidate Name

International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE

MATHEMATICS 0580/3,0581/3 PAPER 3 Wednesday 9 JUNE 1999 Afternoon 2 hours

Candidates answer on the question paper. Additional materials:

Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional)

TIME 2 hours

INSTRUCTIONS TO CANDIDATES

Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown below that question.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 104. 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 T , use either your calculator value or 3.1 42.

FOR EXAMINER’S USE

This question paper consists of 10 printed pages and 2 blank pages. MFK (0710) QF91682 0 UCLES 1999 [Turn over

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1 (a) The normal price of 24 cans of orange drink is $14.40. A supermarket makes a special offer of 24 cans for $9.84.

(i) What is the price reduction per can in the special offer? Give your answer in cents.

[$1 = 100 cents.]

Answer (u)(i) .......................................... cents 131

(ii) What is the percentage reduction in the price?

Answer (u)(ii) ............................................... % [2]

(b) Corn flakes are sold in the supermarket in three differently sized packets.

Size X Size Y Size Z

1 kilogram for $2.30, 750 g for $1.95, 500 g for $1.50.

(i) Work out the cost, in cents, of 100 g of corn flakes from each size of packet.

Answer (b)(i) Size X ............................... cents

Size Y ............................... cents

Size 2 ............................... cents [3]

(ii) Which size of packet gives the best value for money?

Answer @)(ii) Size ........................................... P I

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2 (a) The linex = 4 is the line of symmetry of the graph ofy = x2 - 8x + 17, part of which is shown in the diagram.

(i) Write down the coordinates of the reflection of the point P(2,5) in the line x = 4.

Answer (a)(i> ( ................ , ................ (ii)

(b) The diagram below shows part of the graph of y = 4 - x -x2.

Continue the curve from x = 4 to x = 7.

Use the graph to find

(i) the value of y when x = - 1.5, Answer (b)(i) y = ................................................

(ii) the two values of x when y = 2, Answer(b)(ii) x = ..................... or .....................

(iii) the greatest value of y,

(iv) the two solutions of the equation Answer (b)(iii) ....................................................

4-x-x2 = 0 correct to one decimal place.

Answer @)(iv) x = .................... or .................... ~~

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4

(a) Write down the length and width of three different rectangles, each with area 24 cm2. 3

Length Width

Answer (a) ..................... cm ..................... cm

..................... cm ..................... cm

..................... ..................... cm cm [31

(b) The area of a square is 24 cm2. Calculate

(i) the length of one side of the square,

Answer (b)(i) .............................................. Cm l.11

(ii) the perimeter of the square.

Answer (b)(ii) ............................................. cm [I1

(c) The area of a circle is 24 cm2. Calculate the radius of the circle, [For T , use either your calculator value or 3.142.1

Answer (c) .................................................. cm [3] (d) The area of a triangle ABC is 24 cm2.

(i) The base BC = 12 cm. Calculate the height of the triangle.

.............................................. Answer (d)(i) cm P I (ii) The base BC is drawn below and angle ABC = 30".

Complete an accurate drawing of triangle ABC.

B C E21

(ii) Write down the size of angle BAC.

Answer (d)(iii) Angle BAC = ........................... r11

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4 A telephone directory is made up of 500 sheets of paper. It has a mass of 1.25 kilograms.

(a) Calculate the mass of one sheet of paper. Give your answer in grams.

.................................................... Answer (a) g P I

(b) The directory is 4 cm thick.

(i) Work out the thickness of one sheet of paper. Give your answer in millimetres.

Answer (b)(i) ............................................ mm [2]

(ii) Write your answer to (b)(i) in standard form.

........................................... Answer (b)(ii) - [I1

(c) The directory is 28 cm long, 20 cm wide and 4 cm thick. Calculate the volume of the directory in cubic centimetres.

Answer (c) ................................................ cm3 [2]

(d) A van has a capacity of 8 cubic metres. [ 1 m3 = 1 000 000 cm3.] Estimate, to the nearest 500, how many directories would fit into the van.

....................................................... Answer (d) P I

(e) The van can carry a maximum mass of 3 tonnes. [l tonne = 1000 kg.] How many directories would have a total mass of 3 tonnes?

Answer (e) ........................................................ [2]

( f ) How many directories could the van safely carry?

Answer &I ........................................................ P I I

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5 NOT TO SCALE X

W

6

NOT TO SCALE (b)

A B

WXis a diameter of a circle centre 0, YZ is a chord and XY = XZ. Angle XYZ = 68". Find

(i) angleXZW,

Answer (u)(i) AngleXZW= .................. [11

(ii) angle WZY,

Answer (a)(ii) Angle WZY = ................ P I (iii) angle Ym.

Answer (u)(iii) Angle YXZ = ................. 121

AB is a diameter of a circle and is 10 cm long, Chord AC = 9 cm. Calculate

(i) the length of BC,

Answer (b)(i) BC = .......................... cm [2]

(ii) angle ABC.

Answer (b)(ii) Angle ABC = ................. 121

P, Q and R are three points on the circumference of a circle. Angle PQR = 90" and angle RPQ = 40".

(i) Construct triangle PQR. (The point P has been marked for

(ii) Measure and write down the length of PQ.

YOU.) 121

Answer (c)(ii) PQ = ......................... cm [ 11

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7

-4

(a) (i) Write down the coordinates of P, Q and R.

Answer (a)(i) P = ......... , .........

........ ........ Q = ( , 1 R = ......... , .........

(ii) PQRS is a rectangle. Mark S on the diagram, and write down its coordinates.

........ , ........ Answer (a)(ii) S = ( (iii) Write down the order of rotational symmetry of the rectangle PQRS.

................................................. Answer (a)(iii) 1 1 1

(iv) Write down the coordinates of the centre of rotational symmetry of the rectangle PQRS.

Answer (a)(iv) .......... , .......... PI ---t --+

(b) (i) Write down the vector QR and the vector PS.

Answer (b)(i) QR =

- - + + \ I (ii) What do you notice about the vectors QR and PS?

.................................................................................................................. Answer (b)(ii) P I - - + A

(c) The vector QT = 2QR. Write down

( i ) the vector QT, 4

Answer (c)(i) QT= - i \ (ii) the coordinates of T.

........... ........... Answer (c)(ii) T = , r11

0580/3,05X 1/3/S99 [Turn over

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7

8

Percentage of total

population aged less

than 15 year ‘S

50

40

30

20

10

0

The bar chart shows the percentage of the total population aged less than 15 years in 1975, and in 1995, for different countries.

Write down that percentage for China

(i) in 1975, Answer (a)(i) ................................................ % [ l ]

(ii) in 1995. Answer (a)@) ............................................... % [ 11

The total population of Singapore in 1995 was 2 800 000. How many were aged less than 15 years?

....................................................... Answer (3) P I

In 1995, what percentage of the population of Belgium was aged 15 years or more?

Answer (c) .................................................... % [2]

In which of these countries did the percentage drop the least?

........................................................ Answer (d) [21

[21 In 1975,46% of the population of Kenya were aged less than 15 years. In 1995 the figure was 50%. Draw bars to show this information on the bar chart.

What is different about the figures for Kenya compared with the other five countries?

Answer 0 ................................................................................................................................

................................................................................................................................ P I

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8

9

6

Sq

4

3

2

1

0 1 2 3 4 5 6 5

The graph of x + y = 5 is shown in the diagram above. Find the gradient of this line.

(0

(ii)

(iii)

Answer (a) .......................................................

Complete the table of values for the equation y = &x + 1.

Draw the graph ofy = $x + 1 on the grid above, for 0 6 x 6 6.

Use the graphs to solve the simultaneous equations

x + y = 5 and y = ; x + l ,

giving the value of x and the value of y correct to one decimal place.

Answer (b)(iii) x = ................., y = .................

(c) Use algebra to solve exactly the simultaneous equations

x + y = 5 ,

y = ; x + 1.

Show all your working.

Answer (c) x = .................................................

y = .................................................

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9 The table shows the values of 7p + 5q for different values o fp and q. For example, i fp = 3 and q = 2, then 7p + 5q = 7 x 3 + 5 x 2 = 31. This is ringed in the table.

Write the two missing values in the table. E21

Most of the numbers between 10 and 30 appear in the table. List the missing numbers.

............................................................................................................................... Answer (b) PI Describe the pattern of numbers that you can see in any line going diagonally down the page

(i) from right to left (3 ),

.................................................................................................................. Answer (c) (i) [I1

(ii) from left to right ( 9).

.................................................................................................................. Answer (c)(ii) [11

If negative whole numbers are included as values forp and q, 7p + 5q can equal any whole number. For example, 8 is not in the table but

7 p + 5 q = 8 when p = - 1 and q = 3 .

(i) Write down working to show that this last statement is correct.

................................................................................................................... Answer (d)(i) [I1

PM (b). (ii) Find values o f p and q for which 7p + 5q can equal any three of the numbers in your list in

Answer (d)(ii) ..................................................................................................................

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

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

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

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

......................................................................................................................................... E61

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