2008_maths_olevel_mj_paper1

Extracted Content: 2008_maths_olevel_mj_paper1

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Candidate Name - Centre Number Candidate Number

nse
or Perfurownsre Memseeevaient

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS | 4008/1, 4028/1
PAPER 1

JUNE 2008 SESSION 2 hours 30 minutes_

Candidates answer on the question paper.
Additionaj materials: ,
1

Geometrical instruments : :

TIME 2 hours 30 minutes

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 in the space below that question.
Omission of essential working will result in loss of marks.

Decimal answers which are not exact should be given correct to three significant figures
unless stated otherwise. ;

Mathematical tables, slide rules and calculators should not be brought into the

examination room. :
FOR EXAMINER’S USE ©

This question paper consists of 24 printed pages.

INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end
of each question or part question.

Copyright: Zimbabwe School Examinations Counct!, J2008. .
LL OZ! MSEC 32008 [Turn over

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2

‘

NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR
CALCULATORS MAY BE USED IN THIS PAPER

1 (a) Express 0,000 0526 in standard form.

(b) Estimate by first rounding off each number to one significant figure,
3,04 x 1,98 - 9,48
the value of =" ""

2,91
Answer (a) [1]
@® aD

ss

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2 Express (a) 5,3 km? in hectares, (b) 20 litres in cubic centimetres,

(c) 408 hours in weeks and days.

Answer (a) ha (1)
@) om’ (1)
(c) weeks days [1]

i]

3 “(a) Find the value of the base y such that 6703, - 725, =5756,.

{b) Convert 134; to a number in base two.

Answer (a) (1]

(0) [2]

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4 4 Ina shop one loaf of bread cost $65 000. (a) ‘Find (i) the cost of a dozen loaves of bread,

(if) the number of loaves of bread that could be bought for
$4 550 000.

(b) Write down the type of variation which connects the cost of bread and the
number of loaves of bread bought.

. Answer (a) (i) $ Rota [1]
(i)

(b) variation [1]

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5

Ora 0

5 (a) Write down one capital letter of the alphabet which has rotational symmetry For
of order 2 but no line of symmetry. —
ee
(b} The mean of m, p. g andr is 8.25.
The mean of m, 1, p,q andr is 4,6. }
Find the value of n. : :
x Answer (a) (1)
(b) (2)
|
6 The radius, r cm, of a circle is given as 9 cm, correct ta the nearest whole number. |
{a} Write down the limits between which r must lie.
(b) Calculate the least possible circumference of the circle, giving your answer

in terms of 7.

Answer (a) {1]

(b) em = [2] |

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A B

—_———— see
98

The diagram shows a pattern which is made up of identical semi-circular arcs. The
shortest distance between the ends A and B is 98 cm,

Calculate
(a) the diameter of each semi-circle,

(b) the distance from A to B along the curves.

>
[Takes = 3)
a

Answer : (a em [1]

(b) :_ em [2]

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The Venn diagram shows the universal set, € and the sets P, Q and R with their members.

(a) From the venn diagram, list the members of

@ PNa,
(ii) PIN’.
(b) Find n().
Answer (@ @ epnQ@se. FD
(ii) ping= [1]
AO eel

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Distance * - (Kilometres)

Shopping 364--—~——--——
centre :

Home

5 8

Time (hours)

The diagram is the distance-time graph of a cyclist who goes out shopping and
returns home.

Calculate
(a) the time spent at the shopping centre,

(b) the average speed for the whole journey.

Answer (@) hours [1]

(b) km/h [2]

—_——--

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9 10 A bag contains 60 identical marbles, except for colour. 36 are green. x are red and the rest are blue. :

(a) If the probability of selecting a red marble at random is - find x.

(b) Two marbles are drawn, one after the other, with replacement. Find the
probability that neither marble is green, giving your answer as a common
fraction in its lowest terms.

Answer (a) x= i {]

(b) [2]

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11

10

In the diagram ABCD is a circle centre O. Are AD = are DC, DAO =55° and AOB

is a straight line. :

_ Calculate
@ BCD,
“(b) ACB,
(e) DAC.

Answer . (a)
CO)

2)

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12 Evaluate (a) (-32)*, 1 b eo w) fa

Answer (a)

(b)

13 Factorise completely
(a) 15m+ 18 - 10mn - 12n,

(b) (27x? =-12y?

Answer

ik

(a)
(0)

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12

14 The following is an extract of Mr Dube’s telephone bill for the month of January

2002. x is the number of units used and y is the Value Added Tax (VAT).

DATE ACCOUNT DETAILS AMOUNT

Rental from 01/02/02 to 28/02/02
31 fan 2002 | Metered units 02781 01685 (x units) 2 192,00
Sub Total * 2 332,00

‘| VAT @ 15.0% v
pT VAT @ 15.0% pt
Amount Due

(a) Find,

@ the units used, x
(ii) the cost per unit.

(b) Calculate the Value Added Tax, p.

Answer @ [1]

fi) S$ . 2]
6) 8 0

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13

tae

(a) A triangle has sides of length 7cm, 15cm and x cm. If x is an integer, find
@ the minimum value of x,
Gi) the maximum value of x.

- (b) The sum of the interior angles of an irregular polygon is 5040°, Find the
number of sides of the polygon.

Answer (a) @ minimum x = {1]
(ii) maximum x = (1)
(0) : [2]

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14

16 The selling price of school shoes at a departmental store in January 2005 was
$750 000 per pair.

(a) Calculate the amount paid for one pair of school shoes if a 10% discount was
allowed.

(b) ‘In February 2005 the price rose by 15%. Calculate the new selling price of
one pair of school shoes. ‘

Answer (@ $§ [2]

MO $e (2

i

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15

17

(a

D ec! 15 B

In the diagram DCB is a straight line. BC = 15cm, AC = 10 cm and ACD = @.
Given that sind = =, find
5

(a) cos@,

(b) the area of AABC.

Answer (a) cos@ = , 2]

(b) cm? [2]

ee UE ata Ua I a SUNRISES

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16 18 Bulawayo and Harare are 400 km apart by air.

A helicopter leaves Bulawayo at 2.30 p.m. and arrives in Harare at 4.10 p.m. on the
same day. Calculate

(a) the average speed of the helicopter,

(b) the arrival time in Bulawayo in the 24-hour clock on the return journey if .
the helicopter leaves Harare at 10.36 p.m. and takes 1 hour 49 minutes.

Answer (a) knv/h [2]

(0) 2]

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17

5, i 6 -15
18 _. It is given that p= 4 and q= F

y

(a) Calculate ip\, leaving your answer in surd form.

(b) ‘If p is parallel to q, calculate the value of y.

Answer (a)

(b)

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18

TOES

mere a
+
Tor

oul oa
aa

ote

FTE HAE

=e

THT

ee

ick

Heo =

am

FS
Ht

1-4

+
THE 4

wawewew

eH

In the diagram the line y =mx-+c touches the curve y= x°-4% at (1; -3).

Write down

the value of c,

(a)

the value of m,

(b)
)
qd)

=],

the gradient of y=x°-4x when x

(c

the range of values of x for which mx +c>x?- 4x.

(

(a)

Answer

()

(c)

(@)

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, ox x 21 It is given that M = | x 2x

(a) Find M? in terms of x.

19

(b) Find x given also that |Mj = 48.

Answer

(a)

(b)

7

M=

x=

“or

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20 22 It is given that y varies inversely as x +4. (a) Express y in terms of x and a constant k. (b) Given also that x =6 when y = 2, find the value of &.

(ce) Find the value x when y = 8.

Answer (a7) y= power
0) k= ee BT
Qo fF,

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21

23 (a) At a certain party the ratio men: women: children was 5: 6: 4. If there
were 80 children at the party, calculate the total number of people at the
party.

(b)} The area of a certain country is given as 8,5 x 10°km*. The area of the

country’s map is given as 3,4 x 10° cm?, Find, in the form 1: n, the scale
. used in drawing the map.

Answer (a) — 2]

(b). — * [3]

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24

In the diagram TA and TB are tangents to the circle ABC.

(a) Using a ruler and compasses only, construct
@ the locus of points equidistant from A and Cy
(ii) _the locus of points equidistant from AT and BT.

(b) Write down the radius of the circle.

Answer (@) (i) on diagram,

(ii) on diagram.

(b)

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23

B12; 9)

O x

In the diagram ACE and BCD are straight lines. AB is parallel to DE, AB =9 cm,
BC =3 cm and B is the point (12; 9).

(a) Describe fully the single transformation which maps AABC onto AEDC.

(b) AABC is mapped onto AA’B'C’ by a transformation represented by the

2 0
matrix ( 3} Calculate the coordinates of B’.

Answer (a)

O © —— JE

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26 Given that log2 = 0,3010 and log 3 = 0.4771, calculate
(a) log6,
(b) log1,5,
(¢) log v2.
Answer (@) = log = [2]
(b) log 5 = [2]

() ~— log/2 = [2]

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24 (a) i) Perpendicular bisector 2 (ii) Bisector of ATB 2

(b) 2,6 + 0,2 1

25 (a) Enlargement with centre 3
(b) BB! 924: 27) 2

26 (a) ~—«0,7781 2
(b) —-0,1761 2

(ec) 0,1505 a

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