2008_maths_olevel_nov_paper1

Extracted Content: 2008_maths_olevel_nov_paper1

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‘ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4008/1, 4028/1
PAPER 1

NOVEMBER 2008 SESSION 2 hours 30 minutes
Candidates answer on the question paper.

Additional materials:
Geometrical instruments

TIME = 2 hours 30 minutes

INSTRUCTIONS TO CANDIDATES

Write vour name. Centre number and candidate number in the spaces at the top of this page.

Answer all questions.

Write vour 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 f gures
unless stated otherwise.

Mathematical tables, slide rules and caleulators should not be breught into the
examination room.

INFORMATION FOR CANDIDATES
Tae number of marks is given in brackets { ] at the end

of each question or part question.

This question paper consists of 26 printed pages and 2 blank pages.

Copyright: Zimbabwe Schoo! Examinations Council. N2008.
EZIMSEC N2008 {Turn over

Candidate Name Centre Number Candidate Number

t
1
|
i
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ae ee

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5 “a

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

Te

(a)

Simplify
@ 6.3 x 1,1, giving your answer as a decimal,

- 2 Fw .
(ii) a a giving your answer as a common fraction.

Find 5% of 130 metres.

Answer (@ (i)

(ii)
peel

(b)

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,

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3 2 (a) Evaluate 54, + 305¢. giving your answer in base 6. For

Use
(b) Convert 10011; to a number in base 3.

Answer (a) [1]

(b) [2]

$ Given that 94 x 152 = 14 288, |
(2) find the value of N if 95 x 182 = 14 288=N.,

(b) Write down the exact value of
(69) 0,094 x 1 520, ;

(ii) 0.14 282 + 0,0094.

Answer (a) 1]
eo) wi i]
(ii) [1]

ee
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{a)

(b}

4
Simplify (0,2)° x (0.2)°, giving your answer as a decimal.

Solve the equation

5x-2Ax+ 3)=9.

Answer (a)

(b) x=

4008/1 N2008

{]
[2]

For

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(a} (b)

5
Write 0019 in 12-hour notation,

Tapiwa and Netsai share some money in the ratio 2:5. Given
that Tapiwa’s share is $620 000, calculate Netsai’s share.

Answer (a)

[1]

(o) §$

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[2]

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In the diagram, BCD is a straight line and AB is parallel to ED. Given that BC = AC, ADB = 20° and ACB = 50°. calculate

(a) BAC,
(b) DAC,
(e) ADE.

Answer (a) BAC =

(b) DAC=

() ADE=

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(1]
[1]

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ie

Given that m= 4 x 10° and n= 2,4 x 10° giving each answer in standard form, For
calculate Examiner's
Use
(a) mn,
n
@ 4,
m

Answer (a) {1]

(b) _ [2]

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WXYZ is a cyclic quadrilateral. The diagonals XZ and YW intersect at P and YX is produced to S. YWX = 70°, XYP =25° and YPZ = 43°.

Calculate

(a) -XZY,
(bo) -YXZ,
(ce) SkW.

Answer (a) XZY =

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(a)

(b)

9
The bearing of town B from town A is 141°. Find the bearing
of town A from town B.

The interior angle of a regular polygon is 162°. Find the number
of sides of the polygon.

Answer (@)

(0)

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10

10

(a) In the diagram, the shaded sector AOB is = of the circle centre O.

Calculate AOB.

(b) Calculate the radius of a circle whose area is 154 cm?.

[Fake x to be

Answer

22

vi

(a) (1]
(b) em [2]

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li 1 Taurai is x years old. Zvikomborero, her brother is 9 years older than her. Their father is 3 times as old as Taurai. Their mother is twice as old as Zvikomborero.

(a) Write down and simplify, in terms of x, an expression for the
total age of the four members of the family.

(b) Given that the sum of the ages of the four members is 139 years,
find the value of x.

Answer (a)

(ob) xe

|e

OO |

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I~

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12

12
The scale of a map is 1: 1 000 000.

Find

(2) the length, in cm, of a line on the imap, which represents a road
160 km long, ~

(b) the actual area of a piece of land which i is represented by 2,64 cm?
on the map, giving your answer in km’.

Answer (a)

(b) km? [2]

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cm Ff ry

For

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13

13

If f(x)=x°-7x+5, find

(a)

(b)

f(-1),

the values of x for which f(x) =—7.

Answer (a)

(b)

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14

14 A bag contains red, blue and green counters all of which are identical except z For
for colour. Use

A counter is picked at random from the bag. Its colour is noted and then
itis replaced. The probability that it is red is 0,2 and the probability that
itis blue is 0,5.

(a) Calculate the probability that the counter picked is either blue or
green.

(b) | Two counters are picked at random one after the other, with

replacement. Calculate the probability that one is red and the other
is blue.

Answer (a) [1]

(b) . [2

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15 15 (a) ~—- Factorise x7- y°.

(b} Given that x- y=4 and x*-? = 20, find the value of x and the value te
of y.

Answer (a) {1] |
: |

() x= {1}

y= [3]
i
Se
i
4008/1 N2068 |

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16

16

D

<—_—_——— 4 ——_ >

The diagram shows an isosceles triangle ABC with AB = AC, BC =24 cm
and AD is perpendicular to BC.

Given that the area of the triangle is 108 cm’, find
(a) AD,

(b)} AC.

Answer (a)

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17

1

tw

The diagram shows a cross-section of a swimming poo! which is 25 m
long, ] m deep at the shallow end and 2 m deep at the deep end.

(a) Calculate the area of the cross-section in m*.

(b) Given that the swimming pool is 10 m wide, calculate the volume
of the pool in m’.

Answer (aj m {2}

(b) m 2]

For

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18

18

| For

Given that logs? = 0,431 and logs3 = 0,683, find the value of (Examine
i

Use
I \
(a) loge, !
: |
(b) jog, 3.
|
|
|
|
i
i
H
1
i
i
|
i
Answer (aj [2] |
0) a
|
oe eeeSeeeSSSSSSSSSSSSSSSSS
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1

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19 uae (2) — [-8 19 (a) _ Itis given that AB= 4| and BC = al

Find

al

@

(ii) CX, given that 9GX = BC.
; “s = (3

(b) P is the point (-3; 2) and PQ=|} _|.
-5

Find the coordinates of point Q.

Answer (a) (i) ACs \

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20

Ran

The Venn diagram shows the universal set £, set X and set Y. The letter:
u, Y, w and = represent the numbers of elements in each subset.

Iris given that n(S) = 150; n(X) = 55 and n(Y) = 32.
Find

(a) the smallest possible value of z,

(b) the largest possible value of v,

(c) the value of w ify = 45,

Answer (a) [1]
(b) (1]
(c f)

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bal (a)

(b)

21
During a sale, a shop reduced all its prices by 20%. Calculate the
original price of an article which was sold during the sale for
$440 000.
On a particular day, a bank bought British pounds (£) at a rate of
1 British pound (£) to 35 000 Zimbabwean dollars ($) and sold
British pounds (£) at a rate of $40 000 per £.
Calculate

(i) the amount, in British pounds, bought for $10 500 000,

(ii} the amount, in Zimbabwean dollars, received for selling

£112,
Answer (@ $
) Wi £
(ii) $

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22

|
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22
25 (ee eee eee eee a
20
15 —
Velocity
(m/s)
10
5
0 10 20 30 40 50 60

Time (s)
The diagram shows a velocity-time graph for a particular journey. Calculate

(2) the distance travelled in the first 30 seconds,
(b) the speed when the time is 40 seconds,

(c) the deceleration during the last 10 seconds,

Answer (a) m [2]
(b) m/s [1]
(c) m/s* [2]

For

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23 23 x is partly constant and partly varies as y.

(a) Express x in terms of v and constants » and k.

(b) Given that x =] when y = 8 and that x =3 when} = 12.

calculate the value of
i) ok,
Gi) ok.

(ce) Find the value of x when y = 30.

Answer (a) =
(b) i h=
(ii) k=

(¢) x=

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No of pupils who scored this mark

The table shows the test results of a class of pupils. The test was marked out

of 10.

(a)

(b)

Find

@ the number of pupil, in the class,

(ii) the modal mark.

(iii) the range of marks scored by the pupils.

Calculate the percentage of pupiis who scored less than 5 marks.

Answer {a} @Y ee HJ
Go

(iii) [1]

Oo . % [2

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>

a

The diagram shows the graph of the function y = 2°-2x-1. Use the
graph to find

(a) the roots of the equation x°-2x-1=0,

(b) the minimum value of x7 -2x-1,

2

the equation of the line of symmetry,

(ad) area enclosed by the curve. the x-axis, the y-axis and the line
Ba
Answer (a) = or f2]
(b} Ui]
(ej ij
(d) (2)

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(a) Solve the equation (2x-3)° =

(b)

In the diagram. line m passes through the points (— 4: 0) and (0:4).
The line 3y+5x=15 cuts the x-axis and the )~axis at A and B
respectively.

(i) Write down the coordinates of A and the coordinates of B.

(ii) Find the equation of line m.

(iii) Write down two inequalities, other than }2 0, which define
the region R, ,

Answer *.~ (aj r= : or. RB)
fo) fi) AC: yj

: a | [2]

(ii) [2]

(iit) PB

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