2011_maths_olevel_nov_paper1

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ZIMBABWE SCHOOL EXAMINAATONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4008/1, 4028/1
PAPER 1

NOVEMBER 2011 SESSION 2 hours 30 minutes

Candidates answer on the question paper.
Additional materials:
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.

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

This question paper consists of 21 printed pages and 3 blank pages.

Copyright: Zimbabwe School Examinations Council, N2011.

©ZIMSEC N2011 [Turn over

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

Giving your answer as a common fraction in its lowest terms, find the value
of

1

3
3°

ww

(a)

ii

(b)

w
alte

[1]
[2]

Answer: (a)

(b)

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Given P = —
(9.88 + 23.8)

(a) Rewrite this expression with each number correct to one
significant figure.

(b) Estimate the value of P correct to one significant figure.

Answer: (a) ——__, [2]
( + )
_(b) [1]
(a) Simplify (272°),
(b) If 32% = 2°, find p.
Answer: (a) (1]
() p= [2]

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(a) in standard form,
(b) asa decimal fraction,

(c) as acommon fraction in its lowest terms.

Answer: (a) [1]

() _ {1]
(©) W]

(a) State the number of lines of symmetry of an equilateral triangle.

(b) _ Factorise completely 3x° -12.x.

Answer: (a) fl]

(b) [2]

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x~6y =-4,
9x+3y =-17.

Answer: x=
ye [3]
A and B are sets. Write the following sets in their simplest form.
@) ANa’
(b) AUA!
() (ANB)U(ANBY
Answer: (@) {J
(b) (1)
Oo {1]

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8 It is given that y varies inversely as the square of (x -1). When» = 2,
x=2,
Find the value of y when x = 4.
Answer: y= B]
9 (a) If Ais anon-singular matrix, simplify AAt
1 3/2)

“(b) «=6OoIf B= 5 2heP write down the order of matrix B.

Answer: (a) {]

(b) [2]

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In the diagram AC is 10 units and BA is parallel to CD. BA is the line
y=3x44,

(a)

(b)

Write down
(i) the value of y at C,
(ii) the equation of the line CD which is parallel to y =3x+4.

Find the coordinates of the point D where the line in part (a)(ii)
crosses the x-axis.

Answer: @ * [1]
@ OY
(b) a) Q]

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(b) Express 5° + 4 as a number in base five.

(c) Convert 1349 to a number in base two.

Answer: (a) {1]
(b) (1]
(c) (1)
12 A rectangle is 9,1 cm long and 5,7 cm wide correct to one decimal place.

(a) State the least possible width of the rectangle.

(b) Find the limits within which the perimeter of the rectangle lies.

Answer: (a) {1]

(b) : cm s perimeter < cm [2]

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A

In the diagram ABC and A'B'C! are congruent triangles and Bcc'B!
is a straight line.

Describe fully a single transformation that maps triangle ABC onto triangle
Alsicl,

Answer:

[3]

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14 Solve the equations
2y
a —=-9=0,
(a) 3

(b) x? -5x-6=0.

Answer: (@) yr {2]
(b) x= or (2]
15 A car manufacturer makes a scale model of one of his real cars.

(a) The capacity of the fuel tank of the real car is 64 litres and that
of the model car is 0.512 litres.

Find the ratio of the length of the real car: the length of model car.

(b) The area of the front window of the model is 0.0484 m’. Find the
area of the front window of the real car.

Answer: (a) {2]

(b) mm [2]

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16 (a) Given that y = m? — 4n*, find the value of y when m = 4 and n= 2.

(b) sif = a =1, make x the subject.
a

Answer: (a) 1]
i [3]
T Evaluate
(a) log, 9,
(b) lo. (|
8595)
(c) logayt.
Answer: (a) (1]

Bo [2]
( _ (1]

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18 On a map, a distance of 20 km is represented by a length of 40 cm. The
scale of the map is 1: n.

(a) Calculate the value of n.

(b) The distance between two towns on the map is 70 cm. Calculate
the actual distance in kilometres between the towns.

Answer: (a) n= [2]

(b) km 2]

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P-P=8= 4x2
VioP=12= 4x3
9-3 =16=4x4
6@-p=q =4x5
(a) — Write down the value of
~ @ p

Gi) q.

(b}: _ Write down the 10" line of this pattern.

Answer: (@) () p=

(1)
[1]

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14

rn
sche
: ¥ al a
os aA
: ia aeeaen maceaaces
tn
a: 7 fl a
ct | ral
; cee eaaanee
a: is i rn ct Geoaar pan 4
a: ai He +t ri Si FA,
“ ne m4 it { Trot | 4)
mi t t
* ry aan | A
+ + ¥
; anaes a ba
RA aan : co rs
sRNeeUCN aeDEEETESEE pemnneceeceeeceeee
a Pett
pS Poor ma = janet
: Se ao eee oe
“AE | | t { t
{ cua 7 HH : tA
ott 1 ct Cee e cee
vennel . pee
t t 1 Hu THEA i i
ieieni LHe ‘Merttrcett HT H
Heel MI i tt Haman We

Find the three inequalities that define the unshaded region in the diagram
above.

Answer:

[5]

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For

|Examiner’s

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21

+r 7 ' r rh rE CTO A aeeen

Hat ETE PEELE PEE CHEEEE PEELE CE

r aan ce | : FF oe
Ret AE HAH 1 f Lit a [
cee i sree rH HH HEEL TH H
FEEEEEEPEEEEEEE EEE EE suBEEEEGoEEEGEa

SeceSGReneee HHH am oe i

uauseeeaeabvaesaesae/aes00ssesoeaen_er<steetuseeeavatze

Pre eT Coors am mt EEE

EERE eee tae eee ete
SSE SEES TET seeenEE |

CPP erry

CTE

In the diagram, O is the origin.

Vectors a and b are shown in the diagram.

Write down, in terms of a and/or b.

{a)

the position vector of the point P,

@

PR -QR.

(iii)

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(b) If |b] = 4, write down the value of oR].

Answer: (a fi)
(ii) = PR=
(iii) ~PR-QR =
0) [QR=

1]
[2]

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17

In the diagram, OAB is a sector of a circle centre O and radius 12 cm and
angle AOB = 50°

OCD is a sector of a circle centre O and radius 6 cm and angle COD = 30°,
Calculate, in terms of I,

(a) the area of the shaded part,

(b) _ the perimeter of the shaded area AOCDOBA.

Answer: (a) cm? [3]

) ecm [3]

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23

velocity
in km/min

The diagram is a velocity-time graph of a train journey between two
stations.

Find

(a) the maximum speed of the train in km/h,

(b) the train’s acceleration in the first half minute,
(c) the distance the train travels at maximum speed,

(d) the distance between the stations.

Answer: (a) km/h
(bm / minute”
(c) km
(d) km

time in
minutes

[2]
[2]
{
U1]

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19

B T
A, B, C and D lie on the circumference of a circle centre O.
SCT is a tangent to the circle at C and is parallel to OB.
AOB = 130° and BCT = 45°

(a) Write down the geometrical word which completes the following
statement “ABCD is a...... quadrilateral”.

(b) Find the values of
G) OBC,
(ij) OBA,
(iii) ADC,
(iv) OCT,

(v) reflex angle AOC.

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Answer: (a)

(b) @) OBC =

(ij) OBA=

(iii) ADC=

(iv) OCT,=

(v) reflex angle AOC=

{1}
[H
{1]
(1)
(1
{2]

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Denis must choose a bag ffom which he should pick a ball. The

I
probability that he chooses Bag A is 3

Bag A contains 5 white and 3 black balls. Bag B contains 6 white and
2 black balls. The tree diagram below shows some of this information.

5 white ball

L Bag A
2 black ball

white ball
black ball
(a) Complete the probability tree diagram shown above.

(b) Find the probability that Denis chooses Bag A and then a white
ball.

(c) Find the probability that Denis picks a white ball.

Answer: (a) on diagram

(6)

(c)

[2]

[3]

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