2008_maths_olevel_nov_paper2

Extracted Content: 2008_maths_olevel_nov_paper2

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‘ae Hepatmance Mewarens?

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4008/2
PAPER 2
NOVEMBER 2008 SESSION 2 hours 30 minutes

Additional materials:

H Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables J

~ -Piain paner (1 _shest) : = oa

TIME 2 hours 30 minutes

INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the
answer paper/answer booklet.

Answer all questions ir Section A and any three questions from Section B.

Write your answers on the separate answer paper providec.
1f vou use more than one sheet of paper, fasten the sheets together.

Electronic calculators must not be used.

All working must be clearly shown. It should be done on the same sheet as the rest of the
answer.

Omission of essential working wil! result in loss of marks.

If the degree of accuracy is not specified in the question and if the answer is not exact.
answer should be given to three significant figures. Answers in degrees should be giver
to one decimal place.

INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part
guestion, Mathematical tables may be used io evaluate explicit numerical expressions.

This question paper consists of 11 printed pages and 1 blank page.

Zimbabwe Schoo! Examinations Council. N2008.

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Section A [64 marks]

Answer all the questions in this section.

2 ~13 : Bis i.
(a) Express - - arr as a single fraction in its lowest terms. (2]
(b) Remove the brackets and simplify
3(a+2c)-4(2a~c). (2)
(ce) Solve the equation
4x-5 3 3
=l-. ‘
i 4 6)
(d) Find the number of circular rings each of diameter 6.3 cm which can be
made from a wire 19.§ m long.
[ U 22\
==], 4
ei ] [4]
(a) Factorise completely
() 2x? 4ax-2bx-ab,
(ii) 3-123". [4]
(b) It is given that P(4; 8) and R(-4: -2) are points on the Cartesian plane.

Find
(i) PR as a column vector,

(ii) PRI.

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(¢} Two cyclists, Alice and Jonn, started a journey at the same time from
two villages which are 27 km apart. Alice cycled at x km/h and John
evcled at 2x km/h. They travelied towards each other and met after
4
3
— hour,
4
@ Write Gown, in terms of x. the distance that Alice travelled in
5)
— hour.
Zz
(} Form an equation in x and solve it.
(iii) Hence write down the numerical value of John’s speed. 4
Sua Earth Mars
3a) Qe reece renee @ ~~~ == 22-22-2222 €
In the diagram. the Sun. Earth and Mars are in a straight line. It is given
ee piel . bs.
that the Earth is 1.496 >: 10° kim from the Sun and Mars is
a a q
2.279 x 10° kim from the Sun.
(i) Write down 1,496 x 10° in ordinary form.
(ii) Find. in standard form. the distance of Mars from the Earth. {3}
(b) In a certain year. a paint manufacturer mixed 27 litres of white paint with
9 litres of red pain: to produce 36 iitres of pink paint. If one litre of the
white paint cost $36 800 and the average cosi of the pink paint was
$35 575 per lite. calculate the cost of one litre of the red paint then. {5]
(e) (i) Solve the simultaneous inequalities
2x-6.<5x
¢ your answer in the form a<x<b where a and b are
integers,
(ij Write down the least possible value of x. [4]

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(b)

\
B

in the diagram. ABCD is a quadrilateral in which AD is parallel 1 BC and
AC and BD intersect at }: such that the ratio BX: XD = 3:2. Given that
9 cm” in area,

() calculate the area of AAD,

(ii) name, in correct order. the triangle which is similar 10 ABCX.

(fil) hence calculate the area of ABC. By
. In the diagram. AP and AQ are tangents to the circles ABQ and ABPC
respectively. Given that APB = 30° and AQB = 50°,
calculate
(BAP,
(i) BAQ,
(iii) reflex PBQ,
(Gv) ACP.
[6]

4008/2 N2008

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2n
n+ 3 2
6n+5 2)
(b) Make m the subject of the formula
ge = 5 13]
3m-2-
3 5 5 y
(c) Given that A -( : and B -( 4 find
2 7 : yf SG
® A,
(ii) _ the two possible values of y given that the determinant of the
: matrix Bis Sy+ 1, (5]

Answer the whole of this question on a sheet of plane paper.

Use ruler and compasses only jor ali construction and show clearly all construction lines
and ares.

(a) On a single diagram, construct
(i) aline OP, 9 cm long,
- (i) ~~ accircle centre O and radius 3,5 cm,
(ili) the locus of points which ran cqnidiwant from O and P.

(iv) the circle whose diameter is OP to cut the circle centre O at R
and Q,

(¥) the two tangents to the circle centre O from the point P.

(b} OP represents a certain locus. Describe this locus fully. [2]

(ce) A point T lies inside the quadrilateral PQOR and is such that it is nearer
PQ than PR and nearer O than P. Given also that OT = 3,5 cm, show
by shading clearly the region in which T lies. [2]

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Answer any three questions in this section.

Answer the whole of this question on a sheet of graph paper.

es

Mass (mm kg) S<me45 | 45<m<50 |50<m=55 | 55<ms 60 j abso 70

Frequency p 11 13 8 |

| Frequency density” 0,5 22 2.6 g | 0.3

1 H a

The table gives the masses, m kg, of a group of students at a teachers’ college.

(a) Find the value of p and the value of g. 2
(b) Using a horizontal scale of 2 cm to represent 5 kg and a vertical scale
of 4 cm to repr. sent 1 unit of frequency density. draw a histogram of
the data. 4)

(ce) Calculate an estimate of the mean mass of the students in the group
whose masses are greater than 45 kg. (3)

(4) | Two students are chosen at random from the whole group. Find the
probability that each of them has a mass which is greater than 50 kg. 3]

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(b)

<— Ground
level

SLPPPS POPS ELAPL SS APLA DALAL EAD LD

In the diagram, ABC is a crane lifting a load D. AB and BC are beams and
ACD is a string. Given that the vertical beam AB = 5m, AC= 8 m.
CD =3,6 mand BCA calculate

@ ABC,

(il) the height of D above the ground level. [6]

The diagram shows a vertical cylindrical container with water up to a height
of 9m. The volume of the water in the container is 512 cm’. A metal
solid, of volume 217 cm?, is lowered into the container untii the solid

is completely immersed in water. Calculate the height by which the

water level rises in the container. Give your answer correct to the nearest
millimetre. [6]

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In the diagram, PQR is 2 segment of a circle of radius 6 cm and centre O,
PR=6 om, RS =8 cm, PS= (3x+ 4) cm and PRS =120°,

(a) Calculate the area of the segment PQR. [4]

(b) @ Form an equation in x and show that it reduces to
3x? + 8x-44 =0,

(ii) Solve the equation 3x7+8x-44=0 giving your answers correct
to 2 decimal places. , {8]

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“9
Answer the whole of this question on a sheet of graph paper.

A stone is thrown into the air. Its height metres after r seconds is given by
the formula h = 60 + 30r - 57°.

Below is a table of values for h = 60 + 307 -S?’.

Time (/seconds) {0 |
ji

Height h(metres) | 60

{a) Find the value of p and the value of g.

(b) Using a horizontal scale of 2 cm to represent 1 second and a vertical
scale of 2 cm to represent 20 metres, draw the graph of
h=60+ 307-57 for0<1<8.

(c) Use your graph to find
(3) the maximum height reached by the stone,

ii) the velocity of the stone when r= 2,

(iii) the times when the stone is at a height of 80 m.

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{6}

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it *

The diagram shows a wooden block of length 150 cm, whose cross-section , ABCD is a
trapezium in which AB is parallel to DC. AB =65 cm, AD= BC = 32,5 cm and the
perpendicular height is 30 em.
(a) Calculate

@ the length CD given that the area of the trapezium is 1 575 em’,

(ii) the volume of the block,

(iii) the mass of the block given that the density of the wood of
which it is made, is 0,72 g/cm’,

(iv) the total surface area of the block. [10]
(b) The block i is to be varnished, One litre of varnish covers an area of

2 000 cm” and is bought in 5-litre tins only. Calculate the number of
tins of varnish that need to be bought to varnish the whole block. [2]

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Answer the whole o f this question on a sheet of graph paper.

A quadrilateral E with vertices (—8: —4), (-4; -4), (-6; -12) anc
(-10; -8) is the image of quadrilateral A with vertices (4: 2), (7: 2).
(3: 6) and (3; 4).

Using a seale of ] cm to represent 1 unit on both axes. draw the x and \ axes
for-10<xs6and ~-12<v<8.

{a)

(b)

(ce)

(i) Draw and label clearly the quadrilateral E.
(ii) Draw and label clearly the quadrilateral A.

(iii) | Write down the matrix which represents the transformation
which maps E onto A.

Quadrilateral T with vertices (0; 6), (0: 4). (-4: 5) and ¢-2; 7) is the
image of quadrilateral A under a certain transformation.

(i) Draw and label clearly the quadrilateral T.

(ii) | Describe completely. the single transformation which maps A
onto T.

‘ 0 \
A one-way stretch represented by QO -14 | maps quadrilateral A onto
ae)

quadriiateral S.

Draw and label clearly the quadrilateral S.

14]

cs)

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