2008_maths_olevel_mj_paper2

Extracted Content: 2008_maths_olevel_mj_paper2

Page 1

Extracted Text

f}

(7 z =i

Fre Pajucmunce Meeurerees

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

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

Additional materials:
Answer paper
Geometrical instruments
Graph paper (3 sheets)
Mathematical tables

~ Plain paper (1 sheet) A

TIME 2 hours 30 minutes

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

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

Write your answers on the separate answer paper provided.
If you use more than one sheet of paper, fasten the sheets together.

Electronic calculators must not be used.

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

Omission of essential working will result in loss of marks.

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

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

This question paper consists of 13 printed pages and 3 blank pages.

Copyright: Zimbabwe School Examinations Council, J2008.

OZIMSEC 12008 {Turn over

ee

---

Page 2

Extracted Text

(a)

(b)

(e)

(d)

2

Section A [64 marks]
Answer all the questions in this section.

Solve the equation
ety +4)=x-1.
3

Factorise completely

6y? — y-12.

Express

Given that z=rvn-1,
@ find z when r = 0,3 and n = 50,

(ii) express 7 in terms of z andr.

2 3 ‘ cs G8
is as a single fraction in its lowest terms.
-1 x

13}

[2]

2]

4008/2 12008

---

Page 3

Extracted Text

(a)

In the diagram, TR and TS are tangents to the circle centre O.

SR is parallel to OQ and SOR =116°.

Calculate
(i) SOR,
@i) —- RSQ,

Gil) RTS.

4008/2 J2008

{Turn over

---

Page 4

Extracted Text

(b)

(c)

{a)

(b)

D B Cc
x
A y F B

In the diagram, ABCD is a rectangle and BCEF is a square.

Given that DA = x om, AF=yem, x+y =15 andx-y=7,

Calculate

(@) the value of x, [2]
(ii) the area of ABCD. (1)
Six angles of an octagon are 140° each. The remaining angles are equal.
Find the size of each of the remaining angles. [3]

. 3 1
Given that (x a5 |. (is -7),

¥,

find the value of
@® x, [11
(i) y. [2]
It is given that
E = {all triangles},
A = {all equilateral triangles},
B = {all isosceles triangles} and
e = {all right angled triangles}.
Draw a clearly labelled Venn diagram to illustrate the relationship
between the sets, [3]

4008/2 12008

---

Page 5

Extracted Text

5 Study the number patterns shown in the table.

Column 1 Column 2 Column 3
i 1 1
3 | 3 9
4 | 6 | 36
4 10 100
5 |p
6
66 |
r 78
n w au
( i} Write down the numerical value of
(a) op.
(be) 9,
{c) Pe

ii Express v in terms of w.
! P.

4008/2 J2008

[3]

[Turn over

---

Page 6

Extracted Text

(a)

(b)

EB

5
In this question take x to be 2.

The diagram ABCDEF represents a metal drinking trough made from a
closed cyclindrical drum that was bisected lengthwise.

The trough has a diameter of 56 cm and a capacity of 110 litres.
(i) Calculate

(a) the area of the cross-section ADE,

(b) AB.

(it) The whole drum was bought for $25 500 and this Tepresents
a 70% increase in price of such a drum in the previous year.

Calculate the price of such a drum in the previous year.
Solve the equation

4x? -2x-3=0,
giving your answers correct to 2 significant figures.

4008/2 32008

---

Page 7

Extracted Text

(a)

P = Q

In the diagram PQ =p and PR=q. Misa midpoint of PR, QL: LR=2:1
and MN is parallel to RQ.

@® Express in terms of p and/or q
(a) QR, 11
(b) LR, [1]
(ce) MR. [1]
(ii) Given that NM = kOR, find the scalar &. [2]

(b) —_ In this question take x to be = ‘

A hemispherical bowl is made of wood 2 cm thick.

(i) Given that the bowl has an internal diameter of 14 cm, calculate
© capacity of the bowl in litres. [3]

(ii) Calculate the mass of the bow! given that the density of the wood
is 0,8 g/cem*. [4]

Volume of a sphere = Sam’

4008/2 32008
[Turn over

---

Page 8

Extracted Text

D is €

In the diagram, ABCD is a quadrilateral with AB parallel to DC. Diagonals AC
and BD meet at E. AB=6 em, BE=3 cm and DC= 15cm.

(a) Name, in the correct order, the triangle that is similar 10 AABE. {1]
(b) Calculate DE. [2]

(c) If the area of ABEC is 22,5 cm’, calculate

@) the area of ADEC, ; “ [2]
i} therein —_ in its simplest form. [4]

4008/2 12008

---

Page 9

Extracted Text

9 Section B [36 marks]

Answer any three questions in this section.
Answer the whole of this question on 2 single sheet of graph paper.

Triangle A has vertices (6; 4), (8; 6) and 4; 6).

Using a scale of 2 cm tc represent 2 units on each axis, draw the x and y axes for

(a) Draw and label triangle A.

(b) A reflection in the line py = x+2 maps triangle A onto triangle B.

@ Draw the line y = x+2.
(ii) Draw and label triangle B.
(ce) Triangle C has vertices at

@ Draw and label triangle C.

(ii) - Describe fully the single transformation which maps triangle

A into triangle C.

]
(d) A transformation P represented by the matrix | id

A onto triangle D.
@ Draw and label triangle D.
(ii) State the name of the transformation represented by P.

(e) A clockwise rotation of 90°, centre (0;10) maps triangle A onto
triangle E.

Draw and label triangle E.

4008/2 J2008

0
| maps triangle

1]

2]

[Turn over

---

Page 10

Extracted Text

10 Answer the whole of this question on a sheet of plain paper.

Use ruler and compasses only. All construction arcs and lines must be clearly
shown.

Three schools, P, Q and R are such that the bearing of Q from P is 045° and that
of R from P is 300°. The distance between P and R is 18 km and Q is due east
of R.

(a) @ Using a scale of 1 cm to represent 2 km, construct a single diagram

to show the relative positions of the 3 schools, P, Q and R. [5]
(ii) Use the diagram to find the actual distance between P and Q. [2]
(iii) Construct the perpendicular from R to QP produced. [2]

(b) Calculate the area of the triangular region PQR, giving your answer
sola | E]

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

The following is an incomplete table of values for the graph of y =x? +4 £
fe

[i> is [2 jay Ta
Ip [29 [45 [93
(a) Calculate the value of p and the value of g. | 2]

(b) Taking 4 cm to represent 1 unit on the X-axis and 2 cm to represent
1 unit on the y-axis, draw the graph of

2 1
yex +— for0.25sx<3., [4]
x
(ce) On the same axes draw the graph of 2) =5x42. ; [2]
@ @ Write down the coordinates of their points of intersection of the

graph of y = x? = and graph of 2y =5x+2. [2]

(ii) Estimate the area bounded by yax? + s and 2y=5x4+2
x

and the lines x =1 andx=2, [2]

4008/2 52008

---

Page 11

Extracted Text

LE

10 (a) A vertical aerial mast is 20.5 m high. Calculate, to the nearest degree,
the angle of elevation of the top of the mast from a point on horizontal
ground which is 32,6 m from the foot of the mast. [2]

(b
(b) z

6 a
M 12 ¥
The diagram shows ALMN in which LM = 6 cm, LN =7 cm and
MN = 12 cm.
Calculate MLN. [5]

ig) A co-operative deposited $60 million into a bank for ie years at the

rate of 20% per annum simple interest.

i
After ie years the co-operative was charged 15% tax on the total interest

they seas and $4.32 million as bank charges,

Calculate

@ the interest the co-operative made, (2]
Gi) the tax deducted, {1]
(iii) the net profit they made. , (2]

4008/2 12008
[Turn over

---

Page 12

Extracted Text

ab

12
Answer the whole of this question on a single sheet of graph paper.
A group of 70 students were involved in a 50 km sponsored walk.

The distances covered by the students are shown in the table,

meee 10<x=20 | eae | 25<x<40 | 40<x<50 |
covered (km) : i :

Number of | 30 | Le | w 13 |
students

Frequency 3 | y 1 1,3
density
(2) Find the value of
@ 4, [1]
Gi) ow. [1]

(b) —_- Using a scale of 2 cm to represent 10 km on the horizontal axis and
2 cm to represent | unit on the vertical axis, draw a histogram to
represent the information in the table, {3

(c) State the modal class, fl

(@) A sponsor paid at the rate of $10 000 per km. Calculate an estimate
of the total amount paid to those who walked more than 25 km. (3

(e) Two students were chosen at random from the group. Calculate the
probability that one walked at most 20 km and the other walked more
than 20 kan but less than or equal to 25 km. [3

4008/2 12008

---

Page 13

Extracted Text

13 Answer the whole of this question on a single sheet of graph paper. Mr F. 1ve manufactures tables and chairs using softwood and hardwood. ; A-table requires 5 metres of softwood and 3 metres of hardwood. A chair requires 3 metres of softweod and 4 metres of hardwood. Mr Hove has 45 metres of softwood and 48 metres of hardwood. Let x be the number of tables made and be the number of chairs made.

(2) Using the above information. write down two inequalities other than x > 0
and y > 0 in x and y, which satisfy these conditions. [4]

(b) In order for Mr Hove to make a profit, he should manufacture more than
2 tables and at least 4 chairs, Write down two inequalities. one in x
and the other one in y, which satisfy these conditions. (3

(ce) The point (x; y) represents x tables and » chairs manufactured. Using
a scale of 2 cm to represent 2 tables on the horizontal axis and 2 cm to
2 chairs on the vertical axis, draw the axes for

Osxsl6and0<y<l6.

Indicate clearly by shading the UNWANTED regions. the region in
which (x:3'} should lie. (41

(d Use your graph to write down all possible combinations which give the
maximum number of tables and chairs manufactured. 12]

4006/2 J200%

---

Page 14

Extracted Text

---