2018_maths_olevel_mj_paper2

Extracted Content: 2018_maths_olevel_mj_paper2

Page 1

Extracted Text

Candidate Name Centre Number Candidate Number

Few ticks come

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4030/2

PAPER 2
JUNE 2018 SESSION 2 hours 30 minutes

Candidates answer on the question paper.
Additional materials: | Geometrical! instruments
Mathematical tables/ Electronic calculator

Allow candidates 5 minutes toe count pages before the examination.
is booklet should not be punched or stapled and pages should not be removed.
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 and your Centre number and Candidate number on the top right corner of every
page of this paper.

Check that all the pages are in the booklet and ask the invigilator for a replacement if
there are duplicate or missing pages.

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

Write your answers in the spaces provided on the question paper using black or blue
pens.

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. Answers in degrees should be given correct 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 or Electronic calculators may be used to evaluate explicit numerical
expressions,

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

Copyright: Zimbabwe School Examinations Council, J2018.
‘OZIMSEC 52018 [Turn over

---

Page 2

Extracted Text

Centre Number Candidate Number

2
Section A [64 marks]

Answer ail the questions in this section.

(a) Simplify 0,8 + 7,2 + 0,24.

Answer: (@ (2]

(b) _ By selling an article for $45, a shopkeeper made a loss of 10 % on
the cost price.

Calculate the cost price.

Answer: (B3 [2]

a ei an
$0302 Fs

---

Page 3

Extracted Text

Centre Number Candidate Number

3

1 (c) It is given that f(k) = 2k? - 8.
Calculate
@® f-3),

(ii) the values of & for which f(k) = 0.

Answer: (i) _-—s- (2)

Gor]

Jn the diagram, PAB is a straight line and is parallel to CD.
PAC = 132° and BCD = 43°.

Calculate ACB.

Answer: (a) [2]

4030/2 J2018

---

Page 4

Extracted Text

Centre Number Candidate Number.

a

A
2 (b) —_ Factorise completely
(i) 4a7b ~ 20ab?,
(i) 3a? +7a-6.
Answer: fi) fi]

@P oa BB]

(c) It is given that Y= mp + ; fp.
{i) Calculate the value of H when m= 2, p=3 and f = — 4.

(ii) = Make f the subject of the formula.

Answer: @ (2)

—

(i)

Ci]

nee
4090/2 F018

---

Page 5

Extracted Text

Centre Number Candidate Number

5

(a) The cost of 3 kg of apples and 7 kg of bananas is $16.
The cost of 4 kg of applies and 5 kg of bananas is $17.
Calculate the cost per kg of apples and the cost per kg
of bananas.

Answer: (a) apples $
bananas $ {4]
(b) —_W varies directly as x and inversely as the square root of u.
W=6, whenx=2andu = 9.
@ Express W in terms of x and w.

(ii) = Find W when x = 8 and u= 4,

Answer: fp {2]
(id) (1)

4030/2 J2018

---

Page 6

Extracted Text

(c}

Centre Number Candidate Number

6

Matix A = ($ 7) and mavixB =(7 _9):

Calculate
@ A-2B,
(ii) = AB,

(iii) Aq}, the inverse of matrix A.

Answer: @ (2)

(ii) {2]

(ii) _ [2]

4030/2 J2018

---

Page 7

Extracted Text

Centre Number Candidate Number

(a)

In the diagram, B, C, D and E are points on the circumference of a
circle centre O. TB is a tangent to the circle at B, CBD = 67° and
EBT = 40°.

Caiculate —

@ ‘EBD,

Gi) BCE,

(iii) BEC,

(iv) BDC.

Answer (a) (i) (t]
Gi) {1]
(iii) 1g
(wv) [1]

4030/2 32018
[Turn over

---

Page 8

Extracted Text

(b)

Lemire INuinber Candidate NUMDEL

8

itis given that the Universal set, € is such that
f= {x:-3 <x <3,x is an integer}.

A and B are subsets of & such that

A ={x: -2<x< 2}and

B ={x:-1<x <3}.

{i) List the elements of 1. A,

2. A’ U BY. where A’is the

complement of set A.
{ii) Find n{A MB).
Answer (6) 1. oe eee __
2. ee nte
(ii) a

4030/2 J20138,

[2]

(t]

---

Page 9

Extracted Text

(c)

Centre Number Candidate Number

9

A polygon has a sides, The sum of the interior angles is equal
to the sum of the exterior angles.

@ Find the value of x.

(id State the name of the polygon.

Answer: @ (2}

ii) {1]

4030/2 S2018
{Turn over

---

Page 10

Extracted Text

(a)

Centre Number Candidate Number

10

Peter, John and James share a certain amount of money.

Peter gets = of the amount of money,

John gets : of the remainder and James gets $3,00.

Calculate the total amount of money shared.

Answer: {a) [4]

4030/2 J2918

---

Page 11

Extracted Text

Centre Number Candidate Number

11

5 (b) = Three men working at the same rate can dig a trench, 5m long,
in 4 hours.

Calculate the time that two men working at the same rate would
take to dig a similar trench, 5m long.

Answer: (b) [2]
{c) Find the value of n given that
HH, = Tio.
Answer: (co) (3)

Gg

{Turn over

---

Page 12

Extracted Text

Centre Number Candidate Number

a

12

Answer the whole of this question on page 13.

Use ruler and compasses only for all constructions and show clearly all the
construction lines and ares.

All constructions should be done on a single diagram. Line PQ has been
drawn on page 13.

(a) Construct

(i) triangle PQR in which PQ ='7,5 cm, RPQ = 90° and

POR = 30°, (4
(ii) —_ the locus of points equidistant from Q and R, [2]
(iii) a circle with diameter QR. {]

ob) Measure and write down the length of the
1. radius of circle in a(iii), tj
2. side PR in triangle POR. {1}

(ii) Mark and label the points X and Y on the circle which
are equidistant from Q and R. [2}

(iii) | Write down the special name given to quadrilateral PRYQ. [1}

DO NOT WRITE IN THIS SPACE

4030/2 R18

---

Page 13

Extracted Text

Centre Number

13

Answer the whole of question 6 on this page.

Candidate Number

+ —<strong></strong>—_—__f—

P

Answer

7,5em
@ WW
(i)
(iii)
()
(i)
(iii)
4030/2 12018

Q

On the diagram
On the diagram
On the diagram
1.
2.

on the diagram

{4]
[2]
(1

---

Page 14

Extracted Text

{a)

Centre Number Candidate Number

14

SECTION B (36 marks]
Answer any ‘free questions in this section.
Each question carries 12 marks.
An open cylindrical water container has an internal height of 1,5 m
and internal diameter of 0,75 m.
Calculate the
@ volume of the container, in litres,

(ii) total internal curved surface area of the container.

22
Taken = 7

Answer fi)

(i)

{3}
{3]

4G30/2 )2U18

---

Page 15

Extracted Text

Candidate Number

Centre Number

15

(by i) Show that the equation

--—= > reduces to x? +2x~6 = 0.

[2]
(ii) Solve the equation x? + 2x ~6 = 0, giving the answers
correct to 2 decimal places.
(i) ox or {4}

4030/2 12018
(Turn over

---

Page 16

Extracted Text

16

The following is an incomplete table of values for y = S15 —x?),

{a) Calculate the value of
@
(ii) 4

Answer (i) m= _ Wy
fijn=_ OY

Answer this part of the question on the grid on page 17.
(b) Gi) ~—_—dDraw the graph of y = a5 —x*), [4]

c) Draw the line y = 2 to cut the graph at two points. fy
(c) Use the graph to

103) find the equation of the line of symmetry of the curve, {
(i) estimate correct fo one decimal place, the solution of

the equation Fs —x’) =2, {2}

(iii) find the gradient of the graph of y = as ~ x7) at the
point where x = 2. [2]:

4030/2 12018

---

Page 17

Extracted Text

Centre Number Candidate Number

rs

17
y C
+ 8 : ia ma
HH
Ee 6 :
4
2
~6 “4 -2 ro 2t 4 6 x
~2
i
Answer (b) (i) On the graph [4]
(ii) On the graph {i}
(i (1)
<
(i) x= or [2]
|
4030/2 32018

[Turn over

---

Page 18

Extracted Text

| | :

(a)

18

Three points P, X and Y are on level ground and are such that
P is 200 m from X ona bearing of 064°. Y is ona bearing of
144° from P and is such that Y is due east of X.

Calculate the

(i) length XY,

(ii) distance P is north of X.

“bayer! a)

(ii)

40702 1201S

---

Page 19

Extracted Text

Centre Number Candidate Number

19

(b) Joseph cycles at a speed of 5 metres per second.
Calculate the time, in hours, he takes to cycle a distance
of 18 km.

Answer (b) hr. [2]

(c} A television set has a marked price of $300. A 5 % discount
is given for cash payment. Calculate the cash price. .

Answer (c)

4030/2 S2018

r

(2]

[Turn ever

---

Page 20

Extracted Text

Centre Number Uancdidai: Suralics

20

9 (@) Jane invested a certain amount of money at a rate of 12 %
per annum simple interest. After 11 months the money had
amounted to $555,00.

Calculate the amount of money she invested.

Answer (f) [4]
10 Answer the whole of this question on the grid on page 21.

(a) (i) Triangle ABC has vertices at A(1; 1), BQ; 1) and
Cd; 3).

Draw and label triangle ABC. (1)

(ii) Triangle A; B, Cy has vertices at A, (—2; —2),
By (—6;—2), and C, (-2; —6).

Draw and label triangle A,B,C;. a3]

(iii) Transformation S represents a stretch with invariant
line the x — axis and stretch factor 4.

Draw and label triangle A2B2C2, the image of triangle
ABC under S. (2]

(iv) Transform:tion R represents a rotation 90° clockwise
about the origin.

_ Draw and label the triangle A;B3C3, the image of triangle

ABC under R. [3]

(b) cf) Describe fully the single transformation that maps .
triangle ABC onto triangle AyB;C). B]

(ii) Find the matrix which represents the transformation R. [2]

A032 12018

---

Page 21

Extracted Text

Centre Number Candidate Number

21
10 Answer the whole of question 10 on this page.
12 t
4] th | ot Rana
EE H +t a
ho
i co tt
H 8
t ;
: 4
zt H 4
2
-8 -6 -4 ~2Ft 0 2 HERE 6 FETTFEH 8 EEE x
tH “2
-4
t tH
“6
Answer (a) (i) On the graph ag}
fii} On the graph {1}
(iii) On the graph [2]
(iv) On the graph [3]
6)
(3}
(ti)
[2]
40302 12018

{Turn over

---

Page 22

Extracted Text

Centre Number Candidate Number

22

1t The table shows the distribution of marks obtained by 30 pupils in a
class test.

Mark (x) t<x55/| 5<x510 | 10<e515|] 15<x%<20/20<%x<¢25

Number of
pupil ()

(a) {i} State the modal class.

Answer (a) (i) {1]

a
493G02 32018

---

Page 23

Extracted Text

Centre Number Candidate Number

23

11 (a) (ii) The table shows entries used to calculate the mean of data
using an assumed mean of 12,5,

Class centre | Number of | Deviation f(x - 12,5)
(x) Pupils (f)_| (x - 12,5)
3 ~38

Calculate the values of p. g, r and S.

(iii) Hence or otherwise calculate, an estimate of the mean of the
distribution.

Answer (a) (ii) p=

q=
r=
Se LY

(iii) mean

{2]

4030/2 J20%8

[Turn over

---

Page 24

Extracted Text

11

(6)

Centre Number Candidate Number

rs

24

Two pupils are chosen at random from the class of 30 pupils.
Calculate the probability that

@ one has a mark in the range 10 < x < 15 and the other
a mark of at most 10,

(ti) doth pupils got marks that are more that 20.

Answer (0) (i) [3]

en C2

4930/2 12018

---

Page 25

Extracted Text

Centre Number Candidate Number

25

12 Answer the whole of this question on the grid on page 26.

(a) _ Draw the graphs of these inequalities by shading the unwanted

region.

(i) ax+y = 40, (2]

(ii) x+2y < 48, (2)

di) +20 - [2]

(iv) y>s. (2)
(b) Mark R the region defined by the four inequalities in (a). [Yj

{c) For integral values of x and y,

@ find the coordinates of a point that gives a maximum

value of x + y, Q)
(ii) state the maximum value of x + y. (tJ
DO NOT WRITE IN THIS SPACE
FHT TD a

[Turn over

---

Page 26

Extracted Text

Centre Number Candidate Number 26 12 (a) Answer the whole of question 12 on this page. HY t HH es “t aan H 40 t 30 20 HH a aaa G 10 EEE + 9 10 20 30 40 50 Answer (a) 7] On the graph [2] (ii) On the graph {2] (iii) On the graph [2] (iv) — On the graph (2] (b) On the graph fl} fc) i) [2] (i) [3] 4030/2 12058

1s tne eee amr ens enema E

---