2020_maths_olevel_mj_paper2

Extracted Content: 2020_maths_olevel_mj_paper2

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/2
PAPER 2
JUNE 2020 SESSION 2 hours 30 minutes

Candidates answer on the question paper

Additional materials=

Mathenratical Instruments

Mathematical Tables

Non programmable Electrome Calculator

Allow candidates 5 minutes to count pages before the examination.

This 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.
Write your Centre and Candidate number in the box on the top right comer 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 four questions from Section B.

Write your answers in the spaces provided on the question paper using black or blue pens,
If working 1s needed for any question. it must be shown in the space belaw 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

Decimal answers in degrees should be yiven correct to one decimal place.

Mathematical tables and Electronic calculators may be used to evaluate explicit numerical
expressions,

INFORMATION FOR CANDIDATES
The number of marks is given in brackets [_] atthe end of each question or part question.

This question paper consists of 26 printed pages and 2 blank page(s).
Copytight: Zimbabwe School Examinauons Council, J2020

eAIMSEO g300) [Turn over

PITMAN

PAB rae a key h nct errno rere rom

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2
SECTION A (52 Marks)
Answer all questions in this section

I (a) The difference between two fractions is 2. The smaller fraction is ol F

an “4

Find the other fraction

Answer (a) [2]

PVddeebeanepreasnsennssccensssssenrneny,

(b) The population of a certain country 1s 24,9 million,
Express this population in standard form.

BEHELD) a rspaanitmcercainn ed

(c) Increase $40,00. in the ratio 8:5.

ATW EEG) foi eronaiiainnstaoea

(4) Evaluate (7N5)".

PSWERLMY, | coucaenaarmrmraspncints Ul

he 20200

(ci

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SS ee

3

(e) Simplify 11011: + 243s, giving the answer in base five,

Answer (€) A

2 (a) Two similar cups have diameters of 6 cm and 10 cm.

(i) Write down the ratio of their volumes,

Answer (a)(i) 2]

fanacenaa gang pani Aaebardsbecedenensanes

1 ‘i P \
(ii) Given that the volume of the smaller cup is 100 em ,
calculate the volume of the larger cup,

AMS WEE (ANTI) sesamiae (1
(b) A wooden block is in the form of a prism whose cross-section is a paralleloyram
with base 35 cm, perpendicular height 20 cm and length 1,2 m-

Calculate the

(i) surface area of the cross-section of the block,

Answer(b)(i)

ACME 0b

|MMUOU AA

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[eee ae Pa

4

(ii) volume of the block,

Answer (b)(i1) 2]

(ili) mass of the block if 3 cm’ of the block weigh 2,5 g.

Answer (b){iii) 2]

Meera itectat ier teiey

a (a) Find the value of ¥/ for which i ,
yd) 3 = (-2)

Answer (a) aie [2]

apeeyaesendanseyeeeenpeseaeae:

abba J2020

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3

(b) Find the matrix P such that a se | 1
(; () ) tA (i i}

RS WEE AD) iccciasiastionamitinnder ld
(c) The equation of a straight line is y + 30° = —4

Find the

{i) coordinates of the point where the line crosses the y-axis

Answer (c¢)(i) 2]

sstsanecensgesneadennsersunserenensiges

(ii) gradient of the line,

Answer (2)(i) snsmsnmannsianane, LO]

(iii) equation of a line parallel to the line y 4-3. = —-l and passing through the
point (3; 5),

Answer (¢)Gii) [2]

A004 2 0

{IMTOO

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6

Answer the whole of this question on the blank space below.

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

All constructions should be done on a single diagram,

(a) Construct
(i) tiangle ABC in which AB = 7 em, 73 (+= 45°, BC=8em-.
Answer (a)i)onthe diagram (4d

(ii) the locus of points equidistant from B and C,
Answer (a)(ii) on the diagram

atentdadsvasnernananesueneasonty pre Htesesisnenssnsran nesesrenss

4004-2 17030

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Sees eee

5

(iii) the locus of points § cm from C.
Answer (a)(iii) on the diagram

(b) A point R in triangle ABC is such that it is nearer B than C and is less than 5 em

from C.
Show by shading, the region in which R must lie.
Answer (b)onthe diagram 2]
(c) Measure and write down the size of ABC "
Answer (c)
: 5 9,2 =
5 (®) Show that the equation * — 3 = Fy teduces to Su" — Gr — 5 =U).
Answer (a),

+14)

Wesdbedapeneasdanpetanedananat in crantanehyqaenptavendevaPtasanpyanentaeantqarypegeen Hfaeeengpansaqaepfeeatesenessaesnangeynsneetsneetysennsseeansa race

(b) — Solve the equation 3-7 — 9) — 5 =()-
Give the answers correct to 2 decimal places.

Answer (b)

rennet pteetadeenasaestypentes:

Syn > TH

MOHAN

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(t)

In the diagram, ABCD is a cyclic quadrilateral with centre O. AB is produced to
M.
af Be= ed ape = 40"

Find

i) pep:

Answer (c)(i) {1]

(ii) 4 Rp.

ABSIT (CHIT) eannnsnapsawnie LA

AMM 2 S20

NC

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titi) 4DO

Answer (¢)(iii) [2]

42 T2020,

UNOCAL

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10
SECTION B (48 Marks)
Answer any four questions from this section,

Each question carries 12 marks

iE
b )

In the diagram, ABO is a triangle in which M is the mid-point of OB and N lies

on AB such that r | ON and AM intersect at X_
AN =2AB
a

OA=" MOB = b-

(a) Express. in terms of @ and/or b

(i) OX:

Answer (a)(i) [1]

(ii) yy.

Answer (a){il)

tL 2 DUR)

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titi) ON.

Answer (a)(iii)

(iw) ANY

ANSwET(ONIM) mannan LY

(b) Given that yy = pf 4) y-Show thar OX (1A) + Lab
9

ala eer er

(c) oy = ON: express (7 \ in terms of a, band he

Answer (¢) [1]

Abd INO

IMAI

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See

12

(d) Use the results of (b) and (c) to find the numerical values of f and &,

PSPC ceraniiea Taig aiaeaiy
B]

satebedgaenesentonensaneee! [deen iaeenaeasenarariatisttsennmeeneennened tay

(e) Hence, or otherwise find the ratio of area of triangle OAV to area of triangle

OAM.

Answer (e)

ib 2 ATO

| mn

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a ee eae

12

(d) Use the results of (b) and (c) to find the numerical values of / and k,

Pe EY i senonnialEaamwnimsipeees
GB)

satebeaayeneseneesencaseen {Acer besenaeesnaarsneatisbarcunaeennensenen tat

(e) Hence, or otherwise find the ratio of area of triangle CAN to area of triangle

OAM.

Answer (e)

AMZ AZO211

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7 Answer the whole of this question on the grid below. Use a scale of 2. cm to |
unit on both axes.

(a) Triangle POR has vertices at P(1: 3), Q(2; 1) and R(4; 3).
Draw and label triangle POR.

404-2 J2020

UCT

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Se es

14
(b) Triangle P;Q,R, is the image of triangle POR under a reflectian in the line
a
(i) Draw the line Y= 7?

Answer (b)(i) on diagram

(ii) Draw and label triangle P} Qty,

(iii) A transformation, G, maps triangle PC) onto triangle Qo [7s with vertices
at Py (1;-6), Qo (2:-2) and I?9(4,-6),

Draw and label triangle 7y()o /?a ,
Answer(b)(iii) on diagram _{)

(iv) Describe fully the single transformation, G, which maps triangle POR onto
triangle PyQy Po.

Answer(b)(iv)

(c) The point /?, (-1; 2) is the image of J? under a translation,

(i) Find the translation vector.

Answer (c)(i) (1)

aeanedenenenenns pipennasnseanncennnaaenasnansynenty

Mukeed oT

ilu

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(ii) Write down the coordinates of P3 and (3 the images of P and ()

(a)

UAC

respectively, under the same translation.

Answer (c)(ii)

Pca aanse iis encee mans eR EON [2]
The following ts. table of values for the function ,, — 3 _ 3-2.
(ac Ser ar Ee ee
a a a a 4. (. 0 16
Find the value of 7? .
ATSWET (A) snc 1]
WMD Dita
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2 eae ee ee

16

Answer this part of the question on the grid below. Use a scale of 2 em to 1
uniton the © axis and 2 ent to S units on the !/ axis.

(b) Draw the graph of y= ee IF
Answer (b) on the diagram [4]

004-2 JOR

IM

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(c) Use the graph to find an estimate the

(i) gradient of the curve at the point where “= 3,

ANSWER LENA) oc avaisirnmninasosiacitonids FI
(ii) area bounded by the curve, the !/ -axis and the line /=— 12.
Answer (c)(ii) ~ Ty
(d) Write down. from the graph. the range of values of “ when the curve has a
negative gradient.
AMSWEE (AY taintimainasionsn LE]
(ce) Use the graph to solve the equation -? — 3)? = 9, for positive values of

Answer (¢)

AWD S220

MOU

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at eet || eer

18
9 (a) Factorise completely
i) =.
Amswer(ay(i) rmiminnsanainnnne Ll
fi) 7? Sr +6
Answer (a)(ii) 2]
(iii) Hence or otherwise find the Highest Common Factor (H-C.F.} of)? — 4 and
ad — or + 6.
Answer (ay(iii) aaieaians
(b) Tis given that _ N
3 pe
(i) Find the value of S when “= 81 and /= 1],
3
Answer (b)(i) [2]

seteaannnang hj dnanbdnnesnnnaneaeoenae

ng 2 IMI

MN .

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ees PS

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(ii) Make the subject of the formula

Answer (byt) css [3]
(c} From a group of 30 people at 4 party, it was observed that 17 people até beef’,
16 people ate pork, ” people are both beef and pork and 6 people ate neither

beef nor pork.
Calculate 7. 1he number of people who ate both beef and pork

AAW CC scat

AWM

UIC

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10

K

In the diagram KLNG is a trapezium in which LMN is a straight line and FEL NY

= VV = 90°. MK = Tem, MG = 5 cm, LAL Ey = 60 and y- 76; = 35°.
Calculate the

{a) length of NG,

Answer (a) (2]

(b) size of AY i

ER ccemainaiconinanionan lel

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Nn

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{e) area of triangle KMG,

Answer (c) Pern tnert ee

(a) length of KG,

Answer (d)

(e) size of MING ‘

Answer (e)

40042 FU

NOUN

Candidate Number

seececae SM

oa, EN

canlkl

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oh)

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A group of youths wishes ( make and paint chairs and tables for sale,
Let / be the number of chairs and !/ the number of tables to be produced.

The group wishes to produce at least 5 chairs and not less than 5 tables.

(a)
Write down two inequalities, one in "and the other in // that satisfy these

conditions.

Answer (a)

(b) The group has 48 hours to make the chairs and tables_
Tfit takes 4 hours to make a chair and 3 hours to make a table, write down an

inequality in “and ! that satisfies this condition,

Answer (b)
The group hired a compressor for 14 hours to paint the chairs and tables.

Given that ittakes | hour to painta chair and | hour to paint a table. form an
inequality in “and !/ that satisfies this condition.

Answer (c)

weep DDT

NA

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(d) The point(:r; y) represents * chairs and Y tables.

(i) Construct and show by shading the unwanted regions, the region in which
(©. 1) must lie. Use a scale of 2 cm to 2 units on both axes.

Answer (d)(i) on the diagram [6]

4iuhed $2020

[ON

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(ii)

(a)

(i)
(ii)

(b)

ILI

Centre Number Candidate Number

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The profit on a chair is $10 and the profit on a table is $20,
Use the graph to find the grearest possible profit that can be made.

Answer (d)(ii) [2]

Vaaeasenee lee paaroenseran tien teense

The table below shows the heights, /icm, of a group of 200 children.

Height (em) _| S0<hs60 | 60<h<7 | 70<hs75 | W<h<k0 pes bs

Freguency | 24 AX 53 45 | 4
nanan | 24 | 8 10.6 | p TT
Find the value of
p
eal Mbeneenenn Pantene []
fi

ARS HET (AMID ecinnsanaanensact CAT

Calculate an estimate of the mean height of the children.

Answer (ay(iii)

Hab 2 2020

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(c) Draw a histogram to show the information in the table.
Use a scale of 2 cm to represent 10 units on the /) axis and 2 cm to represent 2
units on the Frequency Density axis.

4004/2 J2020

OITA

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Po eremneeareriiivieécereetcenanm ces: 1

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| Ae

ag

| (d) Two children are chosen at random from the group.
Find the probability that each has a height which is greater than 75 cm.

Answer (c) (2

saseseaveebunnrngnesbtabebterest A aeenteewes

4A J2020

Qn

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BLANK PAGE

404-2 2520

LMA

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