2020_maths_olevel_mj_paper1

Extracted Content: 2020_maths_olevel_mj_paper1

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Candidate Name Centre Number Candidate Number

(- ae Hiern

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/1

PAPER |

JUNE 2020 SESSION 2 hours 30) minutes

Candidates answer on the question paper

Additional materials;
Mathematical Instniments

Allow candidates 5 minutes to count pages before the examination,
This bookict 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 atthe wp of this page.

Write your centre and candidate number in the bax on the top right corer of every page of this
aper.

Cheek thatall the pages are in the booklet und ask the invigilator for a replacement if there

are duplicate or missing pages.

Answer all questions.

Write your answers iu the spaces provided.on the question paper using black or blue petis.

If working is needed fur any question, + must be shown in the space below that question,

Omission of essential working will result in loss. of marks,

Decimal answers which are nat cxact should be given ta three significant figures unless

stated otherwise,

Mathematical tables, slide rules and calculators s)iould not be brought into the examination

room.

INFORMATION FOR CANDIDATES

The number of marks is given. in brackets [ ] al the end ofeach question or part question,

This question paper consists of 20 printed pages.
Copyniyht, Zinibabwe School Examinations Council, 32020;

E.ZIMSEC JN [Turn over

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Candidate Name Centre Number Candidate Number

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Answer all questions . :
NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS
MAY BE USED IN THIS PAPER
1 Express 208,9

{n) in standard form,

AMSWET (8) ceanunereyreneuemenneye (J
(b) correct to 3 significant figures.

Answer(b) ee OT |
{e) correct to the nearest hundred.

AMSWEE (C) nanuncnennmuennion UE]

Zz Evaluate

{a) —10°,

Answer(a) en |
(b) 4 }

(5)
Answer (b)

Seematt

MAAN s2020

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Candidate aime Centre Number Candidate Number

(LN

©
The Venn diagram showsthree sets A, Band C with their respective clements-

{a) List all clements of

i) AME,
Answer (A)(0) nesnnmuneneanenes ET

(iy (AUBIN.

unaware CANNY. sseminnsnenisasun FD
(by Find * (AUC),
Answer (b) _siianinmowmer EL
4 (@) Solve the inequality 2—y < 3y—10
Answer (a) i

samtciminamesonneswiaevonts dnpvvereanameenes

The perfect square, ¥, satisfies both 2— y < 3y— Wand y< 9

{oy TS :
Find the possible values of y.

Answer (b) (|

lasenmcansannonniersssvnnnyanens

operat Suet
[Turn over

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(ree

4
$s Solve the simultaneous equations:
Qrt+y=d
r-y=-2
Answer si
PR eee ete ||
fs fa) Convert 301, to.a number in base 10,

Answer (a)

SMA tVI*Ndnaeannanneynerttationseraennssi® |

{b) Evaluate

(I) (10l2+ 1112, giving the answer in base 2,

Answer (b)(i) , {1

(il) 131s—42s, giving the answer in base 5,

Answer (b)(ji) ox {1}

HOUMOL I2020,

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Candidate Name

( ——— Centre Number Candidate Number

é]
a TI
he menn of'3 numbers is 7. Two.of the numbers are 4 and -S.
Find the third number.
Answet wit py taaaraseearemnninaese 13]
8 Given thal p= | and nm =—2, evaluate
2
(a) moan
Answer (a) mb
ihe SES

_———
meh

Answer (b}

Ser mtn ae

Vie OU
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Candidate Name Centre Number Candidate Number

6
9 Express 2% -—-] asasingle fraction in ils simplest terms.
2—3n n
TL) \3 A eer nee te Soret a [3]
10 The matrix /(74+2) 4 is singular.
6 it!
Find the possible values of *.
pen |
W Given that f (a) = A + 2 and that j uy se 1
3x — 2 3 6
find the value of A.
|
Answer ert [3]

daa) $2020

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Candidate Name ( ee Centre Number Candidale Number

i2

7
Wis piven that p — (;) q> ie and r= /,"\-
Find , ; ) 0)
(ut) |p). Heaving dhe answer in surd form,

Angiver (i)

(th) the valueol’ pnd the value of Zit p—q = 2

Answer (b)

Savaneedabnnean ee paneammecnaness

A salesman's totul monthly salary consists of a basic salary of $200 anda2%

ion his monthly. sales.

commissia
was $560.

In ong month his total salary
Calculate

his commission for that month,

(a)

Amswer(a) ae enammnnns LU

ANI aa
|Yurn over

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Candidate Name Centre Number Candidate Number

8

(b) the sales he made for that month.

ANEW EDD, a ee [2]
14 Itis given that Sin y = 5 and that {/is an acute angle,
13
Find as a common fraction,
@) Cos (180°— y°).
AMEWERS) | saan tases I2]
(b) Tan y°-
Answer (b)

enenaccsciamans |
The table shows grades obtained by 150 candidates in a Mathematics test,

ABI CTOLETU
[5s [25 [3029 21 [a0]

(a) Find the median grade,

Answer (a)

Seterrorommenacec Al

SIMUL 20200

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Cand; Andidate Name ‘Candidate Number

Centre Number

“oh

(b) Collentate the probabil ity that two candidates chosen at random fron the 150
obtained grade 4 or B.

PE OY! airmen

in {a} Point (R(-3; -2) ts mapped onto point Ry by transformation represented by the

matrix; ] Oo}
ts a)

Find the coordinates of Ri

Answer (8) i

Hm VAAL LAUNAEPTE RTH DWHP tonite

annary sun
[Turn aver

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i b Candidate Name Centre Number Candidate Number

10

(b) In the diagram triangle P is the image of triangle Q under a certain
transformation,

i jangle Q.
Describe fully the single transformation that maps triangle P onto triangle Q

Answer (b)

Maer one nacatennaseiay

40uaK1 2020

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Cundidate Name

—>_ = Centre Number Candidate Number
i »
(7 ML is pi | .
Bien Wat go M and &=1 when =2 and r=3.
Find the i
(a) formula connecting g, mr andr.

RI

Answer (a)

\avateendetennen ak OUNH CA VATHNNHRNANT ANNE

(by numerical value of g whens = 10 and r=2

Answer(b)

sreaconannnnivssiecacinn (ed

Am Aad
[Torn aver

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Candidate Name 18 () (by (cj (4)

Centre Number

Candidate Number

Inthe diagram A, B, C atid D are points on the circumference of a circle centre
o

PD {s a tangent to the cirele at D

Calculate

BAD:

CDP:

CAR

BCD:

4004/0) a2020

AB B= 28 md Cp y=

Answer (a)

ciscpnncemoneneny LY

Answer (b) :

wt Seenerevthieenenal Va

Answer (c)

Answer (qd) :

MSA eet Udasert com sey cvagyg I | |

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Candidate Name

———s Centre Number Candidate Number

13
WH) Simplify tb 3 (4 — 2).

POUNCE TOD) winmininmomiesssian tl
(i) Factorise completely
“= f—-a) #4
Ga AU aptrncerrer nent P|
nu (a) Name the regular polygon which has-totational symmetry of order 5.
Ans\wet (a) ye [1]

(by) The sum of the interior angles of « hexagon is 720°, Three of its interior angles
are 140°, 120° and 160°.
The remaining angles are in the ratio 3:3; 5
Calculate the size of the largest of Lhe remaining angles,

Answer (b)

—rincentinneenae, ED

aandep aman
(Turn over

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1d
; es"
2t Wis piven that Loy = Gand Log y = —2
Evaluate
A) Ley (ary).
SERB) acc casi 3]
(b) “mu | )
Vr
PT ya osenscesnapcrmadlens LOE
22 On averiain map, @ length of 2m represents a distance of Skin.
~

{n} Express the seale of the map Riving the answer in the form 1 | ”

(2)
Conve

(b) Calculate the area on the map in cm’ which represents ay actual area of dk?

Ansiver' (b} i

(2|
PUN eeeerHedeseey i neemnttiereey oi

MMOH S20)

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Se ee

= Centre Number Candidate Number

15

2

6

In the diagram AODF and BOCE are Straight lines latersecting at O, AB is
parallel 10 CD and EF,

AB = CD-= Gem, OD = demand DF =8em.

(n) Name

(i) the triangle which is congment to triangle AOB,

Answer (a)(4) ‘

Gi) (Wo triangles whieh are similar to triangle AOR.

Answer (ay(i))

THAN beeeenaeaentontnsned ones’

saciissinty MAT

eaaenmranenasnen cnn HN HHVHHAD Huon

ib) Calculate the length EF

Areveer(h) naming VOD

pep 42020
a [Tura over

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24 (u) A straight line has gradient -1 and passes through ibe point (3; 0).
Find the equation of the fine inthe farm yf =e oe

Answee (a). [2]

(h) Thesolutions of a quadratic equation are ey = —1 and = 3.
Write down the quadratic equation ii tlie form ar the te =0
where tl antl © ure integers,

Ans\ver (b).

B]
INTTTEN A WnseaAVANEAN COSMO N Nonsense tiie os

FOOT U2,

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LAnUiGale Nee

= Centre Number Candidate Number
\7
a
z
we
EN
Gem ¥

The diagram shows triangle XYZ with XY =6em, XZ = 1em and } ‘V za
Use as much of the information given below ag is necessary-

Sin 30° = 0,402 Cos MP = 0. 87: Tan 0? = 0,58)

Calculate the

(a) area of the triangle XYZ,

Answer(a) [2]

WAV Rees eee

een undmeasennersaizasnere

(b) lengilvof YZ leaving the answer in-surd form.

‘Answer (b) ia]

lshensennaneny

qunaegsau20
JTorn over

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e didate Number “Candidate Name Centre Number Can

18
26

Speed m/s

Time (3)
The diagramis a'speed-time gtaph of an object which decelerates uniformly from
a speed of 50 m/s ton speed of 30 m/s in 20 seconds, I! further decelerates
uniformly for 10-seconds uatil it comes to rest,

(a) Find the speed when ¢=S seconds.

Answer (9) <

PTPNCNTETE ASEAN bbs bishddenbe [2]

(bh) Calcutate the

(i) acceleration ofthe object during the last 10 seconds.

Answer {b)(i)

MOHAN 42020,

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(ii) distance travelled during the 30scconds

Angwer (b)(ii)

Feveu aban gan EnE enn nemen

27 (ee

B 22 A
The diagram:shows the cross-section of a concrete drinking (rough which is 3m
long. AB =2,2m, BC = AG= Imand CD=FG = 0.4tn:
DF the diameter of the drinking trough is 1.4m, Take * io be 22.
7
Calculate the

(a) perimeter of the eross-secinn,

Answer (ay 13]

mannan nnn vey EHNNN AAMHAATNN HH pARmEmNS

vnmbas HZ
{Turn over

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20
(b) area of the crass-section,
ATEUETIBD imanainninesnnrenon LN
{ec} volume of the Goncrete used to make the drinking trough.
Answer (¢} sets \2)

MOHAN $2021

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