2018_maths_olevel_nov_paper1

Extracted Content: 2018_maths_olevel_nov_paper1

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Fa Peefareaence Mosurement °

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/1

PAPER 1
NOVEMBER 2018 SESSION 2 hours 30 minutes
Additional materials:

Candidates answer on the question paper
Geometrical Instruments

Allow candidates 5 minutes to count pages before the examination.
This booklet should not be punched or stapled and pages should not be removed.

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 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.
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 essentiat working will result in foss of marks.

Decimal answers which are not exact should be given correct to three significant figures unless
stated otherwise.

Mathematical tables, slide rules and calculators should not be bought into the examination room

INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question

This question paper consists of 20 printed pages and 0 blank page(s).
Copyright Zimbabwe Schoo! Examinations Councit, N2018.

© ZIMSEC NW18 {Torn over

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Answer all questions.

NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS
MAY BE USED IN THIS PAPER.

93

1. a) Simplify z giving the answer as a fraction.

AMNSWED (8) cooecssesssceveesscseesccncrsecesescctssnscatsersasesnees (1]
b) Express
. 3 + .
i) 5 as a decimal fraction,
(D)GI) ceeecccccsseecsceseeeessconsetseaersatseseesesenes {1]

it) 0,125 in standard form.

(DYE) esesesssesserscsssrsecssreencseessccseaeessrssees LED

2. The following is a list of real numbers:

3 3
aT ES 121; -19; 1; V6d.

Choose from the list

a) a square number,

AMSWEL (8) csccecserccrsrseceecesrssescesserenceseeresseesnererae [1]

b) irrational numbers.

(DO) vescccceseeestescereescareenesenseseassteranenceeee [2]

3. a) Express 4x 53 +3 x 5? +2 as a number in base 5.

ADSWEL (8) csessecceeeesscersssestssetecsscssserserseeeee LL]

4004/1 N2018,

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b)

4. a)

b)

c)

b)

3

Evaluate

i) 10111, + 1010, giving the answer in base 2,

(byi) .. fil

ii} 512? -4357 giving the answer in base 7.

(DEI) -seeeseseseresesseseessesersssneseeteaesesseesees (1)

Express 00 45 in 12 hour notation.

ANSWEL (A) o.esecesssessstetserenessseesssensennsteeeeerersereereee LI

Gortha’s local time is 3 hours 45 minutes ahead of Harare’s local time.

Find the time in Harare when the time in Gortha is 21 23. ~

Convert 5 ki? to hectares.

Express 6, 07 x L0* in ordinary form.

AmSWEr (A) vo.ccececcsceeencecserecessceerenevssesesepuecosneaveeee {]

Evaluate 2, 53 x 10' + 6, | x 10°', giving the answer in standard form.

400-471 M2018 [Turn over

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6. B R §
A
Q
In the diagram AQ and BS are parallel lines such that
PQ = PR, APR = 84° and RQS =90°.
Find
a) PRQ,
AMSWET (8) oo.. ce ceseeccsecceseseeeceeceensensceceetagensrneserseee {1]

b) QRB,

(D) escssccsecssecsescnecteesseerenereensesueseerenenenses {1]
ce) QSR.

(OC) cesserrecseesesstevercsesvereseeverencevensnsnesnenenaeese (1)

A041 N2018

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7. Solve the simultaneous equations:
Qe + dy = il
3c -—5y = —-12
ADSWED occ tcereeeeenectsterteerecisscapsncenenannpnestesarest

“#0041 N2018 {Turn over

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The wave length, w, is inversely proportional to its frequency, f.
When f= 90, w = 675,
Find

a) an equation connecting fand w,

AMSWEF (A) cecceccessessessesessesssecserscterseeteatensensensateas (2]
b) the value of fwhen w = 500.

4004/1 N2018

re

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a

9 a)
b)
HW. a)
b)

7

Write 45,3981 correct to 4 significant figures.

ANSWEF (8) ooeeeccsceccssnsscenencsseessesensesescneatsenseeseses (i]
A student spends 8 seconds, correct to the nearest second, to solve a problem.

Find the limits between which this time lies in the form a < t < 6 where a and b are constants
and ¢ is the time.

(CD) eeeecceccenesnsseneenesessescnssesessessareeereseans [2}
Factorise 32% — 15x completely.
Answer (a) ....... dees eanarseeseseesseseneeaaeaeeassausneesentaees [1]
Find the Highest Common Factor (H.C.F.) of
BAL in, 2B im and 36Pmn,

4004/1 N2018 [Turn over

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8

1, The points A(6; 2) and B(8; 5) lie on a straight line.
Find the

a) gradient of the line AB,

AMSWEEF (A) vecsccsssscesssecseessevscrsceseestesrrscssecseronenaes {1]

b) _ equation of the line AB, giving the answer in the form y = max + c.

« [2]

2a+6 at?

12. Simplify 723° pod

AOONT N2018

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13. a) Express the ratio 3,5 kg : 800 g in its simplest form.

Answer (a) .
b) In 2016 a farmer harvested 4,5 tonnes of maize. This was 20% more than what he had
harvested in 2015.
Find the number of tonnes of maize the farmer harvested in 2015.
(D) eects reeeeeneeereee CONNES [2]
14. a) Solve the inequality
4-Sx<2x+8.
Answer (A) ccccccccccccesececcsssessecsescessesseereersaersees . —]
b) Write down the smallest integer that satisfies the inequality
4-S5x<244+8.
(DY cceeceseeeeeeesseeseenteeneasacserssenevaneneeesesense {1]

40041 N2018 (Turn over

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IS. If log a = 3 and log b = 7,
calculate

a) lug ab,

ANSWEF (8) w.eseeceresssssssessssntetstsstcneereerssesssscseesceere PL]

b) log r

c) log Wa,

J004/1 N2618

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u

16. a) Ifa function f (x) = (x + 4) (2x — 1),

find f (3).

AMSWEL (8) cisscccscesccssscctseneeccsenseceeceeaesesesaeetsensoaes [2]

b) | Solve the equation

3m om 1
T3773

4004/1 N2018 [Turn over

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0 x
17. Itis given that vector p = (5) and vector g = (7)
Find

a) p-—qin terms of x in its simplest form,

AMSWeE (A) o.cseccsccseescesescenecetscescssceasenenersesngersersees {1]

b) the possible values of x given that| p — q| = 5.

4004/1 N2018

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18. a) State the special name given to a regular polygon with 4 sides.

ANSWET (8) c.esccsssecrsecesceesecrscersansenevevaseonevansensnsages {1}
b) ‘The angles of a hexagon are 115°, 89°, x°, x°, x° and x°.

Find the value of x.

4004/1 N2018 {Turn over

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19.

14

12cm

H (45

B c B

In the diagram, triangle ABC is right angled at B, BCD is a straight line, AC = 12 cm and
BCA = 45°.
v2

[Sin 45° <8, Cos 45° = >

Using as much of the information given above as is necessary,
calculate

a) BC, leaving the answer in surd form,

AMSWED (2) .oeeeccsssscssssasssessscnscrsvsssesessetcaecensneaneaees {2]

b) Sin AC'D leaving the answer in surd form,

ce} tan ACD,

40041 N2018

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20. The table befow shows the heights, #, of 50 trees in a school orchard.
Height (h) m 2<hs6 6<hs8 8<hs 10 10<h<12
Frequency 16 22

a) Write down the interval which contains

i) the modal height,

AMSWEF (A)(1) cesceesssesssesessectscceterseescesessevsvensevsaeees {g

ii) the median height.

(A)GD) cvecsesrecsestsssecscnsenseeseccereesensertseeeters {1]

b) Calculate an estimate of the mean height of the trees.

40041 N2018 {Tarn over

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i
21. The probability that Themba will score in a match is 3 The probability that Allan will score in the

same match is *
Calculate the probability that in the same match

a) both score,

ANSWET (A) o.eeeccsesssecsseeseerscessssesssvsceesseavecereavenseees [2}
b) neither of them scores,
(DO) cececssceneeseeesesesssessstessesensseserseeesevecenses [2]
c) — onty one of them scores,

4004/1 N2078

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—-

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22. a) Convert a speed of 12 m/s to a speed in km/h.

b)

Answer (8) vse

Speed
mis

Time (s}

The graph shows the motion of an athlete running on level ground at a constant speed of
12 m/s for 5 seconds. The athlete then retards uniformly to rest after a further 3 seconds.

Calculate the

i}

ii)

total distance covered in the 8 seconds,

acceleration of the athlete in the last 3 seconds.

seeesseeaseeeeaeeceneseeseassesaeeeaneness [2]
(DG) ae ceeeeereneseeeseeeee [2]

AQUAE NZOIS

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In the diagram points A, B and C are on the circumference of circle centre O, OB = 7cm

and AOB = 60°.
; . 22
In this question take x to be >
Calculate
a) ACB,
AMSWEL (@) v..ceecesessescssssvesessessecerscsscatcaecevenceernerss
b) OAB,
()) enn
c) the length of minor arc AB,
(C) cescecsssscesesssescasscrseceasrereseseerseenerssescareeee
d)} the area of the minor sector AOB.

4004/1 N18

{2}

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24. Itis given that the universal set , &, has subsets P,S and M such that,
§ = {152;3;4:5;6;7;8:9},
P = {prime aumbers},
S = {perfect square numbers},
M = {multiples of 3}.

a) _ List all elements of set P.
AMSWET (8) ceessssecsesssersscersccesseeeeseserstereessvecseesesesees [2]

b) = Write down n (PSN At}.

c) Complete the Venn Diagram by inserting elements in the correct regions

(C) creeccceeresensetsetesresreanes on the diagram [3]

UL N2018 (Turn over

wee

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The graph shows triangles X and Y.

a)

b)

Triangle Y is an image of triangle X under a certain single transformation.

Describe fully the single transformation which maps triangle X onto triangle Y.

AMSWED (8) ..sceccsssscssorsseneessessesconserersevsesrassene

ssseeaenasessassuesscecsessnesseaesesesenesesessenteneatarsanes secon 13]
Triangle Z is the image of triangle X under an Enlargement of scale factor 2 and
céntre (0; 0).
i) State the matrix that represents the enlargement.
it) Draw and label triangle Z.
(DMG) ieee ON the grid [3]

Total marks: 100

4004 N2018

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