2021_maths_olevel_nov_paper1

Extracted Content: 2021_maths_olevel_nov_paper1

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

4004/1

MATHEMATICS
PAPER 1

NOVEMBER 2021 SESSION 2 hours 30 minutes

Candidates answer on the question paper

Additional materials:
Mathematical 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.

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 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 essential working will result in loss of marks,

Decimal answers which are not exact should be given to three significant figures unless

stated otherwise.
Mathematical tables, slide rules and calculators should not be brought 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 25 printed pages and 3 blank page.
Copyright Zimbabwe School Examinations Council, N2021

© ZIMSEC 2021 [Turn over

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sandidat
Candidate Name Centre Number Candidate Numbg,

Answer all questions

NEITHER MATHEMATICAL, TABLES NOR SLIDE RULE NOR CALCULATORS
MAY BE USED IN THIS PAPER

1 Express 30,098

(a) correet to the nearest tenth,

Answer (a)

(1)
(b) correct to four significant figures.
Answer (b)
(1)
(c) in standard form,
Answer (c)
(1]
2 (a) —_ Express 42 as a recurring decimal,
3
Answer (a)
i

4004/1 N2021

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Centre Number Candidate Number
(b) Find the value of 10 — 10-2 242 ¥ 2,
Answer (b)
[2]
3 (a) Write down the next term in the sequence 2: 3; 5; 8; 12, ....
Answer (a)
1)

4004/1 N2021
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(b)

4

Centre Number Candidate Numbe,

Candidate Name TT

lity JU — & giving your answer as a common fraction in its
Simphly 4U " "* ,

204.8
simplest form,

Answer (b)
[2]
(i) List the prime numbers between 14 and 20,
Answer (ai)
{1}
Gi) Write the number 801 008 in words.
Answer (a)(ii) in answer space
1]
Express 6,65 hours in hours and minutes.
Answer (b)
i!

4004/1] N2021

. |

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TT ee sees

(a) List the first three values of such that | <a <4 where “18. natural
number,

wn

Answer (a)

[2]
(b) Express 270 as a product of its prime factors in index form,
Answer (b)
[2]
6 (a) ‘If the bearing of P from Q is 054 °, find the bearing of Q from P.
Answer (a)
(1)

4004/1 N202)
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Candidate Name

(b) — Caleulate the number of sides of a regular polygon with intenor angles of
1) nle :

162" cach,

Answer (b)
[2]
7 Express 1 1 asasinglc fraction in its simplest form.
ml l+e
Answer
(3]

4004/1 N2021

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iinet Centre Number Candidate Number
8 (a) Write down the largest Tourdigit number in base 5

Answer (a)
U1)
(b) ~—s Convert 111, to a number in base 7. |
Answer (b)
[2]
4004/1 N2021

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Centre Number Candidate y
Candidate Name

— er

) yeh
9 Factonise completely or? (yt 1) — y
Answer
(3]
10 Evaluate
(a) log, 64,
Answer (a)

f1)

4004/1 N2021

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Candidate Name
Centre Number Candidate Number
(b) log 8.
log 16
Answer (b)
[2]
11 Solve the simultancous equations:
ar+y=4
5y — 42 = 13
Answer
[3]
4004/] N2021

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Contre Number Candidate Nutibe,
Candidate Name

ee ge

y
12° For the expressions 10((0 | 1) amd Br + 1)%

find the
(a) Her,
Answer(a)
DY]
(b) L.C.M.
Answer (b)
[2]

4004/1 N2021

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13 Atn .
an, .
Find re heal of lengths $ em, 8 em and 12m
“0 bo d
te smallest angle aya common fraction in its simplest form.

Answer

[3]

14 (a) Solve the equation 5* = 125.

Answer (a)
[2]

4004/1 N2021
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| is HT:

(by Simphity og\ -
(3)

Answer (b)
(2)
15 Given that —-2< r<5and3<y < 10,
calculate the
(a) greatest possible value of y? — 2%
Answer (a)
[2]

4004/1 N2021

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(b) least possible value of CY,

Answer (b)
[2]

16 (a) Solve the simultaneous inequalities 27 — 6 < dar < 10 —.r.
Leave the answer in the form u <a < b. where a and / are integers.

Answer (a)

[3]

4004/1 N2021
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14
‘andidate Name Centre Number Candidate Number
Candic
(b) Represent the solution to part (a) on a number line.

Answer (b)
(1)
17) Given that y2 = y2 4 2as.
make a the subject of the formula,
Answer (a)
5 (2]
(b) Finda whens = 5,u = 2andy = 2.
Answer (b)
(2)

4004/1 N2021

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ee ee ee

15
Centre Number Candidate Number

D vanes jointly as S and T.

(a) Find an equation connecting D, §, T and a constant k

Answer (a)
(1)
(b) Find the value of given that 1) = 24 when $= 4 and J’ = 2.
Answer (b)
U1]
(ce) Find the value of T given that D = 50 and S' = 10 using the value of
kin (b) above.
Answer (c)
[2]
‘so041 N2021 {Turn over

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eS me

19 The universal set ¢ has subsets A and B such that
n(g) = 45, W (A) = 25, n (AN) =O and n(AN B) = n(AVUB) °.

(a) Show this information on a Venn diagram.

Answer (a) on the diagram

[3]

(by) Find (B).
Answer (b)
(I
20. Given that 3.9 # -2,
fe) = 43
find
(a) f(-))
Answer (a)
(1)

4004/1 N2021

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U _ Centre Number Candidate Number

(b) the value of" for which

Answer (b)
[3]

2021 =
soot [Turn over

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Tene tay

The diagram above shows a specd - time graph of a moving object.

The objects decelerates unitormly at 3m/s’ trom a speed of ¥ m/s toa
speed of 15 m/s in 5 seconds,

It maintains the spced of 15 m/s fora further 5 seconds,

It then decelerates uniformly until it comes to rest after 3 seconds,
Calculate

@

Answer (a)

[2]

4004/1 N2021

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2

(b)

()

(a)

(b)

19

the deceleration j
Nin the last 3
St 3 seconds,

Answer (b)
[1]

the distance travelled in the last 8 seconds.

Answer (c)
[2]
By selling an article for $20, 00 a dealer made a profit of 25%.
Calculate the cost price of the article.
Answer (a)
[2]
.-5
Given that 7¢—$ _ s—5t ’
——— =
find the ratio = §
Answer (b)
[3]

4004s! N2021
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Centre Number Candidate Nunite,

Candidate Name

ough the ongin and the point (1,2),

23 A straight line, {passes thi
Find the

(a) gradient of line I,

Answer (a)

11)

b equati
(b) equation of the line |

Answer (b)

[2]

4004/1 N2021

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Centre Number Candidate Number

(c) equation of
the strai i
Bht line through point (0; — 1) which is parallel to lin |
“ Ww rl) to line f.

Answer (¢)
[2]
24 (a) Ona map the distance between point A and point B 1s 10 cm.
The actual distance is gt km.
2
Find the scale on the map, giving the answer in the form I:n.
Answer (a)
[2]

4004/1 N2021 .
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Centre Number Candidate Numbe,

Candidate Name

(by) Caleulate the actual

(i) distance, In metres, between 2 places which are 3 cm apart on the map,

Answer (bXi)

(1)
Gi) area in 477%. represented by an area of 8 cm2 on the map.
Answer (b)(ii )
[2]
400411 N22)

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Centre Number Candidate Number

3s «Given that On ~2\ and
1 OW ( | ) where O is the ongin,
~2

lind
@ AB
Answer (a)
[2]
(b) AB leaving the answer in surd form,
Answer (b)
gqoart N2021 12]
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Tn Me as

(©) ¢) Jf. where M is the midpoint of AB

Answer (c)
[2]
26 Given that matnix A ] 2\and matrix C - 1 —4Y\,
3°04 -—2 3
tind
(a) the determinant of matrix C,
Answer (a)
[2]

4004/] N2021

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>) A-30,

Answer (b)
(c matrix B it B= 5\:
A(
6
Answer (c)
agoa/l N2021

Centre Number

Candidate Number

en meee

(2)

[2]

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Candidate Namo Contre Number Candidate jy
“Mbe,
BLANK PAGE

$0047) N2024

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