2022_maths_olevel_nov_paper1

Extracted Content: 2022_maths_olevel_nov_paper1

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Candidate Name Centre Number Candidate Number

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/1
PAPER 1

NOVEMBER 2022 SESSION = 2 hours 30 minutes

Candidates answer on the question paper

Additional materials:
Mathematical Instruments

Allow candidates § 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
siated 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 19 printed pages and 1 blank page.
Copyright: Zimbabwe School Examinations Council. N2022,

© ZIMSEC N2022 [Turn over

EAQAILUELMM OAM UA

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NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULA’ MAY BE USED IN THIS PAPER

(a) Express
one million and one in figures,

Answer (a)
(e) 13 rsa hoe,
4
Answer (b)
(c) 11,6° im degrees and minutes
Answer (c)

(a) ‘Solve the equanon 132 = 377

Answer (a)

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(b) If vector 3 5\.
+()=(¢)

find vector @ .

Answer (b)
(1]
(c) Write down the largest perfect square integer number less than 20.
Answer (c)
(1)
3 (a) Write the three figure bearing equivalent to North East.
Answer (a)
(1)
(b) Write the first three positive odd integers.
Answer (b)
(1]
4044/1 N2022
[Turn over

FAA MALO RA ETA LANL AE

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Candidate Name Centre Number Candidate Number ")

a

4

(c) Express 0,0456 correct to one significant figure.

Answer (c)
[i].
4 Evaluate
(a) Wy
(5)
Answer (a)
QJ
(b) log; 80 — log; 16.
Answer (b)
[2]
5 (a) Simplify the expression 2x + 3y.
6x + 9y
Answer (a) y
(21

4004/1 N2022

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Candidate Name Centre Number

5
(b) Find 4
5_
9
Answer (b)
6 Solve the equation 22? — 5¢ — 3 = 0.
Answer
7 Given that f (d) = d? — 3d,
find
@ (3)
Answer (a)
(b) the values of d for which if. (d) = 10.
Answer (6)

4044/1 N2022

(AGAR AARON ELCAMA ANE

Candidate Number

[2]

[3]

{y

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rs75

Candidate Name Centre Number Candidate Number 4

(b)

()

6

Solve the simultanecuygggggations:

3m —-n=—-T
2n+n=17

Given that £ = {zr:

- State from € , a

prime number,

multiple of 19,

square number.

Answer

49 <a <58} reZ,

4004/1 N2022

Answer (a)

Answer (b)

Answer (c)

py!

i

i |

(])

ab

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7
10 Find the next two terms in the following sequences:
(a) 1; 3; 6; 10; 15;...
Answer (a)
[2]
1
©) 16; 4; 1; ie
Answer (b)
11 (a) Given thatl1, = 910, [2]
find the value of @ .
Answer (a)
(b) = Convert 2027 to a number in base 5.
2)

Answer (b)

4044/1 N2022

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EERE ALT LEI, te a

8
12 Evaluate
(a) 1 UNS
ras i)
Answer (a)
[2]
(b) 2 £ 12 leaving the answer in it lowest terms.
ae?)
Answer (b)
L4J
13 (a) State the number of lines of symmetry of a rhombus.
Answer (a)
(VY

4004/1 N2022

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(b)

The diagram above shows triangle HI.

Line HI is parallel to line KL. where L_ and K are midpoints of IJ and HJ
respectively.

The area of triangle HJ is 48 cm’.

Calculate the area of the shaded quadrilateral HILK.

Answer (b)
[3]
14 Factorise completely
@) 36p* — 4q’.
Answer (a)
[3]
4044/1 N2022

[Turn over _

| N

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7973

Candidate Name Centre Number Candidate Number

eg ee

10

(b) 10my + liny + 6m + 9n.

Answer (b)
[2]
15 (a) Convert a speed of 10m/s to a speed in kin/h.
Answer (a)
[2]
(b) — Given that matrix 4 =/m, 6 \ is singular, find the two possible
12 2m
values of 77? ,
Answer (b)
[2]
16 A rectangle of length © metres and width of ¥ metres is drawn according to these
conditions:
‘a) The width is greater than one third of the length.
Find an inequality that satisfies this condition.
Answer (a)
(1)

04/1 N2022

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dae Name NH Centre Number Candidate Number = rt

(b) The perimeter is not less than 400 metres but less than 560 metres.
Find an inequality which satisfy this inequality.

Answer (b)
(3]

(a) Given that 2 — 4 > 7, find the smallest possible value of ” if ” is an integer.

Answer (a)

[2]

A triangle ABC is such that AB = 3 em, AC =5 cm, BC =2 cm
and B AC = 120°-

Use as much of the information given below as is necessary to answer the
question. '

[ 1
ee 60° we, cos 60° = 3} tan 60° =V3

Find the value of © .

ras

Answer (b)
[3]

4401 N2022

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12

18 (a) The magnitude of vector (5) is 5. Find the possible values of ” .
3

Answer (a)
[2]
(b) The universal set é has subsets A, B and C such that
E= {1; 25 3) 4. be 6s BBs OL,
A={x: visa factor of 8},
B= {2; -4;. 8}
C ={x: xis a perfect square number}.
(i) List all elements of subset C.
Answer (b)(i)
1]
(ii) Find n (AU B).
Answer (b)(ii)
[1]
(iii) Write down the relationship between sets A and B in set notation.
“i Answer (b)(iii)
(1]

4004/1 N2022

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jae Name Centre Number Candidate Number 13

The midday temperature, in degrees celsius, for ten days in September in a certain
iawn were recorded as follows:

18: 20, 22; 23; 26; 28; 22; 18; 18217.

(a) State the modal temperature.

Answer (a)
{1
Find the median temperature.
Answer (b)
[1]
Find the temperature range.
Answer (c)
O]
Answer (d)
(2]
[Turn over

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14

20 (a)

€ Q D
The diagram above shows two parallel lines AB and CD.
Line QN cuts the parallel lines at Q and N. Line PM cuts QN at P and AB at M

CQP = 4d°, QPM = 3d? and PMN = d?-

(i) Express jy AV Pin terms of d.

Answer (a)(i)
(1)
(ii) Calculate the value of d .

Answer (a)(ii)

4004/1 N2022

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Candidate Name

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15
(b)
The diagram above shows points A, B, C and D on the circumference of a circle
centre O.
AB and DC are chords and AC is the diameter of the circle. Point F is on AB
produced. :
“FBO = 142°
Calculate
@ BAC,
Answer (b)(i)
(1]
Gi) BOC.
Answer (b)(ii)

4044/1 N2022

nA NENA a

‘NUNCA

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‘andidate Number .

Candidate Name Centre Number g
( i my

16
21 (a) The interior angle of a regular polygon is 132:° and the exterior angle is 2a°

(i) Calculate the value of © .

. Answer (a)(i)
[2]
(ii) Find the number of sides of the regular polygon.
Answer (a)(ii)
[2]

(b) A bag contains 20 balls all identical except for colour. There are 3 green
balls, 5 red balls and 12 brown balls.
One ball is picked at random from the bag, its colour noted and is replaced.
A second ball is picked at random and its colour noted and is replaced.
Calculate the probability that both balls are of the same colour.

Answer (b)
[2]

4004/1 N2022

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17

12 (a) The velocity, “m/s, of a moving particle attery-seconds 1s given by the equation
v=5+4t-2
Calculate the value of

(i) Uwhen t = 3 seconds,

Answer (a)(i)
(1]
(i) when v = 0.,

aa aan Answer (a)(ii)
Sor A [3]

| meh
(b) Make A, the subject in the following fotmula, A = Irr?'+ Qarh.

ay Answer (b)

mc.)

iin aodait 2022
Wi [Turn over
) vehement al

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22
18
23 ABCD is an isosceles trapezium with AB ~ S5cm, DC > 17cm and AD ~ BC.
AB is parallel to DC.
The perimeter of the trapezium is 42cm.

Calculate the

(a) perpendicular distance between the two parallel sides,

Answer (a)
[4]

(b) area of the trapezium ABCD.

Answer (b)

L#

24 A dealer made a profit of 20% on the buying price by selling a double bed for $180, 00

(a) Calculate the buying price.

Answer (a)
[2]

4004/1 N2022

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SEAS) 66 ae

19

(b) Calculate the selling ‘price if the same bed had been sold at a loss of 20%.

Answer (b)
[2]

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