2023_maths_olevel_mj_paper1

Extracted Content: 2023_maths_olevel_mj_paper1

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

MATHEMATICS 4004/1
PAPER |

JUNE 2023 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 26 printed pages and 2 blank pages.
Copyright: Zimbabwe School Examinations Council, J2023.

520

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Answer all questions,

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

1 Express

(a) $4,497 correct to the nearest tenth,

Answer (a) SHEEP EEE ER ERE EEAOENORERENER EL AEERE EES EEE EERE SEET TERT Cay
[1]
(b) —_0,000342 in standard form,
Answer (b)
(1]
(c) 478,367 correct to two significant figures,
ANSWER! wicca pune ee
(1)

4004/1 32023 7 Zin sec? fh

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3
2 Simplify, giving the answer as common fraction in its lowest terms
(a) 2 4 l,
7 3
Answer (a)
(1)
(b) 2.
ay 10
Answer (b)
() 18 14.
— x —
35 9 27
Answer (c)
ee ey eee eeee a
3 (a) Evaluate giving the answers as exact decimals
(i) 0, 024 x 0,3,
Answer (a)(i)
“

4004/1 12024

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i.
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a a eae || NPay:

4

i) (0, 4)

Answer (a)(ii)

(b) Express 0, 224 as a percentage.

Answer (b)

4 The universal set€ = {75; 76; 77; 78; 79; 80}
M and R are subsets €.
M = {even numbers},
R= {multiples of 4}.

(a) (i) List elements of set M.

Answer (a)(i)

40041 12028

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5

(ii) List elements of set R.

Answer (a)(ii)

(1)
(b) Find 7) (Ar! U R)
Answer (b)
[1]
§ (a) Simplify 2 (a — 2) — d(a +3)
Answer (a)
(1)
(b) Express 3 2 asasingle fraction.
m—-2 4m+3
Answer (b)
(2]
4004/1 12023
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SSAA AEE

6

6 (a) State the special name of a quadrilateral with four lines of symmetry.

Answer (a)
(1)
(b) A quadrilateral has interior angles of 7°, 2a°, (a + 10)°and(x + 50)°.
Calculate the value of 2 ,

Answer (b)
ac
7 P varies directly as the cube of”. Given that P = 2andr = 4,
Find the

(a) formula connecting P and",

Answer (a)

4004/1 12023 Zimsec Mv

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7
(b) — valueof P whenr = 8,
Answer (b)
8 Given that:
m+ 3n=5
2 2 rR
m<em> —9n</em> = —15
find the numerical
(a) valueofm — 3n,
Answer (a)
asealpcanenceezen eset eases TES icon raf TEE a
(b) values of 7 and
Answer (b)
R]

4004/1 32023

LOA MAA

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errr rere Saeed

9 Given that p= q_,

q¢m

(a) — make "”" the subject of the formula,

Answer (a)

[2]

(b) Find given thatq = 3and p = 2,

Answer (b)

4004/1 12023 Zimse¢ i

LALOR ALD

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In the diagram points Q, S and R are on the circumference of a circle
centre O. Line PQT is a tangent to the circle at Q.

PQS = m°OQS = n°sQOR = p®> QSR = 70° and
ORS = 25°:

Calculate the value of

(a) ™,

Answer (a)

) ”

Answer (b)
au)

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4004/1 320234

WOOO CANAL ICAO

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10
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Answer (c)
me)
11 (a) Evaluate 7669 + 143g giving the answer in base 9.
Answer (a)
cusps ‘ii
(b) — Convert 35. to a number in base 2.
Answer (b)
[2]
40041 12023 Zimsec ae

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(c) Given that f(r) = (4 =r) (ar — 0, 5),
find f (0).

Answer (c)

In the diagram the unshaded region R is defined by three inequalities.

4004/1 32028

(ONIN TA

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eT ny MS

12

Find the three inequalities

Answer

[4]
13. Two similar cylinders have heights of 16cm and 48cm.
(a) Write down, in its simplest form, the ratio of
(i) heights,
Answer (a)(i)
(1)

4004/1 32023 (©) Zimsec 2023

A et

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13

(ii) volumes

Answer (a)(ii)

(b) The curved surface area of the larger cylinder is 500 cm’.
Calculate the curved surface area of the smaller cylinder.

Answer (b)

14 (a) A sum of money is shared in the ratio 2: 3: 4. The smallest share is
$160, 00.
Calculate the total amount of money shared.

Answer (a)

4004/1 52023

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ene Tl Gere aaa

14

(b) Find the time taken for $4000, 00 to earn a simple interest of $400, 00 at a rate
of 5% per annum.

Answer (b)
[2]
15 Solve the following equations:
(a) 3(@-2)=5r+3
Answer (a)
[2]
® (2)? 49
5) ~ 8
Answer (b)
“121

4004/1 12023 (©) Zimsec 2024

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SETS GET

1s

lo (a) Evaluate QO, 0169 \ 2,18 by first estimating each number to one
QW | IS x 2.06
significant {gure

Answer (a)
[3]
(b) Solve the equation 97 — 32441,
Answer (b)
[2]

14 132025

(1 NAA

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ETS SSS, |S,

16

17 Points 2, Fy and G’ have coordinates at (4;

respectively. O is the origin,
(a)

Express as column vectors

@) EF.

Answer (a)(i)
(ii) 13,
—36F
Answer (a)(ii)
(i) BP + FG
Answer (a)(iii)

4004/1 52023

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8),(—4 ; 0) and (—6 ; 4)

[1]

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aa S ni 2

(b) hind lor leaving the answer tn sun form

Answer (b)

(2]
1s (a) Convert 22° yyy to ke! py
Answer (a)
[2]
(b) A map of a town is drawn to a scale of lem to 9.5 km
Calculate the
(i) actual lenyth of the road va ken thats fen long on the map
Answer (by)
a)

Had | DS

HUN

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AAS RE WT

18

(ii) area ofa town on the map in cp? that has an actual area of 361 km’

Answer (b)(ii)
[2]

19 (a) __ Village A is ona bearing of 092 ° from a village B.
Calculate the 3 figure bearing of village B from village A.

Answer (a)

(1]

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(b) p

Q

In the diagram, OPQ is a sector with centre O and radius 9 cm.
POQ = 84°: Take

mt to be =
7

Calculate the

(i) length of arc PQ,

Answer (b)(i)
[2]
(ii) area of the sector OPQ.
Answer (b)(ii)
[2]

4004/1 32023 <
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The table above shows enrollment at a certain school

(a) State the modal form.

Answer (a)
ssa (1)
(b) — Calculate the mean number of learners per form.
Answer (b)
[2]

4004/1 32023 (©) Zimsec 202!
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21
(c) Two learners are chosen at random from the school

Calculate the probability that both learners are in form 4

Answer (c)
[2]
at
(2r4)
G

in the diagram above XDF and YEG are two straight lines which
intersect at O-
XY. ED and GF are parallel lines ON = OD = Tem,
DF = 3cem. ED = (x + 2)em and GF = (2. — 4) em.
(a) Name the triangle in correct order which is

(i) similar but not congruent to thangle NOY,

Atower (avi)
{t]

Wan ips

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he I REGS ORE

22

(ii) = congruent to triangle XOY.

Answer (a)(ii)
ssesesessbs svi scocoensussoeaaabicaa ‘ij
(b) — Calculate length of FG.
Answer (b)
ssa SECG RNS eGR Blo ai
220 Matrix =f 5 —3)\andmatix — /y? 6).
wm (Za) a=( 5)
(a) Find 4! the inverse of matrix M .
Answer (a)
ovis asd 5A aT RNAS IR TR ha
4004/1 12023 (©) Zimsec 2023

WMATA

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SiS eee ie

23
(b) Matrix NV is singular,
Find the possible values of Y.
Answer (b)
[3]
23
r S
24
o o

Q
In the diagram PQRS is a trapezium, PS and QR are parallel lines.
PQR = PRS = 90°, PQ = 24cm, QR = 32cmand PR = 40cm

4004/1 J2023
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BST TUITE

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ES TT TEE

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(a) Express tan RPS as a fraction its lowest terms.

Answer (a)(i)

(b) = Calculate the
@ length of RS,

[1]

Answer (b)(i)

(ii) area of trapezium PQRS.

Answer (b)(ii)

4004/1 12023

IIA

(2]

m1

(©) Zimsec 2023

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The graph shows triangles X and C and a point Q.

(a) Draw and label on the graph

(i) triangle A the image of Triangle X under a translation of (3) ‘
3

Answer (a)(i)
BI

(ii) triangle B the image of triangle X under a rotation of 180 ° with centre

Answer (a)(ii)
(3)
4004/1 J2023

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PTE Ty

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pear erieneereng eelo —Eens a

26

(b) Desenbe fully the single transformation which maps triangle X onto
tnangle C

Answer (b)

[3]

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HU

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