2024_maths_olevel_nov_paper1

Extracted Content: 2024_maths_olevel_nov_paper1

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
ry Level

General Certificate of Education Ordina

MATHEMATICS 4004/1
PAPER 1 2 hours 30 minutes

INOVEMBER 2024 SESSION

Additional materials:
Mathematical Instruments

INSTRUCTIONS TO CANDIDATES

Write your Name, Centre number and Candidate number in the spaces at the top of each page.
Check that all the pages are in the booklet and ask the invigilator for a replacement if there

are duplicate or missing pages.
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.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question.
This paper is marked out of 100.

This question paper consists of 20 printed pages.
Copyright: Zimbabwe School Examinations Council, N2024.

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© ZIMSEC N2024

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a ee

2
Answer all questions.

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

1 Express 0, 09874

(a) @ correct to the nearest tenth,

Answer (a)(i)
(1
(ii) correct to 2 significant figures,
Answer (a)(ii)
{1]
(b) in standard form.
Answer (b)

{]

4004/1 N2024

AN Zimsse 2008

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Candidate Name Centre Number Candidate Number 3 2 (a) Express | 225 as a product of its prime factors in index form. Answer (a) [2]

(b) Hence or otherwise find \/7 995 -

Answer (b)
(1}
3 Kate, James and Jack shared $3 042 in the ratio 4:3: 2 respectively.
Find how much Kate got more than Jack.
Answer
[3]
4004/1 N2024

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UAOAAATAITEUA AMAIA ANE

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Candidate Name Centre Number Candidate Number 4 4 In a school, lessons start at quarter to 8 in the moming and end at 3. 15 pm. (a) Express 3. 15 pm in 24 hour notation. Answer (a) [1] (b) Find total time for lessons on each day. Answer (b) [2] 5 y ep oom xX Jom i) “ é

XQZ and YPZ are straight lines meeting at Z.
XY and QP are parallel.
XY =6em, QP =4cmand XQ =9 cm. QZ=xem.

4004/1 N2024

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WMA ©

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Candidate Name Centre Number Candidate Number 5 (a) Name two triangles that are similar. Answer (a) 1]

(b) Hence find the length of QZ.

Answer (b)
[3]

6 The table below shows the number of learners in each age group of a class.

umber of learners

Use the table to find the

(a) total number of learners in the class.

Answer (a)
[1]

4004/1 N2024
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HARLOW

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_ SS

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6
(b) probability that a learner chosen at random is 13 years old.
Answer (b)
{1}
(c) probability that if two learners are chosen at random, the first is aged 13

years and the second is aged 15 years.

Answer (c)
[2]
7 (a) Find vector p such that /1 7 9 \.
(3) “Pe (°,)
Answer (a)
2]
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(b) Hence find |p}, the magnitude of vector p.

Answer (b)
[2]
8 (a) Solve the inequality 3x —- 2 <10+ x <5r42 giving the
answer in the form a < x < 6, where “and b are numbers.
Answer (a)

[3]

(b) Hence find a perfect square number which satisfies the given inequality,

Answer (b)

(1]

4004/1 N2024

POM AAEM

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8
9 N
M
ke
P Q R

M, N and Q are three points on the circumference of circle O and diameter QN.
PR is a tangent to the circle at Q. Given that MOR = 42°.

Find
(a) QNM,
Answer (a)
1)
(b) QMN,
Answer (b)

[1]

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(c) MOQ.

Answer (c)
[2]

10 A cylindrical floor polish tin is 14cm in diameter and 5em deep.
In this question take ™ to be 3 1

7°

(a) Calculate the volume of the tin.

Answer (a)
[2]
(b) When full the tin contains 840g of floor polish.
Calculate the density of the polish in g/cm’ to 2 decimal places.

Answer (b)

4004/1 N2024

YAMANE

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Candidate Name Centre Number Candidate Number 10 [2] 11 (a) Express 2,35 hours in hours and minutes. Answer (a) [1] (b) Simplify 4135 + 10112 giving the answer in base ten. Answer (b) [3] 12 A map is drawn to a scale of 1cm to 5 kilometres. (a) Express the scale in the form 1: n Answer (a) (1]

tA

4004/1 N2024

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Candidate Name Centre Number Candidate Number 11 (b) Find the actual distance in kilometres between two points which are 3,6 cm apart on the map. Answer (b) [2]

(c) If the actual area of a city is 125 km? , find the area of the city on the map .

Answer (c)

[2]

4004/1 N2024

YADNTALG LMAO A

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13 y varies jointly as the square of “ and directly with z. When ® =2 andz=3,y= 1

(a) Find the relationship between y , x and z.

(b) Find y when x = 5 andz = 4.

14 Given that f( €) = 29°71
find

(a) f(1),

VHA

4004/1 N2024

Answer (a)

Answer (b)

Answer (a)

5°

[3]

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{2]
(b) the value of © for which f( © ) = 32.

Answer (b)

By

15 ws

Line ” passing through point P has equation 2y = + 6.
Line passes through the origin and is parallel to line”.
Find the

(a) distance OP.

Answer (a)

4004/1 N2024

FAAMONUALAAOUYA RA

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a °c Te ee eS SL

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[3]
(b) equation of line /
Answer (a)
[2]
16 (a) Express 2 5 as a single fraction in its simplest form.
a 2—5a
Answer (a)
[3]
(b) Giventhta = 1,b = 0 andc = —2 ,evaluateb—c
3a
Answer (b)
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nee

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[2]
17 Three towns X, Y and Z are on level ground such that Y is 8k to the east of X. Z is due
south of Y. Z is on a bearing of S'G0°F and 10km from X.
(a) Find the

(i) three figure bearing of Z from X

Answer (a)(i)
(1)
(ii) compass bearing of X from Z
Answer (a)(ii)
[1]
(b) Calculate the distance that Z is south of Y.
Answer (b)
[3]

4004/1 N2024

UAL AA ALU

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Candidate Name Centre Number Candidate Number 16 18 4 f2 4 pp fo —4 Matrix A= on 3 Matrix B = G ») a Simpli 1 (a) plify At B

Answer (a)
2]

(b) Find the inverse of matrix B .

Answer (b)
{3]

4004/1 N2024

ATI

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19

The table below shows the number of children in a hospital by age.

(a) Use the table to find the

(i) modal age of the children.

Answer (a)(i)
(1)
(ii) number of children in the hospital.
Answer (a)(ii)
[2]
(b) Calculate the mean age of the children.
Answer (b)
[3]

4004/1 N2024

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UAE 000 ee

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20 Solve the equations:

(a)

(b)

21

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2(3x —1)-10=0
Answer (a)
[2]
1
—-?) =—
(«2% =4
Answer (b)
[4]
Speedin f
+4, ‘
g 3 3 Times

The speed - time graph shows how an object travels at a constant speed of 40m/s
in 6 seconds and then slows down uniformly, coming to rest after 2 seconds.
Use the graph to calculate the

WATE

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a

(a)

| (b)

(c)

HAMANN ACA

19

uniform deceleration of the object in the last 2 seconds.

Answer (a)
[2]
distance travelled by the object in the 8 seconds.
Answer (b)
[2]
average speed of the object during the 8 seconds.
Answer (c)
[2]
4004/1 N2024
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Co)

20

22 The universal set £, has subsets A and B such that;
€= (3; 6;9;12...; 30}
A= {numbers less than 20 }
B = { factors of 30 }.

(a) List the elements of set A.

Answer (a)
[2]
(b) Find n(B')
Answer (b)
[2]
(c) Represent the sets A, B and£ ona clearly labelled Venn diagram.
Answer (c)
[3]

4004/1 N2024

VOILE (© Zimsec 2024

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