2024_maths_olevel_mj_paper2

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ZIMBABWE SCHOOL EXAMINATIONS COUNCIL General Certificate of Education Ordinary Level

MATHEMATICS: 4004/2
PAPER 2 2 hours 30 minutes

JUNE 2024 SESSION

Additional materials:
Mathematical Instruments
Mathematical Tables

Non programmable Electronic Calculator
Answer booklet

INSTRUCTIONS TO CANDIDATES

Write your Name, Centre number and Candidate number in the spaces provided on the answer
booklet. :

Answer all questions in Section A and any four questions from Section B.

If you use more than one booklet, fasten them together.

All working must be clearly shown on the same sheet as the rest of the answer.

Omission of essential working will result in loss of marks.

If the degree of accuracy is not specified in the question and if the answer is not exact, the
answer should be given correct to three significant figures. Answers in degrees should be
given correct to one decimal place.

Mathematical tables and Non-programmable electronic calculators may be used to
evaluate explicit numerical expressions.

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 10 printed pages and 2 blank pages.

Copyright: Zimbabwe School Examinations Council, J2024.
© ZIMSEC 32024 [Turn over

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Section A [52 Marks]
Answer all questions in this section

Mr Moyo's basic monthly salary is $205. He receives a commission of 2% for
any sales above $500.

(i) Calculate his gross salary for the month if his sales were $1550. [3]
(ii) In acertain month the following deductions were made
Pension $3,90
Medical aid $1,65
Income tax $4,50
Calculate his net salary for the month he made sales of $1550. [3]
The sum of the interior angles of a polygon is double the sum of the
exterior angles.
Find the number of sides of the polygon. [2]
Solve the equation62 — 2 = 27 + 8. [2]
Factorise completely
@) 5h? — 20k? [3]
(ii) = 2mp—m-—6npt+3n (2]
Express 3 2 asa single fraction in its simplest form. [3]
Z-y «ety
Mr Dube had an appointment with a doctor at 1400. Mr Dube arrived 14
minutes earlier and the doctor was 15 minutes late.
Find how long Mr Dube had to wait before the doctor arrived. [2]
Find the difference between 4 weeks 3 days and 2 weeks 5 days, giving the
answer in weeks and days. [1]
Mary cycles to and from a school 5 times. The school is Skm away, to the
nearest km.
Calculate the smallest possible distance she cycles, [3]

The population of a town A is 4.52 X 10” and that of town B is 8,7 x 10°.

4004/2 J2024
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4 (a) (b) (c) (d) 5

(i) Calculate the difference between the populations of town A and

town B, giving the answer in standard form.

(ii) Given that 40% of the population of town B are adults,
calculate the number of adults in town B.

Give the answer in ordinary form.

Simplify 0,35 + 0, 25
0,3 x 0,04

Evaluate 435 + 1001), giving the answer in base two.

A rectangular garden measures 15m by 12m to the nearest metre.

Calculate the least possible area of the garden.

Given that @ = 3,12 X 10-3 and b= 4,5 X10 —4
find, giving the answer in standard form, the value of
(i) a+b,

(ii) ab.

Answer the whole of this question on sheet of plain paper.

[2]

[2]

(2]

(3]

[3]

2]
[2]

Use ruler and compasses only for all constructions and show all construction lines

and arcs.

(a)

(b)

On a single diagram, construct.

(i) a quadrilateral ABC D with AD parallel to BC, AB =8cm.

BC =10cm, 4 BC =90° and BCD=60°.
(ii) the locus of points equidistant from A and B.

(iii) the locus of points equidistant from BandC.

(i) Mark and label point P , which is equidistant from A and B, and

also equidistant from B and C.

(ii) | Construct a circle passing through A,B andC.

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(c)

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Region T is such that it is nearer B than C and nearer B than A and lies
inside the quadrilateral A BC D.

Shade region T.

Measure and write down the radius of the circle (b)(ii).

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[2]
[1]

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Section B [48 Marks] Answer any four questions from this section. Each question carries 12 marks.

6 (a) €={x:1<a2< 20, xis an integer}
X = {x: 2 is a prime number}
Y ={2x: 2 is an even number}
Z = {x:2 isa multiple of 5}

(i) List all the elements of set _X.
(ii) Find n (Z) :
(i) Findn (Y UZ).

(iv) Set Pisa subset of € such that P = {10; 20}.

Express set P in set notation, using the sets X , Y and Z.

(b) (i) Solve the inequality -3 < 2r +1 <7.

(ii) Give the integral values which satisfy the inequality in (i).

7 (a) Given that gc 3\:;
a-(03)

(i) find the value of 7 if the determinant of A is 5.
(ii) find the inverse of A.

(b) Solve the following simultaneous equations:

4r + 3y =6
a+2y=-1
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6 (c)

In the diagram points P, Q, R, S and T lie on the circumference of a circle.

QS is the diameter of the circle. PT is parallel to QS.

QST = 68d SOR = 34°-
(i) State briefly why QRS = 90°. 0)
(ii) Find oR. [2]
(iii) Find gp. [2]

8 The following is an incomplete table of values for the function yy — e+ae2—3

| « {| ~-4 | -3 | -2 T -7 7 o [7 i [2 7 3 4

fy | 9 | p | -17[-3[ ¢ [-j[ 3 7 9 |

@ @ Find the value of P. i]
(ii) Find the value of 7. [1]

(b) (i) Draw the graph of y = x? + © — 30n thea sheet of graph paper.
Use a scale of 2cm to | unit on the © axis and 2cm to 2 units on the
Y axis. [4]

(ii) Draw the line of symmetry of the curve. [1]

(c) Use the graph to

(0) find the equation of the line of symmetry, [1]

(ii) find the coordinates of the minimum point of the curve, [2]

(iii) solve the equation x? + 7 — 3 = —9. 2]
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9 ne Survey 80 motorists were each asked the number of hours their journey took. € results were used to draw acumulative frequency curve. Gunulative equency 80] ri) Ssaase : 60) SHAE son + + 40 30 +4 At + ; eres 20) ~ + ; Pr stsee ess 0 . 2 “3 4 5 6 7 ge!

Time (hours)
Use the graph to answer the following questions.

(a) (i) Complete the frequency distribution table below.

ime in
hes (0 Srethsras

Prequencey{ 20 | 25 | i fT
[2]

(ii) Calculate an estimate mean of the number of hours the 80 motorists took

giving your answer to the nearest hour. [3]
(iii) Find the median. [2]
(iv) Find the probability that two motorists chosen at random took more than 5 hours
but less or equal to 7 hours. 22]
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(b)

Marks (m) 17<ms2l QM<m=24| 24<m<27 | 27<ms30 | 30<ms32 | 32<ms40
Frequency 2 3 9 15 9 2

If the information above were to be represented in a histogram, calculate the heights

of the first three class intervals. [3]

10 A S B

10) b Cc

In the diagram OABC is a parallelogram S is the midpoint of AB and R is the midpoint of
BC. OA = 2a and OC = 2b

(a) Express the following vectors in terms of @ and/or b

@® AS [1]

ji) OS 1]

(ii) OR: (1)

(iv) AR: (1
(b) OSand AR intersect at T. Given that AT = hAR: Show that

OT =(2—h)a+2b- (2)
(c) Given that O77 = KOS > &xPress CT in terms of a, b and k. ]

(d) —_ Using these two expressions for ()T;, find the value of hand the value of k. [4]

(e) _ Find the ratio TR : (1)
AR

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10

(i) Given thaty = 2,9 x 10?-
Evaluate /y — J. giving the answer in standard form. (2]

(d) Evaluate 389 + 10014, giving the answer in base 5. [3]

4004/2 204

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