EXAMINATION NO∴______________

MARIST SECONDARY SCHOOL

P. O. Box 46
Malirana Tel: 0999338735 / 0991587988
Dedza, MALAWI E-mail: maristhead@gmail.com

2025 MSCE MOCK TWO EXAMINATIONS

MATHEMATICS
Subject Number: M131/II
th
Friday, 6 June Time Allowed: 2½ hours
8:00 am – 10:30 am
PAPER II
(100 marks)

Instructions
1. This paper contains 18 pages. Please Question Tick if Do not write in
Number answered these columns
check. 1
2. Before beginning, fill in your Exam no 2

at the top of each page of the question 3

paper. 4
5
3. Answer all questions in Section A and
6
any four in Section B.
7
4. Use of electronic calculators is allowed.
8
5. The maximum number of marks for
9
each question is indicated against each
10
question.
11
6. In the table provided on this page, tick
12
against the question number you have
Total 100
answered.
2025 ©MARIST Turn over
 EXAMINATION NO∴_____________
2025 Page 2 of 18 M131/II

Section A (60 marks)

Answer all the six questions in this section in the spaces provided.
1. a. Factorise 𝑥 3 − 3𝑥 2 − 2𝑥 + 8. (4 marks)

b. A cuboid has a square base of area √5 − 2√5 m2 and a volume

of (4√5 − √2) m3. Find the height of the cuboid in the form
(𝑎 + 𝑏√𝑐) m. (4 marks)
 EXAMINATION NO∴_____________
2025 Page 3 of 18 M131/II

2. a. A quantity M is partly constant and partly varies as the square root

of N. Using constants 𝑠 and 𝑡, write down an equation connecting
M and N. If M = 24 when N = 16, and M = 32 when N = 36, find the
values of the constants 𝑠 and 𝑡. (4 marks)
 EXAMINATION NO∴_____________
2025 Page 4 of 18 M131/II

2. (Continued)
b. The length of a rectangle is 4 cm greater than twice the width.
If the length is increased by 4 cm and the width is decreased
by 5 cm, the new rectangle is two-thirds of the area of the original
rectangle. Calculate the dimensions of the original rectangle. (6 marks)
 EXAMINATION NO∴_____________
2025 Page 5 of 18 M131/II

3. a. Each day, an MSCE candidate has to spend at least twice as much of his
study time on practice (𝑥) as in reading (𝑦). He has more than four hours
and not more than six hours of study time daily. He must read for at least
one hour. Write down four inequalities in 𝑥 and 𝑦, in addition to 𝑥 ≥ 0
and 𝑦 ≥ 0, that satisfy the given information. (4 marks)

𝑎2 +𝑎𝑏 𝑎+3𝑏 𝑎𝑏−𝑎2

b. Simplify ÷ × . (5 marks)
𝑎2 −2𝑎𝑏+𝑏 2 𝑎+2𝑏 𝑎2 +3𝑎𝑏+2𝑏2
 EXAMINATION NO∴_____________
2025 Page 6 of 18 M131/II
7
4. a. If log 2 , log(2𝑥 − 5) and log (2𝑥 − ) are in arithmetic progression,
2
find the value of 𝑥. (4 marks)

b. Solve the following equations simultaneously

5𝑥+2 + 7𝑦+1 = 3468

7𝑦 = 5𝑥 − 76 (6 marks)
 EXAMINATION NO∴_____________
2025 Page 7 of 18 M131/II

5. a. Using a ruler and a pair of compasses only;

 Draw a circle centre O of radius 3 cm.
 From a point P, which is 5 cm from the centre of the circle, construct a
tangent PR to the circle at Q such that PR = 10 cm.
 Construct a line RS parallel to QO, such that POS is a straight line.
 Measure and state size of OS. (6 marks)
 EXAMINATION NO∴_____________
2025 Page 8 of 18 M131/II

5. (Continued)
b. Table 1 below shows grouped data scores obtained in a test.
Table 1
Score 1−5 6 − 10 11 − 15 16 − 20 21 − 25 26 − 30
Frequency 13 𝑎 21 𝑏 8 15

If ∑ 𝑓 = 100 and 𝑥 = 15.1, calculate the values of 𝑎 and 𝑏. (6 marks)

 EXAMINATION NO∴_____________
2025 Page 9 of 18 M131/II

6. a. A bag contains four balls each of which is coloured either red or white.
If one ball is drawn at random from the bag but not replaced and then a
1
second ball is drawn at random, the probability that both balls are red is .
2
What is the probability that both balls are white? (6 marks)
 EXAMINATION NO∴_____________
2025 Page 10 of 18 M131/II

6. (Continued)
b. Figure 1 below shows a capsule in a cylindrical shape with hemispheres at
both ends.

Figure 1
Calculate the surface area of the capsule. (5 marks)
 EXAMINATION NO∴_____________
2025 Page 11 of 18 M131/II

Section B (40 marks)

Answer any four questions from this section in the spaces provided.
7. The line through (−3, 8) parallel to 𝑦 = 2𝑥 − 3 meets the
curve (𝑥 + 3)(𝑦 − 2) = 8 at A and B. Find the coordinates of the
midpoint of AB. (10 marks)
 EXAMINATION NO∴_____________
2025 Page 12 of 18 M131/II

8. A theatre has a sitting capacity of 350 people. The charges for an ordinary seat are
K15 000 and K25 000 for VIP seat. It costs K 2 500 000 to stage a show and the
theatre must make a profit. There are never more than 200 ordinary seats and for a
show to take place at least 75 ordinary seats must be occupied. The number of VIP
seats is always less than twice the number of ordinary seats.
a. Taking 𝒙 to represent the number of ordinary seats and 𝒚 to represent
the number of VIP seats, write down all inequalities representing the
above given information. (4 marks)

b. Using a scale of 2 cm representing 50 units on both axes, represent

the inequalities on a graph on page 13 and mark the region H. (4 marks)

c. Determine the number of seats of each type that should be booked

in order to maximize profit and state the maximum profit. (2 marks)
 EXAMINATION NO∴_____________
2025 Page 13 of 18 M131/II
 EXAMINATION NO∴_____________
2025 Page 14 of 18 M131/II

9. There are 150 people at an international medical conference. 40 are Africans, 70 are
women and 110 are doctors. 12 of the women are Africans, 46 of the doctors are
women and 31 of the Africans are doctors. If 5 of the African men are not doctors.
a. Illustrate the information in a Venn diagram. (6 marks)

b. Calculate the number of African women that are doctors. (2 marks)

c. Calculate the number of men that are neither African nor doctors. (2 marks)
 EXAMINATION NO∴_____________
2025 Page 15 of 18 M131/II

10. OABC is a parallelogram with ⃗⃗⃗⃗⃗⃗ 𝐎𝐀 = 𝑎 and ⃗⃗⃗⃗⃗

𝟎𝐂 = 𝑐 . D lies on OC
where OD: DC = 1:2 and E is the midpoint of CB. DB meets AE at T.
⃗⃗⃗⃗⃗⃗ = 𝑝𝐃𝐁
Taking 𝐃𝐓 ⃗⃗⃗⃗⃗⃗ and 𝐀𝐓
⃗⃗⃗⃗⃗ = 𝑞𝐀𝐄 ⃗⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗ , form two vector expressions for 𝐎𝐓
and hence find the values of 𝑝 and 𝑞. (10 marks)
 EXAMINATION NO∴_____________
2025 Page 16 of 18 M131/II

11. The equation of the quadratic function that has an axis of symmetry
at 𝑥 = 2 passes through (5, 12) and cuts the 𝑥 −axis at 3.
a. Find the equation in form of 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐. (6 marks)

b. Sketch the graph of the quadratic function in (a) above, showing

roots, 𝑦 −intercept and coordinates of the turning point. (4 marks)
 EXAMINATION NO∴_____________
2025 Page 17 of 18 M131/II

12. In the figure 2 below, O is the centre of the circle ABQR and lies on the
circumference of the circle APB. The lines AOR and APQ and BPR are all straight
lines.

Figure 2
Prove that:
a. Angle APB = twice angle AQB. (4 marks)
 EXAMINATION NO∴_____________
2025 Page 18 of 18 M131/II

12. (Continued)
b. Triangle BPQ is isosceles. (4 marks)

c. AR is parallel to BQ. (2 marks)

END OF QUESTION PAPER

NB: This paper contains 18 printed pages.