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/I
nd
Monday, 2 June Time Allowed: 2 hours
8:00 am– 10:00 am
PAPER I
(100 marks)

Instructions
1. This paper contains 15 pages. Please Question Tick if Do not write
Number answered in these
check columns
1
2. Answer all the 20 questions in the
2
spaces provided in the question paper. 3
4
3. The maximum number of marks for 5
6
each question is indicated against each
7
question 8
9
4. Calculators may be used. 10
11
5. All working must be clearly shown. 12
6. Write your name at the top of each page 13
14
in the spaces provided. 15
16
7. In the table provided on this page, tick 17
against the question number you have 18
19
answered. 20
Total 100

© 2025 MARIST Turn over

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1 1 1
1. Factorise completely 𝑥 2 − 𝑥𝑦 + 𝑦2. (4 marks)
9 6 16

√6+√2 1
2. Given that sin 75° = , simplify . (4 marks)
4 sin 75°
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3. The surface area of a closed cone of height ℎ and base radius 𝑟 is given
𝐴 2𝜋𝑟 2
by 𝐴 = 𝜋𝑟 2 + 𝜋𝑟√ℎ2 + 𝑟 2 . Show that ℎ = √1 − . (5 marks)
𝜋𝑟 𝐴

𝑓(𝑥+ℎ)−𝑓(𝑥)
4. If 𝑓 (𝑥) = 𝑥 2 + 𝑥 − 3, express in its simplest form. (5 marks)
ℎ
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0 1 𝑞 −7 1 2 0 −2
5. Given that [ ][ ]=[ ]+[ ], find the values
−2 0 𝑝 0 0 −1 6 3𝑟
of 𝑝, 𝑞 and 𝑟 . (4 marks)

6. A cone has diameter 30 cm and a slant height of 28 cm. Calculate the

volume of the cone. (4 marks)
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5
7. The sum of the 1st and 3rd terms of a Geometric progression is and the
8
nd th 1
sum of the 2 and 4 terms is 1 . Find the common ratio. (5 marks)
4

8. The expressions 𝑥 3 − 7𝑥 + 6 and 𝑥 3 − 𝑥 2 − 4𝑥 + 24 have the same

remainder when divided by 𝑥 + 𝑝. Find the possible values of 𝑝. (5 marks)
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9. 𝐀′𝐁′𝐂′𝐃′ is a rectangle and it is an image of ABCD after a rotation

with coordinates 𝐀′(0, 0), 𝐁′(0, −3), 𝐂′(−2, −3) and 𝐃′(−2, 0). Using a
scale of 2 cm to represent 1 unit on both axes, plot the rectangle on the
graph paper provided. If 𝐀(1, 1) and D (1, −1) have the images 𝐀′ and 𝐃′
after the rotation, describe the rotation fully and plot ABCD. (6 marks)
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10. The point A has position vector (31) and point B has position vector (34).
Find the position vector of the point that divides AB in the ratio 3: 4. (5 marks)

1
11. The cube root of varies directly as P and inversely as the square of R. When
𝑇
2
P = , 𝑅 = 2 and 𝑇 = 1.728. Find the relation connecting T, P and R. (4 marks)
3
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12. Figure 1 below shows a circle LMS centre O. MN is a tangent at M to the circle.
ON =13 cm, NM=12 cm and LS= 6 cm.

Figure 1
Calculate the length of chord LM. (5 marks)
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13. The heights of two similar pails are 12 cm and 8 cm. The larger pail
can hold 2 litres. What is the capacity of the smaller pail? (5 marks)

14. The point P (𝑎, 𝑏) lies on the line through A (−1, −2) and B (3, 0) and
PA = √125. Find the values of 𝑎 and 𝑏. (6 marks)
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15. Figure 2 below is a circle AXYZ. SAT is a tangent at A to the circle and XEZT is a
straight line. Angle ATZ = 35°, angle AXE = 40° and angle EXY= 26°.

Figure 2
Calculate angle AEX. (5 marks)
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16. A man walks directly from point A towards the foot of a tall building
240 m away. After covering 180 m, he observes that the angle of elevation
of the building is 45°. Calculate the angle of elevation of the top of the
building from point A. (5 marks)
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17. Figure 3 shows unshaded region (D) bounded by three inequalities

Figure 3
Write down all the inequalities representing the given region D above. (5 marks)
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18. A car accelerates uniformly from rest to reach a speed of 𝑽 m/s in 5 seconds.
It travels at this speed for 20 seconds and then decelerates uniformly to come
to rest in a further 𝑡 seconds. If the distance travelled while decelerating
4
is of the distance travelled while accelerating and that the total distance
5
travelled was 637 m, find the value of 𝒕 and 𝑽. (6 marks)
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19. Table 1 below shows marks from a mathematics test of randomly selected students
in a form four class.
Table 1
Marks 13 14 15 16 17
Frequency 2 5 7 4 3

Calculate the standard deviation of the marks. (6 marks)

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20. Given that 𝑦 = 𝑎𝑥 𝑏 + 3 where 𝑎 > 0 and that 𝑦 = 8 when 𝑥 = 2

and 𝑦 = 48 when 𝑥 = 8, find the values of 𝑎 and 𝑏. (6 marks)

END OF QUESTION PAPER

NB: This paper contains 15 printed pages.