NAME: ______________________________________
MARIST SECONDARY SCHOOL
P. O. Box 46
Malirana Tel: (+265) 0994484899 / 0991587988
Dedza, MALAWI E-mail: maristhead@gmail.com
2025 FORM FOUR MOCK EXAMINATION
ADDITIONAL MATHEMATICS
Thursday,29th May Subject Number: M132/I
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Time Allowed: 2 h
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PAPER I
(100 marks)
Instructions
Question Tick if Do not write in
1. This paper contains 15 printed pages. Please Number answered these columns
check 1
2. Answer all questions in section A and any 2
two questions from section B .
3
3. Section A carries 60 marks and section B
carries 40 marks. 4
4. The maximum number of marks for each 5
question is indicated against each question 6
5. Calculators may be used. 7
6. All working must be clearly shown. 8
7. Write your name at the top of each page in
9
the spaces provided.
10
8. In the table provided on this page, tick
11
against the question number you have
12
answered.
13
Total 100
NAME: _______________________________________
Page 2 of 15 M132/I
Section A (60 marks)
Answer all questions in this section
1. If 𝑓 (𝑥) = 𝑥 − 3, what is the function 𝑔 which makes 𝑔𝑓 (𝑥) = 𝑥 2 − 6𝑥 + 10?
(5 marks)
tan 2𝑥
2. Find lim . (4 marks)
𝑥→0 tan 3𝑥
NAME: _______________________________________
Page 3 of 15 M132/I
𝑥 𝑛 5𝑛
3. The coefficient of 𝑥 3 in the expansion of (1 + ) equals . Find the value of the
2 12
positive integer 𝑛. (6 marks)
NAME: _______________________________________
Page 4 of 15 M132/I
𝑥2 2𝑦 2
4. Variables 𝑥 and 𝑦 are related by the equation + = 1 where 𝑝 and 𝑞 are
𝑝2 𝑞2
positive constants. When the graph of 𝑦 2 against 𝑥 2 is drawn, a straight line is
obtained. Given that the intercept 𝑦 2 −axis is 4.5 and that the gradient of the
line is −0.18. Calculate the values of 𝑝 and 𝑞. (5 marks)
NAME: _______________________________________
Page 5 of 15 M132/I
5. A rectangle has sides of length (2𝑥 + 3) cm and (𝑥 + 1) cm. What is the domain
of 𝑥 if the area of the rectangle lies between 10 cm2 and 36 cm2 inclusive?
(8 marks)
NAME: _______________________________________
Page 6 of 15 M132/I
6. Solve the equation 2 tan 𝜃 − 4 cot 𝜃 = 𝑐𝑜𝑠𝑒𝑐 𝜃 for −𝜋 < 𝜃 < 𝜋. (8 marks)
NAME: _______________________________________
Page 7 of 15 M132/I
7. Express 8𝑐𝑜𝑠 4 𝜃 in the form 𝑎 cos 4𝜃 + 𝑏 cos 2𝜃 + 𝑐 . (7 marks)
NAME: _______________________________________
Page 8 of 15 M132/I
8. Find the area of the shaded region. (6 marks)
NAME: _______________________________________
Page 9 of 15 M132/I
9. Find the value of 𝑘 for which 𝑦 = 2𝑥 + 𝑘 is a normal to 𝑦 = 2𝑥 2 − 3. (6 marks)
3
10. Use calculus to find the approximate value of √64.96. (5 marks)
NAME: _______________________________________
Page 10 of 15 M132/I
Section B (40 marks)
Answer any two questions from this section
11. a. The following results were obtained experimentally for two variables 𝑥 and
𝑦
𝑥 1 2 3 4 5
𝑦 42 120 430 920 2600
It is believed that 𝑥 and 𝑦 are related by the equation 𝑦 = 𝑎𝑏 𝑥 . By drawing a
straight-line graph estimate the value of 𝑎 and 𝑏. (10 marks)
NAME: _______________________________________
Page 11 of 15 M132/I
b. Find the ranges of values of 𝑥 for which 2𝑥 3 − 3𝑥 2 + 𝑥 + 6 < (𝑥 + 2)(𝑥 +
1)(𝑥 − 1). (8 marks)
NAME: _______________________________________
Page 12 of 15 M132/I
12. a. Draw on the same axes the curves 𝑦 = |sin 𝑥 | and 𝑦 = cos 2𝑥 for the interval
0 ≤ 𝑥 ≤ 2𝜋. Use the graphs to solve the inequality |sin 𝑥 | < cos 2𝑥. (12 marks)
NAME: _______________________________________
Page 13 of 15 M132/I
b. If 𝐹 = 3𝑡 + 1, 𝑚 = 4 kg and the body is initially at rest at point O, find 𝑣
(velocity) when 𝑡 = 2 seconds and 𝑠 (displacement) when 𝑡 = 2 seconds.
(10 marks)
NAME: _______________________________________
Page 14 of 15 M132/I
13. a. In the diagram shown an isosceles triangle PQR inscribed in a circle centre 0,
radius 𝑟 cm. PQ = QR and angle 0RP = 𝜃 radians. Triangle PQR has an area of A
cm2.
i. Show that A=𝑟 2 sin 2𝜃 + 𝑟 2 sin 2𝜃 cos 2𝜃
ii. Find the value of 𝜃 for which A has a stationary value and determine the
nature of this stationary value. (10 marks)
NAME: _______________________________________
Page 15 of 15 M132/I
3
b. The diagram below shows part of the curve 𝑦 = 3𝑥 − 𝑥 2 and the lines 𝑦 =
3𝑥 and 𝑦 = 2𝑦 − 3𝑥. Find the area of the shaded area. (10
marks)
END OF QUESTION PAPER
