Page 1 of 16

Name of student:_________________________________ Class__________

NORTHERN EDUCATION DIVISION MOCK

EXAMINATION
ADDITIONAL MATHEMATICS

PAPER I
(100 marks) Subject Number:
M132/I.
Tuesday, 12 March. Time Allowed: 2hours 30 min.
(8:00-10:30) am.
Instructions: Do not
1. This paper contains 15 pages. Please write in
check. Question Tick if these
answered columns
2. Answer all 7 questions in section A and
any two questions from section B. 1
3. Section A carries 60 marks and section 2
B carries 40 marks
3
4. The maximum number of marks for each
answer is indicated against each 4
question. 5
5. Write your answers in the spaces
6
provided on the question paper
6. Calculators may be used. 7
7. All working must be clearly shown. 8
8. Write your name at the top of each page
9
on your question paper in the spaces
provided. 10

Total
9. Write your examination number on top
of
 Page 2 of 16

each page of your question paper.

10.In the table provided on this page, tick against the question number you have
answered.

Section A: (60 marks)

Answer all the seven questions in this section.

1. a. Evaluate lim
x →2
| 6−x−x 2
x−2 | (3 marks)

b. Evaluate ∫ x 2 ( 2 x 3−1 ) dx .
4
(4 marks)
1
 Page 3 of 16

( )
8
2 n
2. a. The coefficient of y 7 in the expansion of y + is four times
y
the coefficient of y 10 . Find the value of n. (4
marks)

b. The tangent to the curve y=2+ sin2 θ is parallel to the normal

to the curve y=cos 2θ . Find the values of θ for 0 0 ≤ θ ≤360 0 .
(5 marks)
 Page 4 of 16

3. a. Given that f ( x )=2−ax and ff (−2 )=14 . Find the values of a .

(4 marks)

b. Solve the equation: 2 sin θ cos 2 θ+sin 2 θ=0 for 0 0 ≤ θ ≤180 0.

(5 marks)
 Page 5 of 16

1
4. a. Find the range of values of x for 1−x ≥ 2 x+1 (5 marks)

b. A spherical balloon is inflated. When the diameter is 10 cm, its

volume increases at a rate of 200 cm3/s. At what rate does its
surface area increases? Give the answer in terms of π .
(4 marks)
 Page 6 of 16

5. a. A piece of wire of length 28 cm is bent into a sector of radius r cm.

Calculate the radius of a sector for which the area is maximum.
(4
marks)

b. Given that x and y are connected by the equation xy +qy =p

where p and q are constants. A line that passes through (1, 6) and
(4, 1) is drawn. Find the values of p and q . (4
marks)
 Page 7 of 16

6. a. Figure 1 below shows the graph of a linear relationship between

two variables.

Q(12,3)

P (7,2)

Figure 1.
Given that the non linear law is of the form 2 y +10=¿ pq x−3 ,
find the values of the constants p and q . (5 marks)
 Page 8 of 16

4 12
b. Given that cosA = 5 and cosB = 13 where A is an acute angle
and
B is reflex. Without using a calculator, evaluate cosec(A+B).
(4
marks)
 Page 9 of 16

2 2
7. a. Given that the function f ( x )= p−x− 3 x has a maximum
153
value of 24 . Find the value of p . (4
marks)

2
b. If V =t n 3 , where t is a constant, find the approximate
percentage change in V if n is increased by 3 % when n = 5.
(5 marks)
 Page 10 of 16

Section B (40 marks)

Answer any two questions in this section.
8. a. Figure 2 shows two curves y=x 2and y=8−x 2 intersecting at Q.

Figure 2.
Calculate the area of the shaded region. (10 marks)
 Page 11 of 16

b. A given mass of air expands adiabatically and the following measurements

are taken of the pressure (P cm of mercury) and volume (V cm3):

V 100 125 150 175 200

P 58.6 42.4 32.8 27.0 22.3
Table 1.
If p=kV n, determine the values of the constants k and n. (10 marks)
 Page 12 of 16

π
2

9. a. Evaluate ∫ ( sin2 x +2 cos2 x ) dx . leaving your answer in terms of π .

−π
4

(10 marks)
 Page 13 of 16

b.
i. Taking a scale of 2 cm to represent 60 0 on the x axis and 4 cm to
represent 1 unit on the y axis, draw the graphs of y=cos 2 x and
y=cosx for 0 0 ≤ x ≤ 3600 . (8 marks)

ii. Using your graph, solve the equation: cos 2 x=cosx . (2 marks)
 Page 14 of 16

10. a.Water is emptied from a cylindrical tank of radius 20 cm at the rate of

2.5 litres per second and fresh water is added at the rate
of 2 litres per second. At what rate is the water level in the
tank changing? (10 marks)
 Page 15 of 16

b. The length of a closed rectangular box is 3 times its width. If its volume
is 972 cm3, calculate the maximum surface area of the box. (10
marks)
 Page 16 of 16

END OF QUESTION PAPER

NB: This paper contains 15 printed pages.