HAAVAD COLLEGE

2ND MOCK EXAMINATION - 2021

FORM THREE (3)

ELECTIVE MATHEMATICS

SECTION A 1 hour: 15 min.

OBJECTIVE TEST

[40 marks]

Answer all the questions in this section

Select the letter corresponding to the correct answer for each question

1. If * + and * +, find .

A. * + B. * +

C. * + D. * +

2. Simplify: .
( √ )

A. √ B. √

C. √ D. √

√
3. Simplify:
√ √

A. √ B. √

C. 3 D. 4

4. A binary operation Δ is defined on the set of real numbers, R, by , where

√
. Evaluate .

A. √ B. √

C. √ D. √

5. The function √ is defined on the set of real numbers, R. find the

domain of f.
 A. B.

C. D.

6. Given that ( ) ( ).

A. – 5 B. – 3 C. 3 D. 5

7. Given that ( ) and ( ) , where , find ( ).

A. ( ) B.

C. D. ( )

8. If has equal roots, find the values of k.

A. 3, 4 B. C. D.

α and ᵝ are the roots of the equation . Use this information to

answer questions 9 and 10.

9. Find (α + ᵝ).
A. – 2 B. C. D. 2

10. Find ( ).

A. B. C. D.

11. A curve is given by . Find the equation of its line of symmetry.

A. B. C. D.

12. If ( ) is a factor of ( ) , find the other factor.

A. ( ) B. ( ) C. ( ) D.

13. Given that , find the value of m.

A. 20 B. 12 C. – 10 D. – 22

14. Solve .

A. 1 and 0 B. 1 or 2 C. 1 or – 2 D. - 1 or 2

15. If , find the value of y.

A. – 2 B. C. D. 2
16. Find the coefficient of x4 in the expansion of ( ) .

A. – 320 B. – 240 C. 240 D. 320

17. A straight line parallel to 2x + 3y = 6, passes through the point (-1, 2). Find the
equation of the line.
A. 2x – 3y = 2
B. 2x + 3y = - 2
C. 2x + 3y = - 4
D. 2x + 3y = 4
18. Find the coordinates of the centre of the circle

A. (- 2 , 4) B. ( ) C. ( ) D. (2, - 4)

19. A circle with centre (4, 5) passes through the y-intercept of the line 5x – 2y +6 = 0.
Find its equation
A.
B.
C.
D.

20. Find the 21st term of the Arithmetic Progression (A.P): - 4, - 1.5, 1, 3.5, ...
A. 43.5 B. 46.0 C. 48.5 D. 51.0

21. The 3rd and 7th terms of a Geometric Progression (G.P) are 81 and 16 respectively.
Find the 5th term.
A. B. C. 27 D. 36

22. Express cos150o in surd form.

√ √
A. √ B. C. D.

23. Given that and , where x and y are acute, find the value of
( )
A. B. C. D.

24. If , find

A. ( )
B. ( )
C. D.
√( ) √( )

25. Differentiate , with respect to x.

A. 10x + 1 B. 10x + 2 C. x(15x +1) D. x(15x +2)

26. Given that ( ) , find the coordinates of the point where the gradient
is 6.
A. (4, 1) B. (4, -2) C. (1, 4) D. (1, -2)

27. The velocity of a particle, in ms-1, after t seconds, is . Find the

acceleration of the particle after 2 seconds.
A. 10 ms-2 B. 13 ms-2 C. 14 ms-2 D. 17 ms-2

28. Given that a = 5i + 4j and b = 3i + 7j, find (3a – 8b).

A. 9i + 44j B. - 9i + 44j C. - 9i – 44j D. 9i - 44j

29. Find the magnitude and direction of the vector p = 5i – 12j.

A. (13, 113.8o) B. (13, 067.38o) C. (13, 025.38o) D. (13, 157.38o)

30. A force (10i + 4j) N acts on a body of mass 2 kg which is at rest. Find the velocity
after 3 seconds.
A. ( ) B. ( )

C. ( ) D. ( )

31. If ( )( ) ( ), find the value of k.

A. 0.20 B. 0.40 C. 0.80 D. 1.25

32. If ( ), find B-1.

A. ( ) B. ( )

C. ( ) D. ( )

33. In a class of 10 boys and 15 girls, the average score in a biology test is 90. If the
average score for the girls is x, find the average score for the boys in terms of x.

A. B. C. D.

34. How many ways can six students be seated around a circular table?
A. 36 B. 48 C. 72 D. 120

35. There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2
boys.
A. 1638 B. 2730 C. 6006 D. 7520

36. A fair die is tossed twice. What is the sample size?

A. 6 B. 12 C. 36 D. 48
 The table shows the results of tossing a fair die 150 times.

Face 1 2 3 4 5 6
Frequency 12 18 y 30 2y 45

Use this information to answer questions 37 and 38.

37. Find the probability of obtaining a 5.

A. B. C. D.

38. Find the mode.

A. 3 B. 4 C. 5 D. 6

39. Given that ( ) , calculate the minimum value of y.

A. 2 B. 1 C. 0 D. – 2

40. Evaluate ∫ ( )( )
A. B. C. D.
 SECTION B 2 hours 15 mins.

ESSAY

[60 marks]

Answer twelve questions in all: eight questions from part I and four questions from part II

PART I

[24 marks]

Answer all the questions in this part

1.
a) The functions f and g are defined on the set of real numbers, R, by f(x) = 2x - 1,
g(x) = 5x. Find g o f -1

b) The point (-3, b) lies on the curve 2y = 2x3 +x2 4x +3, find the value of b.

2. Evaluate: ∫ .
√

3.
a) Given that and , express

√( ) in terms of x, y and z.

b) The radius of a circle is 12 cm. Find, leaving the answer in terms of π, the rate at
which the area is increasing when the radius is increasing at the rate of 0.2 cms-1.

4. If 2x2 7x 15 is a factor of 6x3 13x2 px q, where p and q are constants, find

the values of p and q.

5. Solve ( )

6. The table below shows the lifespan of some batteries manufactured by a company.

Battery lifespan 26 – 30 31 – 35 36 – 40 41 – 45 46 – 50 51 – 55
(days)
Frequency 4 7 13 8 6 2

a) Draw a cumulative frequency curve for the distribution.

b) Using the curve in (a), find the interquartile range.

7. A triangle PQR has vertices P(2 - 3), Q(5, 1) and R(4, 8). Calculate angle PQR.

8. The resultant force of F1(150 N, 030o) and F2(x N, 120o) is R(y N, 090o). Find, correct
to two decimal places, the values of x and y.
 PART II

[36 marks]

Answer only four questions from this part

9.
a) Simplify and express the answer in terms of
.

b) Find the equation of the tangent of the curve y = 4x(x2 - 12) at its maximum
point.

10.

a) Express in partial fractions

( )

b) A circle with centre (-1, 3) passes through the point (1, 2). Find the equation of
the circle.

11.

a) Given ( ) ∫( ) and f(2) = 2, find f(x).

b) The thirteenth term of an Arithmetic Progression (A. P) is 27 and the seventh term
is three times the second term, find the:
(i) first term;
(ii) (ii) common difference ;
(iii)sum of the first ten terms.

12. There are 11 girls and 9 boys in Form 1A and 10 girls and 9 boys in Form 1B in a
school. Eight students are to be selected from each Form to take part in an essay
competition. Find, correct to three decimal places, the probability that equal number
of girls and boys will be selected from:

a) Form 1A;
b) each Form.

13. The table shows the frequency distribution of the ages of some patients in a clinic.

Ages (years) 11 – 20 21 – 25 26 – 30 31 – 35 36 – 40 41 – 50
Number of 8 16 22 19 25 10
patients

a) Draw a histogram for the distribution.

b) Find, correct to two decimal places, the mean age of the patients.
 c) Find the probability of selecting a patient who is at most 25 years.

14.

a) A uniform ladder rests at angle of 60o with a rough horizontal ground and against
a smooth vertical wall. The ladder weighs 60 kg and its length is 10 m.
(i) Sketch the diagram.
(ii) (ii) Find the reactions at the wall and the ground.

[take g = 10 ms-2]

b) A particle starts from rest with uniform acceleration and attains a speed of 48 ms-1
covering a distance of 400 m. Calculate:
(i) its acceleration ;
(ii) the distance covered when its speed is 24 ms-1.

15.

a) A vector pi +qj where p and q are scalars has its magnitude twice that of the
vector i +3j and is parallel to the vector 3i 4j. Find the vector.
b) Find, correct to the nearest degree, the angle between the vectors ( ) and

( ).