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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2011

Objectives



1. A binary operation * is defined on the set of real number R. by a * b = -1. Find the identity element under the operation *

A. -1

B. 0

C. 1

D. 2


2. Express 750 in radains, leaving your answer in terms of *.

A. 5π/12

B. 3π/4

C. 5π/6

D. 7π/6


3. If log93 + 2x = 1, find x.

A. -1/2

B. -1/4

C. 1/4

D. 1/2


4. Evaluate cos (π/2 + π/3 )

A. -2/√3

B. √ - 3/2

C. √ 3/4

D. 4/√ 3


5. Find the remainder when 5x3 + 2x2 – 7x – 5 is divided by (x – 2).

A. -51

B. -23

C. 29

D. 49


ANSWERS



8. Solve 3x2 + 4x + 1> 0

A. x < - 1, x < - 1/3

B. x > -1, x> - 1/3

C. x > - 1/3 , x < - 1

D. x < - 1/3 , x< - 1/3


9. The equation of a circle is 3x2 + 3y2 = 6X – 12Y + 6 = 0. Find its radius.

A. 1

B. 3

C. 11

D. 6


10. f(x) = p + qx, where p and q are constants. If f(1) = 7 and f(5) = 19, find (3).

A. 13

B. 15

C. 17

D. 26


ANSWERS

11. The sum and product of the roots of a quadratic equation are 4/7 and 5/7 respectively. Find its equation.

A. 7x2- 4x – 5 = 0

B. 7x2 - 4x + 5 = 0

C. 7x2 4x + - 5 = 0

D. 7x2 + 4x + 5 = 0


12. f(x) = (x2 + 3)2 is defined on the set of real numbers, R. Find the gradient of f(x) at x = ½.

A. 4.0

B. 6.0

C. 5.0

D. 10.6





15. A line is perpendicular to 3x –y + 11 = 0 and passes through the point (point (1, -5), Find its equation.

A. 3y – x – 14 = 0

B. 3x + y + 1 = 0

C. 3y + x + 1 = 0

D. 3y + x + 14 = 0


ANSWERS



18. If (37 2 x ) (23) = (1229) find the value of x

A. 5

B. 6

C. 7

D. 8


19. The fourth term of a geometric sequence is 2 and the sixth term is 8. Find the common ratio

A. + l

B. + 2

C. + 3

D. + 4


20. What percentage increase in the radius of a sphere will cause its volume to increase by %

A. 10%

B. 15%

C. 20%

D. 25%


ANSWERS

21. Evaluate 1/1-sin 600 , leaving your answer in surd form.

A. 1- √3

B. 2 -√ 3

C. 4 - 2√ 3

D. 4 + 2√ 3


22. Find the equation of a circle with centre (-3 - 8) and radius 4√ 6

A. x2- y2- 6x + 16y + 23 = 0

B. x2 + y2+6x+16y-23 = 0

C.x2+y2+6x-16y + 23 = 0

D. x2 + y2-6x+16y+23 = 0.


23. Determine the coefficient of x2 in the expansion of (a + 3x)6.

A. 18a2

B.45a4

C. 135a4

D. 1215a2


24. The mean of 2,5. (x+2), 7 and 9 is 6. Find the median.

A. 5.5

B. 6.0

C. 6.5

D. 7.0


25. The probability that Kofi and Ama hit a target in a shooting competition are 1/6 and 1/9 respectively. What is the probability that only one of them will hit the target?

A. 1/54

B. 13/54

C. 20/27

D. 41/54


ANSWERS

26. In how many ways can 3 prefects be chosen out of 8 prefects?

A. 6

B. 24

C. 56

D. 336


27. Find the standard deviation of the numbers 3,6,2,1,7 and 5.

A. 2.00

B.2.16

C.2.50 .

D. 2.56


28. The table shows the distribution of marks of students in a class. Find the upper class boundary of the modal

Marks -------------5 - 7 8 - 10 11 - 13 14 -16 17-1 9 20-22

No. of students --4 -----7 -------26 ------41 -----14 ------8

A. 13

B. 16

C. 16.5

D. 22.5


29. If 3xC2 = 15, find the value of x

A. 2

B. 4

C. 5

D. 6


30. Four doctors and two nurses are to sit round a circular table. In how many ways can this be done if the nurses are to sit together?

A. 48

B. 60

C. 240

D. 270


ANSWERS

31. A basket contains 3 red and 1 white identical balls. A ball is drawn from the basket at random. Calculate the probability that it is either white or red.

A. 1/3

B. ½

C. 3/4

D. 1


32. A force of 200 N acting on a body of mass 20kg initially at rest causes it to move a distance of 320m along a straight line for t seconds. Find the value of t.

A. 4s

B. 6s

C. 8s

D. 10s


33. Two forces 10N and 15N act on an object at an angle of 120° to each other. Find the magnitude of the resultant force.

A.5√ 5

B. 5√ 7

C. 7√ 5

D. 7√ 7


34. A body of mass 25 kg changes its speed from 15ms-1 to 35 ms-1 in 5 seconds by the action of an applied force F. Find the value of F. A. 100 N B.375N C.500N D.600N A particle starts from rest and moves in a straight line such that its velocity, V, at time t seconds is given by v = (3t2 - 2t) ms-1. Use this information to answer questions 35 and 36.


35. Calculate the distance covered in the first 2 seconds

A. 2 m

B.4m C.

6 m D.

8 m


ANSWERS

36. Determine the acceptation when t = 2 seconds

A. 4ms-2

B. 6ms-2

C. 8 ms-2

D. 10ms-2


37. Given that q = 9i + 6j and r = 4i - 6j, which of the following statements is true?

A. r and q are collinear.

B. r and q are perpendicular

C. The magnitude of r is 52 units

D. The projection of r on q is ynits.


38. The functions f and g are defined on the set, R, of real numbers by f:x → x2-x-6 and g:x → x-l.Find f 0g(3).

A. -8

B. -6

C. -4

D. -3.


39. Find the unit vector in the direction of -5i + 12j.

A. 1/13 (-5i-12j)

B. 1/13 (5i-12j) 13 13

C. 1/13 (-5i+12j)

D. 1/13 (5i+12j) 13 13


40. Find, correct to two decimal places, the acute angle between P = (13 12) and

q = (14 5 )

A. 23.520

B. 24.500

C. 29.52°

D. 29.82°.



WASSCE JUNE 2011 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

​1. C 2. A 3. C 4. B 5. C 6. B 7. A 8. C 9. B 10. A 11. B 12. B 13. A 14. C 15. D 16. A 17. A 18. A 19. B 20. A 21. D 22. C 23. D 24. C 25. B 26. C 27. B 28. C 29. A 30. A 31. D 32. C 33. B 34. A 35. B 36. D 37. B 38. C 39. C 40. A


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