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FURTHER MATHEMATICS


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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2008

Objectives



1. Simply (√3 + √48) /√6

A. 3 √2

B. 5 √2

C. (5 √2) / 2

D. (3 √2) / 2


2. Find the range of values of x for which 2x2 + 7x – 15>0

A. x<-1/2 or x >5

B. x >- 5 or x >1/2

C. – ½ < x < 5

D. -5 < x < ½





The sum of the first N terms of a linear sequence is Sn = n2 + 2n

Use this information to answer question 4 and 5


4. Find the common different of the sequence.

A. 5

B. 4

C. 3

D. 2


5. Determine the general term of the sequence

A. n = + 1

B. 2n + 1

C. 3n + 1

D. 4n + 1


ANSWERS

6. If f(x) = 2x2- 3x-1, find the values of x for which f(x) is minimum.

A. ½

B. 4/3

C. ¾

D. 2/3


7. The polynomial 2x2 + x2 – 3x + p has a remainder 20 when divided by (x -2). Find the value of constant p.

A. 8

B.6

C. -6

D. -8


8. If 2 log4 2 = x + 1. find the value of x.

A. -2

B. -1

C. 0

D. 1


9. Which of the following quadratic curve will not intersect with the x-axis?

A. y = 2 – 4x – x2

B. y = x2 -5x -1

C. y = 2x2 –x-1

D. y= 3x2 – 2x + 4


10. What is the coordinates of the centre of the circle 5x2 + y2- 15x + 25y – 3 = 0?

A. (15/2 - 25/2 )

B. (3/2 – 5/2 )

C. (-3/2 5/2)

D (-15/2 25/2)


ANSWERS

11. Evaluate ∫30 (2 + 2x – 3x2) dx

A. -2

B. 2

C. 8

D. 10


12. A rectangle has a perimeter of 24m. If its area is to be a maximum, find its dimension. A. 12,12

B. 6,6

C. 4,8

D. 9,3


13. Express 7π/6 radians in degrees.

A. 3150

B. 2100

C. 1050

D. 750


14. IF P = (13 -24) and Q = (-21 30) , find PQ

A. (4-2 19)

B. (-42 19)

C. (-42 313)

D. (-4-2 39)


15. Two statement are represented by p and q as follows: p: He is brilliant. q: He is regular in class. Which of the following symbols represents the statement “ he is regular in class but dull”?

A. qv – p

B. q ^ - p

C. – q ^ - p

D. –q v –p


ANSWERS

16. Find the locus of points which is equidistant from P(4.5) and Q (-6, = 1).

A. 2x – 5y + 13= 0

B. 3x – 5y – 7 = 0

C. 5x – 3y + 7 = 0

D. 5x + 3y + 1 =0


17. A binary operation * is defined on the set R. of real numbers by

a*b = a2 + b + ab. Find the value of x for which 5 * x = 37

A. 7

B. 2

C. -2

D. -7


18. Find the derivative of 3x2 + 1/x2

A. 6x + 2x2

B. 6x + l/2x

C. 6x- 2/x3

D. 6x- 1/2x


19. The coefficient of the 5th term in the binomial expansion of (1 + kx)8, in ascending powers of x is 35/8. Find the value of constant k.

A. 2

B. ½

C. - ½

D. -2


20. Given that ∱1(x) = 3x2 -6x +1 and ∱(3) = 5, find ∫(x).

A. ∱(x) = x3 - 3x2 + x+20

B. ∱(x) = x3-3x2 + x+31

C. ∱(x) = x3 -3x2 + x +2

D. ∱(x) = x3-3x2 + x-13


ANSWERS

21. Express 1/1-sin 45° in surd form

A. 2 + √ 2

B. 2 + √ 3

C. 2 - √ 2

D. 1 + 2 √ 2





23 If events A and B are independent and P (A) = 7/12 and P(A B) = ¼, find P(B).

A. 3/7

B. 4/7

C. 5/7

D. 6/7


24. Given that AB = 5i -3j and AC = 2i + 5j, find BC.

A.-7i-8j

B. -3i+2j

C. 3i-2j

D. 3i+8j


25. The probability of Jide, Atu and Obu solving a given problem are 1/12 , 1/6 and 1/8 respectively. Calculate the probability that only one of them solves the problem.

A. 1/576

B. 55/576

C. 77/576

D. 167/576


ANSWERS

26. Two forces F, = (10N, 020°) and F2 = (7N, 2000) act on a particle. Find the resultant force.

A. (3N,020°)

B. (3N, 200°)

C. (17N,020°)

D. (17N, 200°)


The table shows the distribution of marks by some candidates in a test.


Marks ------------2 3 4 5 6 7 8

No of students 5 7 9 6 3 6 4

Use this information to answer questions 27. to 29.


27. What is the median score?

A. 35

B. 4.0

C. 4.5

D. 5.0


28. Find, correct to one decimal place, the mean of the distribution.

A. 5.5

B. 5.3

C. 5.2

D. 4.7


29. If a student is selected at random, what is the probability that she scored at least 6 marks?

A. 3/40

B. 1/4

C. 3/40

D. 27/40


30. Express r = (12, 2100) in the form a i + bj.

A. 6(i + √3)

B. 6(- i - √3j)

C.6(i- √3j)

D. 6(i+ √3j)


ANSWERS

31. A test consists of 12 questions out of which candidates are to answer 10. If the first 6 questions are compulsory , how many ways can each candidate select her question?

A. 40

B. 25

C. 15

D. 10


32 A body starts from rest and moves in a straight line with uniform acceleration of 5ms-'. How far, in m, does it go in 10 seconds?

A. 50

B. 250

C. 350

D. 500


33. If n items are arranged two at a time, the number obtained is 20 Find the value of n.

A. 5

B. 10

C. 15

D. 40





35. Fins the value of constant k for which a = 4i -kj and b as 31 + 8 j are perpendicular.

A. 2/5

B. 3/2

C. 5

D. 3


ANSWERS

36. A pack of cards has 6 of them with a ⨂ written on them, 5 with ⨁ and 9 with ∅ What is the probability that a single card drawn at random is not a ⨁ ?

A. 1/4

B. 5/9

C. 2/3

D. 3/4


37. The initial and final velocities of an object of mass 5 kg are u (13) and v = (47) respectively. Find the magnitude of its change in momentum.

A. 25

B. 15

C. 3√ 7

D. √10


38. If y = x2- 6x + 11 is written in the form y = a(x -h)2 + k, find the value of (a + h +k).

A. -4

B. -3

C. 0

D.6


39. The distance between P (x, 7) and Q (6,19) is 13 units. Find the values of x.

A. 1 or - 7

B. l or 7

C. l or ll.

  • D. 5 or- 5




WASSCE JUNE 2008 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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