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FURTHER MATHEMATICS


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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2015

Objectives





2. Solve: 2cos x - 1 = 0, for 0 ≤ x ≤ 2π

A 2π/3 , 4π/3

B. π/6 , 5π/6

C. π/5 , 2π/5

D. π/3 , 5π/3


3. Solve 4(2x2) = 8x

A 1 and 2

B. 1 and -2

C. -1 and 2

D. -1 and -2


4. If Log3 x = Log33, find the value of x

A. 32

B. 1/32

C.1/33

D. 1/23


5. Find the third term of (x/2 – 18 ) in descending order of x

A. x7 /8

B. 7x6/16

C. 7x-5/4

D. 35 x4​/8


ANSWERS

6. Given that f: x → x2 and g: x → x + 3, where x ∈ R find fog(2)

A. 25

B. 9

C. 7

D. 5




ANSWERS

8. Given that P = [ -2/-3 1/4 ] and Q = [5/-2 -3/-1] find the PQ - QP

A. [0/0 0/0]

B. [27/-16 12/-15]

C. [-20/-12 -6/-8]

D. [11/-30 12/-11]


9. which of the following is a factor of the polynomial 6x4 + 2x3 +15x + 5?

A. 3x + 1

B. x + 1

C. 2x + 1

D. x + 2





11. If 36, p, 9/4 and q are consecutive terms of an exponential Sequence (G.P.), find the sum of p and q

A. 9/16

B. 81/16

C. 9

D. 99/16


12. Find the minimum value of y = x2 + 6x – 12

A. -21

B. -12

C. -6

D. -3


A line passes through the origin and the point (11/4 , 21/2 )

Use this information to answer questions 13 and 14


13. What is the gradient of the line?

A. 1

B. 2

C. 3

D. 4


14. Find the y coordinate of the line when x = 4

A. 2

B. 4

C. 6

D. 8


15. In how many ways can a committee if five be selected from eight students if two particular students are to be included?

A. 20

B. 28

C. 54

D. 58


ANSWERS

16. If x = : - 3j and y = 6: + j, calculate the angle between x and y

A. 60°

B. 75°

C. 81°

D. 85°


17. The gradient of a curve at the point (-2, 0) is 3x2 - 4x. Find the equation of the curve

A. y = 6x-4

B. y = 6x2 - 4x + 12

C. y = x3-2x2

D. y = x3-2x2 +16


18. If a and P are the roots of x2 + x - 2 = 0, find the value of (1/α2 + 1/β2 )

A. 5/4

B. 3/4

C. 1/4

D. - 3/4


19. Given that x2 + 4x + k = (x + r)2 +1, find the values of k and r

A. k = 5, r = -1

B. k = 5, r = 2

C. k = 2, r = 5

D. k = -1, r = 5


20. Given the statements: p: the subject is difficult q: I will do my best Which of the following is equivalent to "Although the subject is difficult, I will do my best*

A. p v q

B. ~ p v q

C. p ^ (~ q)

D. p ^ q y 8 N


ANSWERS



Forces of magnitude 8 N, 5 N and 5 N act on a body as shown in the diagram above, Use this information to answer question 21 and 22


21. Calculate, correct to 2 decimal places, the resultant force acting at O

A. 14.06 N

B. 13.00 N

C. 9.83 N

D. 8.26 N


22. Calculate, correct to 2 decimal places, the angle that the resultant makes with the horizontal

A. 80. 760

B. 75.000

C. 71.990

D. 15.000


23. Given that r = 2i - j, s = 3i + 5j and t = 6t - 2j, find the magnitude of (2r + s - t)

A. √ l5

B. 4

C. √ 24

D. √ 26


Marks -----------------------0 1 2 3 4 5

Number of Candid\ate 6 4 8 10 9 3


The table above shows the distribution of marks scored by students in a test. Use the information to answer questions 24 and 25


24. How many candidates scored above the median mark?

A. 3

B. 12

C. 22

D. 30


25. Find the inter-quartile range of the distribution

A. 4

B. 3

C. 2

D. 1


ANSWERS

26. A mass of 75 kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with a constant velocity. [Take g = 9.8 ms'2]

A. 750 N

B. 745 N

C. 735 N

D. 98 N


27. Each of the 90 students in a class speak-at least Igbo and Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.

A. 28/45

B. 4/9

C. 8/45

D. 1/9​





30. Find the coordinates of the point when divides the line joining P(-2, 3) and Q (4, 6) internally in the ratio 2 : 3

A (52/5 , 2/5)

B. (2/5 , 52/5)

C. (-2/5 , 52/5)

D. (2/5 , 22/5)


ANSWERS

A particular starts from rest and moves in a straight line such that its acceleration after t seconds is given by a = (3t – 2) ms-2

Use this information to answer questions 31 and 32


31. Find the other time when the velocity would be zero.

A. 1/3 seconds

B. 3/4 seconds

C. 4/3 seconds

D. 2 seconds


32. Find the distance covered after 3 seconds

A. 10 m

B. 9 m

C. 13/3 m

D. 9/2 m


33. Given that y = 4 – 9x and Δx = 0.1. calculate Δy

A. 9.0

B. 0. 9

C. -0.3

D. -0.9


34. Four fair coins are tossed once. Calculate the probability of obtaining equal number of heads and tails.

A. 1/4

B. 3/8

C. 1/2

D. 15/16


35. In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.

A. 24

B. 23

C. 21

D. 19


ANSWERS



37. If 2 sin2θ = 1 + cosθ, 0° ≤ 6 ≤ 90°, find the value of θ

A. 90°

B. 60°

C. 45°

D. 30°


38. A 24 N force acts on a body such that it changes its velocity from 5 ms-1 to 9 ms-1 in 2 seconds. If the body is travelling in a straight line, calculate the distance covered during the period

A. 22 m

B. 18 m

C. 14 m

D. 10 m


39. The sum, Sn of a sequence is given by Sn = 2n2 - 5, Find the 6th term.

A. 112

B. 67

C. 45

D. 22


40. Forces F1 (8 N, 030°) and F2 (10 N, 150°) act on a particle. Find the horizontal component of the resultant force.

A. 1.7 N

B. 4.5 N

C. 9.0 N

D. 13.0 N



WASSCE JUNE 2015 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

​1. C 2. D 3. A 4. B 5. B 6. A 7. C 8. D 9. A 10. A 11. D 12. A 13. B 14. D 15. A 16. C 17. D 18. A 19. B 20. D 21. D 22. A 23. D 24. B 25. B 26. A 27. B 28. D 29. D 30. Not correct 31. C 32. D 33. D 34. B 35. C 36. D 37. B 38. C 39. D 40. C


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