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FURTHER MATHEMATICS


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THEORY QUESTIONS
WAEC SYLLABUS

WASSCE 2009

Objectives



1. L Solvex:-2x-8>0

A. x<- 2 or x> 4

B. x< -4 or x> 2

C. -2 < x < 4

D. -4 < x < 2


2. If (x + 3) is a factor of the polynomial x3 + 3x2 + nx -12, where n is a constant, find the value of n.

A -1

B. -2

C. -3

D. -4


3. The line v = nix - 3 is a tangent to the curve y = 1- 3x + 2x at the point (1.0). Find the value of the constant m.

A -4

B. -l

C. 3

D. 4


4. The coordinates of the centre of a circle is (-2, 3). If its is 25ncm2, find its equation.

A. x2 + y2 -4x-6y -12 = 0

B. x2 + y2 -4x + 6y-12 = 0

C. x2 -y2 +4x + 6y-12=0

D. x2 +y2-4x-6y- 12 = 0


5. Given that sin 0 = 3 where 0 is acute, find the value of tan 2 20. leaving your answer in surd form. A - 3 B. - 3 C. 3 D. 3 2 2


ANSWERS

6. Find the coefficient of x4 in the binomial expansion of (2+x)6.

A. 120

B. 80

C. 60

D. 15


7. Which of the following binary operations is not commutative1

A. a * b = 1 + 1

B. a * b = a + b -ab a b

C. a * b = 2a + 2b + ab

D. a * b = a- b + ab


8. Express 2 / (3 - √7) in the form a + √b, where a and b are integers

A. 6+ √7

B. 3 + √7

C. 3 - √7

D. 6 - √7


9. The roots of the quadratic equation 2x2 - 5x + m = 0 are α and β, where m is a constant.

Find (α2 + β2) in terms of m

A. (25 - m)/4

B. (25 -2m)/4

C. (25 + m)/4

D. (25 -2m)/4


10. Given that 2x = 0.125, find the value of x.

A. 0

B. -l

C. -2

D. -3


ANSWERS

11. The gradient of point P on the curvey = 3x2 - x + 3 is 5.\ Find the coordinates of P.

A. (1.5)

B. (1.7)

C. (l,13)

D. (l.17)


12. An arc of length 10. 8cm subtends an angle of 1.2 rad the centre of a circle. Calculate the radius of a circle

A. 12.6cm

B. 12.0cm

C. 9.6cm

D. 9.0cm


13. The first term of a geometric series is 350. If the sum i infinity is 250. find the common ratio.

A. – 5/7

B. – 2/5

C. 2/5

D. 5/7


14. P and q are statements such that p => q Which of the following is a valid conclusion from the implication1

A. q => p

B. ~ q => p

C ~ q => ~ p

D. ~ p => -q


15. The roots of a quadratic equation are-3 « d I F equation

A. x2 - 3x + l = 0

B. x2- 2x + 1 = 0

C. x2 + 2x - 3 = 0

D. x2 + x – 3 = 0


ANSWERS



17. Simplify (216)-2/3- x (0.16)-3/2

A. 125/288

B. 2/125

C. 4/225

D. 2/225


18. Given that log3 (x - y) = 1 and log3 (2x+y) = 2. fine the value of x.

A. 1

B. 2

C. 3

D. 4






ANSWERS



In the diagram, a ladder PS leaning against a vertical wall PR makes angle x2 with the horizontal floor The ladder slides down to a point QT such that angle QTR = 30° and angle SNT =y.

Use this information to answer questions 21 and 22.


21. Find the relation between x and y.

A. y = ½ x + 30

B. y = ½ x -30

C. y = x + 30

D. y = x -30


22. Find an expression for tan y.

A. √3 tan x-l

B. √3 tanx-1

C. √3 tan x + 1

D. √3 tan x +1


23. If P = (12 11 ). find (P: + P)

A. (46 31)

B (46 34)

C (36 21)

D (36 24)


24. Simplify 2log38 - 3log32

A.-log34

B. -log32

C. 3log32

D. 3log,4


25. Which of the following is the semi-interquartile range of a distribution?

A. Mode - Median

B. Highest score -Lowest score

C. ½ (Upper Quartile - Median)

D. ½ (Upper Quartile - Lower Quartile)


ANSWERS

26. A stone is projected vertically upwards with a speed of 10ms-1 from a point 8 metres above the ground Find the maximum height reached. [Take g = 10ms":]

A. 13 metres

B. 15 metres

C. 18 metres

D. 23 metres


27. The velocity , v ms-1 of a particle moving in a straight line is given by v = 3t2 - 2t + 1 at time t seconds Find the acceleration of the particle after 3 seconds.

A. 26ms-2

B. 18ms-2

C. 17ms-2

D.16ms-2


28. Three mc. P. Q and R aim at a target the probabilities that P. Q and R hit the target are ½, 1/3, and 3/4 respectively. Find the probability that exactly two of them hit the target.

A. 1

B. ½

C. 5/12

D. 1/3


29. The position vectors of A and B are (2i + j) and (-i + 4i) respectively, find |AB|.

A. 3√2

B. √34

C. √38

D. 9 √2


30. Two fair dice, each numbered 1, 2.... 6, are tossed together. Find the probability that they both show even numbers.

A. 1/3

B. 1/4

C. 1/6

D. 1/12


ANSWERS

31. Calculate correct to the nearest degree, the angle between the vectors. (1 3 ) and (1 4)

A. 580

B. 720

C. 740

D. 870


32. Evaluate. (24 31) (2 3)

A. (13, 11)

B. (11, 13)

C (13 11)

D. (11 13)


33. If the mean of -1.0. 9,3, k, 5 is 2, where k is a constant, find the median of the set of numbers.

A. 0

B. 3/2

C. 7/2

D. 6


34. Eight football clubs are to play in a league on home and away basis. How manv matches are possible?

A. 14

B. 28

C. 56 `

D. 128


35. Two balls are drawn from a bag containing 3 red. 4 white and 5 black identical balls. Find the probability that they are all of the same colour.

A. 5/33

B. 13/66

C. 8/33

D. 19/66


ANSWERS

36. A force F acting on a body of mass 12kg increases its speed from 5ms-1 to 35ms-1 in 5 seconds. Find the value of F.

A. 36N

B. 48N

C. 72N

D. 108N


37. Express the force F = (8 N. 1500) in the form (ai + bj) where a and b are constants

A. 4√3i-4j

B. 4i-4√3j

C. -4i + 4√3j

D. -4√3i + 4j


38. Three defective bulbs got mixed op with 7 good ones. If two bulbs are selected at random. What is the probability that both are good?

A. 3/7

B. 21/50

C. 7/15

D. 49/100


39. The ages, in years, of 5 boys are 5.6.6.8 and 10. Calculate, correct to one decimal place, the standard deviation of their ages

A. 3.2 years

B. 2.6 years

C. 19 year

D. 1.8 years


40. A body is acted upon by forces F1 = (10 N. 0900) and F: = (6N. 1800) Find the magnitude of the resultant force, correct to one decimal place

A. 11.6N

B. 11.7N

C.11.8N

D. 11.9N



WASSCE JUNE 2009 FURTHER MATHEMATICS OBJECTIVE TEST

ANSWERS

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


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