- 1. 1. Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j
A) 54.8º
B) 76.3º
C) 66.4º
D) 56.3º
- 2. 2. Find the equation of the normal to the curve y = 3x²+2 at point (1, 5).
A) 6y - x - 29 = 0
B) 6y + x - 31 = 0
C) y - 6x - 1 = 0
D) y - 6x + 1 = 0
A) 21 ms−²
B) 19 ms−²
C) 31 ms−²
D) 41 ms−²
A) 1/7
B) 3 1/6
C) 6/7
D) 1 1/6
- 5. 5. Given that sinx=45 and cosy=12/13, where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).
A) 56/65
B) 16/65
C) 63/65
D) 48/65
A) 3/4
B) −3/4
C) −5/8
D) 5/8
- 8. 8. Find the radius of the circle 2x²+2y²−4x+5y+1=0
A) 33/4
B) √5/6
C) A. √33/4
D) 5/6
- 9. 9. Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
A) √24units
B) √28units
C) √30units
D) √26units
- 10. 10. A particle began to move at 27ms−¹ along a straight line with constant retardation of 9ms−². Calculate the time it took the particle to come to a stop.
A) 2 sec
B) 3 sec
C) 1 sec
D) 4 sec
- 11. 11. Find the fifth term in the binomial expansion of (q+x)⁷.
A) 21q²x⁵
B) B. 21q⁴x³
C) 35q⁵x²
D) 35q³x⁴
- 12. 12. Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q¹).
A) {x : 4 < x < 8}
B) {x : 2 < x ≤ 4}
C) {x : 2 ≤ x ≤ 4}
D) {x : 4 ≤ x ≤ 8}
- 13. 13. Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y ⇒ x?
A) Either the school bus arrived late or Maryam walked to school
B) Emmanuella did not go to school because the school bus arrived late
C) Mary walked to school because the school bus arrived late
D) The school bus arrived early and Kate ran to school
- 14. 14.
Differentiatef(x)=1/ (1−x²)⁵ with respect to x.
A) −10x/(1−x²)⁶
B) 10x/(1−x²)⁶
C) 5x/(1−x²)⁶
D) −5x/(1−x²)⁶
- 15. 15. Express 3/ 3−√6 in the form x+m√y
A) 3 - √6
B) 3 - 3 √6
C) 3 + √6
D) 3 + 3√6
A) 1/4
B) -1/4
C) 3/2
D) -3/2
- 18. 18. Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r - 2n).
A) (62 N , 020º)
B) (62 N , 240º)
C) (62 N , 200º)
D) (62 N , 280º)
- 19. 19. Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º
A) 35.26º
B) 18.43º
C) 19.47º
D) 30.00º
A) √2n+3
B) 8√2n
C) 2n+2 √2
D) 8n√2
- 22. 22. A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms−²]
A) 3.0
B) 2.0
C) 2.5
D) 4.0
- 23. 23. An exponential sequence (G.P.) is given by 9/2,3/4,1/8,....Find its sum to infinity.
A) 13 1/2
B) 5 2/5
C) 4 1/5
D) 6 3/4
- 24. 24. Adu's scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
A) 1.8
B) 1.4
C) 2.0
D) 1.6
- 25. 25. In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
A) 500
B) 210
C) 720
D) 350
- 26. 26. Evaluate: ∫(2x+1)³dx
A) 8(2x+1)²+k
B) 1/6(2x+1)⁴+k
C) 1/8(2x+1)⁴+k
D) 6(2x+1)²+k
- 27. 27. If α and β are the roots of 7x²+12x−4=0,find the value of αβ/(α+β)²
A) -7/36
B) -36/7
C) 7/36
D) 36/7
- 28. 28. If 3x²+px+12=0 has equal roots, find the values of p .
A) ±3
B) ±12
C) ±6
D) ±4
- 30. 30. The velocity of a body of mass 4.56 kg increases from (10ms−¹,060⁰)to(50ms−¹,060⁰) in 16 seconds . Calculate the magnitude of force acting on it.
A) 11.4 N
B) 17.1 N
C) 36.5 N
D) 5.7 N
- 35. 35. The probabilities that Atta and Tunde will hit a target in a shooting contest are 1/6 and 19 respectively. Find the probability that only one of them will hit the target.
A) 13/54
B) 20/27
C) 41/54
D) 15/4
- 37. 37. If m and ( m + 4) are the roots of 4x²−4x−15=0, find the equation whose roots are 2 m and (2 m + 8).
A) x²+2x+15=0
B) x²+8x−15=0
C) x²−8x−15=0
D) x²−2x−15=0
- 39. 39. In how many ways can four Mathematicians be selected from six ?
A) 15
B) 360
C) 90
D) 60
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