POST UTME AL-HIKMAH UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{x^2 + 1}{x^2 - 1} ).
A. ( f'(x) = \frac{2x}{\( x^2 - 1 \)^2} )
B. ( f'(x) = \frac{2x^2}{\( x^2 - 1 \)^2} )
C. ( f'(x) = \frac{2x^3}{\( x^2 - 1 \)^2} )
D. ( f'(x) = \frac{2x^4}{\( x^2 - 1 \)^2} )
Question 2
A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.
A. 160\pi cm^3
B. 320\pi cm^3
C. 480\pi cm^3
D. 640\pi cm^3
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -3 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, 3)
Question 4
Find the area under the curve \( y = x^3 - 6x^2 + 9x + 2 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 20
C. 30
D. 40
Question 5
Find the equation of the circle with center ( (0, 0) ) and radius ( 2 ).
A. \( x^2 + y^2 = 4 \)
B. \( x^2 + y^2 = 8 \)
C. \( x^2 + y^2 = 16 \)
D. \( x^2 + y^2 = 32 \)
Question 6
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. \( \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8 \) cm
B. \( \sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136} \) cm
C. \( \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8 \) cm
D. \( \sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136} \) cm
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 8
A right-angled triangle has a base of 5 cm and a height of 12 cm. Find the length of the hypotenuse.
A. 13 cm
B. 14 cm
C. 15 cm
D. 16 cm
Question 9
A random variable X has a probability distribution given by P\( X = 1 \) = 0.2, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.5. Find E(X).
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 10
A rec\tangular \tank measures 2 m by 3 m by 4 m. Find the volume of the \tank in cubic metres.
A. 24 m^3
B. 30 m^3
C. 36 m^3
D. 48 m^3
Question 11
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, find the probability that it is blue.
A. 1/2
B. 2/7
C. 3/8
D. 5/8
Question 12
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 13
Find the area of the triangle with vertices ( (0, 0) ), ( (2, 0) ), and ( (0, 2) ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 14
A right circular cone has a height of 6 cm and a radius of 4 cm. Find the volume of the cone.
A. 32\pi cm^3
B. 64\pi cm^3
C. 96\pi cm^3
D. 128\pi cm^3
Question 15
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. 16/3
B. 32/3
C. 64/3
D. 128/3

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