POST UTME CALEB UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality [ 2x^2 + 3x - 1 > 0 ].
A. \( -\infty, -1 \) \cup \( 1, \infty \)
B. \( -\infty, 0 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup (0, 1)
D. \( -\infty, 1 \)
Question 2
A circle has a radius of 4 cm. What is the area of the circle?
A. 50.24 cm^2
B. 50.27 cm^2
C. 50.29 cm^2
D. 50.31 cm^2
Question 3
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg?
A. 4 cm
B. 6 cm
C. 8 cm
D. 12 cm
Question 4
Find the equation of the \tangent to the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) at the point where \( x = 1 \).
A. \( y = 2x - 1 \)
B. \( y = x + 2 \)
C. \( y = 2x + 1 \)
D. \( y = x - 2 \)
Question 5
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \sin x = \frac{1}{2}
B. \cos x = \frac{1}{2}
C. \sin x = \frac{1}{3}
D. \cos x = \frac{1}{3}
Question 6
Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ).
A. 6
B. 8
C. 10
D. 12
Question 7
A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity and acceleration at time \( t = 1 \).
A. v(1) = 5, a(1) = -3
B. v(1) = 3, a(1) = 5
C. v(1) = -3, a(1) = 5
D. v(1) = 5, a(1) = -5
Question 8
A histogram of exam scores for a class of 50 students is shown below. Find the mean score.
A. 60
B. 70
C. 80
D. 90
Question 9
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}}
B. f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}}
D. f'(x) = \frac{2x}{\( 1 - x^2 \)^{3/2}}
Question 10
Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. 1
B. 2
C. 3
D. 4
Question 11
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?
A. 75
B. 76
C. 77
D. 78
Question 12
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 13
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 = x - 1
D. y = x + 1
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2}{x^3} )
B. ( f'(x) = \frac{2}{x^3} )
C. ( f'(x) = -\frac{1}{x^3} )
D. ( f'(x) = \frac{1}{x^3} )
Question 15
If f(x) = 3x^2 + 2x - 5 and g(x) = 2x^2 - 3x + 1, find the derivative of f(g(x)) u\sing the chain rule.
A. 6x^3 + 12x^2 - 6x - 1
B. 6x^3 + 12x^2 - 6x + 1
C. 6x^3 + 12x^2 + 6x - 1
D. 6x^3 + 12x^2 + 6x + 1

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