POST UTME COVENANT UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A polynomial function f(x) has a degree of 3 and a leading coefficient of 2. If f\( -2 \) = -23, find the value of f(1).
A. -5
B. -3
C. -1
D. 1
Question 2
Find the area under the curve of ( f(x) = \frac{1}{x^2} ) from \( x = 1 \) to \( x = 2 \).
A. 1
B. 2
C. 3
D. 4
Question 3
A number is 5 times the sum of its digits. If the number is divisible by 3, what is the sum of its digits?
A. 3
B. 4
C. 5
D. 6
Question 4
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{-1}{\( 1 - x^2 \)^{3/2}}
Question 5
A circle has equation \( x - 2 \)^2 + \( y - 3 \)^2 = 4. Find the equation of the \tangent line at point (3, 1).
A. y = -1/2x + 7/2
B. y = 1/2x - 5/2
C. y = -1/2x + 5/2
D. y = 1/2x + 7/2
Question 6
Solve the inequality x^2 + 2x - 3 > 0.
A. x < -3 or x > 1
B. x < 1 or x > 3
C. x < -1 or x > 3
D. x < 1 or x < -3
Question 7
Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 8
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. f'(x) = 2x \sin x + x^2 \cos x
B. f'(x) = x^2 \cos x - 2x \sin x
C. f'(x) = 2x \cos x + x^2 \sin x
D. f'(x) = x^2 \sin x - 2x \cos x
Question 9
Find the probability of drawing two hearts from a s\tandard deck of 52 cards, given that the first card drawn is a heart.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 10
Find the surface area of the sphere with a radius of 5 cm.
A. 50\pi\text{ cm}^2
B. 100\pi\text{ cm}^2
C. 150\pi\text{ cm}^2
D. 200\pi\text{ cm}^2
Question 11
Find the value of \( \sin\( 2x \ \) ) given that \( \cos\( x \ \) = \frac{3}{5} ) and \( \sin\( x \ \) = \frac{4}{5} ).
A. 1
B. 2
C. 3
D. 4
Question 12
Find the area under the curve of the function f(x) = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 17
B. 19
C. 21
D. 23
Question 13
Find the determinant of the matrix \\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\end{bmatrix}.
A. 0
B. 1
C. -1
D. 2
Question 14
Determine the volume of the frustum of a cone with a height of 15 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.
A. 300\pi\text{ cm}^3
B. 400\pi\text{ cm}^3
C. 500\pi\text{ cm}^3
D. 600\pi\text{ cm}^3
Question 15
If f(x) = \frac{1}{x^2 + 1}, find f'(x) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}

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