POST UTME CRAWFORD UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the cylinder with radius 6 and height 8.
A. 288\pi
B. 288\pi
C. 288\pi
D. 288\pi
Question 2
Find the area under the curve of the function ( f(x) = \frac{1}{x^2 + 1} ) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{6} \)
D. \( \frac{pi}{8} \)
Question 3
Find the equation of the circle with center \( -2,3 \) and radius 4.
A. \( x+2 \)^2 + \( y-3 \)^2 = 16
B. \( x-2 \)^2 + \( y+3 \)^2 = 16
C. \( x+2 \)^2 + \( y+3 \)^2 = 16
D. \( x-2 \)^2 + \( y-3 \)^2 = 16
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 5
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?
A. 0.68
B. 0.85
C. 0.95
D. 0.98
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{5}{2} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{2} \)
C. \( x < -\frac{5}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{2} \) or \( x < \frac{3}{2} \)
Question 7
Solve the equation \sin(x) = 0.5 for 0 ≤ x ≤ 2π.
A. π/6
B. π/2
C. 5π/6
D. 3π/2
Question 8
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \( \frac{4}{3} pi \)
B. \( \frac{8}{3} pi \)
C. \( \frac{16}{3} pi \)
D. \( \frac{32}{3} pi \)
Question 9
Solve the inequality \frac{x-2}{x+1} > 0.
A. x < -1 or x > 2
B. x < -1 or x < 2
C. x > -1 or x < 2
D. x > -1 or x > 2
Question 10
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 1 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 2 \end{bmatrix}
Question 11
Find the derivative of the function ( f(x) = \frac{x^2 - 4x + 3}{x^2 + 2x + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) - \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
B. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) - \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^3} )
C. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) + \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^2} )
D. ( f'(x) = \frac{\( 2x - 4 \)\( x^2 + 2x + 1 \) + \( x^2 - 4x + 3 \)\( 2x + 2 \)}{\( x^2 + 2x + 1 \)^3} )
Question 12
Solve the system of linear equations \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -3 \ 3x + y + 2z = 5 \end{cases} \).
A. x = 1, y = 2, z = 3
B. x = 2, y = 3, z = 4
C. x = 3, y = 4, z = 5
D. x = 4, y = 5, z = 6
Question 13
A polynomial $p(x)$ has degree $n$ and has roots $r_1, r_2, \ldots, r_n$. If $p(x) = \( x - r_1 \)\( x - r_2 \) \cdots \( x - r_n \)$, what is the value of $p(1)$?
A. \( 1 - r_1 \)\( 1 - r_2 \) \cdots \( 1 - r_n \)
B. r_1r_2 \cdots r_n
C. 1 - r_1 - r_2 - \cdots - r_n
D. 1 + r_1 + r_2 + \cdots + r_n
Question 14
Find the derivative of the function f(x) = \frac{1}{x^2 + 1} 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{-x}{\( x^2 + 1 \)^2}
Question 15
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \) u\sing integration by substitution.
A. \( \frac{pi}{4} - 1 \)
B. \( \frac{pi}{4} + 1 \)
C. \( \frac{pi}{4} - \frac{1}{2} \)
D. \( \frac{pi}{4} + \frac{1}{2} \)

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