POST UTME BELLS UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. ( 5 )
B. ( 6 )
C. ( 7 )
D. ( 8 )
Question 2
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from x = 0 to x = 1.
A. 0.5
B. 1
C. 1.5
D. 2
Question 3
A bag contains 5 red marbles, 4 blue marbles, and 6 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. \frac{11}{15}
B. \frac{13}{15}
C. \frac{14}{15}
D. \frac{16}{15}
Question 4
Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi/5
B. 64\pi/5
C. 128\pi/5
D. 256\pi/5
Question 5
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 7
A set of exam scores has a mean of 85 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 70 and 90?
A. 0.135
B. 0.25
C. 0.5
D. 0.75
Question 8
Evaluate the definite integral \( int_{0}^{2} \( 2x^3 - 5x^2 + 3x - 1 \ \) dx ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 9
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 4 & 2 \end{pmatrix} ].
A. 14
B. -14
C. 16
D. -16
Question 10
Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 11
Solve the inequality \( \frac{2x + 1}{x - 1} > 0 \).
A. \( x < -1 \) or \( x > 1 \)
B. \( x < 1 \) or \( x > -1 \)
C. \( x < -1 \) or \( x = 1 \)
D. \( x < 1 \) or \( x = -1 \)
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 1 \) to \( x = 4 \).
A. \( \frac{29}{3} \)
B. \( \frac{31}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{33}{3} \)
Question 13
A vector \vec{a} = 2\hat{i} + 3\hat{j} and a vector \vec{b} = -4\hat{i} + 5\hat{j}. Find the magnitude of the cross product of \vec{a} and \vec{b}.
A. 13
B. 15
C. 17
D. 19
Question 14
Solve the equation x^2 + 4x + 4 = 0.
A. -2
B. 0
C. 2
D. 4
Question 15
If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. -\frac{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}

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