POST UTME WELLSPRING UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
In a binary number system, what is the value of the digit in the $2^3$ place in the number $110101_2$?
A. 0
B. 1
C. 2
D. 3
Question 3
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 4
Solve the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -1 \) or \( x = \frac{3}{2} \)
B. \( x = 1 \) or \( x = -\frac{3}{2} \)
C. \( x = -\frac{1}{2} \) or \( x = 3 \)
D. \( x = \frac{1}{2} \) or \( x = -3 \)
Question 5
Simplify the expression \sqrt{\frac{4}{9}}.
A. \frac{2}{3}
B. \frac{4}{9}
C. \frac{6}{9}
D. \frac{8}{9}
Question 6
A random sample of 25 students from a university had an average height of 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6179
Question 7
In the diagram below, the triangle ABC has a base of 6 cm and a height of 8 cm. If the angle B measures 60°, what is the area of the triangle?
A. 24 cm^2
B. 30 cm^2
C. 36 cm^2
D. 40 cm^2
Question 8
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 9
In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. \( \frac{80}{100} \)
B. \( \frac{70}{100} \)
C. \( \frac{90}{100} \)
D. \( \frac{95}{100} \)
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. ( pi (4)^2 )
B. ( 2pi (4)^2 )
C. ( 4pi (4)^2 )
D. ( 16pi (4)^2 )
Question 11
A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.
A. \( y = \frac{2}{3}x + \frac{1}{3} \)
B. \( y = \frac{2}{3}x - \frac{1}{3} \)
C. \( y = \frac{3}{2}x + \frac{1}{2} \)
D. \( y = \frac{3}{2}x - \frac{1}{2} \)
Question 12
If f(x) = 3x^2 + 2x - 5, find the derivative of f(x) u\sing the chain rule.
A. 6x + 2
B. 3x^2 + 2x - 5
C. 12x + 4
D. 9x^2 + 4x - 10
Question 13
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].
A. 1
B. -1
C. 2
D. 3
Question 14
Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 15
Find the value of \( x \) in the equation \( 2 \sin x = \sqrt{3} \).
A. \( \frac{\pi}{6} \)
B. \( \frac{\pi}{3} \)
C. \( \frac{\pi}{2} \)
D. \( \frac{2\pi}{3} \)

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