POST UTME WELLSPRING UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].
A. 1
B. -1
C. 2
D. 3
Question 2
Simplify the expression \sqrt{\frac{4}{9}}.
A. \frac{2}{3}
B. \frac{4}{9}
C. \frac{6}{9}
D. \frac{8}{9}
Question 3
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 4
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 5
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 6
Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 2 \end{align*}.
A. \\begin{pmatrix} 2 \\ 2 \\end{pmatrix}
B. \\begin{pmatrix} 1 \\ 3 \\end{pmatrix}
C. \\begin{pmatrix} 3 \\ 1 \\end{pmatrix}
D. \\begin{pmatrix} 4 \\ 0 \\end{pmatrix}
Question 7
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 18
B. 24
C. 30
D. 36
Question 8
A line passes through points $\( -2, 3 \)$ and $\( 4, -1 \)$. What is the equation of the line in slope-intercept form?
A. y = -x + 5
B. y = x + 2
C. y = -x - 3
D. y = x - 1
Question 9
A random variable X has a probability density function f(x) = \frac{1}{2} for 0 < x < 2. Find the probability that X is greater than 1.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 10
In the diagram below, the circle with center O has a radius of 4 cm. The point P lies on the circle. If the angle POQ measures 60°, what is the length of the chord PQ?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Question 11
Solve the inequality \frac{x - 2}{x + 1} > 0.
A. \( -\\infty, -1 \) \\cup \( 2, \\infty \)
B. \( -\infty, -1 \) \cup \( 2, \infty \) \cup \( 4, \infty \)
C. \( -\infty, -1 \) \cup \( 2, \infty \) \cup \( -\infty, 4 \)
D. \( -\infty, -1 \) \cup \( 2, \infty \) \cup \( -\infty, 4 \) \cup \( 4, \infty \)
Question 12
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 13
Find the derivative of ( 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 14
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 15
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 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28

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