POST UTME MADONNA UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -3 or x > \frac{1}{2}
B. x < -3 or x < \frac{1}{2}
C. x > -3 or x > \frac{1}{2}
D. x < -3 or x > \frac{1}{2}
Question 3
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x - 8 \) - \( x^2 - 4 \)\( 2x + 2 \)}{\( x^2 - 4 \)^2}
C. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x + 8 \) - \( x^2 - 4 \)\( 2x - 2 \)}{\( x^2 - 4 \)^2}
D. f'(x) = \frac{\( x^2 + 2x - 3 \)\( 2x - 2 \) - \( x^2 - 4 \)\( 2x + 2 \)}{\( x^2 - 4 \)^2}
Question 4
Solve for y in the equation \( y^2 + 4y - 5 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 5
A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?
A. 48 km/h
B. 50 km/h
C. 52 km/h
D. 55 km/h
Question 6
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 7
Find the vector projection of the vector \mathbf{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto the vector \mathbf{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.
A. \begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}
B. \begin{pmatrix} \frac{13}{14} \ \frac{15}{14} \ \frac{17}{14} \end{pmatrix}
C. \begin{pmatrix} \frac{15}{14} \ \frac{17}{14} \ \frac{19}{14} \end{pmatrix}
D. \begin{pmatrix} \frac{17}{14} \ \frac{19}{14} \ \frac{21}{14} \end{pmatrix}
Question 8
Find the derivative of the function f(x) = \frac{x^2 + 2x - 3}{x^2 + 1} u\sing the quotient rule.
A. \frac{2x + 2}{\( x^2 + 1 \)^2}
B. \frac{2x + 2}{x^2 + 1}
C. \frac{2x + 2}{\( x^2 + 1 \)^2} + \frac{2x - 1}{x^2 + 1}
D. \frac{2x + 2}{\( x^2 + 1 \)^2} - \frac{2x - 1}{x^2 + 1}
Question 9
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 10
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < 3/2 or x > -1
D. x > 3/2 or x < -1
Question 11
Determine the value of x in the equation \( \frac{x}{3} + \frac{2}{5} = \frac{7}{15} \).
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup (4, 5)
C. \( -3, -1 \) \cup (1, 3) \cup (4, 5) \cup (6, 7)
D. \( -3, -1 \) \cup (1, 3) \cup (4, 5) \cup (6, 7) \cup (8, 9)
Question 13
In the diagram below, what is the equation of the circle with center at point A?
A. \( x^2 + y^2 = 4 \)
B. \( x^2 + y^2 = 9 \)
C. \( x^2 + y^2 = 16 \)
D. \( x^2 + y^2 = 25 \)
Question 14
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 15
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 190
B. 200
C. 210
D. 220

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