POST UTME IMS U 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the region bounded by the curves y = x^2 and y = 2x.
A. \frac{4}{3}
B. \frac{8}{3}
C. \frac{16}{3}
D. \frac{32}{3}
Question 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. 2x
B. -2x
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2x}{\( x^2 + 1 \)^2}
Question 3
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and \( -1, -2 \).
A. \( x + 1 \)^2 + \( y + 2 \)^2 = 18
B. \( x - 1 \)^2 + \( y - 2 \)^2 = 18
C. \( x + 1 \)^2 + \( y - 2 \)^2 = 18
D. \( x - 1 \)^2 + \( y + 2 \)^2 = 18
Question 4
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 5
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 6
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. 1.4
B. 1.7
C. 2.0
D. 2.3
Question 7
Find the area under the curve \( y = x^2 + 2x \) from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 8
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 121
B. 122
C. 123
D. 124
Question 9
If $f(x) = \frac{1}{x^2+1}$, find $f'(x)$ u\sing the chain rule.
A. \( \frac{-2x}{\( x^2+1 \ \)^2} )
B. \( \frac{2x}{\( x^2+1 \ \)^2} )
C. \( \frac{2}{\( x^2+1 \ \)^2} )
D. \( \frac{-2}{\( x^2+1 \ \)^2} )
Question 10
A line passes through the points (2,3) and (4,5). Find the equation of the line.
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 11
A water \tank has a height of 10 meters and a base radius of 5 meters. Find the volume of water in the \tank.
A. 100π
B. 200π
C. 300π
D. 400π
Question 12
Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).
A. x = 1, y = 1
B. x = 2, y = 0
C. x = 0, y = 2
D. x = 1, y = 0
Question 13
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 14
Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 4x + 3} > 0.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -1 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -1 \) \cup (1, 3)
Question 15
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
A. \( x - 0 \)^2 + \( y - 0 \)^2 = 16
B. \( x - 0 \)^2 + \( y - 0 \)^2 = 4
C. \( x - 0 \)^2 + \( y - 0 \)^2 = 9
D. \( x - 0 \)^2 + \( y - 0 \)^2 = 25

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