POST UTME CHRISTOPHER UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = \frac{1}{x^2 + 1} \). Find the derivative of ( f(x) ) u\sing the chain rule and limits.
A. \[ f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \]
B. \[ f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \]
C. \[ f'(x) = \frac{-x}{\( x^2 + 1 \)^2} \]
D. \[ f'(x) = \frac{x}{\( x^2 + 1 \)^2} \]
Question 2
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 = 4 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 4 )
Question 3
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( x < -1 \ \) or \( x > 5 \ \)
B. \( x < 1 \ \) or \( x > 5 \ \)
C. \( x < -1 \ \) or \( x < 5 \ \)
D. \( x > 1 \ \) or \( x < 5 \ \)
Question 4
Find the mean of the data set { 2, 4, 6, 8, 10 }.
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 5
Solve the equation \( \log_{10} \( x^2 \ \) = 4 \) for ( x ).
A. 2
B. 4
C. -2
D. -4
Question 6
Find the value of \( \sin \( 2x \ \) ) given that \( \sin \( x \ \) = \frac{1}{2} ).
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{\sqrt{3}}{3}
D. \frac{1}{3}
Question 7
In a survey of 50 students, the mean height was 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. 0.3085
B. 0.1915
C. 0.1359
D. 0.0228
Question 8
Solve the inequality \( \frac{x-2}{x+1} > 0 \).
A. \( -∞, -1 \) ∪ (2, ∞)
B. \( -∞, -1 \) ∪ (1, 2)
C. \( -∞, -1 \) ∪ (2, ∞) ∪ (1, 2)
D. \( -∞, -1 \) ∪ (1, 2)
Question 9
A binary operation \( * \) on the set of integers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).
A. 13
B. 19
C. 25
D. 37
Question 10
Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).
A. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 \)
B. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 \)
C. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 \)
D. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 \)
Question 11
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.
A. 8
B. 6
C. 10
D. 12
Question 12
Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \ \)
B. \( x = -3 \ \)
C. \( x = 2 \ \)
D. \( x = 3 \ \)
Question 13
Find the volume of the frustum of a cone with height 10cm, lower base radius 4cm, and upper base radius 6cm.
A. 100π cm³
B. 150π cm³
C. 200π cm³
D. 250π cm³
Question 14
Let \( S = \sum_{n=1}^\infty \frac{1}{n^2} \ \). Find the value of ( S ).
A. \[ S = \frac{\pi^2}{6} \]
B. \[ S = \frac{\pi^2}{12} \]
C. \[ S = \frac{\pi^2}{24} \]
D. \[ S = \frac{\pi^2}{48} \]
Question 15
Solve for x in the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 ).
A. 100
B. 10
C. 1000
D. 10000

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