POST UTME LASU 2017 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{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 2
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{2}{\( x^2+1 \ \)^2} )
D. \( \frac{2}{\( x^2+1 \ \)^2} )
Question 3
A population of bacteria grows according to the equation $P(t) = 2000e^{0.2t}$. Find the rate at which the population is growing after 5 hours.
A. 400e^{0.2t}
B. 2000e^{0.2t}
C. 4000e^{0.2t}
D. 8000e^{0.2t}
Question 4
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.9544
B. 0.8413
C. 0.6915
D. 0.6827
Question 7
Find the derivative of ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 8
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 9
Solve the inequality [ 2x^2 + 5x - 3 > 0 ].
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup \( 3, \infty \)
Question 10
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 11
A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of S.
A. 5
B. 6
C. 7
D. 8
Question 12
If [ f(x) = \frac{x^2 - 4}{x + 2} ], find [ f'(x) ].
A. \frac{2x}{\( x + 2 \)^2}
B. \frac{x^2 - 4}{\( x + 2 \)^2}
C. \frac{2x + 4}{\( x + 2 \)^2}
D. \frac{x^2 + 4}{\( x + 2 \)^2}
Question 13
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
A. -120
B. 120
C. -60
D. 60
Question 14
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. ( 30 ) cm³
B. ( 50 ) cm³
C. ( 70 ) cm³
D. ( 90 ) cm³
Question 15
A circle has a radius of 4 cm. Find its area.
A. ( 16pi ) cm²
B. ( 32pi ) cm²
C. ( 64pi ) cm²
D. ( 128pi ) cm²

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