POST UTME LASU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π
Question 2
Find the value of $\int_0^1 x^2 \sin x dx$.
A. -1 + \cos 1
B. 1 - \cos 1
C. -1 - \cos 1
D. 1 + \cos 1
Question 3
Solve the system of equations \( x + y = 4 \) and \( 2x - 3y = 5 \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 1, y = 3 \)
D. \( x = 4, y = 0 \)
Question 4
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 5
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
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. \( y = 3x - 2 \)
D. \( y = 3x + 2 \)
Question 7
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 8
A histogram of exam scores is shown below:\n\n[Diagram Spec]
A. The mean score is 60.
B. The median score is 60.
C. The mode score is 60.
D. The s\tandard deviation is 10.
Question 9
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 10
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 11
Find the area of the circle with radius \( r = 4 \) cm.
A. ( 16pi ) cm^2
B. ( 32pi ) cm^2
C. ( 64pi ) cm^2
D. ( 128pi ) cm^2
Question 12
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 13
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 14
A random experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. What is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 15
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

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