POST UTME LAUTECH 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation: \( \frac{1}{2} \sin^2 x + \frac{1}{4} \cos^2 x = \frac{1}{4} \)
A. x = \frac{\pi}{6}
B. x = \frac{\pi}{4}
C. x = \frac{\pi}{3}
D. x = \frac{\pi}{2}
Question 2
Solve the equation \frac{1}{x + 1} + \frac{1}{x - 1} = \frac{1}{2}
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 3
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
Question 4
If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.15, find P\( A|B \).
A. 0.3
B. 0.6
C. 0.8
D. 1.0
Question 5
Solve the trigonometric equation: \sin^2 x + \cos^2 x = 1.
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \\frac{3\\pi}{4}
D. x = \\frac{5\\pi}{4}
Question 6
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 7
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 8
In the diagram below, identify the part labeled A.
A. Beaker
B. Burette
C. Test Tube
D. Cell
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > -\frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 10
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)
Question 11
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral.
A. \( \frac{64}{3} \)
B. \( \frac{128}{3} \)
C. \( \frac{256}{3} \)
D. \( \frac{512}{3} \)
Question 12
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 13
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}}
B. f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}}
D. f'(x) = \frac{-1}{\( 1 - x^2 \)^{3/2}}
Question 14
Find the value of \log_{10} (1000)
A. 3
B. 4
C. 5
D. 6
Question 15
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{array} ].
A. -3
B. 3
C. -1
D. 1

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