POST UTME BSU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \).
A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{2}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-2}{\( x^2 + 1 \)^2}
Question 2
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 3
Two events A and B are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find ( P(A cap B) ).
A. 0.24
B. 0.24 + 0.36
C. 0.24 - 0.36
D. 0.5
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 12 )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - 12 )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 24 )
Question 5
Solve the inequality |x - 2| > 3.
A. x < -1 or x > 5
B. x < 1 or x > 5
C. x < -1 or x > 2
D. x < 1 or x > 2
Question 6
A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) north of east. Find the magnitude of the vector \( mathbf{a} + mathbf{b} \), where ( mathbf{b} ) is a vector with magnitude 3 and direction \( 60^circ \) south of west.
A. 4
B. 5
C. 6
D. 7
Question 7
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30 cm^3
B. 50 cm^3
C. 60 cm^3
D. 70 cm^3
Question 8
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4} or x = \frac{3\pi}{4}
B. x = \frac{\pi}{4} or x = \frac{5\pi}{4}
C. x = \frac{\pi}{4} or x = \frac{7\pi}{4}
D. x = \frac{\pi}{4} or x = \frac{9\pi}{4}
Question 9
In the diagram below, the graph of \( y = \frac{1}{2} \sin 2x \) is shown. If the graph passes through the point \( \frac{pi}{4}, 1 \ \) ), find the value of ( x ) when \( y = 0.5 \).
A. 0.5
B. 1.2
C. 1.5
D. 2.0
Question 10
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)
Question 11
A die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. 1/6
B. 1/12
C. 1/18
D. 1/24
Question 12
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \) with first term \( a = 2 \) and common ratio \( r = 3 \).
A. \( 2 cdot \frac{3^{10} - 1}{3 - 1} \)
B. \( 2 cdot \frac{3^{10} - 1}{3 - 1} + 1 \)
C. \( 2 cdot \frac{3^{10} - 1}{3 - 1} - 1 \)
D. \( 2 cdot \frac{3^{10} - 1}{3 - 1} + 2 \)
Question 13
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 = 32
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 64
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 256
Question 14
A sequence is defined as \( a_n = 2n^2 + 3n - 1 \). Find the sum of the first 5 terms of the sequence.
A. a_1 + a_2 + a_3 + a_4 + a_5 = 55
B. a_1 + a_2 + a_3 + a_4 + a_5 = 65
C. a_1 + a_2 + a_3 + a_4 + a_5 = 75
D. a_1 + a_2 + a_3 + a_4 + a_5 = 85
Question 15
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 0
D. x = 1

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