POST UTME KSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4, 5 \). Find the probability that X is greater than 3.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 2
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 80.
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 3
Find the equation of the line pas\sing through the points ((2,3)) and ((4,5)).
A. \( y = \frac{2}{2}x + \frac{1}{2} \)
B. \( y = \frac{2}{2}x + \frac{1}{2} \)
C. \( y = \frac{2}{2}x + \frac{1}{2} \)
D. \( y = \frac{2}{2}x + \frac{1}{2} \)
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 + \frac{1}{2} \)
C. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 - \frac{1}{2} \)
D. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 5
Find the value of x in the equation 2^x = 16.
A. 2
B. 3
C. 4
D. 5
Question 6
Simplify the expression \sqrt{48} \times \sqrt{18}.
A. 12\sqrt{3}
B. 24\sqrt{2}
C. 36\sqrt{3}
D. 48\sqrt{2}
Question 7
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, find the value of the 7th bar.
A. 20
B. 30
C. 40
D. 50
Question 8
Find the value of \( \sin 2\theta \) given that \( \cos \theta = \frac{3}{5} \) and \( \sin \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{20}{25} \)
D. \( \frac{12}{25} \)
Question 9
Solve the inequality \( \frac{x}{x+1} > \frac{2}{3} \) for \( x in mathbb{R} setminus {-1} \).
A. \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \)
C. \( x > -1 \) or \( x < \frac{1}{2} \)
D. \( x < -1 \) or \( x > \frac{1}{2} \)
Question 10
A circle has equation \( x^2 + y^2 = 16 \). Find the equation of the \tangent line at point (P(2, 4)).
A. \( y = -x + 6 \)
B. \( y = x + 6 \)
C. \( y = -x - 6 \)
D. \( y = x - 6 \)
Question 11
If \( A = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \) and \( B = egin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} \), find ( AB ).
A. \( AB = egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} \)
B. \( AB = egin{pmatrix} 3 & 1 \ 1 & 3 \end{pmatrix} \)
C. \( AB = egin{pmatrix} 2 & 2 \ 2 & 2 \end{pmatrix} \)
D. \( AB = egin{pmatrix} 3 & 2 \ 2 & 3 \end{pmatrix} \)
Question 12
Find the sum of the infinite geometric series with first term 2 and common ratio 1/2.
A. ( 4 )
B. ( 8 )
C. ( 16 )
D. ( 32 )
Question 13
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis from \( x = 0 \) to \( x = 2 \).
A. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )
B. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx + pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )
C. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx - pi int_{0}^{2} \( x^2 \)^2 - (2x)^2 , dx )
D. \( pi int_{0}^{2} \( 2x \ \)^2 - \( x^2 \)^2 , dx )
Question 14
Find the equation of the circle with center at ((2,3)) and radius 4.
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
Question 15
If ( f(x) = \frac{1}{x^2 - 4} ), find \( f^{-1}\( x \ \) ).
A. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 4} )
B. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 4} )
C. \( f^{-1}\( x \ \) = \frac{1}{x^2 + 2} )
D. \( f^{-1}\( x \ \) = \frac{1}{x^2 - 2} )

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