POST UTME KSU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points (2,3), (4,5), and (6,7).
A. \( x^2 + y^2 - 12x - 6y + 36 = 0 \)
B. \( x^2 + y^2 - 8x - 4y + 16 = 0 \)
C. \( x^2 + y^2 - 10x - 5y + 25 = 0 \)
D. \( x^2 + y^2 - 14x - 7y + 49 = 0 \)
Question 2
Determine the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 3
Given a random sample of 100 students, with a mean height of 175 cm and a s\tandard deviation of 5 cm, calculate the probability that a randomly selected student will have a height between 170 cm and 180 cm.
A. 0.68
B. 0.73
C. 0.83
D. 0.93
Question 4
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
B. 40
C. 50
D. 60
Question 5
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-4} \)
D. \( x = 10^{-2} \)
Question 6
Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 6
B. 8
C. 10
D. 12
Question 7
Solve the inequality \( 2^x + 2^{x+1} > 2^{x+2} \).
A. x < -2
B. x > -2
C. x < -1
D. x > -1
Question 8
Find the area under the curve of the function ( f(x) = \frac{1}{x} ) from \( x = 1 \) to \( x = 2 \).
A. 0.693
B. 0.693
C. 0.693
D. 0.693
Question 9
Solve for $x$ in the equation $\frac{x}{2} + 5 = 11$.
A. 8
B. 12
C. 16
D. 20
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
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( \frac{16pi}{3} \)
B. \( \frac{32pi}{3} \)
C. \( \frac{64pi}{3} \)
D. \( \frac{128pi}{3} \)
Question 12
Convert the \fraction \( \frac{3}{4} \) to its equivalent in base 8.
A. 3
B. 4
C. 5
D. 6
Question 13
Solve the system of 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. x = 1, y = 2
B. x = 2, y = 3
C. x = 3, y = 4
D. x = 4, y = 5
Question 14
Solve for $x$ in the equation $\frac{1}{x} + 2 = 3$.
A. 1
B. 2
C. 3
D. 4
Question 15
Find the value of $\sum_{n=1}^{10} n^2$.
A. 385
B. 3850
C. 38500
D. 385000

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