POST UTME SKYLINE UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 = 20 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )
Question 2
A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line.
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = -2x + 1 \)
D. \( y = 2x - 2 \)
Question 3
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 5 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 3 \ \)^2 + \( y - 5 \)^2 = 25 )
Question 4
Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 2 \ 3x + y - 2z &= 1 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ -1 \ 1 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \ -2 \end{pmatrix}
D. \begin{pmatrix} 4 \ 2 \ 1 \end{pmatrix}
Question 5
Find the area under the curve of the function ( f(x) = \frac{1}{x^2 + 1} ) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{6} \)
D. \( \frac{pi}{8} \)
Question 6
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 7
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. 2
D. 3
Question 8
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is a success. Find the probability of success.
A. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 9
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, what is the value of the 8th bar?
A. 20
B. 22
C. 24
D. 26
Question 10
A sequence is defined by the formula $a_n = 2n^2 - 5n + 1$. Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 11
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has 10 bars, what is the value of the 8th bar?
A. 20
B. 22
C. 24
D. 26
Question 12
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...
A. 124
B. 126
C. 128
D. 130
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 14
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 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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