POST UTME SKYLINE UNIVERSITY 2025 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 = 16 \)
C. \( x + 3 \)^2 + \( y - 2 \)^2 = 16 \)
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16 \)
Question 2
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 4
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 1210
B. 1230
C. 1250
D. 1270
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 128
Question 6
Solve the inequality \( x^2 - 4x + 4 geq 0 \).
A. x \leq 2
B. x \geq 2
C. x < 2
D. x > 2
Question 7
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).
A. \\begin{pmatrix} \\frac{4}{13} \\frac{6}{13} \\end{pmatrix}
B. \\begin{pmatrix} \\frac{2}{13} \\frac{3}{13} \\end{pmatrix}
C. \\begin{pmatrix} \\frac{1}{13} \\frac{2}{13} \\end{pmatrix}
D. \\begin{pmatrix} \\frac{3}{13} \\frac{4}{13} \\end{pmatrix}
Question 8
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 10
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. 16/15
B. 32/15
C. 64/15
D. 128/15
Question 11
Find the equation of the \tangent line to the curve \( y = x^2 \) at the point ( (1, 1) ).
Question 12
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{π}{2}
B. x = \frac{π}{4}
C. x = \frac{3π}{4}
D. x = \frac{5π}{4}
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 14
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 90
D. 100
Question 15
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. \( x - 2 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 3 \)^2 = 16

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