POST UTME SKYLINE UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let \( S = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( S ) that contain exactly two elements.
A. 10
B. 15
C. 20
D. 25
Question 2
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 3
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 4
Find the value of ( x ) in the equation \( x^2 - 6x + 8 = 0 \).
A. 2
B. 3
C. 4
D. 5
Question 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 6
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 7
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. f'(x) = -\frac{1}{2x^{3/2}}
B. f'(x) = \frac{1}{2x^{3/2}}
C. f'(x) = -\frac{1}{x^{3/2}}
D. f'(x) = \frac{1}{x^{3/2}}
Question 8
A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75 and the s\tandard deviation is 10, find the area under the curve between 60 and 80.
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 9
Find the derivative of the function ( f(x) = x^3 - 6x^2 + 9x + 2 ).
A. 3x^2 - 12x + 9
B. 3x^2 - 12x + 10
C. 3x^2 - 12x + 9 + 2
D. 3x^2 - 12x + 9 - 2
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. \( x + 3 \)^2 + \( y - 2 \)^2 = 16 \)
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16 \)
Question 11
Find the equation of the \tangent line to the curve \( y = x^2 \) at the point ( (1, 1) ).
Question 12
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
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 15
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the first five terms of the sequence.
A. [3, 7, 15, 31, 63]
B. [3, 5, 7, 9, 11]
C. [3, 6, 12, 24, 48]
D. [3, 8, 16, 32, 64]

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