POST UTME SKYLINE UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the line pas\sing through the points (2, 3) and (4, 5)
A. y = 1x + 1
B. y = 1x - 1
C. y = -1x + 1
D. y = -1x - 1
Question 2
Find the value of \( \sin \( 2\theta \ \) ) given that \( \sin \theta = \frac{1}{2} \) and \( \cos \theta = \frac{\sqrt{3}}{2} \).
A. \( \frac{\sqrt{3}}{2} \)
B. \( \frac{1}{2} \)
C. \( \frac{\sqrt{5}}{2} \)
D. \( \frac{1}{\sqrt{2}} \)
Question 3
Simplify the expression: \frac{2x^2 + 5x - 3}{x + 3}
A. \frac{2x^2 + 5x - 3}{x + 3} = 2x - 1
B. \frac{2x^2 + 5x - 3}{x + 3} = 2x + 1
C. \frac{2x^2 + 5x - 3}{x + 3} = x - 1
D. \frac{2x^2 + 5x - 3}{x + 3} = x + 1
Question 4
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. 12
B. 15
C. 18
D. 20
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \frac{x}{\( 1 - x^2 \)^{3/2}}
B. \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. \frac{1}{\( 1 - x^2 \)^{3/2}}
D. \frac{-1}{\( 1 - x^2 \)^{3/2}}
Question 6
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 7
Find the derivative of the function: f(x) = 3x^2 + 2x - 5
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 3x^2 + 2
D. f'(x) = 3x^2 - 2
Question 8
A circle with center ( (3, 4) ) and radius ( 5 ) has the equation \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the line \tangent to the circle at the point ( (6, 7) ).
A. y - 7 = \frac{1}{5}\( x - 6 \)
B. y - 7 = -\frac{1}{5}\( x - 6 \)
C. y - 7 = \frac{5}{1}\( x - 6 \)
D. y - 7 = -\frac{5}{1}\( x - 6 \)
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 10
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 11
In a circle with center $O$, a chord $AB$ is drawn such that $OA=3$ and $OB=4$. If $M$ is the midpoint of $AB$, find the area of $\triangle OMA$.
A. 12
B. 16
C. 20
D. 24
Question 12
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 13
A set of 5 points $A,B,C,D,E$ are chosen at random from the set of all points with integer coordinates in the interval $[0,10]$. What is the probability that the points $A,B,C,D,E$ are all distinct?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 14
A sequence is defined recursively by $a_1=1$ and $a_n=a_{n-1}+2$ for $n>1$. Find the value of $a_{10}$.
A. 21
B. 22
C. 23
D. 24
Question 15
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its surface area.
A. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108
B. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108
C. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108
D. 2(6)(4) + 2(6)(3) + 2(4)(3) = 48 + 36 + 24 = 108

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