POST UTME SKYLINE UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = x^2 + 2x + 1 ). Find the value of \( f\( -2 \ \) ).
A. 1
B. 3
C. 5
D. 7
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)
Question 3
A rec\tangular solid has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its surface area.
A. 120 cm^2
B. 150 cm^2
C. 180 cm^2
D. 200 cm^2
Question 4
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \) or \( x = -3 \)
B. \( x = -1 \) or \( x = -6 \)
C. \( x = 2 \) or \( x = 3 \)
D. \( x = 1 \) or \( x = 4 \)
Question 5
A set 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 will be between 60 and 90?
A. 0.9544
B. 0.8413
C. 0.6915
D. 0.6827
Question 6
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 3
B. 4
C. 5
D. 6
Question 7
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 pm \sqrt{5^2 - 4 \times 1 \times 6}}{2 \times 1} \)
B. \( x = \frac{-5 pm \sqrt{5^2 + 4 \times 1 \times 6}}{2 \times 1} \)
C. \( x = \frac{-5 pm \sqrt{5^2 - 4 \times 1 \times 6}}{2 \times 6} \)
D. \( x = \frac{-5 pm \sqrt{5^2 + 4 \times 1 \times 6}}{2 \times 6} \)
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 9
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. \( 2 + 6 + 18 + ldots + 5832 \)
B. \( 2 + 6 + 18 + ldots + 8192 \)
C. \( 2 + 6 + 18 + ldots + 4096 \)
D. \( 2 + 6 + 18 + ldots + 16384 \)
Question 10
Solve the inequality: \[ \begin{align*} 2x - 5 &< 3 \end{align*} \]
A. x < 4
B. x > 4
C. x < 2
D. x > 2
Question 11
Find the derivative of the function ( f(x) = \sqrt{3x + 2} ) u\sing the chain rule.
A. \( \frac{3}{2\sqrt{3x + 2}} \)
B. \( \frac{3}{2\( 3x + 2 \ \)} )
C. \( \frac{3}{2\sqrt{3x + 2}} + \frac{1}{2\sqrt{3x + 2}} \)
D. \( \frac{3}{2\( 3x + 2 \ \)} - \frac{1}{2\( 3x + 2 \)} )
Question 12
A set ( A ) contains 5 elements. If ( A ) is a subset of a set ( B ), and ( B ) has 8 elements, what is the number of elements in the power set of ( B )?
A. 32
B. 64
C. 128
D. 256
Question 13
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 14
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) - 3 \times \( 5 \times 10 - 7 \times 8 \) + 4 \times \( 5 \times 9 - 6 \times 8 \) )
B. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) - 3 \times \( 5 \times 10 - 7 \times 8 \) - 4 \times \( 5 \times 9 - 6 \times 8 \) )
C. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) + 3 \times \( 5 \times 10 - 7 \times 8 \) + 4 \times \( 5 \times 9 - 6 \times 8 \) )
D. \( 2 \times \( 6 \times 10 - 7 \times 9 \ \) + 3 \times \( 5 \times 10 - 7 \times 8 \) - 4 \times \( 5 \times 9 - 6 \times 8 \) )
Question 15
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)

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