POST UTME NOUN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \( f(x) = \frac{x^2}{x^2 + 1} \) u\sing the quotient rule.
A. \frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x^2}{\( x^2 + 1 \)^2}
C. \frac{2x^3}{\( x^2 + 1 \)^2}
D. \frac{2x^4}{\( x^2 + 1 \)^2}
Question 2
Find the sum of the first 10 terms of the geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$.
A. \frac{1023}{2048}
B. \frac{2047}{4096}
C. \frac{4095}{8192}
D. \frac{8191}{16384}
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) )
B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) + \frac{1}{2} )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) - \frac{1}{2} )
Question 4
Find the area under the curve y = 3x^2 + 2x - 5 from x = 0 to x = 2.
A. 26
B. 30
C. 34
D. 38
Question 5
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.
A. ( 72 ) cm^3
B. ( 96 ) cm^3
C. ( 108 ) cm^3
D. ( 120 ) cm^3
Question 6
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 7
A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?
A. 8
B. 10
C. 12
D. 14
Question 8
Solve the inequality \( \frac{x}{x+2} > 1 \) for ( x ) in the interval \( -infty, -2 \ \) cup \( -2, infty \) ).
A. x ∈ \( -∞, -2 \) ∪ (2, ∞)
B. x ∈ \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)
C. x ∈ \( -∞, -2 \) ∪ (2, ∞)
D. x ∈ \( -∞, -2 \) ∪ (0, ∞)
Question 9
Solve the trigonometric equation \( 2\sin^2 x + 3\cos x - 1 = 0 \) for 0 \leq x \leq 2\pi.
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 10
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 + 2
D. y = x - 2
Question 11
A circle with center \( C = \( 2, 3 \ \) ) and radius \( r = 4 \) has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). Write the equation of the circle in s\tandard form.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 12
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 13
A company produces two products, A and B. The profit from the sale of one unit of product A is ₦150, and the profit from the sale of one unit of product B is ₦200. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. ₦20,000
B. ₦25,000
C. ₦30,000
D. ₦35,000
Question 14
Solve for $x$: $\log_{10}\( x^2 \) = 4$.
A. \pm 2
B. \pm 4
C. \pm 6
D. \pm 8
Question 15
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3 or an even number?
A. \( \frac{1}{2} \)
B. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)

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