POST UTME AAUA 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A polynomial function is defined by f(x) = x^3 - 2x^2 + x - 1. Find the value of f\( -1 \).
A. -3
B. -1
C. 1
D. 3
Question 2
Solve the inequality \( \frac{x}{x+1} > 0 \) for ( x in mathbb{R} ).
A. \( -∞, -1 \) ∪ (0, ∞)
B. \( -∞, 0 \) ∪ (1, ∞)
C. \( -∞, 0 \) ∪ (1, ∞)
D. \( -∞, -1 \) ∪ (0, ∞)
Question 3
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. (1, 2, 3)
B. (1, 2, 6)
C. (1, 3, 6)
D. (2, 3, 6)
Question 4
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 4 - x^2 \) about the x-axis.
A. 16π/3
B. 32π/3
C. 64π/3
D. 128π/3
Question 5
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. What is the expected value of X?
A. 1.1
B. 1.9
C. 2.1
D. 2.9
Question 6
Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x - 3} ) u\sing the quotient rule.
A. \( \frac{-2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )
B. \( \frac{2x + 5}{\( 2x^2 + 5x - 3 \ \)^2} )
C. \( \frac{2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )
D. \( \frac{-2x - 5}{\( 2x^2 + 5x - 3 \ \)^2} )
Question 7
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the value of \( lim_{x \to 2} f\( x \ \) ) u\sing L'Hopital's rule.
A. 4
B. 2
C. 0
D. \infty
Question 8
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
A. \left\( x+2\right \)^2 + \left\( y-3\right \)^2 = 16
B. \left\( x-2\right \)^2 + \left\( y+3\right \)^2 = 16
C. \left\( x+2\right \)^2 + \left\( y-3\right \)^2 = 25
D. \left\( x-2\right \)^2 + \left\( y+3\right \)^2 = 25
Question 9
Solve for ( x ) in the equation \( egin{vmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{vmatrix} = 0 \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 10
A circle has a radius of 4 cm. Find the area of the circle.
A. \pi r^2
B. 2\pi r
C. \pi r
D. 2\pi r^2
Question 11
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x - 1 \) with common ratio \( r = -\frac{1}{2} \).
A. \( 2x^2 + 3x - 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \frac{1}{32} + \frac{1}{64} - \frac{1}{128} \)
B. \( 2x^2 + 3x - 1 + \frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + \frac{1}{32} - \frac{1}{64} + \frac{1}{128} \)
C. \( 2x^2 + 3x - 1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{8} - \frac{1}{16} - \frac{1}{32} - \frac{1}{64} - \frac{1}{128} \)
D. \( 2x^2 + 3x - 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} \)
Question 12
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. \left\{0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}\right\}
B. \left\{0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi\right\}
C. \left\{0, \pi, 2\pi\right\}
D. \left\{\frac{\pi}{2}, \frac{3\pi}{2}\right\}
Question 13
A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. What is the mean of the data?
A. 8
B. 10
C. 12
D. 14
Question 14
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 15
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 13
B. 14
C. 15
D. 16

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