POST UTME AAUA 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 3120
B. 3220
C. 3320
D. 3420
Question 2
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. f'(x) = 2 \sin x \cos x
B. f'(x) = 2 \sin x
C. f'(x) = 2 \cos x
D. f'(x) = 2 \sin x \cos x
Question 3
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the prism.
A. 2(5 × 3) + 2(5 × 2) + 2(3 × 2)
B. 2(5 × 3) + 2(5 × 2) + 2(3 × 2) + 2(5 × 3)
C. 2(5 × 3) + 2(5 × 2) + 2(3 × 2)
D. 2(5 × 3) + 2(5 × 2) + 2(3 × 2) + 2(5 × 3)
Question 4
Find the derivative of the function ( f(x) = \sqrt{2x + 1} ) u\sing the chain rule.
A. 1/√\( 2x + 1 \)
B. 1/\( 2√\( 2x + 1 \ \))
C. 1/\( 2√\( 2x + 1 \ \)) * (2)
D. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)
Question 5
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 6
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 7
Solve the equation \( 2^x + 3^x = 5^x \).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 8
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 9
Solve for x in the equation \(\log_{10}\( x^2 \) = 4\).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \frac{1}{2}.
A. 1.999
B. 2.000
C. 2.001
D. 2.002
Question 11
Determine the volume of the frustum of a cone with height 12 cm, lower base radius 6 cm, and upper base radius 4 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 96\pi cm^3
D. 128\pi cm^3
Question 12
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 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)
D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
Question 14
A rec\tangular solid has dimensions 6 cm, 8 cm, and 10 cm. Find the surface area of the solid.
A. 240 cm^2
B. 320 cm^2
C. 400 cm^2
D. 480 cm^2
Question 15
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

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