POST UTME AAUA 2023 Mathematics | Objective

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Question 1 View Details
A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.
A. 2.5 cm
Correct B. 3.5 cm
C. 4.5 cm
D. 5.5 cm

Correct Answer: B

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Question 2 View Details
Solve the inequality \(\frac{x}{2}\)\) - \(3 > 7\).
Correct A. \(x > 26\)
B. \(x < 26\)
C. \(x > 16\)
D. \(x < 16\)

Correct Answer: A

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Question 3 View Details
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
Correct A. 3120
B. 3220
C. 3320
D. 3420

Correct Answer: A

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Question 4 View Details
A company produces 200 units of a product per day. If the production rate is increased by 10% per day, how many units will be produced after 5 days?
A. 1100
B. 1200
C. 1300
Correct D. 1400

Correct Answer: D

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Question 5 View Details
Find the area under the curve \(y = 2x\^2 + 3x - 1\) from \(x = 0\) to \(x = 2\).
A. 13
B. 14
Correct C. 15
D. 16

Correct Answer: C

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Question 6 View Details
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 \(cm^3\)
Correct C. 96\pi \(cm^3\)
D. 128\pi \(cm^3\)

Correct Answer: C

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Question 7 View Details
Solve for x in the equation \(\log_{10} x^2\)\(= 4\)\).
A. 10
B. 100
C. 1000
Correct D. 10000

Correct Answer: D

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Question 8 View Details
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
Correct B. 2.000
C. 2.001
D. 2.002

Correct Answer: B

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Question 9 View Details
A rectangular 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 \(cm^2\)
Correct D. 480 \(cm^2\)

Correct Answer: D

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Question 10 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. \(-\infty, -1\) \cup \(3, \infty\)
B. \(-\infty, 1\) \cup \(3, \infty\)
C. \(-\infty, -1\) \cup \(1, \infty\)
D. \(-\infty, 1\) \cup \(1, \infty\)

Correct Answer: A

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Question 11 View Details
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.5
Correct B. 0.75
C. 0.875
D. 0.9375

Correct Answer: B

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Question 12 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
A. \(-∞, -1\) ∪ (3, ∞)
B. \(-∞, -3\) ∪ (1, ∞)
Correct C. \(-∞, -1\) ∪ (1, ∞)
D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: C

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Question 13 View Details
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
Correct C. 64π/3
D. 128π/3

Correct Answer: C

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Question 14 View Details
Find the derivative of the function ( f(x) = \(\sqrt{2x + 1}\) ) using the chain rule.
A. \(1/√\)\(2x + 1\)
B. 1/\(2√ 2x + 1 \\))
Correct C. 1/\(2√ 2x + 1 \\)) * (2)
D. 1/\(2√ 2x + 1 \\)) * \(2x + 1\)

Correct Answer: C

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Question 15 View Details
Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).
Correct A. (1, 2, 3)
B. (1, 2, 6)
C. (1, 3, 6)
D. (2, 3, 6)

Correct Answer: A

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Question 16 View Details
Let ( f(x) = \(\frac{x^2 - 4}{x - 2}\)\)) ). Find the value of lim_{x \to 2} f\( x \\() ). Find the value of lim_{x to 2} f\ ) using L'Hopital's rule.
A. 4
B. 2
Correct C. 0
D. \infty

Correct Answer: C

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Question 17 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.
A. \left\(-\frac{5}{4}, \frac{3}{2} \right\)
B. \left\(-\frac{3}{2}, \frac{5}{4} \right\)
Correct C. \left\(-\infty, -\frac{3}{2} \right\) \cup \left\(\frac{5}{4}, \infty \right\)
D. \left\(-\infty, \frac{5}{4} \right\) \cup \left\(-\frac{3}{2}, \infty \right\)

Correct Answer: C

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Question 18 View Details
Find the area of the region bounded by the curves \(y = x^2 - 4x + 3\) and \(y = 2x - 3\).
Correct A. \(\frac{13}{3}\)\)
B. \(\frac{17}{3}\)\)
C. \(\frac{23}{3}\)\)
D. \(\frac{29}{3}\)\)

Correct Answer: A

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Question 19 View Details
A binary operation ( ast ) is defined as (x \\(ast y = xy + 2\)\). Find the value of \\((x ast y = xy + 2\(3 \ast 4\).
Correct A. 14
B. 16
C. 18
D. 20

Correct Answer: A

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Question 20 View Details
A set ( A ) contains the elements ( 1, 2, 3, 4, 5 ). Find the number of subsets of ( A ) that contain exactly two elements.
Correct A. 10
B. 12
C. 15
D. 20

Correct Answer: A

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Question 21 View Details
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
Correct B. 1.9
C. 2.1
D. 2.9

Correct Answer: B

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Question 22 View Details
A curve is defined by the equation (y = 2x\^2 + 5x - 3\). Find the area under the curve between \\((y = 2x^2 + 5x - 3\(x = 0\) and \(x = 2\).
A. 13
B. 15
Correct C. 17
D. 19

Correct Answer: C

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Question 23 View Details
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
Correct C. 12
D. 14

Correct Answer: C

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Question 24 View Details
A polynomial function is defined by f(x) = \((x^3 - 2x^2 + x - 1\)\). Find the value of f\(-1\\((x^3 - 2x^2 + x - 1). Find the value of f\).
Correct A. -3
B. -1
C. 1
D. 3

Correct Answer: A

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Question 25 View Details
A set of data has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected value from the set is greater than 12?
A. 0.25
B. 0.5
Correct C. 0.75
D. 0.9

Correct Answer: C

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