Exam Body

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Subject

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POST UTME AAUA 2023 Mathematics | Objective

Are you preparing for POST UTME AAUA exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 2

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

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

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

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

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

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

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

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

Correct D. 480 cm^2

Correct Answer: D

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Question 10

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

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

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

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

Find the derivative of the function ( f(x) = \sqrt{2x + 1} ) u\sing the chain rule.

A. 1/√\( 2x + 1 \)

B. 1/\( 2√\( 2x + 1 \ \))

Correct C. 1/\( 2√\( 2x + 1 \ \)) * (2)

D. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)

Correct Answer: C

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Question 15

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

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

Correct C. 0

D. \infty

Correct Answer: C

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Question 17

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.

A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)

B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)

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

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

A binary operation ( ast ) is defined as \( x \ast y = xy + 2 \). Find the value of \( 3 \ast 4 \).

Correct A. 14

B. 16

C. 18

D. 20

Correct Answer: A

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Question 20

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

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

A curve is defined by the equation y = 2x^2 + 5x - 3. Find the area under the curve between x = 0 and x = 2.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 23

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

A polynomial function is defined by f(x) = x^3 - 2x^2 + x - 1. Find the value of f\( -1 \).

Correct A. -3

B. -1

C. 1

D. 3

Correct Answer: A

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Question 25

A set of data has a mean of 10 and a s\tandard 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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