Exam Body

Year

Subject

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POST UTME AAUA 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the value of ( x ) in the equation \( 2^x + 5^x = 3^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2

Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).

A. 5

Correct B. 7

C. 9

D. 11

Correct Answer: B

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Question 3

A histogram of exam scores is shown below. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 4

Solve the inequality \( x^2 - 4x - 5 > 0 \).

Correct A. \( -\infty, -1 \) \cup \( 5, \infty \)

B. \( -\infty, 1 \) \cup \( 5, \infty \)

C. \( -\infty, -1 \) \cup \( 1, \infty \)

D. \( -\infty, 1 \) \cup \( 5, \infty \)

Correct Answer: A

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Question 5

Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + \cdots \).

Correct A. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5

B. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6

C. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7

D. 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8

Correct Answer: A

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Question 6

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 7

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 8

A histogram is constructed with a bin width of 2. If the total number of data points is 20, what is the number of bins?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 9

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

Correct A. \( 3x^2 - 4x + 3 \)

B. \( 3x^2 - 4x + 2 \)

C. \( 3x^2 - 4x - 2 \)

D. \( 3x^2 - 4x - 3 \)

Correct Answer: A

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Question 10

A random experiment consists of two indep\endent events, A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.2

Correct B. 0.4

C. 0.6

D. 0.8

Correct Answer: B

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Question 11

Solve for x in the equation \( \tan x = \frac{1}{\sqrt{3}} \) and \( 0 leq x leq \frac{pi}{2} \).

Correct A. π/6

B. π/4

C. π/3

D. π/2

Correct Answer: A

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Question 12

Find the value of k in the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} k & 0 \ 0 & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \ 9 & 6 \end{bmatrix} \).

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 13

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 14

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x + 2

D. y = x - 2

Correct Answer: A

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Question 15

A vector \( \vec{a} \) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).

Correct A. x = 4, y = 3

B. x = 3, y = 4

C. x = 4, y = 4

D. x = 3, y = 3

Correct Answer: A

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Question 16

Let ( f(x) = \frac{1}{\sqrt{1 - x^2}} ). Find the derivative of ( f(x) ) u\sing the chain rule.

Correct A. \( f'(x) = \frac{x}{\( 1 - x^2 \)^{3/2}} \)

B. \( f'(x) = \frac{-x}{\( 1 - x^2 \)^{3/2}} \)

C. \( f'(x) = \frac{1}{\( 1 - x^2 \)^{3/2}} \)

D. \( f'(x) = \frac{-1}{\( 1 - x^2 \)^{3/2}} \)

Correct Answer: A

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Question 17

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

Correct A. 0.8413

B. 0.6915

C. 0.6827

D. 0.9332

Correct Answer: A

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Question 18

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 \)

B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 \)

C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 30 \)

D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 30 \)

Correct Answer: A

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Question 19

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

Correct A. \( x < -1 \ \) or \( x > \frac{3}{2} \ \)

B. \( x < -1 \ \) or \( x < \frac{3}{2} \ \)

C. \( x > -1 \ \) or \( x < \frac{3}{2} \ \)

D. \( x > -1 \ \) or \( x > \frac{3}{2} \ \)

Correct Answer: A

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Question 20

Find the derivative of ( f(x) = x^2 \sin x ) u\sing the product rule.

Correct A. ( f'(x) = 2x \sin x + x^2 \cos x \)

B. ( f'(x) = x^2 \cos x - 2x \sin x \)

C. ( f'(x) = 2x \cos x + x^2 \sin x \)

D. ( f'(x) = x^2 \sin x - 2x \cos x \)

Correct Answer: A

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Question 21

In a triangle ABC, angle A = 30°, angle B = 90°, and side AB = 5 cm. Find the area of the triangle.

A. 10 cm²

Correct B. 15 cm²

C. 20 cm²

D. 25 cm²

Correct Answer: B

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Question 22

Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 23

Find the volume of the sphere with radius 4 cm.

A. 32π cm³

B. 64π cm³

Correct C. 128π cm³

D. 256π cm³

Correct Answer: C

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Question 24

A binary operation ∗ on the set of integers is defined as \( a ∗ b = a^2 + b^2 \). Find the value of ( 2 ∗ 3 ).

A. 13

B. 19

Correct C. 25

D. 37

Correct Answer: C

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Question 25

In a probability experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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