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POST UTME AAUA 2021 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$ using the quadratic formula.

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 8 View Details

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 View Details

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 View Details

A random experiment consists of two independent 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 View Details

Solve for x in the equation $$1x = \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 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

Find the equation of the line passing 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 View Details

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}\(\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 View Details

Let ( f(x) = $\frac{1}${\sqrt{1 - $x^2}}$\) ). Find the derivative of ( f(x) ) using 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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

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 View Details

Find the derivative of ( f(x) = $x^2$ \sin x ) using 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 View Details

In a triangle ABC, angle (A = 30\)°, angle $B = 90\\((A = 30)°, angle$°, 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 View Details

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 View Details

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 View Details

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 View Details

In a probability experiment, two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P($A \cap B$).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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