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POST UTME ESUT 2022 Mathematics | Objective

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Question 1 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio $3/2$.

Correct A. 3125

B. 3126

C. 3127

D. 3128

Correct Answer: A

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Question 2 View Details

Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 7 \\ 10 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}

Correct Answer: A

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Question 3 View Details

Find the derivative of the function f(x) = $\frac{1}{x^2 + 1}$\)\) using the chain rule.

Correct A. -$\frac{2x}{x^2 + 1$ ^2}\)\)

B. $\frac{2x}{x^2 + 1$ ^2}\)\)

C. -$\frac{1}{x^2 + 1$ ^2}\)\)

D. $\frac{1}{x^2 + 1$ ^2}\)\)

Correct Answer: A

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Question 4 View Details

Solve the trigonometric equation \$\sin^2$ x + \$\cos^2$ $x = 1$ for x in the interval [0, 2\pi].

Correct A. $\frac{\pi}{4}$\)

B. $\frac{\pi}{2}$\)

C. $\frac{3\pi}{4}$\)

D. \pi

Correct Answer: A

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Question 5 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.

Correct A. $\frac{128\pi}{3}$\)

B. $\frac{64\pi}{3}$\)

C. $\frac{32\pi}{3}$\)

D. $\frac{16\pi}{3}$\)

Correct Answer: A

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Question 6 View Details

Solve the inequality $\frac{x^2 - 4}{x + 2} \geq 0) for x in \(-\infty, -2 \\() for x in (-\ cup -2, \infty$ ).

A. $-2, -1$ ∪ (1, ∞)

B. $-∞, -2$ \cup $-2, 1$\)

Correct C. $-∞, -2$ ∪ (1, ∞)

D. $-2, 1$

Correct Answer: C

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Question 7 View Details

Find the value of ( x ) that satisfies the equation $\log_{10} x^2 \$$= 4 ).$

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 8 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$.

A. $-2, 0$

Correct B. $-∞, -2$ ∪ (0, ∞)

C. $-∞, 0$ ∪ (2, ∞)

D. $-∞, -2$ ∪ (2, ∞)

Correct Answer: B

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Question 9 View Details

A bakery sells a total of 250 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

A. 50

Correct B. 75

C. 100

D. 125

Correct Answer: B

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Question 10 View Details

A car travels from city A to city B at an average speed of 60 $(km/h$\). On the return trip, the car travels at an average speed of 40 $km/h\\((km/h). On the return trip, the car travels at an average speed of 40$. What is the average speed of the car for the entire trip?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 11 View Details

Find the value of x in the equation $\sin^2 x + \cos^2 x = 1$ if $$1x = \frac{3}{5}$.

A. 0

Correct B. $\frac{\pi}{4}$\)

C. $\frac{\pi}{2}$\)

D. $\frac{3\pi}{4}$\)

Correct Answer: B

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Question 12 View Details

A circle has equation $x - 2 \$^2 + $y - 3)^\(2 = 4$ ). Find the equation of the \\\$(()^(2$ = 4\)\tangent line at point ( (3, 5) ).

Correct A. $y = -x + 7$

B. $y = x + 1$

C. $y = -x - 3$

D. $y = x - 2$

Correct Answer: A

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Question 13 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using the chain rule.

Correct A. -$\frac{2x}{x^2 + 1$ ^2}\)\)

B. $\frac{2x}{x^2 + 1$ ^2}\)\)

C. -$\frac{1}{x^2 + 1$ ^2}\)\)

D. $\frac{1}{x^2 + 1$ ^2}\)\)

Correct Answer: A

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Question 14 View Details

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 8, 12, 15, 10, and 5, respectively. Find the mean score of the class.

A. 10

Correct B. 12

C. 15

D. 18

Correct Answer: B

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Question 15 View Details

Solve the equation $x^3 - 6x^2 + 11x - 6 = 0$ using the rational root theorem.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 512\pi $cm^3$

Correct B. 768\pi $cm^3$

C. 1024\pi $cm^3$

D. 1280\pi $cm^3$

Correct Answer: B

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Question 17 View Details

A circle passes through the points (2,3), (4,5), and (6,7). Find the equation of the circle.

Correct A. $x - 4$^2 + $y - 3$^$2 = 5$

B. $x - 3$^2 + $y - 4$^$2 = 5$

C. $x - 5$^2 + $y - 3$^$2 = 5$

D. $x - 3$^2 + $y - 5$^$2 = 5$

Correct Answer: A

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Question 18 View Details

The mean of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.

A. 45

Correct B. 50

C. 55

D. 60

Correct Answer: B

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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 equation of the line passing through the points (2,3) and (4,5).

Correct A. $y =$$\frac{2}{3}$\) x + 1

B. $y =$$\frac{3}{2}$\) x - 1

C. $y =$$\frac{4}{3}$\) x - 1

D. $y =$$\frac{5}{4}$\) x + 1

Correct Answer: A

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Question 21 View Details

A sequence is defined by the recurrence relation a_$n = 2a$_{n-1} + 1, with $a_1 = 3$. Find the value of a_5.

A. 31

B. 32

Correct C. 33

D. 34

Correct Answer: C

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Question 22 View Details

Solve the equation \$(x^2 + 4x - 5$$= 0.$\)

Correct A. x = -5 or $x = 1$

B. x = -1 or $x = 5$

C. x = -1 or x = -5

D. $x = 1$ or $x = 5$

Correct Answer: A

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Question 23 View Details

Find the surface area of the sphere with radius 4cm.

A. 256\pi $cm^2$

Correct B. 512\pi $cm^2$

C. 768\pi $cm^2$

D. 1024\pi $cm^2$

Correct Answer: B

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Question 24 View Details

A set of 5 numbers has a mean of 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.

A. 45

B. 50

C. 55

D. 60

Correct Answer: VIEW ANSWER

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Question 25 View Details

Find the volume of the solid formed by rotating the region bounded by the curves $y = x\^2$ and $y = 4 - x\^2$ about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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