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POST UTME ESUT 2022 Mathematics | Objective

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Question 1

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

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

Find the derivative of the function f(x) = \frac{1}{x^2 + 1} u\sing 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

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

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

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

A. \( -2, -1 \) ∪ (1, ∞)

B. \( -∞, -2 \) ∪ \( -2, 1 \)

Correct C. \( -∞, -2 \) ∪ (1, ∞)

D. \( -2, 1 \)

Correct Answer: C

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Question 7

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

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

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

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. 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

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

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

A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the rational root theorem.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 16

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

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

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

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 equation of the line pas\sing 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

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

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

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

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

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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