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POST UTME OSUSTECH 2024 Mathematics | Objective

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Question 1

Determine the volume of the frustum of a cone with a height of 6 units, a lower base radius of 4 units, and an upper base radius of 2 units.

Correct A. 24π

B. 48π

C. 96π

D. 192π

Correct Answer: A

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Question 2

Solve for x in the equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 4 \end{bmatrix} \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 3

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 4

Convert the binary number 1010 to decimal.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 5

In the circuit below, what is the equivalent resis\tance between points A and B?

A. 2Ω

B. 4Ω

Correct C. 6Ω

D. 8Ω

Correct Answer: C

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)

Correct Answer: A

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Question 7

Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).

Correct A. \( x = 10^4 \)

B. \( x = 10^2 \)

C. \( x = 10^{-4} \)

D. \( x = 10^{-2} \)

Correct Answer: A

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Question 8

Find the derivative of the function \( y = \sin \( 2x \ \) ) u\sing the chain rule.

Correct A. \( \frac{d}{dx} \( \sin (2x \ \) ) = 2 \cos (2x) )

B. \( \frac{d}{dx} \( \sin (2x \ \) ) = \cos (2x) )

C. \( \frac{d}{dx} \( \sin (2x \ \) ) = 2 \sin (2x) )

D. \( \frac{d}{dx} \( \sin (2x \ \) ) = \sin (2x) )

Correct Answer: A

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Question 9

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. \( inom{5}{2} = 10 \)

B. \( inom{5}{3} = 10 \)

C. \( inom{5}{4} = 5 \)

D. \( inom{5}{1} = 5 \)

Correct Answer: A

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Question 10

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

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 11

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

A. 12143

Correct B. 12145

C. 12147

D. 12149

Correct Answer: B

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Question 12

Solve the system of linear equations u\sing matrices: \begin{align*} x + y + z &= 6 \ 2x + 3y - z &= 2 \ 3x - 2y + z &= 4 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}

D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}

Correct Answer: A

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Question 13

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 1/2

B. 1/3

C. 2/3

D. 3/4

Correct Answer: A

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Question 14

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 1 \)

D. \( x = 2 \)

Correct Answer: A

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Question 15

Find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \) u\sing the power rule.

Correct A. \( f'(x) = 6x + 2 \)

B. \( f'(x) = 3x^2 + 2 \)

C. \( f'(x) = 6x - 2 \)

D. \( f'(x) = 3x^2 - 2 \)

Correct Answer: A

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Question 16

Determine the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{8} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

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

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 18

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 0 \) ∪ (1, ∞)

C. \( -∞, -2 \) ∪ (2, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 19

Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).

Correct A. \frac{24}{25}

B. \frac{16}{25}

C. \frac{20}{25}

D. \frac{12}{25}

Correct Answer: A

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Question 20

A binary operation ( ast ) is defined as \( a ast b = ab + 2 \). Find the value of ( 3 ast 4 ).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 21

A geometric sequence has a common ratio of 2 and the first term is 3. If the sum of the first four terms is 67, find the sum of the next three terms.

Correct A. 336

B. 337

C. 338

D. 339

Correct Answer: A

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Question 22

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

Correct A. \frac{160 \pi}{3}

B. \frac{160 \pi}{2}

C. \frac{160 \pi}{1}

D. \frac{160 \pi}{4}

Correct Answer: A

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Question 23

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

Correct A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{1}{2}

D. \frac{2}{3}

Correct Answer: A

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Question 24

Solve the inequality \frac{x-2}{x+1} > 0.

Correct A. x > 2 or x < -1

B. x > 2 and x < -1

C. x < 2 or x > -1

D. x < 2 and x > -1

Correct Answer: A

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Question 25

Find the mean of the numbers 2, 4, 6, 8, 10.

Correct A. 6

B. 7

C. 8

D. 9

Correct Answer: A

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