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POST UTME IMS U 2024 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

Correct A. 0

B. 1

C. π/2

D. π

Correct Answer: A

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Question 2 View Details

Solve for y in the equation \(y = \frac{1}{2} \left x + \frac{1}{x} \right \\) ).

A. x

Correct B. \(x^2\)

C. \(x^3\)

D. \(x^4\)

Correct Answer: B

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Question 3 View Details

Find the determinant of the matrix \(egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}\).

A. 0

B. 1

Correct C. 2

D. 3

Correct Answer: C

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Question 4 View Details

A water \tank has a height of 10 meters and a base radius of 5 meters. Find the volume of water in the \tank.

A. 100π

B. 200π

Correct C. 300π

D. 400π

Correct Answer: C

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Question 5 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -2\) ∪ (2, ∞)

D. \(-∞, -4\) ∪ (4, ∞)

Correct Answer: A

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Question 6 View Details

Find the volume of the solid formed by rotating the region bounded by \(y = x^2\), \(y = 0\)\), and \(x = 2\) about the x-axis.

Correct A. \(\frac{32}{3} \pi\)

B. ( 16 pi )

C. ( 32 pi )

D. ( 64 pi )

Correct Answer: A

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Question 7 View Details

If (f(x) = \(\frac{1}{\(x^2+1}\)\)\), find \\((f(x) = frac{1}{x^2+1}\(f'(x)\) using the chain rule.

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

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

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

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

Correct Answer: A

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Question 8 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 80% of the scores lie within 2 standard deviations of the mean, what is the range of scores?

A. [50, 100]

B. [60, 110]

Correct C. [70, 120]

D. [80, 130]

Correct Answer: C

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Question 9 View Details

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

Correct A. \(x = 0, \pi/2, \pi, 3\pi/2\)

B. \(x = 0, \pi/4, \pi/2, 3\pi/4\)

C. \(x = \pi/4, \pi/2, 3\pi/4, \pi\)

D. \(x = 0, \pi/2, \pi, 3\pi/2, 2\pi\)

Correct Answer: A

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Question 10 View Details

Find the magnitude of the vector \(\vec{a} = 3\hat{i} + 4\hat{j} + 5\hat{k}\).

A. 5

B. 10

Correct C. 15

D. 20

Correct Answer: C

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Question 11 View Details

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

A. 2x

B. -2x

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

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

Correct Answer: C

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Question 12 View Details

A set 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?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 13 View Details

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

Correct A. 121

B. 122

C. 123

D. 124

Correct Answer: A

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Question 14 View Details

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

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, -3\) \cup \(1, \infty\)

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

D. \(-\infty, 1\) \cup \(3, \infty\)

Correct Answer: A

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Question 15 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.27

B. 50.28

C. 50.29

D. 50.30

Correct Answer: A

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Question 16 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17 View Details

A particle moves along the x-axis with a velocity given by ( v(x) = 2x + 5 ). Find the acceleration at \(x = 3\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 18 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19 View Details

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. \(x - 0\)^2 + \(y - 0\)^\(2 = 16\)

B. \(x - 0\)^2 + \(y - 0\)^\(2 = 4\)

C. \(x - 0\)^2 + \(y - 0\)^\(2 = 9\)

D. \(x - 0\)^2 + \(y - 0\)^\(2 = 25\)

Correct Answer: A

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Question 20 View Details

Find the value of x in the equation \(\frac{x^2 - 4x + 4}{x^2 - 4x + 3} = 1\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 21 View Details

Find the value of x in the equation \(2x^2 + 5x - 3 = 0\).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 22 View Details

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

Correct A. x < -1 or \(x > 5\)

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 equation of the circle with center \(-2, 3\) and radius 4.

Correct A. \(x + 2\)^2 + \(y - 3\)^\(2 = 16\) \)

B. \(x - 2\)^2 + \(y + 3\)^\(2 = 16\) \)

C. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\) \)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\) \)

Correct Answer: A

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Question 24 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

A. \(x =\)\(\frac{\pi}{2}\)\)

Correct B. \(x =\)\(\frac{\pi}{4}\)\)

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: B

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Question 25 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{64}{3}\)\)

B. \(\frac{32}{3}\)\)

C. \(\frac{16}{3}\)\)

D. \(\frac{8}{3}\)\)

Correct Answer: A

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