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POST UTME NOUN 2022 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation \(\frac{1}{2}x + 5 = \frac{3}{4}x - 3\)

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 2 View Details

Solve for x in the inequality \(2x - 5 > 3x + 2\)

A. -1

Correct B. 1

C. 3

D. 5

Correct Answer: B

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Question 3 View Details

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... )

Correct A. 120

B. 150

C. 180

D. 200

Correct Answer: A

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Question 4 View Details

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

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 5 View Details

Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) )

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 6 View Details

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

A. \(y = 2x - 1\)

Correct B. \(y = 2x + 1\)

C. \(y = x + 2\)

D. \(y = x - 2\)

Correct Answer: B

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Question 7 View Details

Solve the inequality \(2x^2 + 5x - 3 \geq 0\) using the quadratic formula.

Correct A. x \leq -1 \text{ or } x \geq \(\frac{3}{2}\)\)

B. x \leq -1 \text{ or } x \leq \(\frac{3}{2}\)\)

C. x \geq -1 \text{ or } x \geq \(\frac{3}{2}\)\)

D. x \geq -1 \text{ or } x \leq \(\frac{3}{2}\)\)

Correct Answer: A

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Question 8 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. \(\frac{1}{3}\)\) \pi \(4^2 + 2^2 + 4 \cdot 4 \cdot 2\) (6)

B. \(\frac{1}{3}\)\) \pi \(4^2 + 2^2 + 4 \cdot 4 \cdot 2\) (12)

C. \(\frac{1}{3}\)\) \pi \(4^2 + 2^2 + 4 \cdot 4 \cdot 2\) (18)

D. \(\frac{1}{3}\)\) \pi \(4^2 + 2^2 + 4 \cdot 4 \cdot 2\) (24)

Correct Answer: A

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Question 9 View Details

Solve the system of equations \(x + y = 4\) and \(x - 2y = -3\) using matrices.

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 1 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 7 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 3 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 5 \end{bmatrix}

Correct Answer: A

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Question 10 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. \(x - 3\)^2 + \(y - 4\)^\(2 = 30\)

C. \(x - 3\)^2 + \(y - 4\)^\(2 = 35\)

D. \(x - 3\)^2 + \(y - 4\)^\(2 = 40\)

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 96\pi \(cm^3\)

D. 192\pi \(cm^3\)

Correct Answer: B

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Question 12 View Details

Solve the inequality \(\log_2 x^2 - 4\)\(> 2\)\).

Correct A. \(x > 2\)

B. \(x < -2\)

C. \(x > 4\)

D. \(x < -4\)

Correct Answer: A

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Question 13 View Details

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

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

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

C. \(y = 2x - 3\)

D. \(y = 2x + 3\)

Correct Answer: A

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Question 14 View Details

A set of 5 consecutive integers has a median of 8. Find the sum of the integers.

A. 120

Correct B. 125

C. 130

D. 135

Correct Answer: B

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Question 15 View Details

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 8 cm

Correct B. 6\sqrt{5} cm

C. 8\sqrt{5} cm

D. 10 cm

Correct Answer: B

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Question 16 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard deviation is 6 cm, calculate the standard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 17 View Details

In a set of consecutive integers, the sum of the first and last term is 51. If the sum of the second and second last term is 47, find the sum of the first and second term.

A. 23

Correct B. 24

C. 25

D. 26

Correct Answer: B

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Question 18 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 80?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 19 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 10 terms of the sequence.

A. 110

B. 120

Correct C. 130

D. 140

Correct Answer: C

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Question 20 View Details

A geometric progression has a first term of 2 and a common ratio of 3. Find the sum of the first 5 terms of the progression.

A. 121

B. 122

Correct C. 123

D. 124

Correct Answer: C

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Question 21 View Details

In a random sample of 100 students, the mean height is 175 cm with a standard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.5

D. 0.8413

Correct Answer: A

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Question 22 View Details

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

Correct A. -2

B. -1

C. 0

D. 2

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

Evaluate the definite integral \(\int_0^1 x^2 dx\).

Correct A. \(\frac{1}{3}\)\)

B. \(\frac{1}{2}\)\)

C. \(\frac{2}{3}\)\)

D. \(\frac{3}{4}\)\)

Correct Answer: A

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Question 25 View Details

Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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