Exam Body

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POST UTME UNN 2018 Mathematics | Objective

Are you preparing for POST UTME UNN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

A. 48\pi

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 2

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

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

B. x \in \( -\infty, -3 \) \cup [1, \infty)

C. x \in \( -\infty, 1 \) \cup [3, \infty)

D. x \in \( -\infty, -3 \) \cup [1, \infty)

Correct Answer: A

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Question 3

A circle is inscribed in a square of side length 10 cm. Find the area of the shaded region.

A. 50\pi

Correct B. 100\pi

C. 200\pi

D. 250\pi

Correct Answer: B

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Question 4

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x + 1

D. y = x - 1

Correct Answer: A

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Question 5

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

Correct A. 8\sqrt{3}

B. 6\sqrt{3}

C. 8\sqrt{2}

D. 6\sqrt{2}

Correct Answer: A

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Question 6

A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.

Correct A. 1/4

B. 1/2

C. 3/4

D. 1

Correct Answer: A

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Question 7

Solve the matrix equation AX = B, where A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}, X = \begin{bmatrix} x \\ y \end{bmatrix}, and B = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 1 \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 8

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 9

Solve the trigonometric equation \sin(x) = \cos(x) for 0 ≤ x ≤ 2π.

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

B. \frac{3\pi}{4}

C. \frac{5\pi}{4}

D. \frac{7\pi}{4}

Correct Answer: A

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Question 10

Find the solution to the quadratic equation x^2 + 5x + 6 = 0.

Correct A. \begin{bmatrix} -2 \\ -3 \end{bmatrix}

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

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

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

Correct Answer: A

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Question 11

Determine the mean of the following dataset: {1, 3, 5, 7, 9}.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 12

Find the volume of the solid formed by revolving the region bounded by y = x^2 and the x-axis about the x-axis.

Correct A. \frac{4\pi}{3}

B. \frac{8\pi}{3}

C. \frac{16\pi}{3}

D. \frac{32\pi}{3}

Correct Answer: A

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Question 13

Solve the differential equation \frac{dy}{dx} = \frac{y}{x} u\sing the chain rule.

Correct A. y = \ln|x|

B. y = \ln|x^2|

C. y = \ln|x^3|

D. y = \ln|x^4|

Correct Answer: A

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Question 14

Find the equation of the \tangent line to the curve y = x^2 at the point (1, 1).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = 3x - 1

D. y = 3x + 1

Correct Answer: A

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Question 15

Determine the number of solutions to the equation x^2 + 2x + 2 = 0.

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 16

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

A. 24πcm^3

Correct B. 48πcm^3

C. 96πcm^3

D. 192πcm^3

Correct Answer: B

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Question 17

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 80?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 18

Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 19

Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.

Correct A. x = -1 ± √2

B. x = 1 ± √2

C. x = -1 ± √3

D. x = 1 ± √3

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 = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 21

Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X is greater than 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 23

Find the value of x in the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 24

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

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 25

Find the value of y in the equation \( y = 2x + 3 \), given that x = 2.

Correct A. 7

B. 5

C. 3

D. 1

Correct Answer: A

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