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POST UTME NOUN 2018 Mathematics | Objective

Are you preparing for POST UTME NOUN 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 area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ - left$ \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right $ )

B. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + left$ \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right $ )

C. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ - left$ \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right $ + \frac{1}{2} )

D. $ \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ $ + left$ \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right $ - \frac{1}{2} )

Correct Answer: A

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Question 2

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. $ \frac{1}{6} $

B. $ \frac{1}{3} $

C. $ \frac{1}{2} $

Correct D. $ \frac{2}{3} $

Correct Answer: D

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Question 3

Solve the equation $ x^2 + 4x + 4 = 0 $.

Correct A. $ x = -2 $

B. $ x = 2 $

C. $ x = -1 $

D. $ x = 1 $

Correct Answer: A

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Question 4

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 = 4 )

C. $ x - 2 \ $^2 + $ y - 3 $^2 = 9 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 25 )

Correct Answer: A

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Question 5

A company produces two products, A and B. The profit from the sale of one unit of product A is ₦150, and the profit from the sale of one unit of product B is ₦200. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. ₦20,000

B. ₦25,000

Correct C. ₦30,000

D. ₦35,000

Correct Answer: C

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Question 6

In a probability experiment, two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events A and B occur?

A. 0.24

Correct B. 0.48

C. 0.64

D. 0.76

Correct Answer: B

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Question 7

Find the area under the curve y = 3x^2 + 2x - 5 from x = 0 to x = 2.

A. 26

B. 30

Correct C. 34

D. 38

Correct Answer: C

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Question 8

In a circle with center O and radius 6, what is the length of the arc intercepted by a central angle of 60 degrees?

A. 3.14

Correct B. 6.28

C. 9.42

D. 12.56

Correct Answer: B

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Question 9

Solve the trigonometric equation $ 2\sin^2 x + 3\cos x - 1 = 0 $ for 0 \leq x \leq 2\pi.

A. \frac{\pi}{6}

B. \frac{\pi}{4}

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

D. \frac{\pi}{2}

Correct Answer: C

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Question 10

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 + 2

D. y = x - 2

Correct Answer: A

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Question 11

A random sample of 16 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the probability that a randomly selected student from this population has a height greater than 180 cm.

A. 0.2389

Correct B. 0.2618

C. 0.2915

D. 0.3191

Correct Answer: B

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Question 12

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

Correct A. \frac{2x}{$ x^2 + 1 $^2}

B. \frac{2x^2}{$ x^2 + 1 $^2}

C. \frac{2x^3}{$ x^2 + 1 $^2}

D. \frac{2x^4}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 13

Solve the equation $ 2^x + 3^x = 5^x $ for x.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 14

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle in s\tandard form.

Correct A. $ x - 0 $^2 + $ y - 0 $^2 = 16

B. $ x - 4 $^2 + $ y - 0 $^2 = 16

C. $ x - 0 $^2 + $ y - 4 $^2 = 16

D. $ x - 4 $^2 + $ y - 4 $^2 = 16

Correct Answer: A

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Question 15

Find the magnitude of the vector $ \vec{a} = \langle 3, 4 \rangle $ and the vector $ \vec{b} = \langle -2, 1 \rangle $.

Correct A. \sqrt{3^2 + 4^2} = 5

B. \sqrt{$ -2 $^2 + 1^2} = \sqrt{5}

C. \sqrt{3^2 + $ -2 $^2} = \sqrt{13}

D. \sqrt{4^2 + 1^2} = \sqrt{17}

Correct Answer: A

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Question 16

Determine the value of $\frac{d}{dx}\left$ \frac{1}{x^2+1}\right $$ u\sing 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 17

A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. What is the class width of the histogram?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 18

Solve for $x$: $\log_{10}$ x^2 $ = 4$.

Correct A. \pm 2

B. \pm 4

C. \pm 6

D. \pm 8

Correct Answer: A

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Question 19

Find the sum of the first 10 terms of the geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$.

Correct A. \frac{1023}{2048}

B. \frac{2047}{4096}

C. \frac{4095}{8192}

D. \frac{8191}{16384}

Correct Answer: A

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Question 20

A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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Question 21

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 22

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, 1 $ ∪ (3, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 3 $ ∪ (1, ∞)

Correct Answer: A

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Question 23

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 24

Solve the system of equations $ x + y = 2 $ and $ xy = 1 $.

Correct A. (1, 1)

B. $ 1, -1 $

C. $ -1, 1 $

D. $ -1, -1 $

Correct Answer: A

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Question 25

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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