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POST UTME NOUN 2018 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 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 + \(y - 3\)^\(2 = 4\) )

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 View Details

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 View Details

In a probability experiment, two events A and B are independent. 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 View Details

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 View Details

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 View Details

Solve the trigonometric equation (2\\(sin^2\) x + 3\(1x - 1 = 0\) for 0 \\((2sin^2 x + 3\)\(1x - 1 = 0\)\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 View Details

Find the equation of the line passing 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 View Details

A random sample of 16 students from a university had a mean height of 175.5 cm with a standard 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 View Details

Find the derivative of the function \(f(x) = \frac{x^2}{x^2 + 1}\) using 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 View Details

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 View Details

A circle has a radius of 4 cm and a center at (0, 0). Find the equation of the circle in standard 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 View Details

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

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 View Details

Determine the value of \(\frac{d}{dx}\left \frac{1}{x^2+1}\right\)\) 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 17 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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