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POST UTME KSU 2018 Mathematics | Objective

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Question 1 View Details

Determine the value of \(int_{0}^{1} \frac{1}{x^2 + 1} dx\) using the method of substitution.

Correct A. \(\frac{\pi}{2}\)\)

B. \(\frac{\pi}{4}\)\)

C. \(\frac{\pi}{6}\)\)

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

Correct Answer: A

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Question 2 View Details

A circle has equation \(x - 1 \\)^2 + \(y - 2)^\(2 = 4\) ). Find the equation of the \\\\((()^(2\) = 4\)\tangent line at point ( (3, 5) ).

Correct A. \(y = -\)\(\frac{1}{2}\)\) x + \(\frac{13}{2}\)\)

B. \(y =\)\(\frac{1}{2}\)\) x + \(\frac{13}{2}\)\)

C. \(y = -\)\(\frac{1}{2}\)\) x + \(\frac{9}{2}\)\)

D. \(y =\)\(\frac{1}{2}\)\) x + \(\frac{9}{2}\)\)

Correct Answer: A

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Question 3 View Details

A random variable ( X ) has probability distribution \(P X = 1 \\) = \(\frac{1}{2}\)\) ) and \(P X = 2 \\) = \(\frac{1}{2}\)\) ). Find the probability that ( X ) is greater than 1.

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

B. \(\frac{1}{4}\)\)

Correct C. \(\frac{3}{4}\)\)

D. \(\frac{1}{4}\)\) + \(\frac{1}{2}\)\)

Correct Answer: C

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Question 4 View Details

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

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

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

C. f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 5 View Details

Solve the inequality \(2^x + 2^{x+1} > 2^{x+2}\).

A. \(x < -2\)

Correct B. \(x > -2\)

C. \(x < -1\)

D. \(x > -1\)

Correct Answer: B

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2\)\), the x-axis, and the line \\((y = frac{1}{2}x^2\(x = 2\) about the x-axis.

Correct A. \(\frac{16\pi}{3}\)

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

C. \(\frac{64\pi}{3}\)

D. \(\frac{128\pi}{3}\)

Correct Answer: A

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Question 7 View Details

Solve for ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. \(x = 10^2\)

Correct B. \(x = 10^4\)

C. \(x = 10^{-4}\)

D. \(x = 10^{-2}\)

Correct Answer: B

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Question 8 View Details

Find the area of the triangle formed by the points ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. ( 6 )

B. ( 12 )

Correct C. ( 18 )

D. ( 24 )

Correct Answer: C

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Question 9 View Details

Solve the system of equations \(egin{cases} x + y = 2 \ 2x - y = 3 \end{cases}\).

Correct A. \(x = 1, y = 1\)

B. \(x = 2, y = 0\)

C. \(x = 0, y = 2\)

D. \(x = -1, y = 3\)

Correct Answer: A

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Question 10 View Details

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

Correct A. ( 0 )

B. ( 1 )

C. \(-1\)

D. ( 2 )

Correct Answer: A

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Question 11 View Details

Solve the inequality (\(\frac{x-2}{x+1}\(> 0\)\) for x in \\((frac{x-2}{x+1} > 0\(-\infty, -1 \ cup -1, 2\) cup (2\), infty) ).

Correct A. \(x < -1\) or \(x > 2\)

B. \(x > -1\) and \(x < 2\)

C. \(x < -1\) or \(x = 2\)

D. \(x > -1\) and \(x > 2\)

Correct Answer: A

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Question 12 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 13 View Details

Solve the equation \(2^x + 2^{x+1} = 2^{x+2} + 2^{x+3}\).

Correct A. \(x = -1\)

B. \(x = 0\)

C. \(x = 1\)

D. \(x = 2\)

Correct Answer: A

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Question 14 View Details

Find the value of \(sum_{n = 1}^{10} n^2\).

A. ( 385 )

Correct B. ( 3850 )

C. ( 38500 )

D. ( 385000 )

Correct Answer: B

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Question 15 View Details

Solve the inequality \(\frac{x-1}{x+2} \leq 0) for x in \(-\infty, -2 \\() for x in (-\ cup -2, 1\) cup (1, infty) ).

Correct A. \(x < -2\) or \(x > 1\)

B. \(x > -2\) and \(x < 1\)

C. \(x < -2\) or \(x = 1\)

D. \(x > -2\) and \(x > 1\)

Correct Answer: A

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Question 16 View Details

Determine the mean of the following dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is increased by 2, what is the new mean?

A. 22

Correct B. 24

C. 26

D. 28

Correct Answer: B

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Question 17 View Details

A circle has a diameter of 10 cm. If a chord is drawn from the center of the circle to a point on the circumference, what is the length of the chord?

A. 5 cm

Correct B. 7.07 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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Question 18 View Details

Solve the inequality: \\((2x^2 + 5x - 3\)\(> 0.\)\) What is the solution set?

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the arithmetic progression: 2, 5, 8, 11, ...

A. 55

B. 60

Correct C. 65

D. 70

Correct Answer: C

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Question 20 View Details

A random experiment has two independent events: A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.24

Correct B. 0.36

C. 0.48

D. 0.60

Correct Answer: B

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Question 21 View Details

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 22 View Details

Find the area under the curve of the function ( f(x) = \(\frac{1}{x}\)\) ) from \(x = 1\) to \(x = 2\).

Correct A. 0.693

B. 0.693

C. 0.693

D. 0.693

Correct Answer: A

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Question 23 View Details

Solve the system of equations using matrices: \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

Correct A. \(x = 1\), \(y = 2\)

B. \(x = 2\), \(y = 3\)

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 24 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 25 View Details

Convert the \fraction \(\frac{3}{4}\) to its equivalent in base 8.

A. 3

B. 4

C. 5

Correct D. 6

Correct Answer: D

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