POST UTME AFE BABALOLA UNIVERSITY 2019 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 \\) )
B. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + 3 )
C. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) - 2 )
D. \(\frac{1}{2} \left \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \\) + 2 )

Correct Answer: A

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Question 2 View Details
Solve for ( x ) in the equation \(\sin^2 x + \cos^2 x = 1\).
Correct A. \(x = \frac{\pi}{4}\)
B. \(x = \frac{\pi}{2}\)
C. \(x = \frac{3\pi}{4}\)
D. \(x = \frac{5\pi}{4}\)

Correct Answer: A

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Question 3 View Details
Find the magnitude of the vector \(\vec{a} = egin{pmatrix} 3 \ 4 \end{pmatrix}\).
Correct A. \(\sqrt{3^2 + 4^2}\)
B. \(\sqrt{3^2 - 4^2}\)
C. \(\sqrt{3^2 + 4^2 + 5^2}\)
D. \(\sqrt{3^2 - 4^2 + 5^2}\)

Correct Answer: A

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Question 4 View Details
Solve the inequality \(x^2 - 4x - 5 > 0\).
Correct A. \(x < -1\) or \(x > 5\)
B. \(x < 1\) or \(x > 5\)
C. \(x < -1\) or \(x < 5\)
D. \(x > 1\) or \(x < 5\)

Correct Answer: A

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Question 5 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ).
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 6 View Details
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.25
Correct B. 0.5
C. 0.75
D. 1

Correct Answer: B

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Question 7 View Details
Solve the system of linear equations \(egin{cases} x + y + z = 6 \ 2x - 3y + z = 3 \ x - 2y + 3z = -2 \end{cases}\).
Correct A. \(x = 1\), \(y = 2\), \(z = 3\)
B. \(x = 2\), \(y = 1\), \(z = 3\)
C. \(x = 3\), \(y = 2\), \(z = 1\)
D. \(x = 1\), \(y = 3\), \(z = 2\)

Correct Answer: A

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Question 8 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. \(y = -2x + 1\)
D. \(y = -2x - 1\)

Correct Answer: A

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Question 9 View Details
Solve the quadratic 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 10 View Details
Find the value of \(\log_{10} 1000 \\) ).
A. 3
Correct B. 4
C. 5
D. 6

Correct Answer: B

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