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POST UTME AL-HIKMAH UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Solve for 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 2 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 3 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. \(x = 2\), \(y = 1\)

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

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

Correct Answer: A

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Question 4 View Details

Find the mean and standard deviation of the data set: {1, 2, 3, 4, 5}.

A. \(mean = 3\), std \(dev = 1.414\)

Correct B. \(mean = 3\), std \(dev = 1.732\)

C. \(mean = 3\), std \(dev = 2.236\)

D. \(mean = 3\), std \(dev = 2.828\)

Correct Answer: B

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Question 5 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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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.

A. 4π

B. 8π

Correct C. 16π

D. 32π

Correct Answer: C

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Question 7 View Details

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

A. 2

B. 4

C. 8

Correct D. 16

Correct Answer: D

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Question 8 View Details

A surveyor measures the distance between two points on a straight line as 100 meters. If the angle between the line of sight and the horizontal is 60°, find the height of the point above the horizontal.

A. 50

B. 75

C. 100

Correct D. 150

Correct Answer: D

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Question 9 View Details

Find the area of the triangle with vertices ( 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 10 View Details

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. Find the volume of the box.

Correct A. 48

B. 64

C. 80

D. 96

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ] using the formula for 2x2 matrices.

A. 1

Correct B. 13

C. 5

D. 21

Correct Answer: B

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Question 12 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the die is rolled again. If the number rolled is odd, the die is rolled three more times. What is the probability that the number rolled is greater than 4?

A. \(1/3\)

B. \(1/2\)

Correct C. \(2/3\)

D. \(5/6\)

Correct Answer: C

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Question 13 View Details

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

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

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

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

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

Correct Answer: A

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Question 14 View Details

The mean of a set of numbers is 25. If the set contains 5 numbers, what is the sum of the numbers?

A. 100

Correct B. 125

C. 150

D. 175

Correct Answer: B

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Question 15 View Details

Simplify the expression [ \(\sqrt{16x^2}\)\) \cdot \(\sqrt{9x^2}\)\) \]

A. \(12x^2\)

Correct B. \(4x^2\)

C. \(6x^2\)

D. \(24x^2\)

Correct Answer: B

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Question 16 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\) for x in mathbb{R} setminus {3, -3}.

Correct A. \(-\infty, -3 \\) cup (3, infty) )

B. \(-\infty, -3 \\) cup (3, infty) cup (0, 4) )

C. \(-\infty, -3 \\) cup (3, infty) cup \(-4, 0\) )

D. \(-\infty, -3 \\) cup (3, infty) cup \(-4, 0\) cup (0, 4) )

Correct Answer: A

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Question 17 View Details

Find the area under the curve \(y = \sin^2 x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).

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

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

C. \(\frac{\pi}{2}\)

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

Correct Answer: A

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Question 18 View Details

A histogram of exam scores has a mean of 80 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 19 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 20 View Details

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. ( 25pi )

B. ( 50pi )

C. ( 75pi )

D. ( 100pi )

Correct Answer: A

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Question 21 View Details

In the complex plane, let \(z_1 = 2 - 3i\) and \(z_2 = 1 + 4i\). Find the value of \(|z_1 + z_2|\).

A. 5

B. \(\sqrt{10}\)

Correct C. \(\sqrt{26}\)

D. \(\sqrt{50}\)

Correct Answer: C

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Question 22 View Details

Find the equation of the circle with center at \(-2, 3\)\) 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 23 View Details

Solve the inequality \(\frac{2x + 1}{x - 1} > 0\).

Correct A. \(-\infty, -\frac{1}{2}\) \cup \(1, \infty\)

B. \(-\infty, -\frac{1}{2}\) \cup \(1, \infty\)

C. \(-\infty, -\frac{1}{2}\) \cup \(1, \infty\)

D. \(-\infty, -\frac{1}{2}\) \cup \(1, \infty\)

Correct Answer: A

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Question 24 View Details

Find the value of \(\int_0^1 \frac{1}{x^2 + 1} dx\).

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 25 View Details

Find the value of \(\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix}\).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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