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POST UTME AL-HIKMAH UNIVERSITY 2019 Mathematics | Objective

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Question 1

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

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

Solve the system of equations u\sing 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

Find the mean and s\tandard 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

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

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 $ x = 2 $ about the x-axis.

A. 4π

B. 8π

Correct C. 16π

D. 32π

Correct Answer: C

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Question 7

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

A surveyor measures the dis\tance 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

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

A rec\tangular 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

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

A. 1

Correct B. 13

C. 5

D. 21

Correct Answer: B

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Question 12

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

Find the derivative of the function [ f(x) = \frac{1}{x^2 + 1} ] u\sing 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

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

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

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

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

A histogram of exam scores has a mean of 80 and a s\tandard 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

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing 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

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

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

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

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

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

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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