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POST UTME AL-HIKMAH UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

A researcher conducted a study on the relationship between the number of hours spent studying and the final exam scores of students. The data collected is shown in the histogram below. What is the mean number of hours spent studying by the students?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 2 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 3 View Details

A company produces two products, A and B. The profit from the sale of product A is 10 per unit, and the profit from the sale of product B is15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 4 View Details

A random variable X has a probability distribution given by the following table. What is the expected value of X?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 5 View Details

A curve is defined by the equation (y = $\frac{1}{x}$\). Find the area under the curve between \$(y = frac{1}{x}\(x = 1$ and $x = 2$.

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 6 View Details

Let X be a random variable with probability density function (pdf) given by f(x) = ($\frac{1}{2}\\()x^2$\) for \$(frac{1}{2}x^2\(0 \le x$ ≤ 2. Find the probability that X is greater than 1.

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 inequality $\frac{x^2 - 4}{x^2 - 9} > 0$ for x ≠ ±3.

Correct A. $-∞, -3$ \cup $-3, 3$\)∪ (3, ∞)

B. $-∞, -3$ ∪ (3, ∞)

C. $-3, 3$

D. $-∞, 3$

Correct Answer: A

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Question 8 View Details

Find the area under the curve y = $\frac{1}{x^2}$ from $x = 1$ to $x = 2$.

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 9 View Details

Let S be the set of all real numbers x such that \$(x^2 - 4x + 3$$= 0.$\) Find the set S.

Correct A. {1, 3}

B. {-1, 3}

C. {1, -3}

D. {-1, -3}

Correct Answer: A

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Question 10 View Details

Find the sum of the infinite geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ldots$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 11 View Details

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. 0

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 12 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.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 13 View Details

Solve the equation [ \$\sin^2$ x + \$\cos^2$ $x = 1$ ] for [ x ].

A. 0

B. $\frac{\pi}{2}$\)

Correct C. $\frac{\pi}{4}$\)

D. $\frac{\pi}{6}$\)

Correct Answer: C

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Question 14 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, find P$A \cap B$.

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 15 View Details

Solve the quadratic equation [ \$(x^2 + 5x + 6$$= 0$\) ].

A. -2

Correct B. -3

C. 1

D. 2

Correct Answer: B

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Question 16 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

Correct A. ( 12 )

B. ( 16 )

C. ( 20 )

D. ( 24 )

Correct Answer: A

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Question 17 View Details

In the set $A = {1, 2, 3, 4, 5}$, find the number of subsets that contain exactly two elements.

A. ( 10 )

Correct B. ( 15 )

C. ( 20 )

D. ( 25 )

Correct Answer: B

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Question 18 View Details

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

A. ( 32 pi )

B. ( 64 pi )

Correct C. ( 128 pi )

D. ( 256 pi )

Correct Answer: C

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Question 19 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $x - 3 \$^2 + $y - 4$^$2 = 25$ )

B. $x - 3 \$^2 + $y - 4$^$2 = 30$ )

C. $x - 3 \$^2 + $y - 4$^$2 = 35$ )

D. $x - 3 \$^2 + $y - 4$^$2 = 40$ )

Correct Answer: A

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Question 20 View Details

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, 54, ldots ).

A. ( 5894 )

B. ( 5896 )

Correct C. ( 5898 )

D. ( 5900 )

Correct Answer: C

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Question 21 View Details

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

A. f'$(x) =$$\frac{-x}${ 1 + $x^2$ \)^{$3/2$}}\)

Correct B. f'$(x) =$$\frac{x}${ 1 + $x^2$ \)^{$3/2$}}\)

C. f'$(x) =$$\frac{1}${ 1 + $x^2$ \)^{$3/2$}}\)

D. f'$(x) =$$\frac{-1}${ 1 + $x^2$ \)^{$3/2$}}\)

Correct Answer: B

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Question 22 View Details

Solve the inequality $2x^2 + 5x - 3 > 0$ using the quadratic formula.

Correct A. x < -1 or x > $\frac{3}{2}$\)

B. x > -1 or x < $\frac{3}{2}$\)

C. x < -1 or x < $\frac{3}{2}$\)

D. x > -1 or x > $\frac{3}{2}$\)

Correct Answer: A

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Question 23 View Details

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 24 View Details

Find the determinant of the matrix $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$.

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 25 View Details

Solve the system of equations: $x + y = 4$ and $2x - y = 3$.

A. $x = 1$, $y = 3$

Correct B. $x = 2$, $y = 2$

C. $x = 3$, $y = 1$

D. $x = 4$, $y = 0$

Correct Answer: B

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