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POST UTME IGBINEDION UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Determine the value of \(\frac{d}{dx} \left \frac{1}{x^2 + 1} \right\)\) using the quotient rule.

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

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

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

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

Correct Answer: A

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Question 2 View Details

Solve the inequality \(|x - 2| > 3\).

Correct A. \(-∞, -1\) ∪ (4, ∞)

B. \(-∞, 1\) ∪ (4, ∞)

C. \(-∞, -1\) ∪ (2, 4)

D. \(-∞, 1\) ∪ (2, 4)

Correct Answer: A

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Question 3 View Details

Find the equation of the line passing through the points \(-2, 3\)\) and \(1, -2\)\).

Correct A. \(y = -\)\(\frac{5}{3}\)\) x + \(\frac{13}{3}\)\)

B. \(y =\)\(\frac{5}{3}\)\) x - \(\frac{13}{3}\)\)

C. \(y = -\)\(\frac{1}{5}\)\) x + \(\frac{13}{5}\)\)

D. \(y =\)\(\frac{1}{5}\)\) x - \(\frac{13}{5}\)\)

Correct Answer: A

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Question 4 View Details

Solve the system of equations \(\begin{cases} x + y = 4 \ x - 2y = -3 \end{cases}\) using substitution.

Correct A. (x,\(y) = (1\), 3)

B. (x,\(y) = (3\), 1)

C. (x,\(y) = (1\), 1)

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

Correct Answer: A

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Question 5 View Details

A circle has a radius of 4 cm and a center at the origin. Find the equation of the circle.

Correct A. \(x^2\) + \\((y^2\)\(= 16\)\)

B. \(x^2\) + \\((y^2\)\(= 32\)\)

C. \(x - 0\)^2 + \(y - 0\)^\(2 = 16\)

D. \(x - 0\)^2 + \(y - 0\)^\(2 = 32\)

Correct Answer: A

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Question 6 View Details

Solve the inequality \(\frac{x}{x+1} > \frac{1}{x+1}\) for x in mathbb{R} setminus {-1}.

A. \(x > 0\)

B. \(x < -1\)

Correct C. \(x > -1\)

D. \(x < 0\)

Correct Answer: C

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Question 7 View Details

Find the equation of the circle passing through the points ( (1, 2) ) and \(-2, 3 \\) ).

Correct A. \(x^2 + y^2 - 4x + 2y - 4 = 0\)

B. \(x^2 + y^2 + 4x - 2y - 4 = 0\)

C. \(x^2 + y^2 - 2x - 4y - 4 = 0\)

D. \(x^2 + y^2 + 2x + 4y - 4 = 0\)

Correct Answer: A

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Question 8 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix}\).

A. 2

Correct B. -2

C. 4

D. -4

Correct Answer: B

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Question 9 View Details

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

A. \(x = 0\)

Correct B. \(x = -2\)

C. \(x = 2\)

D. \(x = -4\)

Correct Answer: B

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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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Question 11 View Details

In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the other two sides is 3:4, what is the area of the triangle?

Correct A. 6 \(cm^2\)

B. 8 \(cm^2\)

C. 10 \(cm^2\)

D. 12 \(cm^2\)

Correct Answer: A

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Question 12 View Details

A binary operation \(* \cdot *\) on the set {1, 2, 3, 4, 5\} is defined as follows: \begin{align*} 1 \\({1, 2, 3, 4, 5} is defined as follows: \cdot 1 &= 1, \quad 1 \cdot \(2 = 2\), \quad 1 \cdot \(3 = 3\), \quad 1 \cdot \(4 = 4\), \quad 1 \cdot \(5 = 5\), \quad 2 \cdot \(1 = 2\), \quad 2 \cdot \(2 = 4\), \quad 2 \cdot \(3 = 6\), \quad 2 \cdot \(4 = 8\), \quad 2 \cdot \(5 = 10\), \quad 3 \cdot \(1 = 3\), \quad 3 \cdot \(2 = 6\), \quad 3 \cdot \(3 = 9\), \quad 3 \cdot \(4 = 12\), \quad 3 \cdot \(5 = 15\), \quad 4 \cdot \(1 = 4\), \quad 4 \cdot \(2 = 8\), \quad 4 \cdot \(3 = 12\), \quad 4 \cdot \(4 = 16\), \quad 4 \cdot \(5 = 20\), \quad 5 \cdot \(1 = 5\), \quad 5 \cdot \(2 = 10\), \quad 5 \cdot \(3 = 15\), \quad 5 \cdot \(4 = 20\), \quad 5 \cdot \(5 = 25\). end{align*} If \(a \\\(end{align*} If (a \cdot b = 12), what is the value of \(b \\\(), what is the value of (b \cdot a\)?

Correct A. 12

B. 15

C. 20

D. 25

Correct Answer: A

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Question 13 View Details

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the box?

A. 48 \(cm^3\)

Correct B. 72 \(cm^3\)

C. 96 \(cm^3\)

D. 120 \(cm^3\)

Correct Answer: B

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Question 14 View Details

A histogram of the scores of 10 students on a test is shown below. What is the mean score of the students?

A. 40

Correct B. 42.5

C. 45

D. 50

Correct Answer: B

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Question 15 View Details

A 3x3 matrix is given by \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}. What is the determinant of the matrix?

A. 0

B. 3

C. 6

D. 9

Correct Answer: VIEW ANSWER

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Question 16 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the missing number in the data set?

Correct A. 22

B. 20

C. 18

D. 16

Correct Answer: A

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Question 17 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula. What is the value of x?

A. -2

Correct B. -3

C. -1

D. 1

Correct Answer: B

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Question 18 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?

Correct A. 30

B. 60

C. 90

D. 120

Correct Answer: A

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Question 19 View Details

Find the determinant of the 3x3 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 20 View Details

A histogram is a graphical representation of a frequency distribution. What is the shape of the histogram for the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20?

A. Symmetric

Correct B. Skewed

C. Bell-shaped

D. Uniform

Correct Answer: B

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Question 21 View Details

Let X be a random variable with probability density function f(x) = \(\frac{1}{2}e^{-|x|}\) for -∞\(< x\)< ∞. Find the probability that X is greater than 1.

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 22 View Details

Find the derivative of the function (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'\((x) =\)\(\frac{1}{x^2 + 1\) ^2}\)\) )

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

Correct Answer: A

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Question 23 View Details

Solve the system of linear equations \(egin{cases} x + 2y - z = 1 \ 2x - 3y + 4z = -2 \ 3x + y - 2z = 3 \end{cases}\).

Correct A. [1, 2, 3]

B. [2, 3, 1]

C. [3, 1, 2]

D. [1, 3, 2]

Correct Answer: A

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Question 24 View Details

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 25 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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