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POST UTME IGBINEDION UNIVERSITY 2022 Mathematics | Objective

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Question 1

Determine the value of $\frac{d}{dx} \left$ \frac{1}{x^2 + 1} \right $$ u\sing 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

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

Find the equation of the line pas\sing 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

Solve the system of equations $\begin{cases} x + y = 4 \ x - 2y = -3 \end{cases}$ u\sing 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

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

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

Find the equation of the circle pas\sing 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

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

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

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

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

A binary operation $* \cdot *$ on the set \{1, 2, 3, 4, 5\} is defined as follows: \begin{align*} 1 \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 \cdot b = 12 $, 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

A rec\tangular 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

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

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

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 mis\sing number in the data set?

Correct A. 22

B. 20

C. 18

D. 16

Correct Answer: A

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Question 17

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $ u\sing 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

A rec\tangular 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

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

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

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

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

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

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

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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