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POST UTME IGBINEDION UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME IGBINEDION UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \boxed{\( x + 2 \)^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 2

Let \( S = \{ 1, 2, 3, \ldots, n \} \). Find the sum of the first n terms of the arithmetic sequence with first term 1 and common difference 2.

Correct A. \boxed{\frac{n}{2} [2 + \( n - 1 \)2]}

B. \frac{n}{2} [1 + \( n - 1 \)2]

C. \frac{n}{2} [2 + \( n - 1 \)1]

D. \frac{n}{2} [1 + \( n - 1 \)1]

Correct Answer: A

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Question 3

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 50 and 70.

Correct A. \boxed{0.9545}

B. 0.8413

C. 0.6915

D. 0.5

Correct Answer: A

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Question 4

Solve the trigonometric equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \) for \( 0 \leq x \leq 2 \pi \).

Correct A. \boxed{x = \frac{\pi}{6}, \frac{5\pi}{6}}

B. x = \frac{\pi}{3}, \frac{2\pi}{3}

C. x = \frac{\pi}{4}, \frac{3\pi}{4}

D. x = \frac{\pi}{2}, \frac{3\pi}{2}

Correct Answer: A

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Question 5

Find the magnitude of the vector \( \vec{a} = 2 \hat{i} + 3 \hat{j} \).

Correct A. \boxed{\sqrt{13}}

B. \sqrt{5}

C. \sqrt{2}

D. \sqrt{1}

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 5x - 3} ) u\sing the quotient rule.

Correct A. \frac{-10x + 15}{\( 2x^2 + 5x - 3 \)^2}

B. \frac{10x - 15}{\( 2x^2 + 5x - 3 \)^2}

C. \frac{20x^2 - 10x + 15}{\( 2x^2 + 5x - 3 \)^2}

D. \frac{-20x^2 + 10x - 15}{\( 2x^2 + 5x - 3 \)^2}

Correct Answer: A

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Question 7

Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \frac{pi}{4}

B. \frac{3pi}{4}

C. \frac{5pi}{4}

D. \frac{7pi}{4}

Correct Answer: A

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Question 8

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).

Correct A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

B. \( x - 3 \)^2 + \( y - 2 \)^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 9

Solve the system of equations \( x + y = 2 \) and \( 2x - 3y = - 5 \) u\sing matrices.

Correct A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}

B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -1 \\ 3 \end{bmatrix}

C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ -1 \end{bmatrix}

D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -3 \\ 1 \end{bmatrix}

Correct Answer: A

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Question 10

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 7 \\ 8 & 9 & 10 \end{bmatrix} \).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 11

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 5 & 7 \end{bmatrix} \).

A. 1

B. -1

Correct C. 13

D. 21

Correct Answer: C

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Question 12

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \ \) for ( x ) in the interval \( [0, 2\pi] \).

A. 0

Correct B. \frac{\pi}{4}

C. \frac{\pi}{2}

D. \pi

Correct Answer: B

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Question 13

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. \frac{1}{4}

B. \frac{1}{2}

Correct C. \frac{2}{5}

D. \frac{3}{8}

Correct Answer: C

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Question 14

Simplify the expression \( \sqrt{\frac{16}{25}} \ \).

A. 2

Correct B. \frac{2}{5}

C. \frac{4}{5}

D. 4

Correct Answer: B

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Question 15

Find the vector \( \vec{a} \ \) such that \( \vec{a} \cdot \vec{b} = 12 \ \) and \( \vec{a} \cdot \vec{c} = 9 \ \), where \( \vec{b} = \begin{bmatrix} 2 \ 3 \end{bmatrix} \ \) and \( \vec{c} = \begin{bmatrix} 4 \ 5 \end{bmatrix} \ \).

Correct A. \begin{bmatrix} 3 \ 2 \end{bmatrix}

B. \begin{bmatrix} 4 \ 3 \end{bmatrix}

C. \begin{bmatrix} 5 \ 4 \end{bmatrix}

D. \begin{bmatrix} 6 \ 5 \end{bmatrix}

Correct Answer: A

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Question 16

In a trapezoid, the length of the shorter base is 8 cm, and the length of the longer base is 12 cm. If the height of the trapezoid is 6 cm, what is the area of the trapezoid in square centimeters?

A. 40

B. 48

Correct C. 60

D. 72

Correct Answer: C

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Question 17

A right circular cone has a radius of 4 cm and a height of 8 cm. If the volume of the cone is 32π cubic centimeters, what is the value of x in the equation \( x + 2 \)^2 = 16?

Correct A. 2

B. 4

C. 6

D. 8

Correct Answer: A

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Question 18

A s\tandard six-sided die is rolled. What is the probability that the number on the die is a multiple of 3?

Correct A. 1/6

B. 1/3

C. 1/2

D. 2/3

Correct Answer: A

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Question 19

A function f(x) is defined as f(x) = 2x^2 + 3x - 1. What is the value of f\( -2 \)?

Correct A. -11

B. -9

C. -7

D. -5

Correct Answer: A

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Question 20

A circle has a radius of 5 cm. What is the area of the circle in square centimeters?

Correct A. 25π

B. 50π

C. 75π

D. 100π

Correct Answer: A

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Question 21

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.

Correct A. 170.5 cm, 179.5 cm

B. 172.5 cm, 177.5 cm

C. 173.5 cm, 176.5 cm

D. 174.5 cm, 175.5 cm

Correct Answer: A

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Question 22

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

Correct A. \[f'(x) = \frac{2x}{x^2 + 1} - \frac{2x \log\( x^2 \)}{\( x^2 + 1 \)^2}\]

B. \[f'(x) = \frac{2x}{x^2 + 1} + \frac{2x \log\( x^2 \)}{\( x^2 + 1 \)^2}\]

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

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

Correct Answer: A

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Question 23

A random variable X has a probability distribution given by \[P\( X = x \) = \begin{cases} 0.2 & x = 1 \ 0.3 & x = 2 \ 0.5 & x = 3 \ 0.1 & x = 4 \ 0.1 & x = 5 \ \end{cases}\] Find the probability that X is greater than 3.

A. 0.4

B. 0.5

Correct C. 0.6

D. 0.7

Correct Answer: C

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Question 24

Solve the system of linear equations \[\begin{align*} x + y + z &= 6 \ 2x + 3y + z &= 11 \ x + 2y + 3z &= 7 \ \end{align*}\] u\sing matrices.

Correct A. \[\begin{align*} x &= 1 \ y &= 2 \ z &= 3 \ \end{align*}\]

B. \[\begin{align*} x &= 2 \ y &= 1 \ z &= 3 \ \end{align*}\]

C. \[\begin{align*} x &= 3 \ y &= 1 \ z &= 2 \ \end{align*}\]

D. \[\begin{align*} x &= 1 \ y &= 3 \ z &= 2 \ \end{align*}\]

Correct Answer: A

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Question 25

Find the equation of the circle with center (2, 3) and radius 4.

Correct A. \[\( x - 2 \)^2 + \( y - 3 \)^2 = 16\]

B. \[\( x - 3 \)^2 + \( y - 2 \)^2 = 16\]

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

D. \[\( x - 3 \)^2 + \( y - 3 \)^2 = 16\]

Correct Answer: A

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