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POST UTME IGBINEDION UNIVERSITY 2023 Mathematics | Objective

Prepare for your exams with POST UTME IGBINEDION UNIVERSITY questions? Reviewing past/model 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.

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Question 1 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

Solve the trigonometric equation (2 \$sin^2$ x + 3 $1x - 2 = 0$ for \$(2 sin^2 x + 3$$1x - 2 = 0$$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 View Details

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 View Details

Find the derivative of the function ( f(x) = $\frac{1}{2x^2 + 5x - 3}$\)\) ) using 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 View Details

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

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

B. $\frac{3\pi}{4}$\)

C. $\frac{5\pi}{4}$\)

D. $\frac{7\pi}{4}$\)

Correct Answer: A

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Question 8 View Details

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 View Details

Solve the system of equations $x + y = 2$ and $2x - 3y = - 5$ using 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 View Details

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 View Details

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 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for ( x ) in the interval $[0, 2\\\() 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 View Details

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 View Details

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 View Details

Find the vector $\vec{a} \$ such that $\vec{a} \cdot \vec{b} = 12 \$ and $\vec{a} \cdot \vec{c} = 9$, where $\\(), 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 View Details

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 View Details

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 View Details

A standard 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 View Details

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

Correct A. -11

B. -9

C. -7

D. -5

Correct Answer: A

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Question 20 View Details

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 View Details

A random sample of 25 students from a university had a mean height of 175 cm with a standard deviation of 5 cm. If the population standard 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 View Details

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

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

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

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 View Details

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 View Details

Solve the system of linear equations $\begin{align*} x + y + z & = 6 \ 2x + 3y + z & = 11 \ x + 2y + 3z & = 7 \ \end{align*}$ using 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 View Details

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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