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POST UTME SUMMIT UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME SUMMIT 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.

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Question 1

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm^3

Correct B. 48π cm^3

C. 96π cm^3

D. 192π cm^3

Correct Answer: B

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Question 2

A random variable X has a probability distribution given by P$ X = 1 $ = 1/4, P$ X = 2 $ = 1/2, P$ X = 3 $ = 1/4. Find the probability that X is greater than 2.

A. 1/2

Correct B. 3/4

C. 1/4

D. 0

Correct Answer: B

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Question 3

Solve the matrix equation AX = B, where A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.

Correct A. X = egin{bmatrix} 1 \ 2 \end{bmatrix}

B. X = egin{bmatrix} 2 \ 1 \end{bmatrix}

C. X = egin{bmatrix} 3 \ 4 \end{bmatrix}

D. X = egin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 4

A histogram of the heights of 100 students is shown below. If the mean height is 170 cm, find the s\tandard deviation.

A. 10 cm

Correct B. 15 cm

C. 20 cm

D. 25 cm

Correct Answer: B

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Question 5

Find the surface area of the sphere with radius 5 cm.

A. 100π cm^2

B. 200π cm^2

Correct C. 300π cm^2

D. 400π cm^2

Correct Answer: C

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Question 6

A random variable X follows a binomial distribution with parameters n = 10 and p = 0.4. Find the probability that X is greater than 6.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 7

Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).

Correct A. \[ $ x - 4 $^2 + $ y - 5 $^2 = 9 \]

B. \[ $ x - 3 $^2 + $ y - 4 $^2 = 16 \]

C. \[ $ x - 5 $^2 + $ y - 6 $^2 = 25 \]

D. \[ $ x - 6 $^2 + $ y - 7 $^2 = 36 \]

Correct Answer: A

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Question 8

Solve the inequality \[ 2x^2 + 5x - 3 \geq 0 \].

Correct A. \[ x \leq -1 \text{ or } x \geq \frac{3}{2} \]

B. \[ x \leq -2 \text{ or } x \geq 1 \]

C. \[ x \leq -3 \text{ or } x \geq 2 \]

D. \[ x \leq -4 \text{ or } x \geq 3 \]

Correct Answer: A

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Question 9

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 10

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

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

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

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

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

Correct Answer: A

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Question 11

Find the value of $\lim_{x\to\infty} \left$ \frac{\ln\( x^2 + 1 \ $}{x}\right)$.

Correct A. 0

B. 1

C. \infty

D. undefined

Correct Answer: A

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Question 12

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. 1/6

Correct B. 1/3

C. 2/3

D. 5/6

Correct Answer: B

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Question 13

Solve the equation $\sqrt{x + 5} - 3 = 2$ for $x$.

Correct A. -16

B. -8

C. 4

D. 16

Correct Answer: A

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Question 14

A vector $\mathbf{a}$ has magnitude 5 and direction $\theta = \frac{\pi}{3}$. Find the magnitude of the vector $\mathbf{a} + \mathbf{b}$, where $\mathbf{b}$ is a vector with magnitude 3 and direction $\theta = \frac{\pi}{6}$.

A. 4

B. 5

Correct C. 6

D. 8

Correct Answer: C

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Question 15

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

A. 1/3

B. 1/2

Correct C. 2/3

D. 1

Correct Answer: C

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Question 16

Let X be a random variable with probability density function (pdf) ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the expected value of X.

Correct A. 1/3

B. 1/2

C. 2/3

D. 1

Correct Answer: A

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Question 17

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.9544

Correct B. 0.9772

C. 0.9987

D. 0.9999

Correct Answer: B

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Question 18

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

Correct A. -2x/$ x^2 + 1 $^2

B. 2x/$ x^2 + 1 $^2

C. -1/$ x^2 + 1 $^2

D. 1/$ x^2 + 1 $^2

Correct Answer: A

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Question 19

Solve the system of equations u\sing matrices: $ egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} $.

Correct A. [1, 2]

B. [2, 1]

C. [3, -1]

D. [-1, 3]

Correct Answer: A

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Question 20

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + cdots $.

Correct A. 1048576

B. 1048575

C. 1048574

D. 1048573

Correct Answer: A

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Question 21

In a set of consecutive integers, the sum of the first and last term is 56. If the sum of the second and second last term is 34, find the sum of the first and second term.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 22

Find the equation of the circle with center at $ -2, 3 $ and pas\sing through the point (1, 2).

Correct A. \left$ x + 2 \right $^2 + \left$ y - 3 \right $^2 = 5

B. \left$ x + 2 \right $^2 + \left$ y - 3 \right $^2 = 10

C. \left$ x + 2 \right $^2 + \left$ y - 3 \right $^2 = 15

D. \left$ x + 2 \right $^2 + \left$ y - 3 \right $^2 = 20

Correct Answer: A

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Question 23

Solve the inequality \frac{x - 2}{x + 1} > 0.

Correct A. x < -1 \text{ or } x > 2

B. x < -1 \text{ or } x < 2

C. x > -1 \text{ or } x > 2

D. x > -1 \text{ or } x < 2

Correct Answer: A

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Question 24

Find the value of x in the matrix equation \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 7 \end{bmatrix}.

A. x = 2

B. x = 3

Correct C. x = 4

D. x = 5

Correct Answer: C

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Question 25

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 300

Correct B. 400

C. 500

D. 600

Correct Answer: B

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