Exam Body

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POST UTME UI 2017 Mathematics | Objective

Are you preparing for POST UTME UI exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 2

Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}

Correct A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}

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

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

Correct Answer: A

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Question 3

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{3}{8}

D. \frac{5}{8}

Correct Answer: C

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Question 4

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 5

Solve the trigonometric equation: \sin^2 x + \cos^2 x = 1.

Correct A. x = \frac{\pi}{4}

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

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

D. x = \pi

Correct Answer: A

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Question 6

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

Correct A. \( P\( X > 0.5 \ \) = \frac{1}{2} )

B. \( P\( X > 0.5 \ \) = \frac{1}{4} )

C. \( P\( X > 0.5 \ \) = \frac{3}{4} )

D. \( P\( X > 0.5 \ \) = \frac{1}{3} )

Correct Answer: A

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Question 7

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 95% of the scores lie within 2 s\tandard deviations of the mean, what is the minimum score that 95% of the students scored?

A. 40

Correct B. 50

C. 60

D. 70

Correct Answer: B

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Question 8

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \).

Correct A. \( egin{pmatrix} -15 \ 10 \end{pmatrix} \)

B. \( egin{pmatrix} 10 \ -15 \end{pmatrix} \)

C. \( egin{pmatrix} 15 \ -10 \end{pmatrix} \)

D. \( egin{pmatrix} -10 \ 15 \end{pmatrix} \)

Correct Answer: A

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Question 9

Evaluate the definite integral \( int_{0}^{1} x^2 , dx \).

Correct A. \( \frac{1}{3} \)

B. \( \frac{1}{2} \)

C. \( \frac{2}{3} \)

D. \( \frac{1}{4} \)

Correct Answer: A

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Question 10

Simplify the expression \( \frac{2^3 cdot 3^2}{2^2 cdot 3} \).

Correct A. \( 2^2 cdot 3 \)

B. \( 2^2 cdot 3^2 \)

C. \( 2^3 cdot 3^2 \)

D. \( 2^4 cdot 3^2 \)

Correct Answer: A

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Question 11

Let X and Y be indep\endent random variables with X ~ N(0, 1) and Y ~ N(0, 1). Find the probability that X + Y > 0.

A. 0.5

Correct B. 0.75

C. 0.25

D. 0.33

Correct Answer: B

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Question 12

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

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

B. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

C. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16

D. \left\( x + 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16

Correct Answer: A

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Question 13

Solve the system of equations \begin{align*} x + y &= 2 \ x - y &= 4 \end{align*}.

Correct A. \left\{ \left\( 3, -1 \right \) \right\}

B. \left\{ \left\( 1, 1 \right \) \right\}

C. \left\{ \left\( -1, 3 \right \) \right\}

D. \left\{ \left\( 2, 0 \right \) \right\}

Correct Answer: A

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Question 14

Find the mean and s\tandard deviation of the random variable X with probability mass function \begin{align*} p(x) = \begin{cases} \frac{1}{3} & \text{if } x = 1 \frac{1}{2} & \text{if } x = 2 \frac{1}{6} & \text{if } x = 3 \end{cases} \end{align*}.

Correct A. \text{Mean: } 1.5, \text{ S\tandard Deviation: } 1.1

B. \text{Mean: } 2, \text{ S\tandard Deviation: } 1.2

C. \text{Mean: } 1, \text{ S\tandard Deviation: } 1.3

D. \text{Mean: } 2.5, \text{ S\tandard Deviation: } 1.4

Correct Answer: A

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Question 15

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 16

In the diagram below, the graph of the quadratic equation \( y = ax^2 + bx + c \) has its vertex at \( -2, 3 \ \) ) and passes through the point ( (1, 6) ). Find the equation of the graph in the form \( y = a\( x + 2 \ \)^2 + 3 ).

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

Correct B. y = 2\( x + 2 \)^2 + 3

C. y = -1\( x + 2 \)^2 + 3

D. y = 1\( x + 2 \)^2 + 3

Correct Answer: B

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Question 17

A population of bacteria grows according to the equation ( N(t) = 200e^{0.5t} ), where ( N(t) ) is the number of bacteria at time ( t ) hours. Find the rate of change of the population with respect to time when the population is 1000 bacteria.

A. 10 bacteria/hour

B. 20 bacteria/hour

Correct C. 50 bacteria/hour

D. 100 bacteria/hour

Correct Answer: C

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Question 18

A circle has its center at ( (2, 3) ) and passes through the point ( (6, 5) ). Find the equation of the circle in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).

A. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

Correct B. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 49

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 64

Correct Answer: B

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Question 19

A random variable ( X ) has a probability distribution given by the table below. Find the expected value of ( X ).

A. 2.5

Correct B. 3.5

C. 4.5

D. 5.5

Correct Answer: B

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Question 20

A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of the vector.

Correct A. x = 4, y = 3

B. x = 3, y = 4

C. x = 2, y = 5

D. x = 5, y = 2

Correct Answer: A

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Question 21

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

Correct A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )

B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )

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

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

Correct Answer: A

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Question 22

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

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{3pi}{4} \)

C. \( x = \frac{5pi}{4} \)

D. \( x = \frac{7pi}{4} \)

Correct Answer: A

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Question 23

A histogram of exam scores is shown below. What is the mean score?

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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Question 24

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )

B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )

C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 9 )

D. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 9 )

Correct Answer: A

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Question 25

A firm has a profit function given by ( P(x) = 2x^2 - 10x + 5 ). Find the value of ( x ) that maximizes profit.

Correct A. \( x = 5 \)

B. \( x = 10 \)

C. \( x = 15 \)

D. \( x = 20 \)

Correct Answer: A

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