Exam Body

Year

Subject

Paper Type

POST UTME UI 2017 Mathematics | Objective

Prepare for your exams with POST UTME UI questions? Reviewing past/model 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 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

Solve the system of equations using 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 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. \(\frac{3}{8}\)\)

D. \(\frac{5}{8}\)\)

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. If 95% of the scores lie within 2 standard 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

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

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

Let X and Y be independent 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

Find the mean and standard 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 } \(x = 2\\() & text{if}\) \(\frac{1}{6}\)\) & text{if } \(x = 3\) \\(text{if}\((x = 3\)\end{cases} \end{align*}.

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

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

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

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

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 \\\() ) 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\(\sqrt{x}\)}\) ) using 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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

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

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

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

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

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

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support