Exam Body

Year

Subject

Paper Type

POST UTME UI 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $\frac{d}{dx} \left$ \int_{0}^{x^2} \frac{1}{t} dt \right $$.

A. \frac{1}{x}

Correct B. \frac{2}{x}

C. \frac{1}{x^2}

D. \frac{2}{x^2}

Correct Answer: B

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

Question 2

Solve the equation $\log_{10} $ x^2 $ = 4$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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

Question 3

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

Correct A. \frac{4}{3}

B. \frac{2}{3}

C. \frac{1}{3}

D. \frac{1}{2}

Correct Answer: A

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

Question 4

Solve the inequality $|x - 2| > 3$.

Correct A. $ -\infty, -1 $ \cup $ 5, \infty $

B. $ -\infty, 1 $ \cup $ 5, \infty $

C. $ -\infty, -1 $ \cup (2, 5)

D. $ -\infty, 1 $ \cup (2, 5)

Correct Answer: A

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

Question 5

Find the value of $\sin (2x)$ given that $\sin x = \frac{1}{2}$.

A. \frac{1}{2}

Correct B. \frac{\sqrt{3}}{2}

C. \frac{\sqrt{5}}{2}

D. \frac{\sqrt{7}}{2}

Correct Answer: B

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

Question 6

A random variable X has a probability distribution given by P$ X = 1 $ = 0.3, P$ X = 2 $ = 0.4, and P$ X = 3 $ = 0.3. If Y is another random variable such that Y = 2X - 1, find the probability P$ Y = 3 $.

Correct A. 0.4

B. 0.3

C. 0.2

D. 0.1

Correct Answer: A

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

Question 7

The equation of a circle is given by x^2 + y^2 + 4x - 6y + 5 = 0. Find the coordinates of the center of the circle.

Correct A. $ -2, 3 $

B. $ 2, -3 $

C. $ -3, 2 $

D. $ 3, -2 $

Correct Answer: A

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

Question 8

Solve the equation 2x^3 - 5x^2 + 3x - 1 = 0.

A. 1, 2, 3

Correct B. 1, -1, 2

C. 2, -1, 3

D. -1, 2, 3

Correct Answer: B

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

Question 9

A polynomial f(x) = x^3 - 2x^2 + x - 1 has a root at x = 1. Find the other two roots.

A. 1, 2, 3

Correct B. 1, -1, 2

C. 2, -1, 3

D. -1, 2, 3

Correct Answer: B

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

Question 10

A matrix A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} has an inverse A^{-1}. Find the value of A^{-1} cdot A.

Correct A. \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}

B. \begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}

C. \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}

D. \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}

Correct Answer: A

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

Question 11

Find the equation of the circle pas\sing through the points (2,3), (4,5), and $ -1,2 $.

Correct A. $ x^2 + y^2 + 4x - 6y + 5 = 0 $

B. $ x^2 + y^2 - 4x + 6y + 5 = 0 $

C. $ x^2 + y^2 + 2x - 4y + 5 = 0 $

D. $ x^2 + y^2 - 2x + 4y + 5 = 0 $

Correct Answer: A

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

Question 12

Evaluate the integral $ int_{0}^{1} \frac{1}{x^2 + 1} dx $.

A. $ \frac{1}{2} $

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

C. $ \frac{pi}{2} $

D. $ \frac{3pi}{4} $

Correct Answer: B

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

Question 13

Solve the equation $ \sin^2 x + \cos^2 x = 1 $ for ( x ).

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

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

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

D. $ x = \frac{5pi}{4} $

Correct Answer: A

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

Question 14

Find the value of ( x ) in the equation $ 2^x + 2^{-x} = 3 $.

A. $ x = 1 $

B. $ x = 2 $

Correct C. $ x = \log_2 3 $

D. $ x = -\log_2 3 $

Correct Answer: C

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

Question 15

Find the equation of the line pas\sing through the points (1,2) and (3,4).

Correct A. $ y = 2x - 1 $

B. $ y = 2x + 1 $

C. $ y = 2x - 2 $

D. $ y = 2x + 2 $

Correct Answer: A

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

Question 16

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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

Question 17

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

A. 1/6

B. 1/3

Correct C. 2/3

D. 5/6

Correct Answer: C

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

Question 18

In a set of numbers, the mean is 10 and the median is 8. If the mode is 12, what is the value of the sum of the numbers?

A. 120

B. 150

Correct C. 180

D. 200

Correct Answer: C

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

Question 19

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 2040

B. 2160

Correct C. 2400

D. 2880

Correct Answer: C

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

Question 20

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 80?

A. 0.68

B. 0.72

Correct C. 0.76

D. 0.80

Correct Answer: C

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

Question 21

Solve for ( x ) in the 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 = \\frac{5\\pi}{4}

Correct Answer: A

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

Question 22

A circle has a radius of 4 cm. What is the area of the circle?

A. 16\pi

B. 20\pi

Correct C. 24\pi

D. 32\pi

Correct Answer: C

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

Question 23

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?

A. 8

B. 10

Correct C. 12

D. 14

Correct Answer: C

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

Question 24

A set of numbers has a mean of 20 and a s\tandard deviation of 5. What is the probability that a randomly selected number is greater than 25?

A. 0.16

B. 0.20

Correct C. 0.24

D. 0.28

Correct Answer: C

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

Question 25

A geometric progression has a first term of 2 and a common ratio of 3. What is the sum of the first 5 terms?

A. 243

B. 2430

Correct C. 24300

D. 243000

Correct Answer: C

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