Exam Body

Year

Subject

Paper Type

POST UTME LEAD CITY UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation \( \frac{1}{x} + \frac{1}{2} = \frac{3}{4} \).

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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

Question 2

A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.

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

B. \( x^2 + y^2 = 16 \)

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

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

Correct Answer: A

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

Question 3

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -1 \) or \( x < \frac{3}{2} \)

C. \( x > -1 \) or \( x > \frac{3}{2} \)

D. \( x > -1 \) or \( x < \frac{3}{2} \)

Correct Answer: A

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

Question 4

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. 64

B. 32

C. 16

D. 8

Correct Answer: A

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

Question 5

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_{10} \).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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

Question 6

Determine the value of k in the polynomial equation \( x^3 + 2x^2 - 7x - 12 = k\( x + 3 \)\( x - 1 \ \) ).

Correct A. -3

B. -1

C. 1

D. 3

Correct Answer: A

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

Question 7

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

A. 32

B. 40

Correct C. 48

D. 56

Correct Answer: C

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

Question 8

A set of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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

Question 9

Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \).

A. -1

Correct B. 0

C. 1

D. 2

Correct Answer: B

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

Question 10

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 80?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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

Question 11

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).

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

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

Correct C. \( x = \frac{\pi}{6} \)

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

Correct Answer: C

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

Question 12

A random variable X has a probability distribution given by \( P\( X = x \ \) = \begin{cases} \frac{1}{2} & \text{if } x = 1 \frac{1}{4} & \text{if } x = 2 \frac{1}{4} & \text{if } x = 3 \end{cases} ). Find the expected value of X.

Correct A. ( E(X) = 1.5 )

B. ( E(X) = 2 )

C. ( E(X) = 2.5 )

D. ( E(X) = 3 )

Correct Answer: A

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

Question 13

Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

Correct A. \( x = -2 \pm 2i \)

B. \( x = -1 \pm i \)

C. \( x = -2 \pm i \)

D. \( x = -1 \pm 2i \)

Correct Answer: A

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

Question 14

A function f(x) is defined as ( f(x) = \frac{x^2 - 4}{x + 2} ). Find the domain of the function.

Correct A. \( x \in \( -\infty, -2 \ \) \cup \( -2, \infty \) )

B. \( x \in \( -\infty, 2 \ \) \cup \( 2, \infty \) )

C. \( x \in \( -\infty, -2 \ \) \cup \( 2, \infty \) )

D. \( x \in \( -\infty, 2 \ \) \cup \( -2, \infty \) )

Correct Answer: A

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

Question 15

A curve is defined by the equation \( y = \frac{1}{x} \). Find the equation of the \tangent line to the curve at the point (1, 1).

Correct A. \( y = x - 1 \)

B. \( y = x + 1 \)

C. \( y = -x + 1 \)

D. \( y = x - 2 \)

Correct Answer: A

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

Question 16

Let ( S ) be the set of all ordered pairs ( (x, y) ) such that \( x^2 + y^2 leq 4 \). Find the number of elements in the set ( S ).

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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

Question 17

A sequence is defined by \( a_n = \frac{1}{n} + \frac{1}{n+1} \) for ( n geq 1 ). Find the sum of the first 5 terms of the sequence.

A. 1.5

Correct B. 2.5

C. 3.5

D. 4.5

Correct Answer: B

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

Question 18

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 1/2

B. 1/3

Correct C. 2/5

D. 3/5

Correct Answer: C

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

Question 19

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

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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

Question 20

A polynomial ( p(x) ) is defined by ( p(x) = x^3 + 2x^2 - 5x + 1 ). Find the value of \( p\( -1 \ \) ).

Correct A. -3

B. -2

C. -1

D. 0

Correct Answer: A

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

Question 21

A solid right circular cone has a height of 8 cm and a base radius of 3 cm. Find the volume of the cone in cubic centimeters.

Correct A. 48\pi

B. 64\pi

C. 72\pi

D. 80\pi

Correct Answer: A

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

Question 22

Simplify the expression: \( \frac{2x^2 + 5x - 3}{x + 3} \)

Correct A. 2x - 1

B. 2x + 1

C. x + 2

D. x - 2

Correct Answer: A

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

Question 23

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

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

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

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

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

Correct Answer: A

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

Question 24

A binary operation \( \ast \) is defined as: \( a \ast b = ab + 2 \). Find the value of \( 2 \ast 3 \).

A. 8

Correct B. 10

C. 12

D. 14

Correct Answer: B

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

Question 25

Solve the inequality: \( 2x - 5 > 3x + 2 \).

Correct A. \( x < -\frac{7}{2} \)

B. \( x > -\frac{7}{2} \)

C. \( x < \frac{7}{2} \)

D. \( x > \frac{7}{2} \)

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