Exam Body

Year

Subject

Paper Type

POST UTME CHRISTOPHER UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME CHRISTOPHER UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. 2x

B. -2x

Correct C. \frac{-2x}{\( x^2 + 1 \)^2}

D. \frac{2x}{\( x^2 + 1 \)^2}

Correct Answer: C

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

Question 2

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}{6}

Correct Answer: A

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

Question 3

Solve the inequality \( x^2 - 4x + 4 \geq 0 \).

Correct A. x \leq 2

B. x \geq 2

C. x < 2

D. x > 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 \( x = 2 \).

Correct A. \frac{8}{3}

B. \frac{16}{3}

C. \frac{4}{3}

D. \frac{2}{3}

Correct Answer: A

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

Question 5

Determine the value of ( x ) in the equation \( 2^x = 16 \).

A. 4

B. 2

Correct C. 3

D. 1

Correct Answer: C

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

Question 6

Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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

Question 7

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).

A. \( -∞, -3 \) ∪ (2, ∞)

Correct B. \( -∞, -3 \) ∪ (0, 2) ∪ (3, ∞)

C. \( -∞, -3 \) ∪ (0, 3)

D. \( -∞, -3 \) ∪ (2, 3)

Correct Answer: B

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

Question 8

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( 6, -1 \).

Correct A. \( x^2 + y^2 - 12x - 4y + 20 = 0 \)

B. \( x^2 + y^2 - 8x - 6y + 15 = 0 \)

C. \( x^2 + y^2 - 10x - 2y + 25 = 0 \)

D. \( x^2 + y^2 - 12x - 8y + 32 = 0 \)

Correct Answer: A

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

Question 9

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

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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

Question 10

A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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

Question 11

Determine the mean of the following data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Correct A. 6

B. 5

C. 7

D. 8

Correct Answer: A

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\( X = 1 \) = 0.2, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.5. What is the expected value of X?

A. 1.5

Correct B. 2.0

C. 2.5

D. 3.0

Correct Answer: B

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

Question 13

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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

Question 14

In a circle with center O and radius 5, what is the length of the arc intercepted by a central angle of 60 degrees?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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

Question 15

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 2197

Correct B. 2401

C. 2605

D. 2809

Correct Answer: B

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

Question 16

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{| mathbf{a} |^2} mathbf{a} \).

A. 0

Correct B. \begin{pmatrix} \frac{4}{13} \\ \frac{6}{13} \end{pmatrix}

C. \begin{pmatrix} \frac{2}{13} \\ \frac{3}{13} \end{pmatrix}

D. \begin{pmatrix} \frac{1}{13} \\ \frac{-2}{13} \end{pmatrix}

Correct Answer: B

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

Question 17

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the definite integral \( \int_{a}^{b} f\( x \ \) \, dx ).

A. 64

B. 80

Correct C. 96

D. 128

Correct Answer: C

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

Question 18

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

A. 0

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

C. \frac{\pi}{2}

D. \pi

Correct Answer: B

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

Question 19

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. \( x - 5 \)^2 + \( y - 3 \)^2 = 25

D. \( x - 3 \)^2 + \( y - 5 \)^2 = 25

Correct Answer: A

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

Question 20

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + \cdots \).

A. 4095

Correct B. 4096

C. 4097

D. 4098

Correct Answer: B

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

Question 21

Evaluate the definite integral \( int_{0}^{1} x^2 ln\( x \ \) , dx ) u\sing integration by parts.

A. \frac{1}{4}

B. \frac{1}{3}

Correct C. \frac{1}{2}

D. \frac{1}{6}

Correct Answer: C

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

Question 22

Determine the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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

Question 23

Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, -3 \) \cup \( 1, \infty \)

Correct Answer: A

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

Question 24

Find the area under the curve \( y = x^3 - 6x^2 + 9x + 2 \) from \( x = 0 \) to \( x = 2 \).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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

Question 25

Determine the value of ( x ) in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 1

D. 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