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

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Question 1

Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \).

A. \( x = -2 \ \)

Correct B. \( x = -3 \ \)

C. \( x = 2 \ \)

D. \( x = 3 \ \)

Correct Answer: B

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Question 2

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

Correct A. \( \frac{5}{3} \ \)

B. \( \frac{7}{3} \ \)

C. \( \frac{9}{3} \ \)

D. \( \frac{11}{3} \ \)

Correct Answer: A

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Question 3

Solve the inequality \( x^2 - 4x - 5 > 0 \).

Correct A. \( x < -1 \ \) or \( x > 5 \ \)

B. \( x < 1 \ \) or \( x > 5 \ \)

C. \( x < -1 \ \) or \( x < 5 \ \)

D. \( x > 1 \ \) or \( x < 5 \ \)

Correct Answer: A

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Question 4

Find the value of \( \log_{10} \( 1000 \ \).

A. \( 3 \ \)

Correct B. \( 4 \ \)

C. \( 5 \ \)

D. \( 6 \ \)

Correct Answer: B

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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

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

Correct A. \( \frac{-1}{2x^{3/2}} \)

B. \( \frac{1}{2x^{3/2}} \)

C. \( \frac{1}{x^{3/2}} \)

D. \( \frac{-1}{x^{3/2}} \)

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + ldots \).

Correct A. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 \)

B. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 \)

C. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 \)

D. \( 2x + 3x^2 + 4x^3 + 5x^4 + 6x^5 + 7x^6 + 8x^7 + 9x^8 \)

Correct Answer: A

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Question 9

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

B. \( y = \frac{1}{2}x - \frac{1}{2} \)

C. \( y = 2x - 1 \)

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

Correct Answer: A

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Question 10

Find the mean of the numbers ( 2, 4, 6, 8, 10 ).

Correct A. ( 6 )

B. ( 7 )

C. ( 8 )

D. ( 9 )

Correct Answer: A

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Question 11

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 = 16 )

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

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

Correct Answer: A

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Question 12

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

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

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

Correct C. \( x = \frac{pi}{2} \)

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

Correct Answer: C

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Question 13

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find its volume.

A. ( 400 ) cm³

B. ( 500 ) cm³

Correct C. ( 600 ) cm³

D. ( 800 ) cm³

Correct Answer: C

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Question 14

Find the area of the triangle with vertices ( A(2, 3) ), ( B(4, 5) ), and ( C(6, 7) ).

A. ( 10 ) cm²

B. ( 15 ) cm²

Correct C. ( 20 ) cm²

D. ( 25 ) cm²

Correct Answer: C

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Question 15

Solve the system of equations \( x + y = 3 \) and \( x - y = 1 \).

Correct A. \( x = 2, y = 1 \)

B. \( x = 1, y = 2 \)

C. \( x = 2, y = 2 \)

D. \( x = 1, y = 1 \)

Correct Answer: A

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Question 16

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.

Correct A. ( f'(x) = \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2} \)

B. ( f'(x) = \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2} \)

C. ( f'(x) = \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2} \) + 2

D. ( f'(x) = \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2} \) - 2

Correct Answer: A

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Question 17

In a histogram with 5 classes, the frequency of the first class is 10, the second class is 15, the third class is 20, the fourth class is 25, and the fifth class is 30. What is the mean of the frequencies?

A. 20

Correct B. 22.5

C. 25

D. 27.5

Correct Answer: B

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Question 18

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

A. 2

Correct B. 4

C. -2

D. -4

Correct Answer: B

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Question 19

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 50.27

C. 50.29

D. 50.31

Correct Answer: A

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Question 20

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{3}}{3}

D. \frac{1}{3}

Correct Answer: B

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Question 21

In a survey of 50 students, the mean height was 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.3085

B. 0.1915

C. 0.1359

D. 0.0228

Correct Answer: A

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Question 22

Solve for x in the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 ).

Correct A. 100

B. 10

C. 1000

D. 10000

Correct Answer: A

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Question 23

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.

Correct A. 8

B. 6

C. 10

D. 12

Correct Answer: A

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Question 24

A binary operation \( * \) on the set of integers is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).

A. 13

B. 19

Correct C. 25

D. 37

Correct Answer: C

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Question 25

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment is terminated. What is the probability that the experiment will be terminated on the first roll?

A. 1/2

Correct B. 1/3

C. 2/3

D. 1/6

Correct Answer: B

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