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POST UTME CHRISTOPHER UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \( \frac{1}{2} \)

B. \( \frac{1}{3} \)

C. \( \frac{1}{4} \)

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 2

A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 3

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

Correct A. \( \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} \)

B. \( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} \)

C. \( \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} \)

D. \( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} \)

Correct Answer: A

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Question 4

A histogram is constructed with the following data: \( egin{array}{|c|c|} hline \text{Class} & \text{Frequency} \ hline 0-10 & 5 \ 10-20 & 8 \ 20-30 & 12 \ 30-40 & 15 \ 40-50 & 10 \ hline \end{array} \). Find the mean of the data.

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 5

A solid cylinder has a radius of 4 cm and a height of 10 cm. Find the volume of the cylinder.

Correct A. \( pi \times 4^2 \times 10 \)

B. \( pi \times 4^2 \times 5 \)

C. \( pi \times 4^2 \times 10^2 \)

D. \( pi \times 4^2 \times 10^3 \)

Correct Answer: A

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Question 6

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 7

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

Correct A. x = -2 or x = -3

B. x = -1 or x = -6

C. x = 2 or x = 3

D. x = 1 or x = 6

Correct Answer: A

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Question 8

A binary operation * is defined as \( a * b = ab + 5 \). Find the value of \( 2 * 3 \).

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 9

A particle moves in a straight line with a velocity of \( v = 2t + 5 \) m/s. Find the acceleration of the particle after 3 seconds.

A. 4 m/s^2

B. 6 m/s^2

Correct C. 8 m/s^2

D. 10 m/s^2

Correct Answer: C

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Question 10

A random experiment has two indep\endent events A and B. If P(A) = 0.4 and P(B) = 0.6, find the probability that both events occur.

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 11

A random variable X is uniformly distributed over the interval [0, 1]. Find the probability that X^2 + Y^2 > 1, where Y is an indep\endent random variable uniformly distributed over the interval [0, 1].

A. 0

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: C

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Question 12

Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 13

A solid cylinder of radius 4 cm and height 10 cm has a hole drilled through it with a radius of 2 cm. Find the volume of the remaining solid.

A. 100\pi

Correct B. 200\pi

C. 300\pi

D. 400\pi

Correct Answer: B

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Question 14

The mean of a set of 5 numbers is 10. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 35

B. 40

C. 45

D. 50

Correct Answer: A

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Question 15

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

A. 1023

Correct B. 1024

C. 1025

D. 1026

Correct Answer: B

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Question 16

Let \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \). Find ( AB ) if it exists.

Correct A. \[ \begin{bmatrix} 19 & 22 \\ 43 & 50 \end{bmatrix} \]

B. \[ \begin{bmatrix} 11 & 14 \\ 23 & 28 \end{bmatrix} \]

C. \[ \begin{bmatrix} 3 & 4 \\ 9 & 12 \end{bmatrix} \]

D. \[ \begin{bmatrix} 7 & 8 \\ 15 & 18 \end{bmatrix} \]

Correct Answer: A

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Question 17

Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, 54, ... ).

Correct A. \[ 10494 \]

B. \[ 10494.5 \]

C. \[ 10495 \]

D. \[ 10496 \]

Correct Answer: A

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Question 18

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

A. \[ \frac{\pi}{2} \]

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

C. \[ \frac{3\pi}{4} \]

D. \[ \frac{5\pi}{4} \]

Correct Answer: B

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Question 19

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

Correct A. \[ -\frac{2x}{\( x^2 + 1 \)^2} \]

B. \[ \frac{2x}{\( x^2 + 1 \)^2} \]

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

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

Correct Answer: A

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Question 20

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 = 30 \]

D. \[ \( x - 4 \)^2 + \( y - 3 \)^2 = 30 \]

Correct Answer: A

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Question 21

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

Correct A. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 22

Solve for ( x ) in the equation \( 2^x = 16 \).

A. ( 2 )

Correct B. ( 4 )

C. ( 8 )

D. ( 16 )

Correct Answer: B

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Question 23

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. \( 6x + 2 \)

B. \( 6x - 2 \)

C. \( 6x + 2x - 2 \)

D. \( 6x + 2x + 2 \)

Correct Answer: A

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Question 24

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

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Question 25

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. ( 6 )

B. ( 12 )

Correct C. ( 18 )

D. ( 24 )

Correct Answer: C

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