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POST UTME CHRISTOPHER UNIVERSITY 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 2

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.

Correct A. -1102

B. -1020

C. -1000

D. -980

Correct Answer: A

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Question 3

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

Correct A. 200\pi

B. 400\pi

C. 800\pi

D. 1600\pi

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: A

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Question 5

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

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 6

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.

Correct A. \begin{pmatrix} 11 \ 2 \end{pmatrix}

B. \begin{pmatrix} -11 \ 2 \end{pmatrix}

C. \begin{pmatrix} 11 \ -2 \end{pmatrix}

D. \begin{pmatrix} -11 \ -2 \end{pmatrix}

Correct Answer: A

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Question 7

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

Correct A. \frac{4}{5}

B. \frac{4}{3}

C. \frac{4}{15}

D. \frac{4}{9}

Correct Answer: A

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Question 8

Find the area under the curve \( y = e^x \) from \( x = 0 \) to \( x = 1 \).

Correct A. e - 1

B. e + 1

C. e^2 - 1

D. e^2 + 1

Correct Answer: A

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Question 9

Solve the equation \( x^3 + 2x^2 - 7x + 12 = 0 \) u\sing the rational root theorem.

Correct A. x = 1

B. x = -1

C. x = 3

D. x = -3

Correct Answer: A

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Question 10

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

Correct A. \frac{8}{3}

B. \frac{4}{3}

C. \frac{8}{5}

D. \frac{4}{5}

Correct Answer: A

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Question 11

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. \( y = 2x - 1 \)

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

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

Correct Answer: A

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Question 12

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 13

Find the volume of the frustum of a cone with height \( h = 10 \) cm, and radii of the bases \( r_1 = 4 \) cm and \( r_2 = 6 \) cm.

Correct A. \( \frac{1}{3} pi \( 4^2 + 6^2 + 4 cdot 6 \ \) cdot 10 )

B. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 \ \) cdot 10 )

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

D. \( \frac{1}{3} pi \( 4^2 + 6^2 - 4 cdot 6 \ \) cdot 5 )

Correct Answer: A

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Question 14

Find the sum of the first ( n ) terms of the arithmetic progression ( 2, 5, 8, ldots ).

Correct A. \( \frac{n}{2} [2 + \( n - 1 \ \) cdot 3] )

B. \( \frac{n}{2} [2 + \( n + 1 \ \) cdot 3] )

C. \( \frac{n}{2} [2 + \( n - 1 \ \) cdot 2] )

D. \( \frac{n}{2} [2 + \( n + 1 \ \) cdot 2] )

Correct Answer: A

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Question 15

Solve the system of equations \( x + y = 4 \) and \( x^2 + y^2 = 16 \).

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

B. \( x = 2, y = 2 \) or \( x = -2, y = -2 \)

C. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 0, y = 4 \)

D. \( x = 2, y = 2 \) or \( x = -2, y = -2 \) or \( x = 4, y = 0 \)

Correct Answer: A

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Question 16

Find the area of the triangle with vertices ( (0,0), (3,0), (0,4) ).

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

B. \( \frac{1}{2} cdot 3 cdot 4 cdot \sin 60^circ \)

C. \( \frac{1}{2} cdot 3 cdot 4 cdot \cos 60^circ \)

D. \( \frac{1}{2} cdot 3 cdot 4 cdot \tan 60^circ \)

Correct Answer: A

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Question 17

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

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

B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

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

Correct Answer: A

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Question 18

Find the sum of the first ( n ) terms of the geometric progression ( 2, 6, 18, ldots ).

A. \( 2 cdot \frac{6^n - 1}{5} \)

B. \( 2 cdot \frac{6^n + 1}{5} \)

C. \( 2 cdot \frac{6^n - 1}{6} \)

D. \( 2 cdot \frac{6^n + 1}{6} \)

Correct Answer: VIEW ANSWER

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Question 19

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20

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

Correct A. \frac{-5 + \sqrt{37}}{4}

B. \frac{-5 - \sqrt{37}}{4}

C. \frac{-5 + \sqrt{37}}{2}

D. \frac{-5 - \sqrt{37}}{2}

Correct Answer: A

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Question 21

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

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

B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16

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

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

Correct Answer: A

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Question 22

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}

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

Correct Answer: A

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Question 23

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \) u\sing substitution.

Correct A. x = \frac{3}{2}, y = \frac{1}{2}

B. x = \frac{1}{2}, y = \frac{3}{2}

C. x = 2, y = 1

D. x = 1, y = 2

Correct Answer: A

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Question 24

Find the area of the triangle with vertices \( (0, 0), (3, 0), (0, 4) \) u\sing the formula \( \frac{1}{2} \times \text{base} \times \text{height} \).

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 25

Find the equation of the line pas\sing through the points \( (2, 3) \) and \( (4, 5) \) u\sing the slope-intercept form.

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

B. y = \frac{2}{4}x + 1

C. y = \frac{4}{2}x + 1

D. y = \frac{4}{4}x + 1

Correct Answer: A

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