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POST UTME MADONNA UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME MADONNA 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.

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Question 1

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.

Correct A. 1/4

B. 1/2

C. 3/4

D. 1

Correct Answer: A

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Question 2

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

Correct A. \( x \leq -3 \) or \( x \geq 1 \)

B. \( x \leq -1 \) or \( x \geq 3 \)

C. \( x \leq 1 \) or \( x \geq 3 \)

D. \( x \leq -3 \) or \( x \geq 1 \)

Correct Answer: A

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Question 3

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

Correct A. \( 8/3 \)

B. \( 16/3 \)

C. \( 32/3 \)

D. \( 64/3 \)

Correct Answer: A

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Question 4

Let \( a \) and \( b \) be the roots of the quadratic equation \( x^2 + 2x + 3 = 0 \). Find the value of \( a^2 + b^2 \).

Correct A. \( 4 \)

B. \( 5 \)

C. \( 6 \)

D. \( 7 \)

Correct Answer: A

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Question 5

Solve the system of linear equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \).

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

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

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 6

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 7

Find the value of \( \frac{1}{2} \sin 2x + \frac{1}{4} \cos 2x \) when \( x = \frac{\pi}{6} \).

Correct A. \frac{1}{2}

B. \frac{1}{4}

C. \frac{1}{8}

D. \frac{1}{16}

Correct Answer: A

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Question 8

In the diagram below, the line \( y = 2x - 3 \) intersects the circle \( x^2 + y^2 = 16 \). Find the coordinates of the point of intersection.

A. (3, 3)

Correct B. (4, 5)

C. (5, 7)

D. (6, 9)

Correct Answer: B

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Question 9

Differentiate the function ( f(x) = \frac{x^2}{x^2 + 1} ) with respect to x.

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

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

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

D. \frac{2x^4}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 10

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

Correct A. \( -\infty, -1 \) \cup \( 5, \infty \)

B. \( -\infty, -5 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 5, \infty \)

D. \( -\infty, -5 \) \cup \( 1, \infty \)

Correct Answer: A

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Question 11

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

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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Question 12

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

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

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

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

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

Correct Answer: B

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Question 13

Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = 2x + 3

D. y = 2x - 3

Correct Answer: A

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Question 14

Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 3 \end{align*}.

Correct A. x = 1, y = 3

B. x = 2, y = 2

C. x = 3, y = 1

D. x = 4, y = 0

Correct Answer: A

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Question 15

Find the derivative of the function f(x) = x^3 - 2x^2 + x - 1.

Correct A. 3x^2 - 4x + 1

B. 3x^2 - 4x - 1

C. 3x^2 + 4x + 1

D. 3x^2 + 4x - 1

Correct Answer: A

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Question 16

Find the equation of the plane pas\sing through the points (1, 2, 3), (2, 3, 4), and (3, 4, 5).

Correct A. \( x - y + z - 6 = 0 \)

B. \( x + y - z + 6 = 0 \)

C. \( x - y + z + 6 = 0 \)

D. \( x + y + z + 6 = 0 \)

Correct Answer: A

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Question 17

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 18

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

Correct A. \( \frac{32}{3} pi \)

B. \( \frac{16}{3} pi \)

C. \( \frac{64}{3} pi \)

D. \( \frac{128}{3} pi \)

Correct Answer: A

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Question 19

Find the area under the curve \( y = \sin x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).

Correct A. ( 1 )

B. \( \frac{1}{2} \)

C. \( \frac{pi}{2} \)

D. ( pi )

Correct Answer: A

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Question 20

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

Correct A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)

B. \( x^2 + y^2 + 4x - 6y + 9 = 0 \)

C. \( x^2 + y^2 - 4x + 6y + 9 = 0 \)

D. \( x^2 + y^2 + 4x + 6y + 9 = 0 \)

Correct Answer: A

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Question 21

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

A. 2

Correct B. 61

C. 62

D. 63

Correct Answer: B

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Question 22

Solve the inequality \frac{x^2 - 4}{x + 2} > 0.

Correct A. \( -2, -1 \) \cup \( 1, \infty \)

B. \( -2, 1 \) \cup \( 2, \infty \)

C. \( -2, 1 \) \cup \( 2, \infty \)

D. \( -2, \infty \) \cup \( 1, \infty \)

Correct Answer: A

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Question 23

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

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 24

Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 1, y = 3

D. x = 2, y = 4

Correct Answer: A

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Question 25

Find the area of the circle with radius 4.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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