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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME JOSEPH AYO BABALOLA 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 \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{16}{3} \)

B. \( \frac{32}{3} \)

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

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

Correct Answer: A

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Question 2

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

A. \( x = -\frac{3}{2} \)

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

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

D. \( x = \frac{3}{2} \)

Correct Answer: B

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Question 3

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 4

Find the area of the triangle with vertices ( (0, 0) ), ( (2, 0) ), and ( (0, 3) ).

Correct A. ( 6 )

B. ( 12 )

C. ( 18 )

D. ( 24 )

Correct Answer: A

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Question 5

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

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

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

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 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. ( 20 )

B. ( 24 )

C. ( 28 )

D. ( 32 )

Correct Answer: A

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Question 7

A circle has a radius of 5 cm. Find the area of the circle.

A. \( 50 \pi \)

Correct B. \( 100 \pi \)

C. \( 150 \pi \)

D. \( 200 \pi \)

Correct Answer: B

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Question 8

Find the derivative of the function \( y = 2x^3 - 5x^2 + x - 1 \) u\sing the chain rule.

Correct A. \( 6x^2 - 10x + 1 \)

B. \( 6x^2 - 10x + 2 \)

C. \( 6x^2 - 10x - 1 \)

D. \( 6x^2 - 10x - 2 \)

Correct Answer: A

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Question 9

A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line in slope-intercept form.

Correct A. \( y = x + 1 \)

B. \( y = x - 1 \)

C. \( y = x + 2 \)

D. \( y = x - 2 \)

Correct Answer: A

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Question 10

A random experiment has two indep\endent events ( A ) and ( B ) with probabilities ( P(A) = 0.4 ) and ( P(B) = 0.6 ). Find the probability that both events occur.

A. ( 0.24 )

Correct B. ( 0.36 )

C. ( 0.48 )

D. ( 0.64 )

Correct Answer: B

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Question 11

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} ).

Correct A. \begin{pmatrix} \frac{7}{5} \\ \frac{6}{5} \end{pmatrix}

B. \begin{pmatrix} \frac{1}{5} \\ -\frac{2}{5} \end{pmatrix}

C. \begin{pmatrix} \frac{2}{5} \\ -\frac{3}{5} \end{pmatrix}

D. \begin{pmatrix} -\frac{1}{5} \\ \frac{2}{5} \end{pmatrix}

Correct Answer: A

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Question 12

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

Correct A. 3x + 2y - z = 6

B. 2x + 3y - z = 6

C. x + 2y - 3z = 6

D. x + 3y - 2z = 6

Correct Answer: A

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Question 13

Let ( f(x) = x^2 + 2x + 1 ). Find the equation of the \tangent line to the curve at the point where \( x = 1 \).

Correct A. y = 3x - 2

B. y = 3x + 2

C. y = 3x - 1

D. y = 3x + 1

Correct Answer: A

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Question 14

A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{2}{3}

Correct D. \frac{5}{6}

Correct Answer: D

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Question 15

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

A. 80\pi

B. 160\pi

Correct C. 320\pi

D. 640\pi

Correct Answer: C

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Question 16

Solve for 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 17

Find the value of \( \sin \( 2 \theta \ \) ) given that \( \sin \( \theta \ \) = \frac{3}{5} ) and \( \cos \( \theta \ \) = \frac{4}{5} ).

A. √2

Correct B. √6

C. √10

D. √14

Correct Answer: B

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Question 18

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 19

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

A. -2

Correct B. -3

C. -4

D. -5

Correct Answer: B

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Question 20

A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x and y components of ( vec{a} ).

Correct A. x: 4, y: 4

B. x: 4, y: 3

C. x: 3, y: 4

D. x: 3, y: 3

Correct Answer: A

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Question 21

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: C

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Question 22

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

Correct A. x < -1 or x > 3/2

B. x < -3/2 or x > 1

C. x < 1 or x > -3/2

D. x < 3/2 or x > -1

Correct Answer: A

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Question 23

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 24

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

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 25

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.

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

B. 3x^2 - 4x - 3

C. 3x^2 + 4x + 3

D. 3x^2 - 4x + 1

Correct Answer: A

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