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POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

Correct A. \vec{r} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 2 \end{pmatrix}

B. \vec{r} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 1 \end{pmatrix}

C. \vec{r} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 3 \\ 2 \end{pmatrix}

D. \vec{r} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 1 \\ 3 \end{pmatrix}

Correct Answer: A

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Question 2

Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.

A. \frac{-4 \pm \sqrt{16 - 16}}{2}

B. \frac{-4 \pm \sqrt{16 + 16}}{2}

Correct C. \frac{-4 \pm \sqrt{16 - 4}}{2}

D. \frac{-4 \pm \sqrt{16 + 4}}{2}

Correct Answer: C

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Question 3

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

C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16

D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16

Correct Answer: A

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Question 4

Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.

Correct A. \left\( x - 1 \right \) \left\( x - 3 \right \) > 0

B. \left\( x - 2 \right \) \left\( x - 2 \right \) > 0

C. \left\( x - 3 \right \) \left\( x - 1 \right \) > 0

D. \left\( x - 1 \right \) \left\( x - 3 \right \) < 0

Correct Answer: A

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Question 5

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

A. y = 1x + 1

Correct B. y = 2x + 2

C. y = 3x + 3

D. y = 4x + 4

Correct Answer: B

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Question 6

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

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

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

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

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

Correct Answer: A

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Question 7

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 student scored above 90?

A. 0.1587

B. 0.3413

C. 0.4772

Correct D. 0.6915

Correct Answer: D

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Question 8

Solve the trigonometric equation \( \tan^2 x + 2 \tan x - 6 = 0 \) for ( x ) in the interval ( [0, 2 pi] ).

A. \frac{3 pi}{12}

Correct B. \frac{5 pi}{12}

C. \frac{7 pi}{12}

D. \frac{11 pi}{12}

Correct Answer: B

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Question 9

A random experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. What is the probability that both events occur?

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.64

Correct Answer: A

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Question 10

Find the equation of the \tangent line to the curve \( y = x^3 - 6x^2 + 9x + 2 \) at the point \( 1, -4 \ \) ).

Correct A. y = 3x - 5

B. y = 3x - 7

C. y = 3x - 9

D. y = 3x - 11

Correct Answer: A

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Question 11

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of the university students.

A. 173.5 cm to 177.5 cm

Correct B. 171.5 cm to 179.5 cm

C. 174.5 cm to 176.5 cm

D. 172.5 cm to 178.5 cm

Correct Answer: B

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Question 12

Solve the system of equations u\sing matrices: \[\begin{align*} x + y + z &= 6 \ 2x + 3y - z &= 2 \ -x + 2y + 3z &= -1 \end{align*}\]

Correct A. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}\]

B. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 2 \ 1 \ 3 \end{bmatrix}\]

C. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 3 \ 2 \ 1 \end{bmatrix}\]

D. \[\begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 3 \ 2 \end{bmatrix}\]

Correct Answer: A

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Question 13

Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).

Correct A. \( x - 4 \)^2 + \( y - 5 \)^2 = 9

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

C. \( x - 5 \)^2 + \( y - 6 \)^2 = 25

D. \( x - 6 \)^2 + \( y - 7 \)^2 = 36

Correct Answer: A

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Question 14

A binary operation \(*\) on the set \{1, 2, 3, 4, 5\} is defined as \[\begin{align*} *: \{1, 2, 3, 4, 5\} \times \{1, 2, 3, 4, 5\} &\to \{1, 2, 3, 4, 5\} \end{align*}\]. If \(a * b = 3\), find the value of \(a\) and \(b\).

Correct A. \(a = 2, b = 1\)

B. \(a = 3, b = 2\)

C. \(a = 4, b = 3\)

D. \(a = 5, b = 4\)

Correct Answer: A

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Question 15

Solve the equation \(\frac{1}{x + 1} + \frac{1}{x - 1} = \frac{1}{2}\) for \(x\).

Correct A. \(x = 2\)

B. \(x = -2\)

C. \(x = 1\)

D. \(x = -1\)

Correct Answer: A

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Question 16

Solve the inequality \( \frac{x}{x-2} > 0 \) for \( x in \( -infty, infty \ \) ).

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

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

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

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

Correct Answer: A

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Question 17

Find the volume of the frustum of a cone with height \( h = 6 \) cm, and radii of the bases \( r_1 = 4 \) cm and \( r_2 = 2 \) cm.

A. 48\pi

B. 64\pi

Correct C. 72\pi

D. 80\pi

Correct Answer: C

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Question 18

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

Correct A. \left\{ (2, 2) \right\}

B. \left\{ (2, 2), \( -2, -2 \) \right\}

C. \left\{ (2, 2), \( -2, 2 \) \right\}

D. \left\{ (2, 2), \( 2, -2 \) \right\}

Correct Answer: A

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Question 19

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 20

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. \left\{ -2 \right\}

B. \left\{ -1, -3 \right\}

C. \left\{ -2, 2 \right\}

D. \left\{ -2, -4 \right\}

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.

Correct A. 1.999999999

B. 2.999999999

C. 3.999999999

D. 4.999999999

Correct Answer: A

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Question 22

A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16. What is the class width?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 23

Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 4).

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

A polynomial f(x) has roots at x = -2, x = 1, and x = 3. What is the product of the roots?

Correct A. -6

B. -12

C. -18

D. -24

Correct Answer: A

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Question 25

Find the area under the curve y = x^2 from x = 0 to x = 4.

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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