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POST UTME AFE BABALOLA UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME AFE 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.

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Question 1

In a circle with center at point O and radius 6 units, what is the length of the arc intercepted by a central angle of 60 degrees?

Correct A. 6\pi

B. 3\pi

C. 2\pi

D. \pi

Correct Answer: A

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Question 2

Find the sum of the first 10 terms of the arithmetic sequence 3, 6, 9, ...

A. 60

B. 90

Correct C. 120

D. 150

Correct Answer: C

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Question 3

Solve the system of linear equations:\begin{align*} x + y &= 4 \ 2x - 3y &= -1 \end{align*}

Correct A. (1, 3)

B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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Question 4

A histogram is constructed with a bin width of 5 units. If the mean of the data is 15 and the median is 10, what is the mode?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 5

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 = -2x + 1

D. y = -2x - 1

Correct Answer: A

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Question 6

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).

Correct A. x = 3, y = 2

B. x = 2, y = 3

C. x = 1, y = 4

D. x = 4, y = 1

Correct Answer: A

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Question 8

Find the value of ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).

A. 0

B. 30

Correct C. 45

D. 60

Correct Answer: C

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Question 9

Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, ... ).

A. 100

B. 120

Correct C. 140

D. 160

Correct Answer: C

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Question 10

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

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 11

A histogram is a graphical representation of the distribution of a set of data. What is the primary advantage of u\sing a histogram over a bar chart?

Correct A. It provides a more detailed view of the data distribution

B. It is easier to read and unders\tand

C. It is more suitable for large datasets

D. It is more visually appealing

Correct Answer: A

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Question 12

Given the equation \( y = \frac{1}{2} \sin \( 2x \ \) ), find the value of ( y ) when \( x = \frac{pi}{4} \).

Correct A. 0.7071

B. 0.7072

C. 0.7073

D. 0.7074

Correct Answer: A

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Question 13

A curve has an equation of the form \( y = ax^2 + bx + c \). If the curve passes through the points ( (1, 4) ), ( (2, 9) ), and ( (3, 16) ), find the value of ( a ).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 14

A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.

Correct A. 452.389

B. 452.390

C. 452.391

D. 452.392

Correct Answer: A

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Question 15

A curve has an equation of the form \( y = \frac{1}{x} \). Find the derivative of the curve.

Correct A. -1/x^2

B. 1/x^2

C. -1/x

D. 1/x

Correct Answer: A

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Question 16

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. \frac{1}{4}

B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{5}{8}

Correct Answer: A

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Question 17

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 18

Find the mean and s\tandard deviation of the random variable X with probability density function f_X(x) = \frac{1}{2}x, 0 < x < 2.

Correct A. \mu = 1, \sigma = \frac{1}{\sqrt{3}}

B. \mu = 1, \sigma = \frac{1}{\sqrt{2}}

C. \mu = 1, \sigma = \frac{1}{\sqrt{5}}

D. \mu = 1, \sigma = \frac{1}{\sqrt{6}}

Correct Answer: A

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Question 19

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

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

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

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

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

Correct Answer: A

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Question 20

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. -1

D. 2

Correct Answer: A

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Question 21

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in mathbb{R} setminus { -2 } \).

Correct A. \( -∞, -2 \) ∪ (2, ∞)

B. \( -∞, -2 \) ∪ \( -2, 2 \)

C. \( -∞, 2 \)

D. (2, ∞)

Correct Answer: A

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Question 22

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ) in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ).

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

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

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

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

Correct Answer: A

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Question 23

If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ) 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 24

Solve the system of linear equations \( egin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases} \).

Correct A. x = 2, y = 1

B. x = 1, y = 2

C. x = 2, y = 2

D. x = 1, y = 1

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) ).

Correct A. 6

B. 8

C. 12

D. 16

Correct Answer: A

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