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POST UTME BELLS UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME BELLS 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

Determine the mean of the following set of numbers: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

B. 8

C. 10

Correct D. 12

Correct Answer: D

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Question 2

A histogram is constructed with the following data: 2, 4, 6, 8, 10. The height of the bars is proportional to the frequency of the data. What is the mode of the data?

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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Question 3

A dep\endent event is defined as an event whose probability of occurrence is affected by the occurrence of another event. What is the probability of drawing a red card from a deck of 52 cards if the first card drawn is a red card?

Correct A. 1/2

B. 1/3

C. 2/3

D. 3/4

Correct Answer: A

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Question 4

A 3x3 matrix is given by the following equation: [ A = egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} ]. What is the determinant of matrix A?

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

A sequence is given by the following equation: [ a_n = 2n + 1 ]. What is the 5th term of the sequence?

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 6

In a survey of 100 students, the mean height was 170 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

Correct A. 0.1587

B. 0.3413

C. 0.4772

D. 0.6827

Correct Answer: A

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Question 7

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism?

A. 400 cm^3

B. 500 cm^3

Correct C. 600 cm^3

D. 800 cm^3

Correct Answer: C

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Question 8

Solve the system of equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \)

Correct A. \( egin{bmatrix} -1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} 1 \ -2 \end{bmatrix} \)

C. \( egin{bmatrix} 2 \ -1 \end{bmatrix} \)

D. \( egin{bmatrix} -2 \ 1 \end{bmatrix} \)

Correct Answer: A

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Question 9

A circle has a radius of 4 cm. What is the area of the circle?

A. 50.24 cm^2

Correct B. 100.48 cm^2

C. 200.96 cm^2

D. 50.24 cm^2

Correct Answer: B

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Question 10

A histogram shows the distribution of exam scores for a class of 100 students. The histogram has 5 bars, with the heights of the bars being 10, 20, 30, 20, and 20. What is the mean of the exam scores?

A. 20

B. 22

Correct C. 25

D. 28

Correct Answer: C

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Question 11

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12

Solve the matrix equation \( \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 8 \end{bmatrix} \).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 13

Find the value of ( x ) in the equation \( 2^x = 16 \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 14

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (1, ∞)

Correct Answer: A

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Question 15

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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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

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 18

Solve the equation \sin^2(x) + \cos^2(x) = 1 for x.

Correct A. x = \frac{\pi}{4}

B. x = \frac{\pi}{2}

C. x = \frac{3\pi}{4}

D. x = \pi

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 quotient rule.

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

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

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

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

Correct Answer: C

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Question 20

Evaluate the definite integral \int_0^1 x^2 dx.

Correct A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

D. 1

Correct Answer: A

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Question 21

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice; otherwise, the coin is flipped only once. What is the probability that at least one of the coin flips shows heads?

A. 1/4

Correct B. 1/2

C. 3/4

D. 2/3

Correct Answer: B

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Question 22

The volume of a sphere (V) is given by the formula \( V = \frac{4}{3} \pi r^3 \ \). If the radius of the sphere is increased by 20%, what percentage increase will occur in its volume?

A. 4%

B. 12%

Correct C. 24%

D. 48%

Correct Answer: C

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Question 23

The mean of five numbers is 20. If one of the numbers is increased by 10, what will be the new mean?

A. 20

Correct B. 21

C. 22

D. 23

Correct Answer: B

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Question 24

Solve the system of equations: \( x + y = 4 \) and \( 2x - 3y = - 6 \).

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

B. \( x = 3, y = 1 \)

C. \( x = 4, y = 0 \)

D. \( x = 5, y = -1 \)

Correct Answer: A

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Question 25

Find the derivative of the function \( f(x) = 3x^2 \sin x \).

Correct A. \( f'(x) = 3x^2 \cos x + 6x \sin x \)

B. \( f'(x) = 3x^2 \sin x \)

C. \( f'(x) = 3x \cos x \)

D. \( f'(x) = 3x \sin x \)

Correct Answer: A

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