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POST UTME BOWEN UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME BOWEN UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In a certain number base, the representation of the number 27 is 101. What is the value of the number base?

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 2

A set 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 will be between 70 and 80?

Correct A. 0.34

B. 0.68

C. 0.85

D. 0.95

Correct Answer: A

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Question 3

A binary operation * is defined as follows: a * b = a^2 + b^2. Find the value of \( 2 * 3 \) * 4.

A. 32

B. 40

Correct C. 48

D. 64

Correct Answer: C

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Question 4

A histogram of exam scores is shown below. What is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 5

A vector →A is given by →A = 2→i + 3→j. Find the magnitude of →A.

A. √13

Correct B. √15

C. √17

D. √19

Correct Answer: B

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Question 6

In a certain number base, the digits 1, 2, and 3 represent the values 2, 5, and 8, respectively. What is the value of the number 432 in this base?

A. 19

Correct B. 21

C. 23

D. 25

Correct Answer: B

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Question 7

A right circular cone has a height of 12 cm and a base radius of 6 cm. If a smaller cone is formed by melting 1/4 of the original cone, what is the volume of the smaller cone?

Correct A. 288π cm^3

B. 384π cm^3

C. 576π cm^3

D. 768π cm^3

Correct Answer: A

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Question 8

A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. 1/6

B. 1/12

Correct C. 1/18

D. 1/36

Correct Answer: C

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Question 9

In a certain trigonometric identity, \sin\( x+y \) = \sin\( x)\cos(y \) + \cos\( x)\sin(y \). If x = 30° and y = 60°, what is the value of \sin\( x+y \)?

Correct A. √3/2

B. 1/2

C. √2/2

D. 1/√2

Correct Answer: A

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Question 10

The area under the curve y = x^2 from x = 0 to x = 4 can be calculated u\sing the definite integral. What is the value of this integral?

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 11

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.

A. 8

Correct B. 12

C. 16

D. 20

Correct Answer: B

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Question 12

A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } x = 1, \\ 0.3 & \text{if } x = 2, \\ 0.5 & \text{if } x = 3. \end{cases} \] Find the mean of X.

A. 1.5

B. 2.0

Correct C. 2.5

D. 3.0

Correct Answer: C

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Question 13

Solve the system of equations \[ \begin{cases} x + y + z = 6, \\ 2x + 2y + 3z = 12. \end{cases} \] u\sing matrices.

Correct A. \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 4 \\ 5 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 5 \\ 6 \end{bmatrix}

Correct Answer: A

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Question 14

A polynomial function f(x) has a degree of 4 and the following properties: f(1) = 2, f\( -1 \) = -2, f(0) = 0, f(2) = 10. Find the value of f(3).

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 15

Two events A and B are indep\endent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events A and B occur.

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 16

Find the equation of the circle with centre \( -2, 3 \) and radius 4.

Correct A. \boxed{\( x + 2 \)^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 17

Solve the inequality \frac{x - 2}{x + 1} > 0.

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

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

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

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

Correct Answer: A

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Question 18

Find the value of \sum_{n=1}^{\infty} \frac{1}{n^2}.

Correct A. \boxed{\frac{\pi^2}{6}}

B. \frac{\pi^2}{12}

C. \frac{\pi^2}{24}

D. \frac{\pi^2}{48}

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. \boxed{y = 1x + 1}

B. y = 2x + 1

C. y = x + 1

D. y = 2x - 1

Correct Answer: A

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Question 20

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

Correct A. \boxed{x = \pm 10}

B. x = 10

C. x = -10

D. x = 5

Correct Answer: A

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Question 21

In a binary system, what is the decimal equivalent of the binary number 1011?

A. 11

Correct B. 13

C. 15

D. 17

Correct Answer: B

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Question 22

A histogram is a graphical representation of the distribution of a set of data. What is the primary purpose of a histogram?

A. To show the mean of the data

B. To show the median of the data

Correct C. To show the distribution of the data

D. To show the range of the data

Correct Answer: C

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Question 23

A vector Δπ is defined as Δπ = πₑ - πₒ. What is the magnitude of Δπ?

A. |Δπ| = |πₑ| - |πₒ|

B. |Δπ| = |πₑ| + |πₒ|

Correct C. |Δπ| = |πₑ| - |πₒ|

D. |Δπ| = |πₑ| × |πₒ|

Correct Answer: C

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Question 24

A polynomial function f(x) = x^3 - 6x^2 + 11x - 6 is given. What is the value of f\( -1 \)?

Correct A. 1

B. -1

C. 0

D. 6

Correct Answer: A

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Question 25

A curve is defined by the equation y = x^2 + 2x - 3. What is the area under the curve between x = -1 and x = 2?

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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