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POST UTME BABCOCK UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME BABCOCK 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

Determine the value of $k$ in the quadratic equation $x^2 + kx + 16 = 0$, given that one of the roots is $-4$.

Correct A. -8

B. -4

C. 8

D. 4

Correct Answer: A

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Question 2

A particle moves along the x-axis with its position given by the equation $s(t) = 2t^3 - 5t^2 + 3t + 1$. Find the velocity of the particle at time $t = 2$ seconds.

A. -14

Correct B. 14

C. -28

D. 28

Correct Answer: B

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Question 3

In the diagram below, $ABCD$ is a rec\tangle with $AB = 6$ cm and $BC = 8$ cm. Find the area of the shaded region.

A. 24

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 4

A bag contains 5 red marbles, 8 blue marbles, and 12 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. 1/3

Correct B. 2/3

C. 3/5

D. 4/5

Correct Answer: B

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Question 5

Solve the inequality $|2x - 1| geq 3$.

Correct A. $x leq -1$ or $x geq 2$

B. $x < -1$ or $x > 2$

C. $x leq 2$ or $x geq -1$

D. $x < 2$ or $x > -1$

Correct Answer: A

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Question 6

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 7

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

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 8

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $.

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 9

Find the value of $ \sin \( 2x \ $ ) given that $ \sin \( x \ $ = \frac{1}{2} ).

Correct A. \frac{\sqrt{3}}{2}

B. \frac{1}{2}

C. \frac{\sqrt{3}}{3}

D. \frac{1}{3}

Correct Answer: A

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Question 10

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

Correct A. 5, 2.5

B. 2.5, 5

C. 4, 3

D. 3, 4

Correct Answer: A

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Question 11

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pi\text{ cm}^3

B. 300\pi\text{ cm}^3

Correct C. 400\pi\text{ cm}^3

D. 500\pi\text{ cm}^3

Correct Answer: C

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Question 12

Solve for x in the equation $ \log_2\( x^2 \ $ = 4\).

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 13

A survey of 100 students found that 60% of them preferred Mathematics, 20% preferred Science, and 20% preferred English. If a student is randomly selected, what is the probability that the student prefers Mathematics or Science?

A. 0.4

Correct B. 0.6

C. 0.8

D. 1.0

Correct Answer: B

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Question 14

Find the surface area of the sphere with radius 8 cm.

A. 256\pi\text{ cm}^2

B. 512\pi\text{ cm}^2

Correct C. 768\pi\text{ cm}^2

D. 1024\pi\text{ cm}^2

Correct Answer: C

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Question 15

A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4 cm

B. 6 cm

Correct C. 8 cm

D. 10 cm

Correct Answer: C

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Question 16

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 17

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

Correct A. \\begin{pmatrix} 1 \\ 1 \\end{pmatrix}

B. \\begin{pmatrix} -1 \\ 3 \\end{pmatrix}

C. \\begin{pmatrix} 2 \\ -1 \\end{pmatrix}

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

Correct Answer: A

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Question 18

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

Correct A. \frac{-2x}{$ x^2 + 1 $^2}

B. \frac{2x}{$ x^2 + 1 $^2}

C. \frac{x}{$ x^2 + 1 $^2}

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

Correct Answer: A

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Question 19

Solve the matrix equation AX = B, where A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}, X = \begin{pmatrix} x \ y \end{pmatrix}, and B = \begin{pmatrix} 5 \ 6 \end{pmatrix}.

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

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

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

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

Correct Answer: A

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Question 20

Find the area of the triangle formed by the points (0, 0), (2, 0), and (1, 2).

Correct A. \frac{1}{2}bh

B. bh

C. \frac{1}{4}bh

D. \frac{1}{8}bh

Correct Answer: A

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Question 21

Solve the inequality x^2 - 4x - 5 > 0.

Correct A. $ -\\infty, -1 $ \\cup $ 5, \\infty $

B. $ -\\infty, 1 $ \\cup $ 5, \\infty $

C. $ -\\infty, -5 $ \\cup $ 1, \\infty $

D. $ -\\infty, 5 $ \\cup $ 1, \\infty $

Correct Answer: A

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Question 22

Find the derivative of the function f(x) = \frac{1}{x^2 - 4} u\sing the quotient rule.

Correct A. \frac{2x}{$ x^2 - 4 $^2}

B. \frac{-2x}{$ x^2 - 4 $^2}

C. \frac{x}{$ x^2 - 4 $^2}

D. \frac{-x}{$ x^2 - 4 $^2}

Correct Answer: A

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Question 23

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

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

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

C. \\begin{pmatrix} 3 \\ 0 \\end{pmatrix}

D. \\begin{pmatrix} 0 \\ 3 \\end{pmatrix}

Correct Answer: A

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Question 24

In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both Mathematics and Science. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.7

B. 0.6

C. 0.5

D. 0.4

Correct Answer: A

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Question 25

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 12\pi

Correct B. 24\pi

C. 36\pi

D. 48\pi

Correct Answer: B

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