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POST UTME BABCOCK UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details

Determine the value of (k\) in the quadratic equation $x^2 + kx + 16 = 0\\((k) in the quadratic equation$, 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 View Details

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 $t = 2\\((s(t) = 2t^3 - 5t^2 + 3t + 1). Find the velocity of the particle at time$ seconds.

A. -14

Correct B. 14

C. -28

D. 28

Correct Answer: B

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Question 3 View Details

In the diagram below, (ABCD\) is a rectangle with $AB = 6\\((ABCD) is a rectangle with$ 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the value of ($12x \$ ) given that \$($12x $$1x \$ = $\frac{1}{2}$\) ).

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 View Details

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}\(\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 View Details

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\pitext{ cm}^3

B. 300\pitext{ cm}^3

Correct C. 400\pitext{ cm}^3

D. 500\pitext{ cm}^3

Correct Answer: C

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Question 12 View Details

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 View Details

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 View Details

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

A. 256\pitext{ cm}^2

B. 512\pitext{ cm}^2

Correct C. 768\pitext{ cm}^2

D. 1024\pitext{ cm}^2

Correct Answer: C

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Question 15 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function f(x) = $\frac{1}{x^2 + 1}$\)\) using 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 View Details

Solve the matrix equation (AX = B\), where A = \begin{pmatrix} 1 & 2 \\$((AX = B)$, where A = \ 3 & 4 \end{pmatrix},$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 View Details

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 View Details

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 View Details

Find the derivative of the function f(x) = $\frac{1}{x^2 - 4}$\)\) using 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 View Details

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 View Details

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 View Details

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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