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POST UTME FUTO 2017 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = $\frac{1}{2}\\()x^2$\) about the x-axis, from \$(y = frac{1}{2}x^2\(x = 0$ to $x = 2$.

Correct A. 4π

B. 8π

C. 16π

D. 32π

Correct Answer: A

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Question 2 View Details

If ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ), find ( f'(x) ) using the chain rule.

Correct A. ( f'$(x) =$$\frac{x - 2 (2x)}{x - 2 ^2}$\) )

B. ( f'$(x) =$$\frac{x - 2 2x - 4}{x - 2 ^2}$\) )

C. ( f'$(x) =$$\frac{x - 2 x + 2}{x - 2 ^2}$\) )

D. ( f'$(x) =$$\frac{x - 2 x - 4}{x - 2 ^2}$\) )

Correct Answer: A

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Question 3 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. $x - 3 \$^2 + $y - 4$^$2 = 25$ )

B. $x - 4 \$^2 + $y - 3$^$2 = 25$ )

C. $x - 5 \$^2 + $y - 3$^$2 = 25$ )

D. $x - 3 \$^2 + $y - 5$^$2 = 25$ )

Correct Answer: A

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Question 4 View Details

Solve the inequality $2^x > 3^x$ for ( x ).

A. $x < 0$

Correct B. $x > 0$

C. $x < 1$

D. $x > 1$

Correct Answer: B

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Question 5 View Details

Find the area under the curve $y = \frac{1}{x}$ from $x = 1$ to $x = 2$.

Correct A. $\(12 -$11\)

B. $\(12 -$12\)

C. $\(11 -$12\)

D. $\(12 -$13\)

Correct Answer: A

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Question 6 View Details

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 using the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 7 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24 $cm^2$

B. 100.48 $cm^2$

C. 200.96 $cm^2$

D. 400.96 $cm^2$

Correct Answer: A

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Question 8 View Details

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

A. $1/6$

Correct B. $1/12$

C. $1/24$

D. $1/36$

Correct Answer: B

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Question 9 View Details

A histogram is shown below. What is the mean of the data?

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 10 View Details

A line passes through the points (2,3) and (4,5). Find the equation of the line in slope-intercept form.

A. $y = 2x - 1$

Correct B. $y = 2x + 1$

C. $y = -2x + 1$

D. $y = -2x - 1$

Correct Answer: B

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Question 11 View Details

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

A. $x = -2$

Correct B. $x = -3$

C. $x = 2$

D. $x = 3$

Correct Answer: B

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Question 12 View Details

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. $1/2$

B. $1/3$

Correct C. $2/5$

D. $3/8$

Correct Answer: C

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Question 13 View Details

Find the derivative of the function ( f(x) = $3x^2 + 2x - 5$ ) using the chain rule.

Correct A. 6x + 2

B. $6x^2 + 2x$

C. $6x^2 + 4x$

D. $6x^2 - 2x$

Correct Answer: A

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Question 14 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30 $cm^3$

B. 40 $cm^3$

C. 50 $cm^3$

D. 60 $cm^3$

Correct Answer: A

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Question 15 View Details

A company produces two products, A and B. The profit from the sale of product A is 10 per unit, and the profit from the sale of product B is15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 16 View Details

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the expected value of X.

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

B. $\frac{3}{4}$

C. $\frac{5}{6}$

D. $\frac{7}{8}$

Correct Answer: A

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. ( 0.9544 )

Correct B. ( 0.9772 )

C. ( 0.9987 )

D. ( 0.9999 )

Correct Answer: B

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Question 18 View Details

Solve the quadratic equation $x^2 + 4x + 4 = 0$.

Correct A. $x = -2$

B. $x = -1$

C. $x = 0$

D. $x = 2$

Correct Answer: A

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Question 19 View Details

Let $\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}$. Find the cross product $\mathbf{a} \times \mathbf{b}$.

Correct A. $egin{pmatrix} -3 \ 6 \ -3 \end{pmatrix}$

B. $egin{pmatrix} 3 \ -6 \ 3 \end{pmatrix}$

C. $egin{pmatrix} 6 \ -3 \ -6 \end{pmatrix}$

D. $egin{pmatrix} -6 \ 3 \ 6 \end{pmatrix}$

Correct Answer: A

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Question 20 View Details

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

Correct A. ( f'$(x) = 2$\sin$x)\cos(x$ )

B. ( f'$(x) =$\sin(x) )

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

D. ( f'$(x) = 2$\cos(x) )

Correct Answer: A

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

Correct A. $\frac{16\pi}{3}$\)

B. $\frac{32\pi}{3}$\)

C. $\frac{64\pi}{3}$\)

D. $\frac{128\pi}{3}$\)

Correct Answer: A

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Question 22 View Details

Solve the inequality $|x - 2| > 3$.

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

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

C. $-\infty, -1$ \cup (2, 5)

D. $-\infty, 1$ \cup (2, 5)

Correct Answer: A

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Question 23 View Details

A binary operation (\ast\) is defined as \$(ast\(a ast b = a^2 + b^2$. Find the value of $2 \\(ast b = a^2 + b^2). Find the value of \ast 3$.

A. 13

Correct B. 25

C. 37

D. 49

Correct Answer: B

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Question 24 View Details

A die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. $\frac{1}{3}$\)

B. $\frac{1}{6}$\)

C. $\frac{1}{2}$\)

D. $\frac{2}{3}$\)

Correct Answer: A

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Question 25 View Details

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ with respect to x.

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

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

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

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

Correct Answer: A

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