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  • Questions count: 14
  • Passing grade: 90%
  • Time limit: 5 days
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1.

Find the derivative of the function.

\[f(x) = 3x^4 - 5x^2 + 7x - 2\]

$f'(x) = 12x^4 - 10x^2 + 7$
$f'(x) = 4x^3 - 10x + 7$
$f'(x) = 12x^3 - 10x - 7$
$f'(x) = 12x^3 - 10x + 7$
2.

Divide and simplify. Assume all expressions under radicals are positive.

\[\frac{\sqrt{486x^{12}y^{22}}}{\sqrt[4]{6x^4y}}\]

$3xy\sqrt{6}$
$18x^2y^5\sqrt[4]{y}$
$3x^2y^5\sqrt[4]{y}$
$x^2\sqrt[4]{81y^{21}}$
3.

Simplify the expression. Write the answer with positive exponents only.

\[\left(\frac{x^3 y^{-2}}{x^{-1} y^4}\right)^2\]

$\frac{x^8}{y^{12}}$
$\frac{x^6}{y^8}$
$\frac{x^4}{y^6}$
$x^8 y^{12}$
4.

Solve for x using the quadratic formula. 23

\[2x^2 - 5x + 2 = 0\]

$x = -2 \text{ or } x = \frac{1}{2}$
$x = 2 \text{ or } x = -\frac{1}{2}$
$x = 1 \text{ or } x = \frac{1}{4}$
$x = 2 \text{ or } x = \frac{1}{2}$
5.

Divide and simplify. Assume all expressions under radicals are positive.

\[\frac{\sqrt{486x^{12}y^{22}}}{\sqrt[4]{6x^4y}}\]

$3x^2y^5\sqrt[4]{y}$
$3xy\sqrt{6}$
$x^2\sqrt[4]{81y^{21}}$
$18x^2y^5\sqrt[4]{y}$
6.

Find the derivative of the function.

\[f(x) = 3x^4 - 5x^2 + 7x - 2\]

$f'(x) = 12x^4 - 10x^2 + 7$
$f'(x) = 4x^3 - 10x + 7$
$f'(x) = 12x^3 - 10x + 7$
$f'(x) = 12x^3 - 10x - 7$
7.

Solve for x using the quadratic formula.

\[2x^2 - 5x + 2 = 0\]

$x = 2 \text{ or } x = \frac{1}{2}$
$x = 1 \text{ or } x = \frac{1}{4}$
$x = 2 \text{ or } x = -\frac{1}{2}$
$x = -2 \text{ or } x = \frac{1}{2}$
8.

Simplify the expression. Write the answer with positive exponents only.

\[\left(\frac{x^3 y^{-2}}{x^{-1} y^4}\right)^2\]

$x^8 y^{12}$
$\frac{x^8}{y^{12}}$
$\frac{x^6}{y^8}$
$\frac{x^4}{y^6}$
9.

Divide and simplify. Assume all expressions under radicals are positive. 22222

\[\frac{\sqrt{486x^{12}y^{22}}}{\sqrt[4]{6x^4y}}\]

$18x^2y^5\sqrt[4]{y}$
$18x^2y^5\sqrt[4]{y}$
$3x^2y^5\sqrt[4]{y}$
$3xy\sqrt{6}$
10.

Find the derivative of the function.

\[f(x) = 3x^4 - 5x^2 + 7x - 2\]

$f'(x) = 4x^3 - 10x + 7$
$f'(x) = 12x^4 - 10x^2 + 7$
$f'(x) = 12x^3 - 10x + 7$
$f'(x) = 12x^3 - 10x - 7$
11.

Simplify the expression. Write the answer with positive exponents only.

\[\left(\frac{x^3 y^{-2}}{x^{-1} y^4}\right)^2\]

$\frac{x^8}{y^{12}}$
$\frac{x^4}{y^6}$
$x^8 y^{12}$
$\frac{x^6}{y^8}$
12.

Divide and simplify. Assume all expressions under radicals are positive.

\[\frac{\sqrt{486x^{12}y^{22}}}{\sqrt[4]{6x^4y}}\]

$3x^2y^5\sqrt[4]{y}$
$x^2\sqrt[4]{81y^{21}}$
$18x^2y^5\sqrt[4]{y}$
$3xy\sqrt{6}$
13.

Divide and simplify. Assume all expressions under radicals are positive.

\[\frac{\sqrt{486x^{12}y^{22}}}{\sqrt[4]{6x^4y}}\]

$18x^2y^5\sqrt[4]{y}$
$3xy\sqrt{6}$
$3x^2y^5\sqrt[4]{y}$
$x^2\sqrt[4]{81y^{21}}$
14.

Solve for x using the quadratic formula.

\[2x^2 - 5x + 2 = 0\]

$x = 2 \text{ or } x = -\frac{1}{2}$
$x = 1 \text{ or } x = \frac{1}{4}$
$x = 2 \text{ or } x = \frac{1}{2}$
$x = -2 \text{ or } x = \frac{1}{2}$
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