Final Exam Review Adv Algebra Day 2

Dividing Complex numbers

Multiple Choice

What is the conjugate of 2 + 3i?

• 2 - 3i

• -2 + 3i

• -2 - 3i

• 2 + 3i

Multiple Choice

What is the conjugate of -5 + 4i

• 5 + 4i

• 5 - 4i

• -5 - 4i

• -5 + 4i

Multiple Choice

What is the conjugate of 4i?

• 4i

• 4 + 4i

• 4-4i

• -4i

Multiple Choice

$$\frac{5-8i}{3+2i}$$  , what do you do to divide?

• Multiply the top and bottom by 3-2i

• Multiply the top and bottom by 5 + 8i

• multiply the top by 5 + 8i and the bottom by 3 - 2i

• Multiply the top and bottom by -3 - 2i

Multiple Choice

Simplify

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

4.6 Add/Subtract Unlike denominators

Notes

Multiple Choice

$$\frac{u-v}{8v}+\frac{6u-3v}{8v}$$  

• $$\frac{7u-4v}{16v}$$  

• $$\frac{7u-4v}{8v}$$  

• $$\frac{7u+2v}{8v}$$  

• $$\frac{7u+2v}{16v}$$  

Multiple Choice

Lets multiply, Only distribute the NUMERATOR (top)

$$\frac{m-3}{m-3\ }\cdot\frac{4}{5m+4}$$  

• $$\frac{4m-12}{\left(m-3\right)\left(5m+4\right)}$$  

• $$\frac{4m-12}{m-3}$$  

• $$\frac{4m-12}{5m+4}$$  

• $$\frac{m-3}{5m+4}$$  

• $$\frac{4}{m-3}$$  

Multiple Choice

Simplify.

$$\frac{4m-12}{\left(m-3\right)\left(5m+4\right)}+\frac{10m^2+8m}{\left(m-3\right)\left(5m+4\right)}$$  

• $$\frac{3m+3}{m-1}$$  

• $$\frac{10m^2+12m-12}{\left(m-3\right)\left(5m+4\right)}$$  

• $$\frac{4+2m}{6m+1}$$  

• $$\frac{21m-56}{5\left(m-6\right)}$$  

What does the problem look like now?

Multiple Choice

$$\frac{5x^2+30x}{3\left(x+6\right)}-\frac{3}{3\left(x+6\right)}$$  

• $$\frac{5x^2+31x+4}{3\left(x+6\right)}$$  

• $$\frac{5x^2+31x+6}{2}$$  

• $$\frac{x}{1-x^2-6x}$$  

• $$\frac{5x^2+30x-3}{3\left(x+6\right)}$$  

Multiplying Rational Expressions

Multiple Choice

Multiply and simplify: $$\frac{v+4}{7v^2\left(v+4\right)}\times\frac{7v^2\left(v+1\right)}{10}$$

• $$\frac{7v^2\left(v+1\right)}{10}$$

• $$v+1$$

• $$\frac{1}{10}$$

• $$\frac{v+1}{10}$$

Multiple Choice

• n - 1

• 
  $$\frac{2\left(n-1\right)}{2}$$

• 2(n - 1)

• $$\frac{\left(n-1\right)}{2}$$

Multiple Choice

DIVIDE the rational expressions:

$$\frac{x+8}{\left(x+4\right)\left(x-3\right)}\div\frac{x+8}{5\left(x+4\right)}$$  

• $$\frac{x+8}{5}$$  

• $$\frac{5}{x+4}$$  

• $$\frac{5}{x-3}$$  

• $$\frac{1}{x-3}$$  

Multiple Choice

DIVIDE the rational expressions:

$$\frac{x+8}{\left(x+4\right)\left(x-3\right)}\div\frac{x+8}{5\left(x+4\right)}$$  

• $$\frac{x+8}{5}$$  

• $$\frac{5}{x+4}$$  

• $$\frac{5}{x-3}$$  

• $$\frac{1}{x-3}$$  

Sum and Differences of Cubes

Multiple Choice

Level 2 Question 14
8x⁶ - 64

• Prime
• 8(x² - 2)³
• 8(x²-2)(x⁴+2x²+4)
• 8(x-2)⁶

Multiple Choice

Factor:   x³ + 1

• (x + 1)³
• (x+1)(x² - x + 1)
• (x - 1) (x² + x - 1)
• (x + 1)(x² - 2x + 1)

Multiple Choice

Write the expression in radical form:
$$3^{\frac{5}{4}}$$  

• $$^5\sqrt{3^4}$$  

• $$^4\sqrt{3^5}$$  

• $$\sqrt{3^4}$$  

• $$\sqrt{3^{\frac{5}{4}}}$$  

Multiple Choice

Write the expression in radical form:
$$\left(ab\right)^{\frac{3}{4}}$$  

• $$^4\sqrt{\left(ab\right)^3}$$  

• $$^4\sqrt{\left(ab^3\right)}$$  

• $$^3\sqrt{\left(ab\right)^4}$$  

Multiple Choice

Write the expression in exponential form:

$$^4\sqrt{k^5}$$  

• $$k^{\frac{5}{4}}$$  

• $$k^{\frac{4}{5}}$$  

• $$\frac{k^4}{5}$$  

Multiple Choice

Write the expression in exponential form:
$$\left(\sqrt{3m}\right)^7$$  

• $$\left(\sqrt{3m}\right)^{\frac{1}{2}}$$  

• $$\left(\left(3m\right)^{\frac{1}{2}}\right)^7$$  

• $$\left(3m\right)^{\frac{7}{2}}$$  

• $$3m^{\frac{7}{2}}$$  

Multiple Choice

Solve the radical equation

• 25

• 50

• 125

• 5

Multiple Choice

• 4

• -4

• 2

• -2

Multiple Choice

Solve

• -14
• 14
• no solution
• 28

The base of the log is 10 and the base of the the exponent is also 10.

Multiple Choice

Rewrite the equation in logarithmic form.

• A
• B
• C
• D

Multiple Choice

Rewrite the equation in logarithmic form.

• A
• B
• C
• D

Multiple Choice

Rewrite in exponential form.

• A
• B
• C
• D

Multiple Choice

Rewrite in exponential form.

• A
• B
• C
• D