Q3 Test Review

Fraction Operations (How-To)

100

What is the FIRST thing you should do before doing any operations?

FACTOR all the parts of the fractions!

200

When MULTIPLYING fractions, you...

Multiply all terms straight across the top and straight across the bottom.

300

When ADDING or SUBTRACTING fractions, you need...

Common Denominators!

400

When DIVIDING fractions, you...

Keep, change, flip!

(Keep first fraction the same, change operation to multiplication, and flip the 2nd fraction)

500

When SOLVING an equation with multiple fractions, you need to...

Get common denominators and then they cancel out when solving! 

Radical Operations

100

When simplifying a radical, how do you know how many numbers should be circled in a group?

Look at the index! (the baby number on the root)

200

When simplifying radicals, how do you simplify variables/exponents?

Option 1: Divide index by exponent. Any remainders STAY in the root.

Option 2: Write out appropriate number of variables and create groups of them based on the index.

300

When ADDING or SUBTRACTING radicals, you first need...

Like-Radicals (the radicals need to match!)

400

When adding like radicals, what numbers change? (Ex: the coefficients, the indexes, the numbers under the root, etc)

ONLY the coefficients change!

500

When MULTIPLYING radicals:

A. Do you need like radicals?

B. Which numbers do you combine?

A. You do NOT need like radicals to multiply.

B. Multiply all coefficients together AND multiply all numbers under the root together. Simplify the root afterwards. 

Solving Radical Equations

100

What operation "undoes" an exponent?

A root with an index that matches the exponent. 

200

What operation "undoes" a radical?

An exponent that is the same as the index.

300

When taking an EVEN root, how many answers should you get?

TWO answers. (Use a plus/minus immediately after taking the root of both sides)

400

Can you take the ODD root of a negative number? (Ex: cube root of -64)

YES! Check in your calc!

500

Solve: 2(x-3)²=18

x=6, 0

Logarithms

100

What is the base of a common log (log)?

10

200

What is the base of a natural log (ln)?

e

300

Change to exponential form: log(3x)=7

10⁷=3x

400

Expand Completely: ln(2x²y⁷)⁵

5ln2 + 10lnx + 35lny

OR

ln32 + 10lnx + 35lny

500

Condense completely: log2 - 6logx + 9logy - logz

log (2y⁹)/(x⁶z)

Solving Logarithms

100

What can you NOT take the log of?

You can't take the log of 0 or a negative number.

200

When do you need to check your answers when solving?

When your problem begins with multiple logs.

300

Solve: log(x+1)=3

x=999

400

Solve: ln(3x+2) = ln(4x-5)

x = 7

500

Solve: log(x) + log (4x) = 2

x = 5

1.Condense logs. 

2.Change forms

3. Solve for x.

4. Check answers.