WEEK 1

DONE Unit 2: Verb Agreement

1 Topic | 3 Quizzes
DONE Unit 3: Punctuation

3 Topics | 3 Quizzes
DONE Unit 4: Apostrophes

3 Quizzes
DONE Unit 6: Using Desmos

3 Quizzes
DONE Unit 7: Ratios, Rates, and Conversions

1 Topic | 3 Quizzes
DONE Unit 8: Slope Intercept

3 Quizzes
DONE Unit 10: Line Graphs and Bar Graphs

3 Quizzes
DONE Unit 11: Scatterplots

3 Quizzes
WEEK 2

DONE Unit 12: Words in Context

3 Quizzes
DONE Unit 13: Passage Summarization

3 Quizzes
DONE Unit 14: Pronouns

3 Quizzes
DONE Unit 15: Transition Words and Phrases Part 1

1 Topic | 3 Quizzes
DONE Unit 16: Word Choice

3 Quizzes
Unit 17: Linear Word Problems – Type 1: Numbers

2 Topics | 2 Quizzes
Unit 18: Transforming Equations (Single Variable)

1 Topic | 2 Quizzes
DONE Unit 19: Systems of Linear Equations

1 Topic | 3 Quizzes
DONE Unit 20: Systems of Inequalities

1 Topic | 3 Quizzes
DONE Unit 21: Systems Word Problems

3 Quizzes
WEEK 3

DONE Unit 22: Figures and Tables

3 Quizzes
DONE Unit 23: Author’s Objective

3 Quizzes
DONE Unit 24: Misplaced Modifiers

3 Quizzes
DONE Unit 26: Statistics

1 Topic | 3 Quizzes
DONE Unit 27: Average from a Table

3 Quizzes
DONE Unit 28: Probabilities

3 Quizzes
DONE Unit 29: Percentages

1 Topic | 3 Quizzes
DONE Unit 30: Angle Problems

1 Topic | 3 Quizzes
DONE Unit 31: Circle Basics

1 Topic | 3 Quizzes
DONE Unit 32: Triangles

3 Quizzes
WEEK 4

DONE Unit 33: Accomplish the Goal

1 Topic | 3 Quizzes
DONE Unit 34: Punctuation Part 2

1 Topic | 1 Quiz
DONE Unit 35: Command of Evidence

3 Quizzes
DONE Unit 36: Parabolas and Factoring

2 Topics | 3 Quizzes
DONE Unit 37: Non-Linear Systems

1 Topic | 3 Quizzes
DONE Unit 38: Quadratic and Discriminant

3 Quizzes
DONE Unit 39: Zeros in Quadratics

3 Quizzes
DONE Unit 41: SohCahToa

3 Quizzes
WEEK 5

DONE Unit 42: Inferences

3 Quizzes
DONE Unit 43: Complete the Text

3 Quizzes
DONE Unit 44: Dual Passages

3 Quizzes
DONE Unit 45: Functions

1 Topic | 3 Quizzes
DONE Unit 46: Functions with Coordinate Box

1 Topic | 3 Quizzes
DONE Unit 47: Exponents and Radicals

1 Topic | 3 Quizzes
DONE Unit 48: Constants

1 Topic | 3 Quizzes
DONE Unit 49: Surveys and Studies

3 Quizzes
WEEK 6

DONE Unit 51: Equal Polynomials

3 Quizzes
DONE Unit 53: Area and Volume

3 Quizzes
DONE Unit 54: Absolute Value

3 Quizzes
DONE Unit 55: Box Plots

3 Quizzes
DONE Unit 56: Polynomial Graphs

3 Quizzes
DONE Unit 57: Translations

3 Quizzes
DONE Unit 58: Vertex Form of a Parabola

3 Quizzes
DONE Unit 59: Creative Geometry

3 Quizzes
EXTRA

Logical Comparisons

2 Quizzes
Here’s a crazy looking radical problem:

For which of the following values of *w* does $$\sqrt[4]{16w^3x^\frac9w}=(2)(3^\frac34)(x^\frac34)$$

A) 2

B) 3

C) 4

D) 6

**Strategy****:**

**Separate terms underneath a radical.****Consider writing the radicals as fractional exponents then using the exponent rules.****Always check for extraneous solutions!**

__Radical Rules__

- This property allows you to pull numbers out from the square root sign: $$\sqrt{xy}=\sqrt x\;\times\;\sqrt y\\\sqrt{32}=\sqrt{2\times16}=\sqrt2\;\times\;\sqrt{16}=4\sqrt2$$
- $$\sqrt{\frac xy}=\frac{\sqrt x}{\sqrt y}$$
- If we have different roots, we have to first convert to exponents to combine. $$\sqrt8\;\times\;\sqrt[3]8\;\neq\;\sqrt[4]8$$
- Instead, we must do $$\sqrt8\;\times\;\sqrt[3]8=8^\frac12\;\times\;8^\frac13=8^\frac56=\sqrt[6]{8^5}$$

Now, back to our crazy example:

This is the kind of problem the SAT wants you to look at and freak out about because it looks so complex. But as always, getting to the answer isn’t so hard if you know your rules!

We see on the right side we have fractional exponents. This is a big clue that we need to convert the left side. We start by getting rid of our radical.

$$(16w^3x^\frac9w)^\frac14$$

Remember that when we have an exponent raised to an exponent, we multiply. Don’t forget about the coefficient!

$$16^\frac14{\;w}^\frac34\;x^\frac9{4w}=(2)(3^\frac34)(x^\frac34)$$

We want the value of *w*. If we look at our middle terms, we can now easily find *w* has to equal 3. We only had to do two steps to find this!

__Extraneous Solutions__

One more note on radicals. Anytime you start with a radical in an equation and square both sides to get rid of it, you risk introducing what is known as an **extraneous solution**. This is a false answer that won’t work in the original equation. For example:

$$\sqrt{x-a}=x-4$$

If *a* = 2, what is the solution set of the equation above?

A) {3, 6}

B) {2}

C) {3}

D) {6}

The first thing we need to do is plug in our constant.

$$\sqrt{x-2}=x-4$$

Then, a quick look at our answers tells us there are only 3 possibilities (2, 3, and 6). This equation is simple enough that you should just plug them in and solve three times.

However, if you forgot to do that, or just like a little extra pain on your SAT, you could square both sides to get

$$x-2=(x-4)(x-4)\\x-2=x^2-8x+16\\0=x^2-9x+18\\0=(x-3)(x-6)$$

So 3,6 is our solution set. But you already see where this one is going by the section we’re in. If we plug 3 back into our original equation, we get

$$\sqrt{3-2\;}=3-4\\\sqrt1=-1\\1=-1$$

Clearly false! Always check for extraneous solutions when you square to clear away radicals.

**Extraneous solutions**

We can’t stress this enough: test your solutions when dealing with radicals or variables in denominators. Almost always, one of the solutions is extraneous (doesn’t work).

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