Module 1 Review

Module 1 Review

This activity is a COMBINATION of review resources created by your classmates! Work TOGETHER, sharing IDEAS, not ANSWERS. Tag Ms. Perrin in the chat if you need help, but let your expert in the group help first!

You should move through the activity together. If you can't finish a section in time, move on! This will take some of your asynchronous time, but there is no other asynchronous assignment! Yay!

Section 1 - Multiplying Binomials and Trinomials

Period 2 should work on this section from 11:00 until 11:10. The experts are Daniel, Luka, John, Eva, and Minh.

Period 3 should work on this section from 1:00 until 1:10. The experts are Caroline, Wyatt, Violet, and Katherine.

At that time, you should move on to section 2. Pick a timekeeper to keep your team on track!

Definition (from Eva)

• A binomial is an algebraic expression of the sum or the difference of two terms.

• A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Multiple Choice

Violet & Caroline's Problem: Multiply:

 $(3x^2+6x-12)(x-4)$  

•  $3x^3-6x^2-36x+48$  

•  $-18x^5-36x+48$  

•  $3x^2+6x-12x-4$  

•  $3x^3+6x^2-36x-48$  

Multiple Choice

Eva's Problem: Multiply

 $\left(y^2+3y^3\right)\left(6y+3y^3+4+6y^2\right)$  

•  $6y^3+9y^6+4y^2+18y^5$  

•  $9y^6+21y^5+24y^4+18y^3+4y^2$  

•  $y^2+18y^4+3y^3+4+6y^2$  

•  $9y^6+15y^5+12y^4+6y^3+4y^2$  

Open Ended

John's Discussion Question: When you multiply two polynomials, what can happen to the total number of terms?

Increase?

Decrease?

Stay the same?

Section 2 - Adding and Subtracting Polynomials

Period 2 should work on this section from 11:10 until 11:20. The experts are Caroline, Amanda, Tra, and Kara.

Period 3 should work on this section from 1:10 until 1:20. The experts are Ammran, Neena, Neko, Natalie, and Jack.

At that time, you should move on to section 3. Pick a timekeeper to keep your team on track!

Multiple Choice

Kara's Problem

Find the difference: 
 $\left(3b^2-b+7\right)-\left(b^2-b+8\right)$  

•  $2b^2-2b-1$  

•  $2b^2-1$  

•  $2b^2-2b+15$  

•  $2b^2+15$  

Multiple Choice

Natalie's Problem:  $\frac{1}{2}\left(7x+8x^2\right)-2x^2\left(3-4x+8x^2\right)$  

•  $-16x^4+6x^2+\frac{7}{2}x$  

•  $16x^4-8x^3-2x^2+\frac{7}{2}x$  

•  $10x^2-\frac{1}{2}x+3$  

•  $-16x^4+8x^3-2x^2+\frac{7}{2}x$  

Open Ended

Group discussion question: If you are adding two polynomials with the same degree, can the degree of the sum be...

Greater than the original degrees?

The same as the original degrees?

Less than the original degrees?

How do you know?

Section 3 - Solving Equations & Inequalities with Set Notation & Properties

Period 2 should work on this section from 11:20 until 11:30. The experts are Maeve, Perry, Klemens, Sam, and Etan.

Period 3 should work on this section from 1:20 until 1:30. The experts are Finn, Ripley, Tate, and Carmine.

At that time, you should move on to section 4. Pick a timekeeper to keep your team on track!

Multiple Choice

Finn's Problem

 $-3\left(-5x+x-10\right)\le5x+15$ 

•  $\left\{R\parallel x\le\frac{-15}{7}\right\}$  

•  $\left\{R\parallel x\le\frac{-15}{13}\right\}$  

•  $\left\{R\parallel x\ge\frac{-15}{7}\right\}$  

•  $\left\{R\parallel x\ge\frac{-15}{13}\right\}$  

Multiple Choice

 $-7\left(x-3\right)+bx>6$  

Ms. Perrin's Problem!
Solve for x when b = 2.

•  $x>\frac{17}{7}$  

•  $x<\frac{17}{7}$  

•  $x>3$  

•  $x<3$  

Open Ended

Discussion Question: Why does it make sense that the inequality sign flips when you multiply or divide by a negative number on both sides?

Section 4 - Solving Inequalities with And/Or and Set Notation

Period 2 should work on this section from 11:30 until 11:40. The experts are Naia, Charlie, Satoshi, Santi, and James.

Period 3 should work on this section from 1:30 until 1:40. The experts are Pablo, Ryan, Clara, and Mark.

At that time, you should move on to section 5. Pick a timekeeper to keep your team on track!

Fill in the Blank

Clara's Question:

____ inequalities require that BOTH inequalities are true, which means you are looking for the overlap.

Fill in the Blank

Clara's Question (continued): ____ inequalities require that AT LEAST ONE of the inequalities be true, which means that you are looking for the areas where either (or both) is shaded.

Multiple Select

Satoshi's Problem
This number line shows the graph of x>-5 and the graph of x>5. Which area (or areas) would be shaded for the compound inequality

 $x>-5\ OR\ x>5$  ? 

• 1

• 2

• 3

• None

OR Inequalities are satisfied when EITHER is true.

That means that the final graph of the inequality would look like this, because:

1. Neither inequality is true to the left of -5
2. x>-5 is true between -5 and 5
3. Both inequalities are true to the right of 5.

Multiple Select

Satoshi's Problem
This number line shows the graph of x>-5 and the graph of x>5. Which area (or areas) would be shaded for the compound inequality

 $x>-5\ AND\ x>5$  ? 

• 1

• 2

• 3

• None

AND Inequalities are satisfied when BOTH are true.

That means that the final graph of the inequality would look like this, because:

1. Neither inequality is true to the left of -5
2. Only x>-5 is true between -5 and 5
3. Both inequalities are true to the right of 5.

Multiple Choice

Pablo's Problem:

 $20x\le140\ AND\ 7x\ge49$  

•  $R$  

•  $\left\{7\right\}$  

•  $\phi$  

•  $\left\{R\parallel x\le7\right\}$  

•  $\left\{R\parallel x\ge7\right\}$  

Multiple Choice

Solve for x:

 $-9x+2>18\ \ \ OR\ \ \ 13x+15\le-4$  

•  $x\le-\frac{19}{13}$  

•  $x<-\frac{16}{9}$  

•  $-\frac{16}{9}<x\le-\frac{19}{13}$  

• All real numbers

• No Solution

Open Ended

Discussion question: What is a compound inequality (with AND/OR) that would have no solution?

Section 5 - Graphing Lines

Period 2 should work on this section from 11:40 until 11:50. The experts are Andrew, Will, and Ben.

Period 3 should work on this section from 1:40 until 1:50. The experts are Eli, Oscar, Charlie, and Efe.

At that time, you should move on to section 6. Pick a timekeeper to keep your team on track!

Fill in the Blank

Andrew, Will, and Ben's Problem:

What is the slope of the line shown? Write as an integer or a simplified fraction using /.

Multiple Choice

A variation on Oscar's Problem!

What is the equation of a line with a slope of 5 that contains (includes) the point (8,3)?

• $8x+3y=5$

• $y=5x-37$

• $3y=5x+8$

• $y=5x+3$

You did this in Math 8!

Multiple Select

Part 1: A line passes through the points (5, 0) and (8, -4).
Which two of these represent an equation of the line? 

•  $8x-4y=5$  

•  $4x+3y=20$  

•  $y=-\frac{4}{3}x+\frac{20}{3}$  

•  $y=-\frac{3}{4}x+5$  

Multiple Select

Part 2: A line passes through the points (5, 0) and (8, -4). We figured out that the equations  $4x+3y=20$  and  $y=-\frac{4}{3}x+\frac{20}{3}$  represent the line through these points. 

Which of the following points is ALSO on the line? 

•  $\left(-\frac{4}{3},\frac{20}{3}\right)$  
  

•  $\left(4,3\right)$  
  

•  $\left(2,4\right)$  
  

•  $\left(3,4\right)$  
  

Open Ended

Discussion Question: What is a strategy you can use to graph a line in the form $Ax+By=C$ ? 

Section 6 - Graphing Inequalities

Period 2 should work on this section from 11:50 until 12:00. The experts are Sophie & Meredith.

Period 3 should work on this section from 1:50 until 12:00. The experts are Amelia & Eleanor.

Then you're done! Remember that other students' review resources have been posted on our class page.

Multiple Choice

Which graph represents the inequality  $3x-4y>2$  ? 

Multiple Choice

Which inequality is represented by this graph?

• $y>-\frac{1}{2}x-3$

• $y\ge-\frac{1}{2}x-3$

• $y>\frac{1}{2}x-3$

• $y\ge\frac{1}{2}x-3$

Multiple Choice

Which system of inequalities is represented by this graph?

• 
  

  $y>2x-1$
  

  
  $y\le-\frac{1}{3}x+2$
  

• $y\ge2x-1$
  $y<-\frac{1}{3}x+2$
  

• $y<2x-1$
  $y\ge-\frac{1}{3}x+2$
  

• $y>2x-1$ $y\ge-\frac{1}{3}x+2$

Believe in your brain!

We will take our ANet assessment on Monday. Your homework is to complete your study guide (and ALEKS, as always!) - no exit ticket or discussion posts!