Algebra 1 3rd 9 Weeks Review

Algebra 1

3rd 9 Weeks Review

• Correlation coefficient

• Linear Regression

• System of Equations - solution at intersection

• Inequalities - solving algebraically, solutions on graph

• System of Inequalities - solutions in overlap region

• Properties of Exponents

Correlation Coefficient (r)

How closely scatterplot data aligns with a linear equation

r= -1 r= 0 r= 1

Strong negative NONE Strong positive

Multiple Choice

What is the correlation for the following Scatter Plot.

• Weak Positive

• No Correlation

• Strong Negative

• Weak Negative

• Strong Positive

Multiple Choice

What is the correlation for the following Scatter Plot.

• Weak Positive

• No Correlation

• Strong Negative

• Weak Negative

• Strong Positive

Multiple Choice

What is the correlation for the following Scatter Plot.

• Weak Positive

• No Correlation

• Strong Negative

• Weak Negative

• Strong Positive

Multiple Choice

Given the following Scatter Plot, select the option that is most likely the r value.

• $$r=.27$$

• $$r=-.862$$

• $$r=.934$$

• $$r=.54$$

Multiple Choice

Given the following Scatter Plot, select the option that is most likely the r value.

• $$r=-.45$$

• $$r=-.981$$

• $$r=.728$$

• $$r=.12$$

Multiple Choice

Given the following Scatter Plot, select the option that is most likely the r value.

• $$r=-.1$$

• $$r=-.981$$

• $$r=.92$$

• $$r=.765$$

Multiple Choice

Correlation coefficient is the statistic that measures the strength and direction of a linear association between two quantitative variables.

• True

• False

Multiple Choice

If r=0, there is a strong correlation.

• True

• False

Multiple Choice

r = -0.3 is considered to have...

• moderate negative correlation

• weak negative correlation

• no correlation

• strong negative correlation

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Linear Regression

Table: STAT-> Edit L1 for x L2 for y

STAT--> CALC #4 LinReg, Enter 3x

2nd 0 to turn "Diagnostic On" for r value

Example

A group of scientists were conducting a study on a particular type of crime in Lexington, Kentucky. They conducted the study over 10 years and the results are shown in the table below, where x represents the year and y represents the number of times that crime was committed.

You Try It

The profit of a company is based on the price of the product it sells. The table below shows how the profit of a company (y) is related to the cost of one of its products (x).

Multiple Choice

 B) What is the correlation coefficient, r? (Round to the nearest hundreth.)

• $$r=0.5$$  

• $$r=-0.67$$  

• $$r=-0.32$$  

Solutions to System of Equations

​Where the lines intersect

*Use your calculator y = then graph,

2nd Calc Trace for intersection

Example: 3x + 4y = 12. --> y = (12 - 3x)/4

Multiple Choice

Solve:
y = -1x - 5
4x - 8y = 4

• (-3, -2)

• (5, -7)

• (3, 9)

• (-5, 4)

Multiple Choice

Solve the system of Equation (x,y)
3x + y = –14
–2x – y = 9

• (-5,1)

• (5,-1)

• (1,4)

• (-1,4)

Multiple Choice

Solve the system of Equation (x,y)
3x + y = –21
x + y = –5  

• (-3,8)

• (8,-3)

• (3,-8)

• (-8,3)

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

PLUG IN METHOD

Multiple Choice

Will the solution (-3, -7) make the following system of equations a true statement?

y = 4x + 5

y = x – 4

• YES

• NO

Multiple Choice

How many solutions does this system have?

y = 7x - 3

y = 7x +6

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does this system have?

y = 8x + 8

y = 8x + 8

• One Solution

• No Solution

• Infinitely Many Solutions

Multiple Choice

Lines that are parallel have __________.

• no solutions

• infinitely many solutions

• one solution

Multiple Choice

Lines that intersect once have __________.

• no solutions

• infinitely many solutions

• one solution

Solving Inequalities

​Move y to left by itself

Move everything else to right

LAST STEP divide by coefficient in front of y

*If it is NEGATIVE flip the inequality

Example: 8x - 4y > 12

-4y > 12 - 8x

y < -3 + 2x

Multiple Choice

-4 + y < -8

• y < 4

• y < -12

• y < -4

• y < 12

Multiple Choice

Does the sign need to flip when solving?
8y < (-40)

• YES

• NO

Multiple Choice

- 2k > 18

• k is greater than 20

• k is less than negative 9

• k is greater than negative 9

• k is less than 36 

Multiple Choice

-8x < 48

• x < -6

• x > -6

• x < 6

• x > 6

Multiple Choice

Solve 

• a≤1

• a≤25

• a>1

• a<25

Replace this with your body text.

​Happy teaching!

Multiple Choice

Select the correct graph for y > 1/3x + 2

• A

• B

• C

• D

Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

Multiple Choice

Which of the following equations match the given graph?

• y > 2x - 5

• y ≥ 7/4x + 2

• x < -5

• x > -5

Multiple Choice

Identify the inequality.

• y > 2

• y ≤ 1

• x ≥ 2

• y ≥ 1

Multiple Choice

Select the graph for y >  -2x - 3

• A

• B

• C

• D

Multiple Choice

which equation best represents this graph?

• y < 1/2x + 1

• y < 1/2x + 2

• y >1/2x + 2

• y > 2x

Graphing Inequalities

​With your calculator

y = ( )/coefficient

Move cursor to left and select / for shaded above or below

Then graph

Systems of Inequalities

*Solution in OVERLAP of shaded region

Hotspot

Select all of the coordinates that ARE solutions to the system of inequalities shown.

Hotspot

Place a dot on the solution of the system:

$$2x-3y=-12$$

$$y=-\frac{1}{2}x+4$$

Drag and Drop

The reason (2, 0) is NOT a solution is because ​

Placeholder

Drag these tiles and drop them in the correct blank above

it is on the dotted line.

it is in the shaded region.

it is an intercept.

it doesn't work.

False, it is a solution. Don't try to trick me!

Multiple Choice

The maximum capacity for the Movie Theatre is 455 people.

• <

• >

• <

• >

Multiple Choice

Little Italy's special events room can seat at most 50 guests.

• >

• >

• <

• <

Multiple Choice

The minimum height to ride the Intimidator roller coaster at Carowinds is 4'6".

• >

• <

• >

• <

Multiple Choice

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Multiple Choice

Which graph represents the system of inequalities?

$$y<\frac{1}{2}x-1$$  

$$y\ge-3x+4$$   

Multiple Choice

Is (0,0) a solution to the system?

• Solution

• Not a solution

Multiple Choice

Which of the following points is a solution to the system of inequalities?

• (0,0)

• (4,10)

• (6,-4)

• The system has no solutions.

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Solve the system of inequalities by graphing. $$8x\ +4y\ge10\ and\ 3x-6y>12$$  

Multiple Choice

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

Power:

(a^m)ⁿ = a^mn

Product:

a^m x aⁿ = a^m+n

Properties of Exponents

Multiple Choice

(2m³)(3m⁴) =

• 5m⁷

• 6m¹²

• 5m¹²

• 6m⁷

Multiple Choice

According to the product rule, when when multiplying two powers that have the same base, you can ______the exponents

• add

• subtrct

• multiply

• divide

Multiple Choice

Simplify

$$x^3y^4\left(x^2y^2\right)$$  

• $$x^6y^6$$  

• $$x^5y^6$$  

• $$x^5y^8$$  

• $$x^6y^8$$  

Multiple Choice

According to the quotient rule, when we divide two powers with the same base, we can ______ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

Simplify

$$\frac{x^7y^5}{xy^2}$$  

• $$x^6y^7$$  

• $$x^8y^7$$  

• $$x^7y^{10}$$  

• $$x^6y^3$$  

Multiple Choice

According to the power rule, when we raise a power to a power, we ___ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

Simplify

$$\left(xy^5\right)^2$$  

• $$x^2y^{10}$$  

• $$x^2y^3$$  

• $$xy^3$$  

• $$xy^{10}$$  

Multiple Choice

Simplify

$$\left(3a^2c\right)^3$$  

• $$9a^6c^3$$  

• $$27a^5c^3$$  

• $$27a^6c^3$$  

• $$9a^5c^3$$  

Multiple Choice

Simplify

$$\left(\frac{x^4}{y^5}\right)^3$$  

• $$\frac{x^7}{y^8}$$  

• $$\frac{x^{12}}{y^{15}}$$  

• $$\frac{x^7}{y^{15}}$$  

• $$\frac{x^{12}}{y^8}$$  

Multiple Choice

What does anything to the zero power equals to?

• 0

• 1

• itself

• the variable

Multiple Choice

Simplify

$$x^2y^{-3}$$  

• $$\frac{y^{-3}}{x^2}$$  

• $$\frac{x^2}{y^3}$$  

• $$\frac{y^3}{x^{-2}}$$  

• $$\frac{y^3}{x^2}$$  

Multiple Choice

Which of the following is in radical form?

• $$\sqrt[4]{5^3}$$  

• $$5^{\frac{3}{2}}$$  

Multiple Choice

Which of the following is in exponential form?

• $$\sqrt[4]{8^{ }}$$  

• $$8^{\frac{1}{4}}$$  

Multiple Choice

Write the following expression in radical form: $$81^{\frac{1}{2}}$$  

• $$\sqrt[]{81}$$  

• $$\sqrt[]{81^2}$$  

• $$\sqrt[1]{81^2}$$  

• $$81^2$$  

Multiple Choice

Write the following expression in radical form: $$64^{\frac{1}{3}}$$  

• $$\sqrt[]{64^3}$$   

• $$\sqrt[1]{64^3}$$   

• $$\sqrt[3]{64}$$  

Match

Match each expression to it's radical form:

• $$\sqrt[]{25^5}$$  

• $$\sqrt[5]{25^2}$$  

• $$\sqrt[]{5^{25}}$$  

• $$\sqrt[25]{5^2}$$  

 

 

 

 

• $$25^{\frac{5}{2}}$$  

• $$25^{\frac{2}{5}}$$  

• $$5^{\frac{25}{2}}$$  

• $$5^{\frac{2}{25}}$$  

Multiple Choice

Simplify:

√100

• 1

• 10

• 10²

• Already simplified

Multiple Choice

Simplify:
3√16

• 12
• 48
• √12
• 3√4

Multiple Choice

Simplify:

√45

• 9√5

• 3√5

• 5√9

• 3√15

Multiple Choice

Simplify the following radical: √32

• 3√2

• 4√8

• 16√2

• 4√2

Multiple Choice

√45x⁴y⁷

• 3x²y³√5

• 9x²y³√5y

• 3x²y³√5y

• 3x⁴y⁷