What is your Goal Score for the EOC?

If your goal is “Good,” you should be able to:1. Distinguish between causation and correlation in applied

contexts that can be represented by linear models.

Correlation means that two factors may increase or decrease at the same rate or similar rates. The correlation coefficient can range from a perfect 1 to a perfect -1. The higher the value, the more closely the two data sets are related.

Causation means that one variable is caused by another variable. Just because two things may appear to be related does not mean one caused the other.

Example:

There is a high correlation coefficient on this graph, meaning the two increase and decrease at about the same rate over time… but does eating less margarine really mean that less marriages will end in divorce? Eating less margarine does not cause a marriage to succeed.

Bonus Question: Do the two lines on this graph represent functions?

What are the input variables?

What are the output variables?

Extra practice here: http://www.mathworksheetsland.com/stats/10corrvscause/ip.pdf

2. Interpret and describe relationships between quantities on a scatter plot.

Example:

Does this graph represent a function?_____________________________

What is the independent variable/ input?__________________________

What is the dependent variable/ output?___________________________

What type of correlation does this show?___________________________

Does this graph represent a causation?____________________________

Extra Practice Here:http://www.cheney268.com/chs/math/jones%20folder/makeup1/9.9%20scatter%20plot%20ws_correlation.pdf

https://cdn.kutasoftware.com/Worksheets/PreAlg/Scatter%20Plots.pdf

3. Identify the domain of a function from a list, table, or graph.Remember that the domain of a function is its set of x values, which are also called input values.

List: (0,1); (2,3); (4,5); (6,7); (8,9)

What is the domain? ______________________________

Is this a function? ________________________________

Table:

What is the domain? ______________________________

Is this a function? ________________________________

What type of correlation does this table model? __________________

Does it also show causation?______________________________________

Graph 1: Graph 2:

What is the domain?What is the range?What type of graph is this?Does it represent a function?

What is the domain?What is the range?Does it represent a function?

Graph 3:

What is the domain?What is the range?What type of graph is this?Does it represent a function?

Graph 4:

What is the domain?What is the range?Does it represent a function?

More practice on domain and range here: Activity file

4. Rearrange a formula by solving for a specific variable. Example: The formula for area of a triangle is one-half base times height. What if you know the area and don’t know the height? How would you solve for h?A = ½ b*h*2 = *2

2A = b*h b = b

2A = h b

5. Interpret and analyze applied contexts modeled by tables, graphs, or verbal statements in linear and non-linear relationships.

Linear Graph: Price in dollars per kg of Silver

Is this a function?What is the domain?What is the range?Why can’t domain or range include negative numbers? Describe the correlation.Is there also causation?What is the equation for this line?What does the slope represent?

Non-linear Graph:

Is this a function?What is the domain?What is the range?Why can’t domain or range include negative numbers? What does the domain represent?What does the range represent?

Verbal statement:Farmer Joe started his strawberry farm with two acres of land that produced about 100 pounds of strawberries. Each year he bought an additional acre of land, which increased the amount of strawberries by an additional 50 pounds. Complete the table.

x f(x) g(x)1 2 1002 3 150

What does the domain represent for these functions?What does f(x) represent?What does g(x) represent?Write an equation for f(x) and explain it.

Write an equation for g(x) and explain it.6. Write linear equations and inequalities in one variable to

interpret and solve problems.

Equation from word problem: Andrea was building onto a Lego tower in Ms. Benedetto’s classroom. The tower was 12 inches when she started. She added 2 inches per day (d). Write an equation to represent the height after Andrea added onto the tower for 4 days.

Solve the equation.

Inequality from word problem: Kayleigh makes $10 per hour babysitting. She needs to earn at least $300 before Prom to buy the dress she wants and maybe have some extras. Write an inequality for Kayleigh to determine how many hours she needs to work to meet her goal.

Solve the inequality.

7. Identify and interpret slope and intercepts (x and y) of a linear function modeled by tables, graphs, equations, or verbal statements.

Table:Slope: Change in y change in x

x-intercept(s)

y-intercept

Equation

Quadratic Graph (Parabola):x-intercept(s)

y-intercept

Equation

Vertex

Linear Graph:Slope:

x-intercept(s)

y-intercept

Equation

Equation in Slope-Intercept Form:y = 2x – 4 Slope

x-intercept(s)y-intercept

Equation in Standard Form:2x+3y=13 Slope

x-intercept(s)y-intercept

8. Create and interpret systems of equations that represent applied contexts.

Example:The choir students decided to put on a concert to raise money for their competition. They sold 50 student tickets and 40 parent tickets on the first night and brought in $400. On the second night, they sold 150 student tickets and 80 parent tickets for $1400. What was the cost of student tickets? Parent tickets?

Let x=Let y=

Solve by substitution or elimination:

Parent tickets=Student tickets=

9. Graph inequalities in one variable.

Example:

10. Analyze and use appropriate units of measurement or scales.

11. Interpret, rewrite, and simplify algebraic expressions.

Combining Like Terms with Addition or Subtraction:4x2 + 8x – 3 + 2x2 - 3x - 5

Product of Powers:4x2y3 * 3x3y4

Power of Powers:(6xy2z3)2

Quotient of Powers:8x 6 y 4 z 4x4yz

If your goal is “Excellent,” you should also be able to:1. Choose a level of accuracy appropriate for a given set of

measurements.

Level of accuracy of a measurement is +/- ½ the distance between intervals. If something is measured in inches, then the level of accuracy is +/- ½ inch.

If something is measured to ¼ inches, then the level of accuracy is +/- 1/8 inch because ½ of ¼ = 1/8.

2. Interpret the meaning of “average rate of change” for a given time frame from verbal statements, tables, or graphs.

Verbal statement: Each month between April and August, Jasmine measured the daily temperature and calculated an average for each month. In April, the average was 78°F. In May, the average was 85°F. In June, the average was 92°F. In July, the average was 99°F. In August, the average was 101°F. What was the average rate of change in temperature for April to August?

Table:What was the average rate of change for sightings of sea turtles in Hawaii between September and December?

July August

September

October

November

December

59 63 72 69 56 42

3. Graph and compare two functions to determine intersections, intercepts, and slopes.

f(x)= 2/3 x-5g(x)= -3x+5

Graph the functions:

f(x) g(x)SlopeX-interceptY-interceptIntersection

4. Determine the effect on a graph by replacing f(x) with f(x+k), f(x-k), f(x*k), f(x)+k, and f(x)-k

5. Analyze and interpret key features such as minima and maxima of non-linear functions.

6. Simplify polynomials in applied contexts

Remember to use your exponent rules (Product of Powers, Quotient of Powers, Power of Powers…)

FOIL: (30-x)(200+5x)

Multiply polynomials:

Divide polynomials:

Factor Polynomials:

Difference of Squares:*

Regular Polynomials:

7. Create and graph inequalities in two variables.Example:

8. Given a line of best fit for a data set, write the equation of the line and/or interpret slope and y-intercept.

Scatter Plot:

Equation of Line of Best Fit:What does the slope represent?

9. Analyze and explain any errors in steps used to solve systems of equations/ quadratics by factoring or completing the square.

Error in solving system of equations by substitution:

Original Equations 2x + y = 143x – 2y = 7

Step 1 y= -2x + 14Step 2 3x -2(-2x + 14) =7Step 3 3x-4x+28=7Step 4 -x+28=7Step 5 -x=-21Step 6 x=21Step 7 2(21)+y=14Step 8 42+y=14Step 9 y=-30Solution (21,-30)

Error in solving system of equations by elimination:

Error in solving quadratics by factoring:Original Equation x2+x-5= -2x+5Step 1 x2+x-10= -2xStep 2 x2+3x-10 =0Step 3 (x-5)(x+2)=0Step 4 x-5=0 and x+2=0Solution x= {-2,5}

Original Equations

-x + 3y = 112x + 3y = 32

Step 1 2(-x + 3y = 11)Step 2 -2x + 3y = 22

2x + 3y = 32Step 3 6y = 54Step 4 y = 9Step 5 2x + 3(9) = 32Step 6 2x + 27 = 32Step 7 2x = 5Step 8 x=2.5Solution (2.5, 9)

Error in solving quadratics by completing the square:Original Equation 2x2 – 3x + 2= 5x + 2Step 1 2x2 - 8x + 2 = 2Step 2 2x2 – 8x = 0Step 3 x2 – 4x = 0Step 4 x2 – 4x + 4 = 4Step 5 (x+4)2 = 4Step 6 x + 4 = 2Solution x = -2