Unit 2 Semester A Important Concepts
Provide a definition, rules, examples to represent each concept
Inverse Operations:
Distributive Property:
Reciprocal:
Inequality:
Steps to solve an equation:
Steps to solve an inequality:
How many solutions an equation can have (show specific examples of one solution, no solution and infinite solutions!):
What do you need to do if you get to the last step in solving an equation and get -x=3?
Solving Equations & Justify Steps - Practice
1) 5-2(3-x)=4x+10
2) 9x-5=14(16x+60)
Identifying Number of Solutions - Practice
3) 3x+12+x=8+4+x
4) 4(x+1) = 4x+1
Rearranging Equations - Practice
5) Solve for x: 3x+4y=7
6) Solve for F: C=59(F-32)
Solving Inequalities & Justify Steps - Practice
7) 3(x-5)< -2x
8) x5+46
Real World Applications - Practice
9) Chris makes 7 dollars per hour plus a weekly bonus of 10 dollars a week. If his paycheck this week was $94, how many hours did he work?
10) Aiden borrows a book from a public library. He read a few pages on day one. On day two, he reads twice the number of pages than he read on day one. On the third day, he reads six pages less than what he read on the first day. If he read the entire book that contains 458 pages in three days, how many pages did he read on day three?
Extra Practice
11) Find and correct the error:
x4+6>3
x+6>12
x>6
12) Find and correct the error:
-2(1-x)=2x-7
-2+2x=2x-7
-2= -7
x= -7
Unit 3 Semester A Important Concepts
Provide a definition, rules, steps, examples to represent each concept
Proportional vs. Non-Proportional Relationships:
Unit Rate:
Slope(give an example of a real-world problem that would be a linear equation -has an initial value and constant rate of change- and explain what the slope is in the problem):
Y-Intercept (give an example of a real-world problem that would be a linear equation- has an initial value and a constant rate of change- and explain what the y-intercept is in the problem):
Positive Slope, Negative Slope,0 Slope:
Slope Intercept Form:
Graphing a Linear Equation:
Show y = mx + b as a translation of y = mx:
Practice
1) Determine the following:
Is this a proportional relationship?
What is the unit rate?
What does the unit rate mean in context of the scenario?
2)
Is this a proportional relationship?
What is the y-intercept?
What does the y-intercept mean in context of the scenario?
What is the slope?
What does the slope mean in context of the scenario?
3) The cost of a gym membership can be represented by 25 + 5x, where x is the number of visits to the gym.
How many times can you visit if you have a $100 budget?
What is the y-intercept? What does it mean in context?
What is the slope? What does it mean in context?
4)
Calculate the slope.
Determine the y-intercept.
5) Create an equation of the line in slope intercept form:
6) Determine the following:
Slope from point A to C.
Slope from point C to E.
What type of triangles are ABC and CDE?
Will the slope be the same for any two points on this line?
Write the equation for the line in slope intercept form.
7) Which container of peanut butter is the better deal?
8) Determine the following:
Label which line is proportional and which one is not. How did you know?
How was the bottom line shifted to get to the top line? (How many units did it move & in what direction?)
Calculate the slope for both lines.
9) Determine the following:
Does this represent a proportional relationship?
What is the y-intercept? What does it mean in context?
What is the slope? What does it mean in context?
How could you move this line to have it represent a proportional relationship?
10) Determine the following:
Which panda has the steeper slope?
What does the slope represent in this situation?
What is the y-intercept for each panda? What does it mean in the scenario?
Unit 4 Semester A Important Concepts
Provide a definition, rules, examples to represent each concept
Systems of linear equations:
Solution of a system of linear equations:
How to solve a system of linear equations graphically :
How to solve a system of linear equations with substitution:
How to solve a system of linear equations using elimination:
Additional notes:
Solve Systems - Practice
1.
What is the solution to this system?
3. Solve using systems of equations:
Jayden took a total of 58 quarters and dimes to trade in for cash at the bank. He got back exactly $10.
Let d=the number of dimes
Let q= the number of quarters
Make an equation that shows when you add the number of dimes and number of quarters you get 58 coins:
Make an equation to show the total number of quarters plus the total number of dimes equals $10. (hint: think about how much each coin is worth.)
2. Solve the system:
-x +9y=9
2x-3y=12
4. Use the equations you created in question 3 to solve the system of equations and find the total number of quarters and dimes Jayden had.
5. Solve using systems of equations:
A movie theater charges different prices for children and adults. On Friday, 10 adults and 25 children went to the movie and it cost $670. On Sunday 5 adults and 10 children went and it cost $290. How much does the movie charge for adults?
Let c=the price of a child’s ticket
Let a= the price of an adult ticket
Make an equation that shows the cost of going to the movie on Friday:
Make an equation to show the cost to go to the theater on Sunday:
6. Use the equations in problem 5 to figure out the cost of each adult ticket.
Unit 5 Semester A Important Concepts
Provide a definition, rules, examples to represent each concept
Bivariate data:
Scatter Plot:
Negative vs Positive Association :
Trend Line/Line of Best Fit:
Determine if the relation is a function - Practice
1)Classify the scatter plot as positive, negative, or no correlation:
2) Draw a line of best fit for the data:
How would you describe the relationship between the variables shown in the scatter plot above?
People who studied longer generally made ____ grades than people who studied less time.
3. The amount 8 different baseball hitting instructors charge for lessons are shown in the table below.
Lesson Length (minutes)
Cost
(Dollars)
15
20
60
50
20
25
10
5
30
30
45
39
40
30
25
30
Draw a scatter plot of the data.
Unit 6 Semester A Important Concepts
Provide a definition, rules, examples to represent each concept
How to tell if a group of coordinates is a function or just a relation:
X-value/input/domain/independent variable:
y-value/output/range/dependent variable :
Vertical Line Test:
Increasing/Decreasing Functions:
Slope-intercept/Standard/Point-Slope Form:
Key Characteristics of a linear graph:
Interval Notation
Inequality Notation
Interval Notation
Determine if the relation is a function - Practice
1)
2) y=2x3
3)
Finding Domain and Range of Graphs - Practice
Example:
How would you write the answer for domain and range in interval and notation?
Give the domain and range of the function in interval and inequality notation
Unit 2 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Rational Numbers:
Irrational Numbers:
Integers:
Whole Numbers:
Natural Numbers:
Perfect Squares:
Perfect Cubes:
Square roots:
Cube roots:
Estimating roots:
Classifying Numbers - Practice
Determine which specific category each number would fall into and WHY:
⅔
0.101001001000…
0.4
0
0.73737373…
-2
-8.1
2
Determine whether the number is rational or irrational and WHY:
81
42
327
Estimating Roots & Fractions - Practice
Estimate the value of 50 and place the value on a number line
Convert 0.454545… into a fraction.
Unit 3 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Exponents:
Product Rule:
Quotient Rule:
Zero Power Rule:
Power Rule:
Negative Power Rule:
Simplifying Expressions - Practice
Simplify the expression using exponent rules: 7x3y514x4y
Simplify the expression using exponent rules: (2x0)-3
Unit 4 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Standard Form:
Scientific Notation:
How to compare numbers in scientific notation:
Adding/Subtracting numbers in scientific notation:
Multiplying/Dividing numbers in scientific notation:
Other notes:
Scientific Notation - Practice
Write the numbers in scientific notation:
0.0000876
1,567,000
A thai pepper has a hotness rating of 7.5104 and the red savina habanero has a hotness rating of 4.6105. How many times hotter is the red savina than the thai pepper?
The mass of the moon is about 7.31022. The mass of Earth is about 5.91024. Find the combined mass of the moon and the Earth.
Order the numbers from least to greatest.
547,000
62,000
4.1102
9.2105
Unit 5 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Scatter Plot:
Correlation:
Outliers:
Trend Line:
Regression Line:
Scatter Plot & Correlation - Practice
1) Determine whether the scatter plot shows a positive, negative, or no correlation:
Correlation = _____ (positive, negative, no correlation)
Is there an outlier in the data? If yes, which point is the outlier?
2) Draw a trend line or line of best fit for the scatter plot below:
3) Using the trend line, make a prediction for y when x = 10.
Regression Line - Practice
1) Calculate the regression line for the following data set:
(2, 4), (3, 6), (4, 7), (5, 9)
2) On the regression line, what is the predicted value of y when x = 6?
Outliers - Practice
1) Identify the outlier in the data set below and explain why it is an outlier:
(2, 4), (3, 6), (4, 20), (5, 9)
2) How does an outlier affect the regression line of a scatter plot?
Unit 6 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Function Notation:
Inverse Functions:
Composite Functions:
Domain and Range of Functions:
Composition of Functions - Practice
1) Given the functions f(x) = 3x - 5 and g(x) = x^2 + 1, find f(g(x)).
2) Given the functions f(x) = x + 2 and g(x) = 2x - 3, find g(f(x)).
Domain and Range - Practice
1) Find the domain and range of the function f(x) = √(x - 2).
2) Find the domain and range of the function f(x) = 2x^2 - 4x + 3.
Unit 7 Semester B Important Concepts
Provide a definition, rules, examples to represent each concept
Parallel lines:
Perpendicular lines:
Point-slope form:
Slope-intercept form:
Writing Equations of Lines - Practice
1) Write the equation of the line that passes through the point (2, 4) and has a slope of 3.
2) Write the equation of the line that is perpendicular to y = 2x + 1 and passes through the point (3, 5).
Parallel and Perpendicular Lines - Practice
1) Determine if the two lines are parallel, perpendicular, or neither:
y = 2x + 3
y = -2x + 3
2) Determine if the two lines are parallel, perpendicular, or neither:
y = 2x + 1
y = -0.5x + 5