Name: Checking solutions of equations with graphing calculator Inequalities Translating to and from words

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1 Name: Midterm Review Units 1, 2, 3, and 4 *Use notes, activities, quizzes, and tests to help remember how to solve problems* Unit 1: Patterns Graphing Extending the line? Connecting points? Title the graph, labeling and scaling axes Tables Independent/Dependent Variables Filling in the table with values Equations Simplifying to find an output Solving to find an input Writing Explicit Rules Getting information from a rule: terms number, common ratio, common difference Using rule to solve for a term or for a term number Writing Recursive Rules (with or without the context) Starting with the term, add/multiply to get to the next term. Arithmetic Sequences What are they? Write recursive rule, explicit rule, fill in the table, what does the graph look like, solve equations to find the term number, simplify expressions to find the term, find next term(s) in a sequence Geometric Sequences What are they? Write recursive rule, explicit rule, fill in the table, what does the graph look like, solve equations to find the term number, simplify expressions to find the term, find next term(s) in a sequence Explain if sequence is arithmetic or geometric Order of Operations Simplify expressions with rational numbers (integers, fractions, decimals) Exponents: ( 3) 2 vs 3 2 Unit 2: Equalities and Inequalities Expressions Evaluating Expressions o Substituting with parentheses Translating words to algebraic expressions Writing expressions from word problems/stories Simplifying by combining like terms/distributive property Equations Solving Equations o 1-Step, 2-Step, multi-step o o Combining Like Terms/Distributive Property Variables on both sides Special Cases: Infinitely Many and No Solution Fraction busters o Literal (these equations will be simple no craziness) Solving Equations Reminders Simplify both sides COMPLETELY, then solve Checking solutions of equations with graphing calculator Inequalities Translating to and from words

2 Open vs. Closed Circle When do we flip the inequality symbol Number Lines Real World: possible solutions (points or arrow)? Writing equations/inequalities from real world problems Unit 3: Functions Function notation Relation à Function Table Mapping Diagram Ordered Pairs Equation Graph Vertical Line Test what does this state? Situation (words) Domain/Range From a graph From a table From an equation Independent Variable Dependent Variable Input/Output Equations/Graph/Table Dependent Variable is a function of the Independent Variable Types of functions Using graphing calculator Find input, output, domain, range for linear, quadratic, cubic, exponential, and reciprocal functions Unit 4: Linear Functions Linear Function Increasing/Decreasing Functions Rate of Change x-intercept/y-intercept Meaning of the coordinate Distance-Rate-Time Graphs (Motion graphs) Drawing a graph from a story Determining if a linear function graph, table, or equation Slope Formula and Slope from a graph Meaning of slope Horizontal and Vertical Lines Is a line steep? Not steep? Flat? Slope-intercept form Standard form Direct variation Point-slope form Create a graph from the different forms Write a linear equation from a graph in any form Transform equations in any form to either slope-intercept of standard form Write an equation given two points Write an equation given a point and a slope Write an equation given slope and the y-intercept Parallel lines Perpendicular lines

3 3 Unit 1 Review 1.) Stages 0 2 of a triangular pattern are shown below. Use the pattern to answer the following questions. In the space above, draw stage 3 of the pattern. Complete the table below comparing the stage number to the perimeter of the large triangle. Make a graph showing the relationship between the stage number and the perimeter of the triangle. Label and scale the axes appropriately. Stage Number Perimeter Write a recursive rule to explain the pattern. e.) Write an explicit rule for the perimeter of the pattern. Define the variables. f.) Use either rule to determine what the perimeter will be at stage 10. Show your work or explain your reasoning. g.) Does the perimeter form an arithmetic sequence, geometric sequence, or neither? Explain.

4 2.) A fish store was breeding guppies. It started off with 3 pregnant fish. Each of the fish hatched 5 female guppies. One month later, those fish hatched 5 guppies. The next month, those fish each had 5 female babies. Use this pattern to answer the following questions. Complete the table below comparing the month number to the number of guppies born. Make a graph showing the relationship between the number of months and the number of new fish born that month. 4 # of months # of guppies Write a recursive rule to explain the pattern. Write an explicit rule to explain the pattern. Define the variables. e.) If this pattern continues, how many fish will be in the tank after 6 months? Show all work. f.) Does this pattern represent an arithmetic sequence, geometric sequence, or neither? Explain. 3.) The first three terms of a sequence are given in each problem below. Find the next 3 terms, circle if the sequence is arithmetic or geometric, give the explicit rule to find a term in the sequence, and give the recursive rule. 5, 3, 1,,, arithmetic or geometric Explicit Rule: Recursive Rule:

5 48, 72, 108,,, arithmetic or geometric 5 Explicit Rule: Recursive Rule: 1, 2, 5,,, arithmetic or geometric Explicit Rule: Recursive Rule: 12, 4, 4,,, 3 arithmetic or geometric Explicit Rule: Recursive Rule: e.) 2, 2 3, 2,,, 9 arithmetic or geometric Explicit Rule: Recursive Rule: 4.) Using the explicit rule from 3a, what is the ninth term? 5.) Using the explicit rule from 3b, what is the fifteenth term? If necessary, round to the thousandth. 6.) Using the explicit rule from 3d, what is the tenth term? Keep your answer as a simplified fraction.

6 6 7.) Determine if the tables below represent an arithmetic sequence, a geometric sequence, or neither. If it is arithmetic or geometric, write an explicit rule. Term # Term Term # Term Term # Term Term # Term ) Simplify the following expressions. Show ALL work. ( ) ( 3 8) ( 12 3 ) 3 ( 4 2 ) ( 8)

7 9.) Evaluate the following expressions. 4x 2 6x( 4 x) for x = 5 6x 2x ( ) for x = ) Evaluate the following expressions for x = 5 5x 2 + 2x 6 3 2x 3 ( ) 2 4( x 7) 11.) Simplify the following expressions. ( ) 3( x 2) 5 3x ( 4 + y) 4( 2y 6) 6h 5( h 5) 8 5( x 7)

8 Unit 2 Review 12.) Justin wants to rent a violin. The store has two rental options. Option 1: Charges a $25 down payment to rent a violin, and then $8 per month. Option 2: $0 down, but $11 per month. 8 Write an expression for the amount of money Justin will pay if he rents the violin for m months on Option 1. Write an expression for the amount of money Justin will pay if he rents the violin for m months on Option 2. If Justin rents the violin for 12 months, which store would be the best deal? Show your work and explain your reasoning. 13.) Solve the following equations. Show ALL work. 18 4x = 6 h 17 = x + 9 = 24 8( x 5) = 40

9 e.) 6y + 4y + 5 = 25 i.) 3x 7 + 5x + 2 = 4( 2x 3) f.) 7( e 8) = 5 4e j.) 5( a + 1) 4 = 9 g.) 2( 5 3x) = 6x + 10 k.) 3 4 x x = 7 10 x + 4 h.) 11x 16 = 4x + 19 l.) 4 3 x = 5 6 x + 5 9

10 10 14.) The formula A = 1 ( is used to find the area of a trapezoid when given the two bases 2 b + b 1 2)h ( b 1 and b 2 ) and the height (h). Use the formula to find the area of a trapezoid with bases of length 7.5cm and 9.2cm, and a height of 8.9cm. Use the formula to solve for the height, when the bases measure 8cm and 15cm, and the area is 126.5cm 2. Solve the formula for h. Solve the formula for. b 1 15.) The volume of a cone is found using the formula V = 1. Solve this formula for h. 3 πr2 h 16.) The equations for surface area of a cylinder is: ( ) S = 2πr h + r Find the surface area of a cylinder with a radius of 5 cm and a height of 12 cm.

11 The surface area of a cylinder is cm 2 and the radius is 8 cm, what is the height? 11 Solve the equation for h. 17.) Solve the equation for p: m = 3n 7p 9 18.) Solve the equation for w: e = 3( w + z) 5w 19.) Translate each real world situation in to an inequality using an appropriate inequality symbol. In order to ride the rollercoaster, your height, h, must be at least 48 inches. To beat the high score in a video game you must get a score, s, of more than 205,800 points. To qualify for the skiing championship, you have to complete the course in less than 23.5 seconds. Use t for time it takes to complete the course.

12 20.) Solve the inequality, check your solution, graph the solution on the number line > 2x 16 x x + 3 < 4x 15

13 3( 2x 4) ) Sam wanted to sell buttons for a student council fundraiser. The button machine costs $85 to buy and each button costs $0.15 to make. He plans on selling the buttons for $0.75. Sam wants to make sure that he makes a profit so wants to know how many buttons he needs to sell before his income is more than his expenses. Define the variable. Write an inequality. Solve, check, and graph the inequality. State your answer in a complete sentence. Unit 3: Functions 22.) For each relation, determine if it is a function. Explain why it is or why it is not. Use correct vocabulary. {( 1,0 ),( 3,5), ( 4,5), ( 5,7) } ( 5,2), ( 3, 2), ( 4, 8), 3, 10 { ( )}

14 x y e.) 23.) This table compares the height of ten apple trees at Bishop s Orchards with the pounds of apples harvested from each tree. What is the independent variable? What is the dependent variable? Is this relation a function? Explain. Apples Tree Height Harvested (feet) (pounds) Using just this table of values, what is the domain? e.) Using just this table of values, what is the range?

15 f.) About how many pounds of apples would you expect from a tree that is 4 feet tall? Explain. 15 g.) If a tree produced 100 pounds of apples, approximately what height would you expect the tree to be? Explain. 24.) Determine if each of the situations below illustrate a function. Explain your reasoning. Monica has sold Girl Scout cookies for the past 6 years. Is the amount of cookies sold a function of the year? Explain. Is the year a function of the number of cookies sold? Explain Justin measured the height of his grass every Saturday morning during the summer. The grass never got mowed. Is the week a function of the grass height? Explain. Is the grass height a function of the week? Explain. e.) Is the number of points scored a function of the players? Explain. f.) Are the players a function of the number of points scored? Explain.

16 16 25.) The Jones family decided they wanted to join the Soundview YMCA. There is a one-time, $100 joining fee, and then it costs $79 per month for the family to be members. Write a function to represent the situation where m represents the number of months and c represents the total cost. Write an equation in function notation that represents the given situation. Use the equation to find c( 4). If the total cost came to $653, use the equation to find the number of months paid. If the Jones wanted to join for 1.5 months, how much would it cost? 26.) Tommy decided to open a bank account on the first day of the month. The graph below shows how much money was in Tommy s bank account on the first day of each month. State the domain of the function. State the range of the function. What is amount of money at 7 months? Money in account in dollars What does the point (3, 30) mean in the context of this problem? Months since bank account opened

17 17 27.) State the domain and range of the function below. Unit 4 Review Plot the points from the given tables. State whether the graph represents a linear function. Use the rate of change to explain your reasoning. 28.) x y ) x y

18 18 30.) On the first day of the school year, Lara put $22 on her lunch card. She buys lunch every day for $2.75. Make a table and a graph of the given situation. Label axes. Days of school Money remaining on lunch card Does the line represent and increasing or decreasing function? Explain. What is the meaning of the point (4, 11)? What is the y-intercept? What is the meaning of this coordinate? What is the x-intercept? What is the meaning of this coordinate? 31.) Use the graph of the line below to answer the following questions. What is the slope of the line? What is the y-intercept of the line? What is the x-intercept of the line?

19 19 32.) Jimmy and his family went for a drive while on vacation in New Hampshire to look for moose. They left their campsite and drove slowly for the first 20 minutes looking out their window in hopes of seeing a moose. At 20 minutes they thought they saw a moose in a lake, so they immediately stopped the car and got out. They stayed there for 5 minutes, but realized that what they had seen was just a fallen log. They got back in their car and continued their journey. This time, they drove even slower for the next 10 minutes until Jimmy s little sister yelled out that she saw something in the forest. They again stopped the car and a moose came out of the woods! They were overjoyed and spent the next 15 minutes taking pictures and celebrating. Finally the moose ran away. Jimmy and his family got back into the car and drove faster and faster back to their campsite as Jimmy needed to use the restroom. Make a graph that represents this situation. Distance from campsite in miles Time in Minutes 33.) Graph each line on the coordinate plane provided and then find the slope. y = 8 x = 4 Slope: Slope:

20 ( ) y = 2 3 x 4 y + 6 = 3 x 2 20 Slope: Slope: 34.) Using the formula, what is the slope of the line that contains the coordinates ( 4,12) and ( 6, 4)? ( ) 35.) Write an equation that is parallel to the equation in #33a and goes through the point 5, 9. ( ) 36.) Write an equation that is parallel to the equation in #33c and goes through the point 5, 9. ( ) 37.) Write an equation that is perpendicular to the equation in #33b and goes through the point 5, 9. ( ) 38.) Write an equation that is perpendicular to the equation in #33d and goes through the point 5, 9.

21 39.) Given the coordinates: ( 6,4) and ( 4, 8) Write an equation for the line in point-slope form through the two points. 21 Transform the equation in part 39a into slope-intercept form. Transform the equation in part 39a into standard form. Write an equation of a line in point-slope form that is perpendicular to the line in 39a through ( ) the point 11, 3. e.) Write an equation of a line in point-slope form that is parallel to the line in 39a through the point ( 2,7).

22 For 40 42, use the window to the right to answer the following questions. 22 ( ) = 3w 2 24w ) Given: k w Sketch the graph. ( ) Using the graphing calculator, what is k 6? ( ) = 0 Using the graphing calculator, what is k w? What is the domain of the function? e.) What is the range of the function? ( ) = 7 x 41.) Given: y x Sketch the graph. ( ) Using the graphing calculator, what is y 28? ( ) = 0.14 Using the graphing calculator, what is y x? What is the domain of the function? e.) What is the range of the function? ( ) = x ) Given: f x Sketch the graph. ( ) Using the graphing calculator, what is f 6? ( ) = 0 Using the graphing calculator, what is f x? What is the domain of the function? e.) What is the range of the function?