Using Graphs to Relate Two Quantities

Size: px
Start display at page:

Transcription

1 - Think About a Plan Using Graphs to Relate Two Quantities Skiing Sketch a graph of each situation. Are the graphs the same? Explain. a. your speed as you travel from the bottom of a ski slope to the top b. your speed as you travel from the top of a ski slope to the bottom Understanding the Problem. What is likely to be true about your speed as you go from the bottom of the ski slope to the top?. What is likely to be true about your speed as you go from the top of the ski slope to the bottom? Planning the Solution. What will the graph tend to look like relating to your speed as you go up the ski slope?. What will the graph tend to look like relating to your speed as you go down the ski slope? Getting an Answer. Sketch the graph as you travel to the top of the slope. Speed. Sketch the graph as you travel to the bottom of the slope. Distance Speed. Are the graphs the same? Explain. Distance

2 - Practice Form G Using Graphs to Relate Two Quantities What are the variables in each graph? Describe how the variables are related at various points on the graph.. Volume of Pool Water. Temperature of Water. Plant Height Volume Temp (F) Plant Height Time Depth Time Match each graph with its related table. Explain your answers.... Distance (mi) Time (h) Distance (mi) Time (h) Distance (mi) Time (h) A. Time Distance B. Time Distance C. (h) (mi) (h) (mi) Time (h) Distance (mi)

3 - Practice (continued) Form G Using Graphs to Relate Two Quantities Sketch a graph to represent the situation. Label each section.. You buy two shirts. The third one is free.. You warm up for gym class, play basketball, and then cool down.. The temperature warms up during the day and then decreases at night.. Error Analysis DVDs cost \$. each for the first purchased. After that, they cost \$. each. Describe and correct the error in sketching a graph to represent the relationship between the total cost and the number of DVDs purchased. Cost (\$) Number of DVDs. Sketch a graph of each situation. Are the graphs the same? Explain. a. your distance from school as you leave your house and walk to school b. your distance from school as you leave school and walk to your house

4 - Standardized Test Prep Using Graphs to Relate Two Quantities Multiple Choice For Exercises, choose the correct letter.. The graph shows your distance from the practice field as you go home after practice. You received a ride from a friend back to his house where you ate supper. You then walked home from there. Which point represents a time when you are walking home? A. A B. B C. C D. D Distance B A C Time D. Which table is related to the graph at the right? F. Time Temp. H. (h) (F) Time (h) Temp. (F) Temp (ºF) Time (h) G. Temp. Time I. (F) (h) Temp. (F) Time (h). How are the variables related on the graph? A. as speed decreases, height stay constant B. as speed decreases, height increases C. as speed increases, height decreases D. as speed increases, height increases Height Short Response Speed. For the race you swim mile, run miles, and bike miles. Sketch a graph to represent the relationship. Label the axes with the related variables. What are the important points on the graph?

5 - Think About a Plan Patterns and Linear Functions Electric Car An automaker produces a car that can travel mi on its charged battery before it begins to use gas. Then the car travels mi for each gallon of gas used. Represent the relationship between the amount of gas used and the distance traveled using a table, an equation, and a graph. Is total distance traveled a function of the gas used? What are the independent and dependent variables? Explain. Understanding the Problem. Describe the miles that the car can travel on the different types of fuel. Planning the Solution. Give a verbal description of the relationship between the miles the car travels and gallons of gas it uses. Getting an Answer. Represent this relationship with an equation.. Represent this relationship with a table.. Represent this relationship with a graph. Gallons of gas, g Miles Traveled, m Miles traveled, m Gallons of gas, g. Is total distance traveled a function of the gas used? What are the independent and dependent variables? Explain.

6 - Practice Form G Patterns and Linear Functions For each diagram, find the relationship between the number of shapes and the perimeter of the figure they form. Represent this relationship using a table, words, an equation, and a graph.. triangle triangles triangles triangles Triangles n Perimeter. square squares squares Squares n Perimeter For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph.. x y. x y

7 - Practice (continued) Form G Patterns and Linear Functions For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph.. Distance Traveled. Time (h) Distance (mi) Calories Burned Minutes (min) Calories (C). Reasoning Graph the set of ordered pairs (, ), (, ), (, ), (, ). Determine whether the relationship is a linear function. Explain how you know.. You can make a bubble solution by mixing cup of liquid soap with cups of water. Represent the relationship between the cups of liquid soap and the cups of bubble solution made using a table, an equation, and a graph. Is the amount of bubble solution made a function of the amount of liquid soap used? Explain.

8 - Standardized Test Prep Patterns and Linear Functions Multiple Choice For Exercises, choose the correct letter.. Which equation represents the relationship shown in the table at the right? A. y x C. y x B. y x D. y x. In a relationship between variables, what is the variable called that changes in response to another variable? F. function H. independent variable G. input function I. dependent variable x y. A lawn care company charges a \$ trip fee plus \$. per square foot of x square feet of lawn for fertilization. Which equation represents the relationship? A. x.y B. y.x C. y x. D. x y.. Which equation represents the relationship shown in the graph? F. y x H. y x G. y x I. y x Short Response. The table below shows the relationship between the number of teachers and the number of students going on a field trip. How can the relationship be described using words, an equation, and a graph? y x Teachers Students Field Trip

9 - Think About a Plan Patterns and Nonlinear Functions Fountain A designer wants to make a circular fountain inside a square of grass as shown at the right. What is a rule for the area A of the grass as a function of r? r r Understanding the Problem. What shapes are involved in the areas of grass and the fountain?. What are the formulas for the areas of these shapes? Planning the Solution. Using r as shown in the drawing, what is a rule for the area of the square?. Using r as shown in the drawing, what is a rule for the area of the circle?. How will you find the area of the remaining grass after the fountain is placed in the grass? Getting an Answer. What is a rule for the area A of the grass as a function of r after the fountain is placed in the grass?

10 - Practice Form G Patterns and Nonlinear Functions. A student s earnings E, in dollars, is a function of the number h of hours worked. Graph the function shown by the table. Tell whether the function is linear or nonlinear. Hours, h Earnings (\$), E Graph the function shown by each table. Tell whether the function is linear or nonlinear.. x y. x y

11 - Practice (continued) Form G Patterns and Nonlinear Functions Each set of ordered pairs represents a function. Write a rule that represents the function.. (, ), (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ), (, ). (, ), (,.), (,.), (,.), (,.). (, ), (, ), (, ), (, ), (, ). Reasoning A certain function fits the following description: As the value of x increases by each time, the value of y decreases by the square of x. Is this function linear or nonlinear? Explain your reasoning.. Writing The rule C.r gives the approximate circumference C of a circle as a function of its radius r. Identify the independent and dependent variables in this relationship. Explain your reasoning. r. Open-Ended What is a rule for the function represented by (, ), (, ), (, ), (, )? Explain your reasoning.. A landscape architect wants to make a triangular garden inside a square of land as shown at the right. What is a rule for the area A of the garden as a function of s? S

12 - Standardized Test Prep Patterns and Nonlinear Functions Multiple Choice For Exercises, choose the correct letter.. Which ordered pair represents a linear function? A. (, ), (, ), (, ), (, ), and (, ) B. (, ), (, ), (, ), (, ), and (, ) C. (, ), (, ), (, ), (, ) and (, ) D. (, ), (, ), (, ), (, ), and (, ). The following ordered pairs represent a function: (, ), (, ), (, ), (, ), and (, ). Which equation could represent the function? F. y x G. y x H. y x I. y x. Which rule could represent the function shown by the table at the right? A. y x B. y x C. y x D. y x x y. The ordered pairs (, ), (, ), (, ), (, ), and (, ) represent a function. Which rule could represent the function? F. y x G. y x H. y x I. y x. Which ordered pair represents a nonlinear function? A. (, ), (, ), (, ), (, ), and (, ) C. (, ), (, ), (, ), (, ), and (, ) B. (, ), (, ), (, ), and (, ) D. (, ), (, ), (, ), (, ), and (, ) Short Response. Graph the function shown in the table below. Is the function linear or nonlinear? x y

14 - Practice Form G Graphing a Function Rule Graph each function rule.. y x. y x. y x Graph each function rule. Explain your choice of intervals on the axes of the graph. Tell whether the graph is continuous or discrete.. The cost C, in dollars, for a health club membership depends on the number m of whole months you join. This situation is represented by the function rule C m.. The cost C, in dollars, for bananas depends on the weight w, in pounds, of the bananas. This situation is represented by the function rule C.w.

15 - Practice (continued) Form G Graphing a Function Rule Graph each function rule.. y u xu. y x. y u xu. y u x u. y x. y x. Open-Ended Sketch a graph of a quadratic function that has x-intercepts at and.. Writing Describe the general shape of the graphs of functions of the form y ax.

16 - Standardized Test Prep Graphing a Function Rule Multiple Choice For Exercises, choose the correct letter.. Which table of values can be used to graph the function y x? A. x y C. x y B. x y D. x y. Which term best describes a function whose graph is composed of isolated points? F. continuous G. linear H. discrete I. nonlinear. Which relationship is continuous? A. the number of cows a farmer has owned over the years B. the number of cookies Stan baked for the party C. the number of people attending the assembly D. the distance a runner ran during training. The total cost c a painter charges to paint a house depends on the number h of hours it takes to paint the house. This situation can be represented by the function rule c h. What is the total cost if the painter works for. hours? F. \$ G. \$. H. \$. I. \$. Short Response. The profit y on the number x of items a store sells is represented by the rule y x. What does a table of values for the function rule and the graph of the function look like?

17 - Think About a Plan Writing a Function Rule Projectors You consult your new projector s instruction manual before mounting it to the ceiling. The manual says multiply the desired image width by. to find the correct distance of the projector lens from the wall. a. Write a rule to describe the distance of the lens from the wall as a function of desired image width. b. The diagram shows the room in which the projector will be installed. Will you be able to project an image ft wide? Explain. c. What is the maximum image width you can project in the room?. What represents the desired image width in the drawing? ft? ft. What variables will you use in writing the rule and what do they represent?. Write a rule to describe the distance of the lens from the wall as a function of desired image width.. How can you determine if the room is large enough to project an image that is ft wide?. Is the room large enough to project an image that is ft wide? Explain.. How can you determine the maximum image width that can be projected in this room?. What is the maximum image width you can project in the room? Show your work.

18 - Practice Form G Writing a Function Rule Write a function rule that represents each sentence.. less than one fourth of x is y.. more than the quotient of a number n and is.. P is more than half of q.. more than times a number is... more than the quotient of a and is b. For Exercises, write a function rule that represents each situation.. The price p of an ice cream is \$. plus \$. for each topping t on the ice cream.. A babysitter s earnings e are a function of the number of hours n worked at a rate of \$. per hour.. The price p of a club s membership is \$ for an enrollment fee and \$ per week w to be a member.. A plumber s fees f are \$ for a house call and \$ per hour h for each hour worked.. A hot dog d costs \$ more than one-half the cost of a hamburger h.. José is years younger than times his brother s age. Write a rule that represents José s age j as a function of his brother s age b. How old is José if his brother is?. A taxicab charges \$. for the first mile and \$. for each additional mile. Write a rule for describing the total rate r as a function of the total miles m. What is the taxi rate for miles?

19 - Practice (continued) Form G Writing a Function Rule. Write a function rule for the area of a rectangle whose length is in. more than its width. What is the area of the rectangle when its width is in.?. Write a function rule for the area of a rectangle with a length ft more than two times its width. What is the area of the rectangle when its width is ft?. Write a function rule for the area of a triangle with a base m less than times its height. What is the area of the triangle when its height is m?. Reasoning Write a rule that is an example of a nonlinear function that fits the following description. When b is, a is, and a is a function of b.. Open-Ended Describe a real-world situation that represents a nonlinear function.. Writing Explain whether or not the relationship between inches and feet represents a function.. Multiple Representations Use the table shown at the right. a. Graph the ordered pairs on a coordinate plane. b. Write an equation that can be used to find y for any x value. c. Is the equation a function? Explain. x y

20 - Standardized Test Prep Writing a Function Rule Multiple Choice For Exercises, choose the correct letter.. Jill earns \$ per hour. Using p for her pay and h for the hours she works, what function rule represents the situation? A. h p B. p h C. h p D. p h. What is a function rule for the perimeter P of a building with a rectangular base if the width w is two times the length l? F. p l G. p w H. p l I. p w. Which function rule can be used to represent the area of a triangle with a base b in. longer than twice the height h in terms of the height? A. A bh C. A h h B. A h(h ) D. A (h)(h ). Which equation represents the sentence d is less than the quotient of n and? F. d n H. d n G. d n I. d n. The function rule for the profit a company expects to earn is P m, where P represents profit and m represents the number of months the company has been in business. How much profit should the company earn after months in business? A. \$, B. \$, C. \$, D. \$, Extended Response. A plane was flying at an altitude of, feet when it began the descent toward the airport. The airplane descends at a rate of feet per minute. a. What is the function rule that describes this situation? b. What is the altitude of the plane after it has descended for minutes? Show your work. c. How long will it take for the airplane to land on the ground if it continues to descend at the same rate? Show your work.

21 - Think About a Plan Formalizing Relations and Functions Car Wash A theater group is having a carwash fundraiser. The liquid soap costs \$ and is enough to wash cars. Each car is charged \$. a. If c is the total number of cars washed and p is the profit, which is the independent variable and which is the dependent variable? b. Is the relationship between c and p a function? Explain. c. Write an equation that shows this relationship. d. Find a reasonable domain and range for the situation. Understanding the Problem. What are the expenses associated with the car wash?. If c is the total number of cars washed and p is the profit, which is the independent variable and which is the dependent variable? Explain. Planning the Solution. How do you know if a relation is a function?. How are a reasonable domain and range determined for a function?. What limitations does the domain of this function have? Getting an Answer. Is the relationship between c and p a function? Explain.. Write an equation that shows this relationship.. Describe a reasonable domain and range for the situation.

22 - Practice Form G Formalizing Relations and Functions Identify the domain and range of each relation. Use a mapping diagram to determine whether the relation is a function.. {(, ), (, ), (, ) (, )}. {(,.), (,.), (,.), (,.)}. (, ), (, ), (, ), (, ). {(.,.), (.,.), (.,.), (.,.)} Use the vertical line test to determine whether the relation is a function.. y. y x O x O. The function w(x) x represents the number of words w(x) you can type in x minutes. How many words can you type in minutes?. Sound travels about meters per second. The function d(t) t gives the distance d(t) in meters that sound travels in t seconds. How far does sound travel in seconds?

23 - Practice (continued) Form G Formalizing Relations and Functions Find the range of each function for the given domain.. f (x) x ;,,,,. f (x) x ;,.,,.,. f (x) x ;,,,,. f (x) x ;,,,, Find a reasonable domain and range for each function. Then graph the function.. A high school is having a pancake breakfast fundraiser. They have packages of pancake mix that each feed people. The function N(p) p represents the number of people N(p) that p packages of pancake mix feed.. A charter boat travels at a maximum rate of miles per hour. The function d(x) x represents the distance d(x), in miles, that the boat can travel in x hours. The charter boat travels a maximum distance of miles from the shore.. Reasoning If f (x) x and f (a), what is the value of a? Explain.. Open-Ended What is a value of x that makes the relation {(, ), (, ), (, x)} a function?

24 - Standardized Test Prep Formalizing Relations and Functions Gridded Response Solve each exercise and enter your answer on the grid provided.. What is f () for the function f (x) x?. You have returned some merchandise to a store and received a store credit of \$. In the same store, you are purchasing picture frames that cost \$ each. The function f (x) x represents your total cost f (x) if you purchase x picture frames. How many dollars will you pay if you purchase picture frames?. If f (x) x, what is the range value for the domain value?. When Jerome travels on the highway, he sets his cruise control at mi/h. The function f (x) x represents his total distance f (x) when he has traveled x hours. How many miles will he have travelled after. hours of driving on the highway?. For what value of x is the value of f (x) x equal to?

25 - Think About a Plan Sequences and Functions Transportation Buses on your route run every minutes from : a.m. to : a.m. You get to the bus stop at : a.m. How long will you wait for a bus? Understanding the Problem. What is the maximum amount of time you should have to wait for a bus?. How many minutes after the buses begin running at : a.m. do you arrive at the bus stop?. What time does the first bus of the day arrive at your bus stop? Planning the Solution. Fill in the table at the right showing the times a bus will stop at your stop. Stop Time. What is the common difference?. According to the table, when will the next bus arrive at your bus stop? Getting an Answer. How long will you wait for a bus?

26 - Practice Form G Sequences and Functions Describe the pattern in each sequence. Then find the next two terms of the sequence..,,,,.,,,,..,.,,.,..,.,.,.,..,.,.,.,.,,,,.,,,,.,,,,.,,,, Tell whether the sequence is arithmetic. If it is, identify the common difference..,,,,.,,,,.,,,,.,,,,.,,,,.,,,,.,,,,.,.,.,,.,,,,.,,,,.,,,,.,,,,. You have a gift card for a coffee shop worth \$. Each day you use the card to get a coffee for \$.. Write a rule to represent the amount of money left on the card as an arithmetic sequence. What is the value of the card after buying coffees?. You start a savings account with \$ and save \$ each month. Write a rule to represent the amount of money you invest into your savings account as an arithmetic sequence. How much money will you have invested after months?

27 - Practice (continued) Form G Sequences and Functions Find the third, fifth, and tenth terms of the sequence described by each rule.. A(n) (n )(). A(n) (n )(). A(n). (n )(). A(n) (n )(.). A(n) (n )(). A(n). (n )(). A(n) (n )(). A(n). (n )(.) Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a function rule to represent it...,.,,.,.,,,,.,,,,.,,,,..,.,.,.,.,,,,. Open-Ended Write an arithmetic sequence whose common difference is... Error Analysis Your friend writes A() ()() as a rule for finding the eighth term of the arithmetic sequence,,,, Describe and correct your friend s error.. The local traffic update is given on a radio channel every minutes from : p.m. to : p.m. You turn the radio on at : p.m. How long will you wait for the local traffic update?

28 - Standardized Test Prep Sequences and Functions Multiple Choice For Exercises, choose the correct letter.. What are the next two terms of the following sequence?,,,, A., B., C., D.,. What are the next two terms of the following sequence?,,,, F., G., H., I.,. What is the common difference of the following arithmetic sequence?,,,, A. B. C. D.. What is the ninth term of the arithmetic sequence defined by the rule A(n) (n )()? F. G. H. I.. Each time a touchdown is scored in a football game, points are added to the score of the scoring team. A team already has points. What rule represents the number of points as an arithmetic sequence? A. A(n) n C. A(n) (n )() B. A(n) (n )() D. A(n) (n ) Short Response. A friend opens a savings account by depositing \$. He deposits an additional \$ into the account each month. a. What is a rule that represents the amount of money in the account as an arithmetic sequence? b. How much money is in the account after months? Show your work.

Using Graphs to Relate Two Quantities

- Using Graphs to Relate Two Quantities For Eercises, choose the correct letter.. The graph shows our distance from the practice field as ou go home after practice. You received a ride from a friend back

Algebra I Practice Exam

Algebra I This practice assessment represents selected TEKS student expectations for each reporting category. These questions do not represent all the student expectations eligible for assessment. Copyright

1-1 Practice. Patterns and Expressions. Describe each pattern using words. Draw the next figure in each pattern.

1-1 Practice Patterns and Expressions Describe each pattern using words. Draw the next figure in each pattern. 1. 2. 3. Copy and complete each table. Include a process column. 4. 5. 6. Input Output Input

Station State whether the following represent discrete or continuous graphs. Sketch a graph to represent the situation. Label each section.

Station 1 1. Describe the relationship between the variables. 2. State whether the following represent discrete or continuous graphs. Sketch a graph to represent the situation. Label each section. a. The

Rate of Change and slope. Objective: To find rates of change from tables. To find slope.

Linear Functions Rate of Change and slope Objective: To find rates of change from tables. To find slope. Objectives I can find the rate of change using a table. I can find the slope of an equation using

Algebra 1 Semester 1 Review

Class: Date: Algebra 1 Semester 1 Review 2013-2014 1. 7 4 2. What is the simplified form of each expression? 343 16,384 16,807 2,401 Ê ËÁ 4 7 ˆ 3 343 64 64 343 21952 407 What is the simplified form of

Which of the following is an irrational number? a) 2.8 b) 19

Which of the following is an irrational number? a) 2.8 b) 19 c)!! d) 81 A discounted ticket for a football game costs \$12.50 less than the original price p. You pay \$63 for a discounted ticket. Write and

Name Class Date. Describe each pattern using words. Draw the next figure in each pattern Input Output

1-1 Practice Patterns and Expressions Form G Describe each pattern using words. Draw the next figure in each pattern. 1. 2. 3. Copy and complete each table. Include a process column. 4. 5. 6. Input Output

IM1 Summative Practice #1 Show all your Work

IM1 Summative Practice #1 Name: Show all your Work Period: Simplify each expression below. 1. 5x (7 3x) 2. 5(x 12) + 15(x + y) 3. 8 2(x 2 3x) (9 3x 2 ) Solve each equation. Justify each step with a property

St. Michael s Episcopal School. Summer Math

St. Michael s Episcopal School Summer Math for rising 7th & 8 th grade Algebra students 2017 Eighth Grade students should know the formulas for the perimeter and area of triangles and rectangles, the circumference

Algebra 1 Fall Review

Name Algebra 1 Fall Review 2013-2014 Date 1. Write an inequality to best represent the graph shown at right. (A.1.D.) m: b: inequality: 2. Write an inequality to best describe the graph shown at right.

Algebra I STAAR Practice Test A

Algebra I STAAR Practice Test A 1 What is the value of if (, ) is a solution to the equation 3 1 5 1? A C B 3 D 5 5 A plumber charges \$5 for a service call and \$15 per hour for repairs. She uses the graph

8-3 Writing Equations

Translate each sentence into an equation. 1. The quotient of a number and 3, less 8, is 16. Translate each sentence into an equation. 7. Eighteen more than half a number is 8. 2. Tiffani spent \$95 for

Algebra 1 Unit 3 Practice

Lesson 1-1 Use the table for Items 1 and. Canoe Rental Days Cost (\$) 1 5 3 78 5 1 7 13 1. Use function notation to write a linear function that gives the cost C in dollars of renting a canoe for t days.

A C E. Applications. Applications Connections Extensions. Student 1 Student Below are some results from the bridge experiment in a CMP class.

A C E Applications Connections Extensions Applications 1. Below are some results from the bridge experiment in a CMP class. Bridge-Thickness Experiment Number of Layers 2 4 6 8 Breaking Weight (pennies)

x 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12

Factor the GCF from each expression 4 5 1. 15x 3x. 16x 4 Name: a. b. 4 7 3 6 5 3. 18x y 36x y 4x y 5 4. 3x x 3 x 3 c. d. Not all may be possible. 1. Find two numbers that sum to 8 and have a product of

- Think About a Plan Quadratic Graphs and Their Properties Physics In a physics class demonstration, a ball is dropped from the roof of a building, feet above the ground. The height h (in feet) of the

Grade 7, Unit 2 Practice Problems - Open Up Resources. Lesson 1. Problem 1. Problem 2. Yes, since 3 times 1.5 is 4 and 2 times 1.5 is 3.

9//7, 0) AM Lesson Problem Which one of these shapes is not like the others? Explain what makes it different by representing each width and height pair with a ratio. C is different from A and B. For both

Solving and Graphing Linear Inequalities Chapter Questions. 2. Explain the steps to graphing an inequality on a number line.

Solving and Graphing Linear Inequalities Chapter Questions 1. How do we translate a statement into an inequality? 2. Explain the steps to graphing an inequality on a number line. 3. How is solving an inequality

Student Name P Grade Test Booklet Practice Test TEST BOOKLET SECURITY BARCODE Unit 1 Unit 1 Directions: Today, you will take Unit 1 of the Grade Practice Test. Unit 1 has two sections. In the first section,

On Your Own. Applications. Unit 1. 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars.

Applications 1 p = 7.5n - 55, where n represents the number of car washes and p represents the profit in dollars. 2 t = 0.5 + 2a, where a represents the area of the grass and t represents the time in hours

Franklin Math Bowl Algebra I All answers are presented accurate to three decimal places unless otherwise noted. Good luck! c.

Franklin Math Bowl Algebra I 2009 All answers are presented accurate to three decimal places unless otherwise noted. Good luck! 1. Assuming that x 2 5x + 6 0, simplify x2 6x+9 x 2 5x+6. a. 3 x 2 b. x 2

Review Unit 4: Linear Functions

Review Unit 4: Linear Functions You may use a calculator. Unit 4 Goals Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships

EOC FSA Practice Test. Algebra 1. Calculator Portion

EOC FSA Practice Test Algebra 1 Calculator Portion FSA Mathematics Reference Sheets Packet Algebra 1 EOC FSA Mathematics Reference Sheet Customary Conversions 1 foot = 12 inches 1 yard = 3 feet 1 mile

Name. Algebra I Period

Name Algebra I Period 1 Simplify the following expression: 1 (8 2 4) 8 4 2 4 4 In slope-intercept form, what is the equation of a line with an x-intercept of -3 and a y-intercept of 5? Record your answer

Sample. Test Booklet. Subject: MA, Grade: 08 STAAR Grade 8 Math signup at to remove - Student name:

Test Booklet Subject: MA, Grade: 08 Student name: Author: Texas District: Texas Released Tests Printed: Tuesday February 12, 2019 1 A fishbowl shaped like a sphere is filled with water. The fishbowl has

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

Name: Period: Date: Algebra 1 Common Semester 1 Final Review Like PS4 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3.

Practice EOC Questions

Practice EOC Questions 1 One of the events at a high school track meet is the pole vault. The pole vaulter runs toward the crossbar and uses a pole to attempt to vault over the bar. Josh collects data

8, x 2. 4and. 4, y 1. y 2. x 1. Name. Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1.

MATH 099 PRACTICE FINAL EXAMINATION Fall 2016 Name Part 1: (Skills) Each question is worth 2 points. SHOW ALL WORK IN THE SPACE PROVIDED. 1. Determine whether 4, 3 is a solution to the equation 3x 3y 21

Name: Class: Date: ID: A

Name: Class: Date: ID: A 6A Short Answer Solve the equation. 1.!5d! 24 =!4(d + 6)! d Write the inequality for the graph. 2. 3. 4. 5. Solve the inequality. 6. p + 7

Indiana Core 40 End-of-Course Assessment Algebra I Blueprint*

Types of items on the Algebra I End-of-Course Assessment: Multiple-choice 1 point per problem The answer to the question can be found in one of four answer choices provided. Numeric response 1 point per

1. The sum of four consecutive even numbers is 52. What is the largest of these numbers?

1. The sum of four consecutive even numbers is 52. What is the largest of these numbers? 26 22 C 16 10 2. In a high school basketball game, Sarah scored 10 points in the first half of the game. In the

Part 1 1 st 6weeks material

Name Date Period Part 1 1 st 6weeks material 1. Write an expression that can be used to determine the number of blocks in the n th figure. 2. Write an expression to represent the sequence below: 5, 8,

Name: Period: Date: Algebra 1 1st Semester Review Which best describes the solution(s) for this equation? 3 ( 8x 12) = 33 2x

Name: Period: ate: lgebra 1 1st Semester Review 2011 1 Which algebraic expression could NOT match the pictorial representation below? 5 Which best describes the solution(s) for this equation? 3 ( 8x 12)

Grade 8. Functions 8.F.1-3. Student Pages

THE NEWARK PUBLIC SCHOOLS THE OFFICE OF MATHEMATICS Grade 8 Functions 8.F.1-3 Student Pages 2012 2012 COMMON CORE CORE STATE STATE STANDARDS ALIGNED ALIGNED MODULES Grade 8 - Lesson 1 Introductory Task

Skills Practice Skills Practice for Lesson 5.1

Skills Practice Skills Practice for Lesson. Name Date Widgets, Dumbbells, and Dumpsters Multiple Representations of Linear Functions Vocabular Write the term that best completes each statement.. A(n) is

Topic 1. Solving Equations and Inequalities 1. Solve the following equation

Topic 1. Solving Equations and Inequalities 1. Solve the following equation Algebraically 2( x 3) = 12 Graphically 2( x 3) = 12 2. Solve the following equations algebraically a. 5w 15 2w = 2(w 5) b. 1

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3

SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want

Name: Class: Date: ID: A. c. the quotient of z and 28 z divided by 28 b. z subtracted from 28 z less than 28

Name: Class: Date: ID: A Review for Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic expression z 28 in words.

Lesson 9.1 Skills Practice

Lesson 9.1 Skills Practice Name Date Call to Order Inequalities Vocabulary Write the term that best completes each statement. 1. A(n) graph of an inequality in one variable is the set of all points on

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the

Practice - Solving Two-Step Equations Solve each equation. Check your answer.. a +. +. b +. 9 + t. a +. -t + Write an equation to model each situation. Then solve.. You want to buy a bouquet of yellow

Name. 1. Given the solution (3, y), what is the value of y if x + y = 6? 7. The graph of y = x 2 is shown below. A. 3 B. 4 C. 5 D.

Name 1. Given the solution (, y), what is the value of y if x + y = 6? 7. The graph of y = x is shown below. 5 D. 6. What are the solutions to the equation x - x = 0? x = - or x = - x = - or x = 1 x =

Systems of Equations Unit Five ONE NONE INFINITE

Systems of Equations Unit Five ONE NONE INFINITE Standards: 8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables

SY14-15 Algebra Exit Exam - PRACTICE Version

Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your

Math 8 Unit 4: A Study of Linear Equations

Math 8 Unit 4: A Study of Linear Equations By the end of this unit, students should be able to: 1) Show that the slope of a line can be calculated as rise/run. Explain why the slope is the same between

Lesson 8: Representing Proportional Relationships with Equations

Lesson 8: Representing Proportional Relationships with Equations Student Outcomes Students use the constant of proportionality to represent proportional relationships by equations in real world contexts

3. Find the area for each question below. a. (3x 2)(2x + 5) b. 4. Simplify the expressions below. is equal to 1, what is the value of a?

Permitted resources: 2018 2019 Algebra 1 Midterm Review FSA Approved calculator Algebra 1 FSA Reference Sheet 1. The expression 13x + 5 represents the number of marbles you have after shopping at the game

UNIT 5 INEQUALITIES CCM6+/7+ Name: Math Teacher:

UNIT 5 INEQUALITIES 2015-2016 CCM6+/7+ Name: Math Teacher: Topic(s) Page(s) Unit 5 Vocabulary 2 Writing and Graphing Inequalities 3 8 Solving One-Step Inequalities 9 15 Solving Multi-Step Inequalities

QUESTIONS 1-46 REVIEW THE OBJECTIVES OF CHAPTER 2.

MAT 101 Course Review Questions Valid for Fall 2014, Spring 2015 and Summer 2015 MIDTERM EXAM FINAL EXAM Questions 1-86 are covered on the Midterm. There are 25 questions on the midterm, all multiple choice,

Chapter 2. Worked-Out Solutions. Chapter 2 Mathematical Practices (p. 52) Chapter 2 Maintaining Mathematical Proficiency (p. 51)

Chapter Chapter Maintaining Mathematical Proficiency (p. ). 6 8 Chapter Mathematical Practices (p. ). x + < x. x > x +.. = 6. =. The solution is x .. x + x +. + = + =. = = 6. + =

ALGEBRA 1 SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Algebra 1 S1 (#2201) and Foundations in Algebra 1 S1 (#7769)

Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Ramal goes to the grocery store and buys pounds of apples and pounds of bananas. Apples cost dollars per

Lesson Lesson Tutorials

7.4 Lesson Lesson Tutorials An equation in two variables represents two quantities that change in relationship to one another. A solution of an equation in two variables is an ordered pair that makes the

MATH 021 TEST 3 REVIEW SHEET

TO THE STUDENT: MATH 021 TEST 3 REVIEW SHEET This Review Sheet gives an outline of the topics covered on Test 3 as well as practice problems. Answers for all problems begin on page 8. In several instances,

Pattern & Algebra Practice Problems

Pattern & Algebra Practice Problems Solve Linear Inequalities 1. Solve for x. A. x > -3 B. x > 0 C. x < 0 D. x < -3 4x < -6 + 2x Symbolize Problem Situations 2. Scott is draining his swimming pool. The

Unit 1 Study Guide [MGSE9-12.N.Q.1-3, MGSE9-12.A.CED.1]

Name: Class: Date: Unit 1 Study Guide [MGSE9-12.N.Q.1-3, MGSE9-12.A.CED.1] Matching a. algebraic expression f. variable b. numerical expression g. constant c. like terms h. solution of an equation d. absolute

Sample. Test Booklet. Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1. - signup at to remove - Student name:

Test Booklet Subject: MA, Grade: HS PSSA 2013 Keystone Algebra 1 Student name: Author: Pennsylvania District: Pennsylvania Released Tests Printed: Friday May 31, 2013 1 Which of the following inequalities

Name Date Class A 3.12, B 3.12, 10, 3.24, C 10, 3.12, 3.24, D 3.12, 3.24,

. Which label or labels could replace A In the diagram below? A Rational Numbers only B Rational Numbers or Integers C Integers only D Irrational Numbers. Between which two integers does the value of 88

Chapter 1 ( )? Chapter 1 Opener. Section 1.1. Worked-Out Solutions. 2π π = π. Try It Yourself (p. 1) So, x = 95.3.

Chapter Chapter Opener Try It Yourself (p. ). + ( ) 7.. + 8. ( ) +. 7. ( 7) + 7 7. 8 () 0 + 8. 7. ( 7) 8 0.. 8. Section.. Activity (pp. ). Triangle Angle A (degrees) Angle B (degrees). a. The sum of the

Algebra 1, Chapter 4 Post Test

Class: Date: Algebra 1, Chapter 4 Post Test Review 4.1.1: I can represent mathematical relationships using graphs. 1. (2 points) Sketch a graph of the speed of a city bus on a daily route. Label each section.

2(m + 3) + 5 = 7(4 m) 5m Simplify both sides of the equation using order of operations. Solution

Unit 2, Activity 2, Split-Page Notetaking Example 2(m + 3) + 5 = 7(4 m) 5m Simplify both sides of the equation using order of operations. 2m + 6 + 5 = 28 7m 5m 2m + 11 = 28 12m +12m +12m 14m + 11 = 28-11

Word problems in Slope-intercept form

Accelerated Algebra I Section 8.5: Linear Equation Word Problems Word problems in Slope-intercept form When a word problem involves a constant rate or speed and a beginning amount, it can be written in

Algebra 1 End-of-Course Assessment Practice Test with Solutions

Algebra 1 End-of-Course Assessment Practice Test with Solutions For Multiple Choice Items, circle the correct response. For Fill-in Response Items, write your answer in the box provided, placing one digit

Name Period Date DRAFT

Name Period Date Equations and Inequalities Student Packet 4: Inequalities EQ4.1 EQ4.2 EQ4.3 Linear Inequalities in One Variable Add, subtract, multiply, and divide integers. Write expressions, equations,

3.1 NOTES Solving Systems of Linear Equations Graphically

3.1 NOTES Solving Systems of Linear Equations Graphically A system of two linear equations in two variables x and y consist of two equations of the following form: Ax + By = C Equation 1 Dx + Ey = F Equation

Applications of Systems of Linear Equations

5.2 Applications of Systems of Linear Equations 5.2 OBJECTIVE 1. Use a system of equations to solve an application We are now ready to apply our equation-solving skills to solving various applications

Algebra - Chapter 5 Review

Name Hour Algebra - Chapter 5 Review 1. Write an equation in slope-intercept form of the graph. 10 y 10 x 10 2. The cost of a school banquet is \$95 plus \$15 for each person attending. Write an equation

8 th Grade Domain 2: Algebra and Functions (40%) Sara

8 th Grade Domain 2: Algebra and Functions (40%) 1. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at different times. Find the slope of the line and tell

1. The area of the surface of the Atlantic Ocean is approximately 31,830,000 square miles. How is this area written in scientific notation?

1. The area of the surface of the tlantic Ocean is approximately 31,830,000 square miles. How is this area written in scientific notation? 3.183 x 10 4 B 3.183 x 10 5 C 3.183 x 10 6 D 3.183 x 10 7 2. In

Lesson 9.1 Skills Practice

Lesson 9.1 Skills Practice Name Date Call to Order Inequalities Vocabulary Write the term that best completes each statement. 1. A(n) in one variable is the set of all points on a number line that makes

Unit 4 Linear Functions

Algebra I: Unit 4 Revised 10/16 Unit 4 Linear Functions Name: 1 P a g e CONTENTS 3.4 Direct Variation 3.5 Arithmetic Sequences 2.3 Consecutive Numbers Unit 4 Assessment #1 (3.4, 3.5, 2.3) 4.1 Graphing

Name: Class: Date: ID: A

Name: Class: Date: 8th Grade Advanced Topic III, Linear Equations and Systems of Linear Equations, MA.8.A.1.1, MA.8.1.1.2, MA.8.A.1.3, *MA.8.A.1.4, MA.8.A.1.5, MA.8.A.1.6 Multiple Choice Identify the choice

The steps in Raya s solution to 2.5 (6.25x + 0.5) = 11 are shown. Select the correct reason for line 4 of Raya s solution.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear functions. Unit 2: Reasoning with Linear Equations and Inequalities The perimeter

2-1 Writing Equations

Translate each sentence into an equation. 1. Three times r less than 15 equals 6. Rewrite the verbal sentence so it is easier to translate. Three times r less than 15 equals 6 is the same as 15 minus 3

Algebra 1 STAAR Review Name: Date:

Algebra 1 STAAR Review Name: Date: 1. Which graph does not represent y as a function of x? I. II. III. A) I only B) II only C) III only D) I and III E) I and II 2. Which expression is equivalent to? 3.

Name Class Date. You can use the properties of equality to solve equations. Subtraction is the inverse of addition.

2-1 Reteaching Solving One-Step Equations You can use the properties of equality to solve equations. Subtraction is the inverse of addition. What is the solution of + 5 =? In the equation, + 5 =, 5 is

A C E. Answers Investigation 2. Applications. Age (wk) Weight (oz) 1. a. Accept any line that approximates the data. Here is one possibility:

Answers Applications 1. a. Accept any line that approximates the data. Here is one possibility: 4. a. Lines will vary. Here is one possibility: b. y = 8.5x 2.5. Students might come up with a simpler model

Summer Math Packet Grade 8 / Course 3

SHOW WORK FOR EVERY PROBLEM 1. If Michelle rollerblades around a circular track with a radius of 80 meters, how far does she skate? Use 3.14 for π. Round to the nearest tenth. 4. The weight of an object

3. A beam or staircase frame from CSP costs \$2.25 for each rod, plus \$50 for shipping and handling.

Pg. 13: #3 3. A beam or staircase frame from CSP costs \$2.25 for each rod, plus \$50 for shipping and handling. a. Complete the following table to show the costs for beams of different lengths. Beam Length

Dear Parents, Guardians, and Students:

Dear Parents, Guardians, and Students: During the summer, students who will be enrolled in Algebra net year are required to complete a portfolio of mathematics problems. The purpose of this eperience is

f (x) = 25x 2 11 f (x) = 10x + 4 x 24 14x + 35 x 25 f (x) = f ( x ) = 91 44x 2 17 x f ( x ) = f ( x ) = 2x

1 Let the function f be defined by the equation y = f (x), where x and f (x) are real numbers. Find the domain of the function f (x) = 25x 2 11 2 Let the function f be defined by the equation y = f (x),

HW A) SWBAT identify the properties of operations Create flashcards or a some type of foldable that shows the following properties of operations

HW A) SWBAT identify the properties of operations Create flashcards or a some type of foldable that shows the following properties of operations including examples: HW B) SWBAT apply properties of operations

Linear Functions. Unit 3

Linear Functions Unit 3 Standards: 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and

Name Date Class. 5 y x + 7

Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6?

Summer Prep Work for Students Entering Geometry

Summer Prep Work for Students Entering Geometry Operations, Expressions, and Equations 4 1. Evaluate when a =, b = 0.5, c =, d = (cd) + ab. The expression x(x + ) is the same as: a.) x + b.) x + c.) x

a. Bob: 7, Bridget: 4, Brian 1 b. Bob: 7, Bridget: 4, Brian 3 c. Bob: 7, Bridget: 14, Brian 3 a. 100 b. 150 c c. 2 d.

Period: Date: K. Williams 8th Grade Year Review: Chapters -4. A neighborhood pool charges \$22 for a pool membership plus an additional \$2 for each visit to the pool. If Elliot visited the pool 6 times,

4. The table shows the number of toll booths driven through compared to the cost of using a Toll Tag.

ALGEBRA 1 Fall 2016 Semester Exam Review Name 1. According to the data shown below, which would be the best prediction of the average cost of a -bedroom house in Georgetown in the year 2018? Year Average

7-6 Growth and Decay. Let t = 7 in the salary equation above. So, Ms. Acosta will earn about \$37, in 7 years.

1. SALARY Ms. Acosta received a job as a teacher with a starting salary of \$34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in

Practice - TAKS OBJECTIVE 1 & 2. 1) Which inequality best describes the graph shown below?

Name: Period Practice - TAKS OBJECTIVE 1 & 2 1) Which inequality best describes the graph shown below? A y 2x B y x 2 C y 2x 2 D y x 2 2) If y is a function of x in the equation y = x 2 9, which statement

DIRECT, JOINT, AND INVERSE VARIATION

DIRECT, JOINT, AND INVERSE VARIATION DIRECT VARIATION A linear equation of the form y = kx with k! 0 is called direct variation. The variable y varies directly with the variable x. In other words, the

Notes/Examples. To solve multi-step linear equations using inverse operations. To use multi-step linear equations to solve real-life problems.

1.2 Explain Solving Multi-Step Equations - Notes Essential Question: How can you use multi-step equations to solve real-life problems? Main Ideas/ Questions Notes/Examples What You Will Learn To solve

Write an inequality for the graph. Then, in words, describe all the values of x that make the inequality true

Name Date. Practice A Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true... 6 8 0 6 Write the word sentence as an inequality.. A number is at most..

MATH ALGEBRA AND FUNCTIONS

Students: 1. Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations and graph and interpret their results.

Directions: Simplify completely! 1) 7 ) 7 10 ) 5 + 6 + 7 4 7 4) 4 11 5) ( ) 6) (6w 8 w ) 7) 0 8 48 75 4 5 8) 7 (10 5 5 ) 9) 4 4 5 8 10) 90m n 11) 1) 5m 8 m 0 0 10 80 r r r 1) 5 18k m 14) 7 km 7km Directions:

NAME DATE PER. REVIEW: FUNCTIONS PART 2

NAME DATE PER. REVIEW: FUNCTIONS PART 2 Match graphs A - G to each description. Then identify the independent & dependent variable. Description Graph (letter) x-axis (independent) y-axis (dependent) 1.

MATH ALGEBRA AND FUNCTIONS

Students: 1. Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and their graphs. 1. Use variables and appropriate operations to write an expression,

0.3 Domain and Range: Relations vs Functions, Domain, Range, and Vertical Line Test Worksheet 3 #1-7

Unit 0 Check Sheet Function Families Check sheet must be turned in to receive Homework & Quiz points. All quiz corrections must be done for test score to replace quiz scores. No check sheet = No Points.