Complete Week 18 Package

Size: px
Start display at page:

Download "Complete Week 18 Package"

Transcription

1 Complete Week 18 Package Jeanette Stein

2 Table of Contents Unit 4 Pacing Chart Day 86 Bellringer Day 86 Practice Day 87 Bellringer Day 87 Practice Day 88 Bellringer Day 88 Activity Day 88 Practice Day 88 Practice Day 89 Bellringer Day 89 Exit Slip Weekly Assessment

3 CCSS Algebra 1 Pacing Chart Unit 7 Unit Week Day CCSS Standards Mathematical Practices Objective I Can Statements 7 Sequences and Functions 7 Sequences and Functions 7 Sequences and Functions 7 Sequences and Functions 18 Understan ding Interest 18 Understan ding Interest 18 Understan ding Interest 18 Understan ding Interest CCSS.MATH.CONTENT.HSF.LE.A.1.A Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. CCSS.MATH.CONTENT.HSF.LE.A.1.B Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. CCSS.MATH.CONTENT.HSF.LE.A.1.C Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. CCSS.MATH.CONTENT.HSF.BF.A.1 Write a function that describes a relationship between two quantities.* CCSS.MATH.CONTENT.HSF.BF.A.1.A Determine an explicit expression, a recursive process, or steps for calculation from a context. CCSS.MATH.CONTENT.HSF.BF.A.1.B Combine standard function types using CCSS.MATH.PRACTICE. MP4 Model with mathematics. CCSS.MATH.PRACTICE. MP8 Look for and express regularity in repeated reasoning. CCSS.MATH.PRACTICE. MP6 Attend to precision. CCSS.MATH.PRACTICE. MP4 Model with mathematics. CCSS.MATH.PRACTICE. MP8 Look for and express regularity in repeated reasoning. The student will be able to recognize situations that can be modeled linearly or exponentially and describe the rate of change per unit as constant or the growth factor as a constant percent. The student will be able to justify the fact that the linear functions grow by equal differences over equal intervals using graphs and tables. The student will be able to justify the fact that exponential functions grow by equal factors over equal intervals using tables and graphs. Given a linear or exponential context, students will find an expression, recursive process, or steps to model a context with mathematical representations. I can recognize situations that can be modeled linearly or exponentially and describe the rate of change per unit as constant or the growth factor as a constant percent. I can justify the fact that the linear functions grow by equal differences over equal intervals using graphs and tables. I can justify the fact that exponential functions grow by equal factors over equal intervals using tables and graphs. Given a linear or exponential context, I can find an expression, recursive process, or steps to model a context with 2015 Page 1

4 CCSS Algebra 1 Pacing Chart Unit 7 7 Sequences and Functions 18 Understan ding Interest arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. CCSS.MATH.CONTENT.HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. mathematical representations. 90 Assessment Assessment Assessment Assessment 2015 Page 2

5 Day 86 Bellringer Name Day 86 Identify the linear situations below. 1. Ben walks at a rate of 3 miles per hour. He runs at a rate of 6 miles per hour. In one week, the combined distance that he walks and runs is 210 miles. Linear or Nonlinear? 2. A salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year. Linear or Nonlinear? 3. An account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years. Linear or Nonlinear? 4. You have inherited land that was purchased for $30,000 in The value of the land increased by approximately 5% per year for 10 years. Linear or Nonlinear? 2015 Page 3

6 Day 86 Bellringer Name Answer Key Day Linear 2. Linear 3. Nonlinear 4. Nonlinear 2015 Page 4

7 Day 86 Practice Name Write the given time period as a fraction of a year months months 2. 6 months months Find the simple interest earned. 5. Principal: $135 Annual rate: 4.3% Time: 30 months 7. Principal: $1200 Annual rate: 1.9% Time: 5 years 6. Principal: $575 Annual rate: 2.6% Time: 3.3 years 8. Principal: $850 Annual rate: 5.1% Time: 54 months Find the simple interest paid. 9. Principal: $350 Annual rate: 4% Time: 3 years 11. Principal: $345 Annual rate: 5.5% Time: 42 months 10. Principal: $2575 Annual rate: 8.2% Time: 10 years 12. Principal: $600 Annual rate: 6.2% Time: 8 years Find the balance of the account. 13. Principal: $200 Annual rate: 3% Time: 2 years 15. Principal: $800 Annual rate: 2.56% Time: 15 months 14. Principal: $1020 Annual rate: 4.1% Time: 18 months 16. Principal: $1580 Annual rate: 3.75% Time: 2.5 years 2015 Page 5

8 Day 86 Practice Name Write the rate as a decimal. Then find the amount of simple interest. Explain your answer. 17. Tameka borrowed $300 to buy a digital music player. She will pay the money back in 1 year at 5% simple interest. How much money will Tameka pay in interest? 18. Victor deposited $2350 in a savings account that pays 4.5% simple annual interest. If Victor keeps the money in the account for 30 months, how much interest will he earn? Find the balance of the account after time t using the simple interest method. 19. $375 at 4% interest compounded annually for 3 years 20. $975 at 8.2% interest compounded annually for 2 years 21. $135 at 2.3% interest compounded annually for 7 years 22. $250 at 3.1% interest compounded annually for 4 years 2015 Page 6

9 Day 86 Practice Name Find the balance of the account after time t using the compound interest formula. 23. $1200 at 2.5% interest compounded annually for 8 years 24. $750 at 4.6% interest compounded annually for 4 years 25. $435 at 1.7% interest compounded annually for 10 years 26. $815 at 5% interest compounded annually for 6.5 years How many steps of simple interest need to be performed? Solve the problem. 27. Solve the problem using the compound interest formula. Jong deposits $500 in an account that earns 2.5% interest compounded annually and keeps the money in the account for 3 years. Monty deposits $500 in an account that earns 5.1% interest compounded annually and keeps the money in the account for 2 years. Who has more money when he closes his account? Explain your reasoning Page 7

10 Day 86 Practice Name Answer Key year year 3. Sample answer: 7 4 or years 4. Sample answer: 8 3 or years 5. $ $ $ $ $ $ $ $ $ $ $ $ Write the rate as a decimal. Then find the amount of simple interest ; $15.00; Sample answer: 300 x 0.05 x 1 = ; $264.38; Sample answer: 2350 x x 2.5 = Find the balance of the account after time t using the simple interest method. 19. $ $ $ $ Find the balance of the account after time t using the compound interest formula. 23. $ $ $ $ How many steps of simple interest need to be performed? Solve the problem. 27. Monty; Sample answer: The amount in Jong s account is $538.45, and the amount in Monty s account is $ Page 8

11 Day 87 Bellringer Name Day 87 Create a table for the linear functions. 1. f(x) = 2x f(x) = x + 1 x f(x) x f(x) 2. f(x) = 2 3 x f(x) = 7 x f(x) x f(x) 2015 Page 9

12 Day 87 Bellringer Name Answer Key Day f(x) = 2x f(x) = x + 1 x f(x) x f(x) f(x) = f(x) = 2 3 x + 4 x f(x) x f(x) Page 10

13 Day 87 Activity Name Exploring Exponential Growth and Decay Teacher Notes Overview: Students explore exponential growth and decay with a paper-folding activity and yarn-cutting activity. Objective: Students will work in pairs to collect data, explore patterns in their collected data, and find exponential models that represent their data. They will display their findings graphically. Materials Needed: Paper (one sheet for each pair of students) Yarn (one piece, about 1 yard, for each pair of students) Calculator Graph Paper Rulers Scissors Activity: 1. Students work in pairs on the exponential growth activity, following the directions on the activity sheet. (One group of 3 may be necessary.) 2. After the students complete the exponential growth activity, the teacher should lead a discussion of questions After completing the exponential growth activity, the students should work on the exponential decay activity, following the directions on the activity sheet. 4. After the students complete the exponential decay activity, the teacher should lead a discussion of questions Page 11

14 Day 87 Activity Name Paper-Folding Activity Part I 1) Look at your sheet of paper and determine the number of sections the paper has when it is completely unfolded. Record this data in the table below. 2) Fold your piece of paper in half and determine the number of sections the paper has after you have made a fold. Record this data in the table below. 3) Fold the piece of paper in half again and determine the new number of sections. Record your data in the table. Continue in the same manner, folding the paper and recording the data, until it becomes too hard to fold the paper any more. (This will probably happen around the 6 th fold.) Paper-Folding Data Number of Folds Number of Sections 4) Which column of your table is the input? Which column is the output? 5) Using graph paper, make a scatter plot of the data. 6) By studying the graph and/or table, predict what you think the number of sections will be for 10 folds. 7) Determine a mathematical model (equation) that represents this data by examining the patterns in the table Page 12

15 Day 87 Activity Name Yarn-Cutting Activity Part II 1) Begin with one piece of yarn and consider it to be one unit long. This data is recorded in the table below. 2) Fold your piece of yarn in half and cut it. You should now have two pieces of yarn, each half the length of the original piece. This information has also been recorded for you in the table below. 3) Continue in the same manner, cutting each piece of yarn in half and recording the new number of pieces and new length, until it becomes too hard to cut the yarn. (This will probably happen around the 5 th cut.) Be sure to record your data in the table. Yarn-Cutting Data Number of Pieces Length of Each New Piece /2 3) Which column of your table is the input? Which column is the output? 4) Using graph paper, make a scatter plot of the data. 5) By studying the graph and/or table, predict what you think the length of each new piece will be after the 10 th cut. 6) Determine a mathematical model (equation) that represents this data by examining the patterns in the table Page 13

16 Day 87 Activity Name 2015 Page 14

17 Day 87 Activity Name Answer Key Part 1 3. Number of Number of Folds Sections input-folds, output-sections = y=2 x Part 2 3. Number of Pieces Length of Each New Piece /2 3 1/4 4 1/8 5 1/16 6 1/32 7 1/64 8 1/ / Page 15

18 Day 87 Activity Name 4. Input number of pieces, output-length y = 1 2 x 2015 Page 16

19 Day 87 Practice Name Discussion Questions 1. What is the meaning of an exponent? 2. Does 5 4 = 4 5? If they are not equal, which is greater? 3. Would 3 6 be greater that or less than 6 3? 4. Given two different whole numbers would you get a greater answer, if you use the smaller number or the larger number in the base? Are there any exceptions? 2015 Page 17

20 Day 87 Practice Name Group Activity Sheet You are at an Interview for a Job. While there, you are asked which salary you would prefer. Salary A would pay $500 the first day and give you a $100 daily increase. Salary B would pay 1 cent for the first day and every successive day you will be paid double the amount. Questions: 5. Create a table of values that would show patterns for salary A and salary B #of days Pay A Pay B 6. Determine the function for each salary. Payment A: Payment B: 7. By using the equations, sketch the graphs of the two functions. Tell where the lines intersect and explain what it means 8. Would you rather be given salary A or salary 13, Explain Page 18

21 Day 87 Practice Name Create a table and make a sketch the graph of each function. 9. y = 4.2 x 11. y = 4 ( 1 2 )x 10. y = 5.2 x 12. y = 4 ( 1 2 )x Page 19

22 Day 87 Practice Name Answer Key. 1. Exponents are repeated multiplications. An exponent tells how many fines the base s used as a factor. For example 6 2 = 6*6*6. 2. No it is not the same. 5 4 = 625 and 4 5 = > 6 3 since 3 6 = 729 and 6 3 = You would get a greater answer if you put the smaller number in the base. The exceptions would be found if at least one of the numbers is 0 or 1. Also note2 4 = Create a table of values that would show patterns for salary A and salary B. #of days Pay A Pay B Salary A: y = 100(x 1) Salary B: y = 0.01 (2x 1) 7. The two lines intersect. This means about 19 th jay both salary A and salary B. will equal 8. It all depends. If you are one the job more than 18 days you would start to earn more money per day, if you use salary B. (However don t forget the total money you have earned in the past. At day 19, Salary A yields $26,600 versus salary B whose total is $5, Page 20

23 Day 87 Practice Name Page 21

24 Day 88 Bellringer Name Day 88 Evaluate each function at the given table. 1. f(x) = 1 2 4x at x = 2 2. f(x) = 6 3 x at x = 3 3. f(x) = ( 2 3 )x at x = 4 4. f(x) = 1 3 2x at x = Page 22

25 Day 88 Bellringer Name Answer Key Day Page 23

26 Day 88 Activity Name Open the TI-Nspire document Compare_Linear_Exponential.tns. In this activity, you will explore the values of the expressions 3x and 3 x as x changes from 0 to 5. You will compare the two expressions by investigating patterns in how their values change both in a table and graphically. 1. Complete the table below. Which column is growing faster? x 3x 3 x a. As x increases from 2 to 3 in the table, how does the value of 3x change? b. As x increases by 1, describe the pattern in the numbers in the 3x column of the table. 3. a. As x increases from 2 to 3 in the table, how does the value of 3 x change? b. As x increases from 3 to 4 in the table, how does the value of 3 x change? c. As x increases by 1, describe the pattern you notice in the numbers in the 3 x column of the table Page 24

27 Day 88 Activity Name 4. Graph the points in Desmos. Compare the two graphs 5. What is the domain when the values for 3 x increasing faster than the values for 3x? 6. Aaron says that the values of f(x) = 5 x will increase faster than the values of the linear function f(x) = 5x. Do you agree or disagree? Support your answer. Define the domain where this is true. Define the domain where this is false Page 25

28 Day 88 Activity Name Answer Key 1. x 3x 3 x a. Increases by 3 b. you can add 3 each time 3. a. multiplied by 3, goes up by 18 b. multiplied by 3, goes up by 54 c. multiplied by x>1 6. a. Answers will vary b. x > 1 c. x Page 26

29 Day 88 Practice Name Calculate the total amount of the investment or total paid in a loan in the following situations: 1.) You borrow $56,700 for 2 years at 6.3% that is compounded annually. What is the total amount you pay back? Answer: 2.) You invested $4,400 for 2 years at 7.3% compounded semi. What is your total after 2 years? Answer: 3.) You lent $12,200 for 2 years at 8.2% and interest is compounded quarterly for 2 years. What is the total amount you ll see after 2 years? Answer: 4.) You borrowed $30,200 for 5 years at an interest rate of 13.6% and it s compounded Semi annually. How much in total will you have paid after 5 years? Answer: 2015 Page 27

30 Day 88 Practice Name 5.) Your $730 investment gets 6.8% interest compounded monthly for 1 year. How much is your $730 worth after 1 year? Answer: 6.) What is your total investment of $16,000 over 2 years worth if it gets 7% interest compounded semi annually? Answer: 7.) Your uncle charges you 13% compounded semi annually for 2 years to lend you $155. What total amount will you pay after the 2 years? Answer: 8.) If you invested $305 at 7.2% interest compounded monthly for 7 years, how much money would you have after 7 years? Answer: 2015 Page 28

31 Day 88 Practice Name 9.) You invested $140 for 2 years at an interest rate of 7.3% compounded annually for 2 years. What total do you have after 2 years? Answer: 10.) Your second mortgage is $53,000 for 8 years with an interest rate of 1% compounded annually for 8 years. What total will you have paid after 8 years? Answer: 2015 Page 29

32 Day 88 Practice Name Answer Key 1.) $64, ) $5, ) $14, ) $58, ) $ ) $18, ) $ ) $ ) $ ) $57, Page 30

33 Day 88 Practice 2 Name Linear vs. Exponential Word Problems At separate times in the course, you ve learned about linear functions and exponential functions, and done word problems involving each type of function. Today s assignment combines those two types of problems. In each problem, you ll need to make a choice of whether to use a linear function or an exponential function. Below is some advice that will help you decide. Linear Function f(x) = mx + b or f(x) = m(x x 1) + y 1 b is the starting value, m is the rate or the slope. m is positive for growth, negative for decay. Exponential Function f(x) = a b x a is the starting value, b is the base or the multiplier. b > 1 for growth, 0 < b < 1 for decay. See below for ways to find the base b. Choosing linear vs. exponential In growth and decay problems (that is, problems involving a quantity increasing or decreasing), here s how to decide whether to choose a linear function or an exponential function. If the growth or decay involves increasing or decreasing by a fixed number, use a linear function. The equation will look like: y = mx + b f(x) = (rate) x + (starting amount). If the growth or decay is expressed using multiplication (including words like doubling or halving ) use an exponential function. The equation will look like: f(x) = (starting amount) (base) x. PRACTICE 1. Decide whether the word problem represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula. a. A library has 8000 books, and is adding 500 more books each year. Linear or exponential? y =. b. A gym s customers must pay $50 for a membership, plus $3 for each time they use the gym. Linear or exponential? y =. c. A bank account starts with $10. Every month, the amount of money in the account is tripled. Linear or exponential? y = Page 31

34 Day 88 Practice 2 Name d. At the start of a carnival, you have 50 ride tickets. Each time you ride the roller coaster, you have to pay 6 tickets. Linear or exponential? y =. e. There are 20,000 owls in the wild. Every decade, the number of owls is halved. Linear or exponential? y =. 2. Decide whether the table represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula. a. x y Linear or exponential? y =. b. x y Linear or exponential? y =. c. x y Linear or exponential? y =. d. x y Linear or exponential? y = e. x y Linear or exponential? y = 2015 Page 32

35 Day 88 Practice 2 Name f. x y Linear or exponential? y = g. x y Linear or exponential? y = 3. Without a calculator, make a table for f(x) = 1 x 8 2. x f(x) = 1 x Without a calculator, make a table for f(x) = ( ) x. Express answers as fractions. x 1 f(x) = 8 ( 2 ) in fractions x 2015 Page 33

36 Day 88 Practice 2 Name 5. A science experiment involves periodically measuring the number of mold cells present on a piece of bread. At the start of the experiment, there are 50 mold cells. Each time a periodic observation is made, the number of mold cells triples. For example, at observation #1, there are 150 mold cells. a. Write a function formula equation (y = ) for the number of mold cells present, where x stands for the observation number. b. Fill in the missing outputs of this table. x = observation number y = mold cell count c. Suppose that the mold begins to be visible as green coloration when the mold cell count exceeds 100,000. On which observation will this happen? d. What will be the mold cell count on the 20th observation? When you find the answer on your calculator, it will be so large that it displays in scientific notation (E notation). Rewrite the answer as an ordinary big number. 6. Julie gets a pre-paid cell phone. Initially she has a $40.00 balance on the phone. Each minute of talking costs $0.15. Let x stand for the amount of time in minutes that Julie has talked on the phone, and let f(x) stand for the remaining dollar value of the phone. a. Is f(x) a linear function or an exponential function? Explain how you know. b. Find a function formula equation f(x) = c. Find the value of f(0) and explain its meaning in terms of the cell phone. d. Find the value of f(100) and explain its meaning in terms of the cell phone Page 34

37 Day 88 Practice 2 Name e. Find the value of x that makes f(x) = 10, and explain its meaning in terms of the cell phone. f. Find the value of x that makes f(x) = 0, and explain its meaning in terms of the cell phone. 7. Sketch a graph of the function Be sure to label the y-intercept. y 3 2 x Hint: the y-intercept is the starting amount on the axes below Sketch a graph of the function y 5 on the axes below. 4 Be sure to label the y-intercept. x 2015 Page 35

38 Day 88 Practice 2 Name 9. Sketch a graph of the function Be sure to label the y-intercept. y 5 2 x on the axes below Page 36

39 Day 88 Practice 2 Name Answer Key 1. a. Linear; y= 500x+8000 b. Linear; t = 50+3x c. Exponential; y=10(3) x d. Linear; y = 50-6x e. Exponential; y = 20000( 1 2 )x 2. a. Linear; y = 3x+2 b. Exponential; y = 3(2) x c. Exponential; y = 10( 1 2 )x d. Linear; y = 12 4x e. Exponential; y = 50(0.7) x f. Linear; y = 40 5x g. Exponential; y = 0.4(1.5) x 3. x f(x) = 1 2 x x = observat ion number y = mold cell count 5. a. b. x f(x) = 8 ( 1 2 )x /2 5 1/4 6 1/ c. 7 th observation d. y = 50(3) x 50(3) 20 = 17,433,922,005 (number will be rounded depending on the calculator) 6. a. Linear; the bill goes up the same amount for each minute. b. f(x) = x c this is the amount on her prepaid card the moment she buys it. d (100) = 25 after talking for 100 minutes, Julie will have $25 left on her pre-paid card. e (200) = 10 when Julie has $10, she has used 200 minutes Page 37

40 Day 88 Practice 2 Name f x = 0 x 267 When Julie has spent all her money, she will Have 267 minutes Page 38

41 Day 89 Bellringer Name Day How much interest does a $318 investment earn at 9% over one year? 2. How much interest is earned on $470 at 4% for seven years? 3. If the balance at the end of eight years on an investment of $630 that has been invested at a rate of 9% is $1,083.60, how much was the interest? 4. If you borrow $675 for six years at an interest rate of 10%, how much interest will you pay? 2015 Page 39

42 Day 89 Bellringer Name Answer Key Day $ $ $ $ Page 40

43 Day 89 Exit Slip Name You have $500 to invest over the next 5 years. If your bank offered you an annual interest rate of 6.3% compounded annually or 0.72% compounded monthly, which interest program would you choose? Explain your reasoning Page 41

44 Day 89 Exit Slip Name Answer Key The best option is the account that is compounded monthly. You would have almost $100 more at the end of the 5 years Page 42

45 Algebra 1 Teachers Weekly Assessment Package Units 7 Created by: Jeanette Stein & Phil Adams 2015 Algebra 1 Teachers

46 Complete Week 18 Algebra 1 Common Core Semester 2 Skills Week Unit CCSS Skill 18 7 F.LE.1b F.LE.1c Distinguish between linear and exponential function 18 7 F.LE.1a Prove that a function is either linear or exponential 18 7 F.BF.1a Write a function that describes a relationship between two quantities 19 7 F.IF.3 Recognize that sequences are functions, sometimes defined recursively 19 7 F.BF F.LE.2 Write arithmetic and geometric sequences both recursively and with an explicit formula Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs 44 Semester 2 Skills Algebra1Teachers.com

47 Complete Week 18 Unit 7 - Sequences & Functions Weekly Assessments 45 Unit 7 - Sequences & Functions Algebra1Teachers.com

48 Complete Week 18 Week #18 - Understanding Interest 1. Classify the following functions. (Circle the correct answer.) a. y = 2x Linear Exponential b. You have $100 and add $20 per week Linear Exponential 2. Graph the function. f(x) = 3 x x f(x) c. y = 2 x Linear Exponential d. You begin with a penny and double it every week. Linear Exponential e. y = 1 2 x Linear Exponential 3. Evaluate the following function. Show your work. f(x) = ( 2) x + 1 a. f(0) = b. f(1) = c. f(3) = 4. Which situation will give you a better return on your money? (show your work) a. $100 per day for one year. b. $0.01 doubled every day for one month (30 days). 46 Unit 7 - Sequences & Functions Algebra1Teachers.com

49 Complete Week Unit 7 - Sequences & Functions Algebra1Teachers.com

50 Complete Week 18 Unit 7 - KEYS Weekly Assessments 48 Unit 7 - KEYS Algebra1Teachers.com

51 Complete Week 18 Week #18 - Answer Key 1. Classify the following functions. (Circle the correct answer.) a. y = 2x Linear Exponential b. You have $100 and add $20 per week Linear Exponential c. y = 2 x Linear Exponential 2. Graph the function. f(x) = 3 x x f(x) 1/ d. You begin with a penny and double it every week. Linear Exponential e. y = 1 2 x Linear Exponential 3. Evaluate the following function. Show your work. f(x) = ( 2) x + 1 a. f(0) = (-2) = = 2 b. f(1) = (-2) = = -1 c. f(3) = (-2) = = Which situation will give you a better return on your money? (show your work) a. $100 per day for one year. Money = 100(days) = 100(365) = $36, b. $0.01 doubled every day for one month (30 days). Money = 0.01(2) number of days Money = 0.01(2) 30 = $10,737, Situation b will give you a better return on investment. 49 Unit 7 - KEYS Algebra1Teachers.com

Linear vs. Exponential Word Problems

Linear vs. Exponential Word Problems Linear vs. Eponential Word Problems At separate times in the course, you ve learned about linear functions and eponential functions, and done word problems involving each type of function. Today s assignment

More information

Math 1 Exponential Functions Unit 2018

Math 1 Exponential Functions Unit 2018 1 Math 1 Exponential Functions Unit 2018 Points: /10 Name: Graphing Exponential Functions/Domain and Range Exponential Functions (Growth and Decay) Tables/Word Problems Linear vs Exponential Functions

More information

Linear vs. Exponential Word Problems

Linear vs. Exponential Word Problems Linear vs. Exponential Word Problems At separate ti es i the ourse, ou e lear ed a out li ear fu tio s a d e po e tial fu tio s, a d do e ord pro le s i ol i g ea h t pe of fu tio. Toda s assig e t o i

More information

Algebra 1 Teachers Weekly Assessment Package Units 10. Created by: Jeanette Stein & Phill Adams Algebra 1 Teachers

Algebra 1 Teachers Weekly Assessment Package Units 10. Created by: Jeanette Stein & Phill Adams Algebra 1 Teachers Algebra 1 Teachers Weekly Assessment Package Units 10 Created by: Jeanette Stein & Phill Adams 2015 Algebra 1 Teachers Contents SEMESTER 2 SKILLS...3 UNIT 10 - UNDERSTAND QUADRATIC FUNCTIONS...6 WEEK #25

More information

FUNCTIONS Families of Functions Common Core Standards F-LE.A.1 Distinguish between situations that can be

FUNCTIONS Families of Functions Common Core Standards F-LE.A.1 Distinguish between situations that can be M Functions, Lesson 5, Families of Functions (r. 2018) FUNCTIONS Families of Functions Common Core Standards F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential

More information

UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable

UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES. Solving Equations and Inequalities in One Variable UNIT 2: REASONING WITH LINEAR EQUATIONS AND INEQUALITIES This unit investigates linear equations and inequalities. Students create linear equations and inequalities and use them to solve problems. They

More information

Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1

Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1 Section 8: Summary of Functions Section 8 Topic 1 Comparing Linear, Quadratic, and Exponential Functions Part 1 Complete the table below to describe the characteristics of linear functions. Linear Functions

More information

Function: State whether the following examples are functions. Then state the domain and range. Use interval notation.

Function: State whether the following examples are functions. Then state the domain and range. Use interval notation. Name Period Date MIDTERM REVIEW Algebra 31 1. What is the definition of a function? Functions 2. How can you determine whether a GRAPH is a function? State whether the following examples are functions.

More information

Mathematics High School Algebra I

Mathematics High School Algebra I Mathematics High School Algebra I All West Virginia teachers are responsible for classroom instruction that integrates content standards and mathematical habits of mind. Students in this course will focus

More information

LINEAR EQUATIONS Modeling Linear Equations Common Core Standards

LINEAR EQUATIONS Modeling Linear Equations Common Core Standards E Linear Equations, Lesson 1, Modeling Linear Functions (r. 2018) LINEAR EQUATIONS Modeling Linear Equations Common Core Standards F-BF.A.1 Write a function that describes a relationship between two quantities.

More information

Unit 3: Linear and Exponential Functions

Unit 3: Linear and Exponential Functions Unit 3: Linear and Exponential Functions In Unit 3, students will learn function notation and develop the concepts of domain and range. They will discover that functions can be combined in ways similar

More information

Unit 4. Exponential Function

Unit 4. Exponential Function Unit 4. Exponential Function In mathematics, an exponential function is a function of the form, f(x) = a(b) x + c + d, where b is a base, c and d are the constants, x is the independent variable, and f(x)

More information

Complete Week 6 Package

Complete Week 6 Package Complete Week 6 Package HighSchoolMathTeachers@2018 Table of Contents Unit 2 Pacing Chart -------------------------------------------------------------------------------------------- 1 Day 26 Bellringer

More information

Lesson 26: Problem Set Sample Solutions

Lesson 26: Problem Set Sample Solutions Problem Set Sample Solutions Problems and 2 provide students with more practice converting arithmetic and geometric sequences between explicit and recursive forms. Fluency with geometric sequences is required

More information

Name: Linear and Exponential Functions 4.1H

Name: Linear and Exponential Functions 4.1H TE-18 Name: Linear and Exponential Functions 4.1H Ready, Set, Go! Ready Topic: Recognizing arithmetic and geometric sequences Predict the next 2 terms in the sequence. State whether the sequence is arithmetic,

More information

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Algebra I

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Algebra I Georgia Standards of Excellence Curriculum Map Mathematics GSE Algebra I These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Standards

More information

GSE Algebra I Curriculum Map 1 st Semester 2 nd Semester

GSE Algebra I Curriculum Map 1 st Semester 2 nd Semester GSE Algebra I Curriculum Map 1 st Semester 2 nd Semester Unit 1 (3 4 weeks) Unit 2 (5 6 weeks) Unit 3 (7 8 weeks) Unit 4 (6 7 weeks) Unit 5 (3 4 weeks) Unit 6 (3 4 weeks) Relationships Between Quantities

More information

Mathematics. Algebra Course Syllabus

Mathematics. Algebra Course Syllabus Prerequisites: Successful completion of Math 8 or Foundations for Algebra Credits: 1.0 Math, Merit Mathematics Algebra 1 2018 2019 Course Syllabus Algebra I formalizes and extends the mathematics students

More information

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Algebra I

Georgia Standards of Excellence Curriculum Map. Mathematics. GSE Algebra I Georgia Standards of Excellence Curriculum Map Mathematics GSE Algebra I These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Department

More information

Standard Description Agile Mind Lesson / Activity Page / Link to Resource

Standard Description Agile Mind Lesson / Activity Page / Link to Resource Publisher: Agile Mind, Inc Date: 19-May-14 Course and/or Algebra I Grade Level: TN Core Standard Standard Description Agile Mind Lesson / Activity Page / Link to Resource Create equations that describe

More information

Complete Week 14 Package

Complete Week 14 Package Complete Week 14 Package Algebra1Teachers @ 2015 Table of Contents Unit 4 Pacing Chart -------------------------------------------------------------------------------------------- 1 Day 66 Bellringer --------------------------------------------------------------------------------------------

More information

Mathematics. Number and Quantity The Real Number System

Mathematics. Number and Quantity The Real Number System Number and Quantity The Real Number System Extend the properties of exponents to rational exponents. 1. Explain how the definition of the meaning of rational exponents follows from extending the properties

More information

California Common Core State Standards for Mathematics Standards Map Algebra I

California Common Core State Standards for Mathematics Standards Map Algebra I A Correlation of Pearson CME Project Algebra 1 Common Core 2013 to the California Common Core State s for Mathematics s Map Algebra I California Common Core State s for Mathematics s Map Algebra I Indicates

More information

CHAPTER 6. Exponential Functions

CHAPTER 6. Exponential Functions CHAPTER 6 Eponential Functions 6.1 EXPLORING THE CHARACTERISTICS OF EXPONENTIAL FUNCTIONS Chapter 6 EXPONENTIAL FUNCTIONS An eponential function is a function that has an in the eponent. Standard form:

More information

MBF3C S3L1 Sine Law and Cosine Law Review May 08, 2018

MBF3C S3L1 Sine Law and Cosine Law Review May 08, 2018 MBF3C S3L1 Sine Law and Cosine Law Review May 08, 2018 Topic : Review of previous spiral I remember how to apply the formulas for Sine Law and Cosine Law Review of Sine Law and Cosine Law Remember when

More information

Transitional Algebra. Semester 1 & 2. Length of Unit. Standards: Functions

Transitional Algebra. Semester 1 & 2. Length of Unit. Standards: Functions Semester 1 & 2 MP.1 MP.2 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Length of Unit Progress Monitoring Short cycle Weekly or bi-weekly formative assessment

More information

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER Use the diagram below. 9.3 cm. A = (9.3 cm) (6.2 cm) = cm 2. 6.

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER Use the diagram below. 9.3 cm. A = (9.3 cm) (6.2 cm) = cm 2. 6. 1. Use the diagram below. 9.3 cm A = (9.3 cm) (6.2 cm) = 57.66 cm 2 6.2 cm A rectangle s sides are measured to be 6.2 cm and 9.3 cm. What is the rectangle s area rounded to the correct number of significant

More information

GSE Algebra 1. Unit Two Information. Curriculum Map: Reasoning with Linear Equations & Inequalities

GSE Algebra 1. Unit Two Information. Curriculum Map: Reasoning with Linear Equations & Inequalities GSE Algebra 1 Unit Two Information EOCT Domain & Weight: Equations 30% Curriculum Map: Reasoning with Linear Equations & Inequalities Content Descriptors: Concept 1: Create equations that describe numbers

More information

Unit 3: Linear and Exponential Functions

Unit 3: Linear and Exponential Functions Unit 3: Linear and Exponential Functions In Unit 3, students will learn function notation and develop the concepts of domain and range. They will discover that functions can be combined in ways similar

More information

NRSD Curriculum - Algebra 1

NRSD Curriculum - Algebra 1 NUMBER AND QUANTITY The Real Number System NRSD Curriculum - Algebra 1 Extend the properties of exponents to rational exponents. 9-12.N-RN.1 Explain how the definition of the meaning of rational exponents

More information

1. Consider the following graphs and choose the correct name of each function.

1. Consider the following graphs and choose the correct name of each function. Name Date Summary of Functions Comparing Linear, Quadratic, and Exponential Functions - Part 1 Independent Practice 1. Consider the following graphs and choose the correct name of each function. Part A:

More information

Unit 3 Multiple Choice Test Questions

Unit 3 Multiple Choice Test Questions Name: Date: Unit Multiple Choice Test Questions MCC9.F.IF. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one

More information

ALGEBRA I CCR MATH STANDARDS

ALGEBRA I CCR MATH STANDARDS RELATIONSHIPS BETWEEN QUANTITIES AND REASONING WITH EQUATIONS M.A1HS.1 M.A1HS.2 M.A1HS.3 M.A1HS.4 M.A1HS.5 M.A1HS.6 M.A1HS.7 M.A1HS.8 M.A1HS.9 M.A1HS.10 Reason quantitatively and use units to solve problems.

More information

Subject Area Algebra I Grade Level 9_

Subject Area Algebra I Grade Level 9_ MVNTA COMMON CORE TEMPLATE Subject Area Algebra I Grade Level 9_ BUCKET ONE BIG ROCKS Reason quantitatively and use units to solve problems. Understand the concept of a function and use function notation.

More information

Common Core State Standards with California Additions 1 Standards Map. Algebra I

Common Core State Standards with California Additions 1 Standards Map. Algebra I Common Core State s with California Additions 1 s Map Algebra I *Indicates a modeling standard linking mathematics to everyday life, work, and decision-making N-RN 1. N-RN 2. Publisher Language 2 Primary

More information

Algebra I Curriculum Crosswalk

Algebra I Curriculum Crosswalk Algebra I Curriculum Crosswalk The following document is to be used to compare the 2003 North Carolina Mathematics Course of Study for Algebra I and the State s for Mathematics Algebra I course. As noted

More information

Section 2 Equations and Inequalities

Section 2 Equations and Inequalities Section 2 Equations and Inequalities The following Mathematics Florida Standards will be covered in this section: MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. MAFS.912.A-REI.1.1

More information

The units on the average rate of change in this situation are. change, and we would expect the graph to be. ab where a 0 and b 0.

The units on the average rate of change in this situation are. change, and we would expect the graph to be. ab where a 0 and b 0. Lesson 9: Exponential Functions Outline Objectives: I can analyze and interpret the behavior of exponential functions. I can solve exponential equations analytically and graphically. I can determine the

More information

Equations and Inequalities in One Variable

Equations and Inequalities in One Variable Name Date lass Equations and Inequalities in One Variable. Which of the following is ( r ) 5 + + s evaluated for r = 8 and s =? A 3 B 50 58. Solve 3x 9= for x. A B 7 3. What is the best first step for

More information

Georgia Standards of Excellence Algebra I

Georgia Standards of Excellence Algebra I A Correlation of 2018 To the Table of Contents Mathematical Practices... 1 Content Standards... 5 Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved. Mathematical Practices

More information

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Algebra II Unit 3 Exponential and Logarithmic Functions Last edit: 22 April 2015 UNDERSTANDING & OVERVIEW In this unit, students synthesize and generalize what they have learned about a variety of function

More information

Algebra I EOC Review (Part 2)

Algebra I EOC Review (Part 2) 1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = 22 2. A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider

More information

Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.

Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number. L7-1 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of

More information

MATHEMATICS COURSE SYLLABUS

MATHEMATICS COURSE SYLLABUS Course Title: Algebra 1 Honors Department: Mathematics MATHEMATICS COURSE SYLLABUS Primary Course Materials: Big Ideas Math Algebra I Book Authors: Ron Larson & Laurie Boswell Algebra I Student Workbooks

More information

0115AI Common Core State Standards

0115AI Common Core State Standards 0115AI Common Core State Standards 1 The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = 8600

More information

Algebra 1. Mathematics Course Syllabus

Algebra 1. Mathematics Course Syllabus Mathematics Algebra 1 2017 2018 Course Syllabus Prerequisites: Successful completion of Math 8 or Foundations for Algebra Credits: 1.0 Math, Merit The fundamental purpose of this course is to formalize

More information

MATHEMATICS Math I. Number and Quantity The Real Number System

MATHEMATICS Math I. Number and Quantity The Real Number System MATHEMATICS Math I The high school mathematics curriculum is designed to develop deep understanding of foundational math ideas. In order to allow time for such understanding, each level focuses on concepts

More information

Learning Target #1: I am learning to compare tables, equations, and graphs to model and solve linear & nonlinear situations.

Learning Target #1: I am learning to compare tables, equations, and graphs to model and solve linear & nonlinear situations. 8 th Grade Honors Name: Chapter 2 Examples of Rigor Learning Target #: I am learning to compare tables, equations, and graphs to model and solve linear & nonlinear situations. Success Criteria I know I

More information

Comparing linear and exponential growth

Comparing linear and exponential growth Januar 16, 2009 Comparing Linear and Exponential Growth page 1 Comparing linear and exponential growth How does exponential growth, which we ve been studing this week, compare to linear growth, which we

More information

Curriculum Scope & Sequence. Subject/Grade Level: MATHEMATICS/HIGH SCHOOL (GRADE 7, GRADE 8, COLLEGE PREP)

Curriculum Scope & Sequence. Subject/Grade Level: MATHEMATICS/HIGH SCHOOL (GRADE 7, GRADE 8, COLLEGE PREP) BOE APPROVED 9/27/11 Curriculum Scope & Sequence Subject/Grade Level: MATHEMATICS/HIGH SCHOOL Course: ALGEBRA I (GRADE 7, GRADE 8, COLLEGE PREP) Unit Duration Common Core Standards / Unit Goals Transfer

More information

N-Q2. Define appropriate quantities for the purpose of descriptive modeling.

N-Q2. Define appropriate quantities for the purpose of descriptive modeling. Unit 1 Expressions Use properties of rational and irrational numbers. N-RN3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number

More information

TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III

TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III TransMath Third Edition Correlated to the South Carolina High School Credential Courses: Essentials of Math I, II, and III TransMath correlated to the South Carolina High School Credential Courses: Essentials

More information

2007 First-Class Mail Rates for Flats* Weight (oz) Rate (dollars) Weight (oz) Rate (dollars)

2007 First-Class Mail Rates for Flats* Weight (oz) Rate (dollars) Weight (oz) Rate (dollars) Lesson 3-9 Step Functions BIG IDEA Step functions have applications in many situations that involve rounding. In 2007, the U.S. postage rate for first class flats (certain large envelopes) was $0.70 for

More information

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?

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

More information

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS KEY SEMESTER 1. Selected Response Key

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS KEY SEMESTER 1. Selected Response Key Selected Response Key # Question Type Unit Common Core State Standard(s) DOK Level Key 1 MC 1 N.Q.3 1 C 2 MC 1 N.Q.1 2 D 3 MC 1 8.EE.1 1 D 4 MTF 1 A.REI.1 1 A 5 MTF 1 A.REI.1 1 B 6 MC 1 A.CED.4 1 D 7 MC

More information

Unit 2 Linear Functions and Systems of Linear Functions Algebra 1

Unit 2 Linear Functions and Systems of Linear Functions Algebra 1 Number of Days: MS 44 10/16/17 12/22/17 HS 44 10/16/17 12/22/17 Unit Goals Stage 1 Unit Description: Unit 2 builds upon students prior knowledge of linear models. Students learn function notation and develop

More information

Algebra Curriculum Map

Algebra Curriculum Map Unit Title: Ratios, Rates, and Proportions Unit: 1 Approximate Days: 8 Academic Year: 2013-2014 Essential Question: How can we translate quantitative relationships into equations to model situations and

More information

Continuously Compounded Interest. Simple Interest Growth. Simple Interest. Logarithms and Exponential Functions

Continuously Compounded Interest. Simple Interest Growth. Simple Interest. Logarithms and Exponential Functions Exponential Models Clues in the word problems tell you which formula to use. If there s no mention of compounding, use a growth or decay model. If your interest is compounded, check for the word continuous.

More information

Study Island. Linear and Exponential Models

Study Island. Linear and Exponential Models Study Island Copyright 2014 Edmentum - All rights reserved. 1. A company is holding a dinner reception in a hotel ballroom. The graph represents the total cost of the ballroom rental and dinner. 3. In

More information

0814AI Common Core State Standards

0814AI Common Core State Standards 0814AI Common Core State Standards 1 Which statement is not always true? 1) The product of two irrational numbers is irrational. 2) The product of two rational numbers is rational. 3) The sum of two rational

More information

Performance Task Name: Content Addressed. Lesson Number and Name of Lesson

Performance Task Name: Content Addressed. Lesson Number and Name of Lesson Unit 1: Relationships Between Quantities Standards in Unit: Reason quantitatively and use units to solve problems. MCC9-12.N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step

More information

Algebra I. 60 Higher Mathematics Courses Algebra I

Algebra I. 60 Higher Mathematics Courses Algebra I The fundamental purpose of the course is to formalize and extend the mathematics that students learned in the middle grades. This course includes standards from the conceptual categories of Number and

More information

Algebra 1 Standards Curriculum Map Bourbon County Schools. Days Unit/Topic Standards Activities Learning Targets ( I Can Statements) 1-19 Unit 1

Algebra 1 Standards Curriculum Map Bourbon County Schools. Days Unit/Topic Standards Activities Learning Targets ( I Can Statements) 1-19 Unit 1 Algebra 1 Standards Curriculum Map Bourbon County Schools Level: Grade and/or Course: Updated: e.g. = Example only Days Unit/Topic Standards Activities Learning Targets ( I 1-19 Unit 1 A.SSE.1 Interpret

More information

Algebra 2 - Semester 2 - Final Exam Review

Algebra 2 - Semester 2 - Final Exam Review Algebra 2 - Semester 2 - Final Exam Review Your final exam will be 60 multiple choice questions coving the following content. This review is intended to show examples of problems you may see on the final.

More information

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?

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.

More information

Name: Class: Date: Describe a pattern in each sequence. What are the next two terms of each sequence?

Name: Class: Date: Describe a pattern in each sequence. What are the next two terms of each sequence? Class: Date: Unit 3 Practice Test Describe a pattern in each sequence. What are the next two terms of each sequence? 1. 24, 22, 20, 18,... Tell whether the sequence is arithmetic. If it is, what is the

More information

3. If 4x = 0, the roots of the equation are (1) 25 and 25 (2) 25, only (3) 5 and 5 (4) 5, only 3

3. If 4x = 0, the roots of the equation are (1) 25 and 25 (2) 25, only (3) 5 and 5 (4) 5, only 3 ALGEBRA 1 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that,

More information

O5C1: Graphing Exponential Functions

O5C1: Graphing Exponential Functions Name: Class Period: Date: Algebra 2 Honors O5C1-4 REVIEW O5C1: Graphing Exponential Functions Graph the exponential function and fill in the table to the right. You will need to draw in the x- and y- axis.

More information

Chapter 3 Exponential and Logarithmic Functions

Chapter 3 Exponential and Logarithmic Functions Chapter 3 Exponential and Logarithmic Functions Overview: 3.1 Exponential Functions and Their Graphs 3.2 Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Exponential and

More information

Subject Algebra 1 Unit 1 Relationships between Quantities and Reasoning with Equations

Subject Algebra 1 Unit 1 Relationships between Quantities and Reasoning with Equations Subject Algebra 1 Unit 1 Relationships between Quantities and Reasoning with Equations Time Frame: Description: Work with expressions and equations through understanding quantities and the relationships

More information

Math 101 Final Exam Review Solutions. Eric Schmutz

Math 101 Final Exam Review Solutions. Eric Schmutz Math 101 Final Exam Review Solutions Eric Schmutz Problem 1. Write an equation of the line passing through (,7) and (-1,1). Let (x 1, y 1 ) = (, 7) and (x, y ) = ( 1, 1). The slope is m = y y 1 x x 1 =

More information

Solving Quadratic Equations Using Multiple Methods and Solving Systems of Linear and Quadratic Equations

Solving Quadratic Equations Using Multiple Methods and Solving Systems of Linear and Quadratic Equations Algebra 1, Quarter 4, Unit 4.1 Solving Quadratic Equations Using Multiple Methods and Solving Systems of Linear and Quadratic Equations Overview Number of instructional days: 13 (1 day = 45 minutes) Content

More information

Equations. 2 3 x 1 4 = 2 3 (x 1 4 ) 4. Four times a number is two less than six times the same number minus ten. What is the number?

Equations. 2 3 x 1 4 = 2 3 (x 1 4 ) 4. Four times a number is two less than six times the same number minus ten. What is the number? Semester Exam Review Packet *This packet is not necessarily comprehensive. In other words, this packet is not a promise in terms of level of difficulty or full scope of material. Equations 1. 9 2(n 1)

More information

Materials: Hw #9-6 answers handout; Do Now and answers overhead; Special note-taking template; Pair Work and answers overhead; hw #9-7

Materials: Hw #9-6 answers handout; Do Now and answers overhead; Special note-taking template; Pair Work and answers overhead; hw #9-7 Pre-AP Algebra 2 Unit 9 - Lesson 7 Compound Interest and the Number e Objectives: Students will be able to calculate compounded and continuously compounded interest. Students know that e is an irrational

More information

Model Traditional Pathway: Model Algebra I Content Standards [AI]

Model Traditional Pathway: Model Algebra I Content Standards [AI] Model Traditional Pathway: Model Algebra I Content Standards [AI] Number and Quantity The Real Number System AI.N-RN A. Extend the properties of exponents to rational exponents. 1. Explain how the definition

More information

Name Class Date. Geometric Sequences and Series Going Deeper. Writing Rules for a Geometric Sequence

Name Class Date. Geometric Sequences and Series Going Deeper. Writing Rules for a Geometric Sequence Name Class Date 5-3 Geometric Sequences and Series Going Deeper Essential question: How can you write a rule for a geometric sequence and find the sum of a finite geometric series? In a geometric sequence,

More information

Eighth Grade Algebra I Mathematics

Eighth Grade Algebra I Mathematics Description The Appleton Area School District middle school mathematics program provides students opportunities to develop mathematical skills in thinking and applying problem-solving strategies. The framework

More information

Logarithmic and Exponential Equations and Inequalities College Costs

Logarithmic and Exponential Equations and Inequalities College Costs Logarithmic and Exponential Equations and Inequalities ACTIVITY 2.6 SUGGESTED LEARNING STRATEGIES: Summarize/ Paraphrase/Retell, Create Representations Wesley is researching college costs. He is considering

More information

Chapter 11 Logarithms

Chapter 11 Logarithms Chapter 11 Logarithms Lesson 1: Introduction to Logs Lesson 2: Graphs of Logs Lesson 3: The Natural Log Lesson 4: Log Laws Lesson 5: Equations of Logs using Log Laws Lesson 6: Exponential Equations using

More information

Algebra I, Common Core Correlation Document

Algebra I, Common Core Correlation Document Resource Title: Publisher: 1 st Year Algebra (MTHH031060 and MTHH032060) University of Nebraska High School Algebra I, Common Core Correlation Document Indicates a modeling standard linking mathematics

More information

ALGEBRA 1 Mathematics Map/Pacing Guide

ALGEBRA 1 Mathematics Map/Pacing Guide Topics & Standards Quarter 1 Time Frame Weeks 1-8 ALGEBRA - SEEING STRUCTURE IN EXPRESSIONS Interpret the structure of expressions A.SSE.1 Interpret expressions that represent a quantity in terms of its

More information

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

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

More information

Grade 11 Mathematics Page 1 of 6 Final Exam Review (updated 2013)

Grade 11 Mathematics Page 1 of 6 Final Exam Review (updated 2013) Grade Mathematics Page of Final Eam Review (updated 0) REVIEW CHAPTER Algebraic Tools for Operating With Functions. Simplify ( 9 ) (7 ).. Epand and simplify. ( ) ( ) ( ) ( 0 )( ). Simplify each of the

More information

ALGEBRA I INSTRUCTIONAL PACING GUIDE (DAYS BASED ON 90 MINUTES DAILY) FIRST NINE WEEKS

ALGEBRA I INSTRUCTIONAL PACING GUIDE (DAYS BASED ON 90 MINUTES DAILY) FIRST NINE WEEKS FIRST NINE WEEKS Unit 1: Relationships Between Quantities and Reasoning with Equations Quantities and Relationships F.LE.1.b. Recognize situations in which one quantity changes at a constant rate per unit

More information

0115AI Common Core State Standards

0115AI Common Core State Standards 0115AI Common Core State Standards 1 The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = 8600

More information

Cumberland County Schools

Cumberland County Schools Cumberland County Schools MATHEMATICS Algebra II The high school mathematics curriculum is designed to develop deep understanding of foundational math ideas. In order to allow time for such understanding,

More information

HW#1. Unit 4B Logarithmic Functions HW #1. 1) Which of the following is equivalent to y=log7 x? (1) y =x 7 (3) x = 7 y (2) x =y 7 (4) y =x 1/7

HW#1. Unit 4B Logarithmic Functions HW #1. 1) Which of the following is equivalent to y=log7 x? (1) y =x 7 (3) x = 7 y (2) x =y 7 (4) y =x 1/7 HW#1 Name Unit 4B Logarithmic Functions HW #1 Algebra II Mrs. Dailey 1) Which of the following is equivalent to y=log7 x? (1) y =x 7 (3) x = 7 y (2) x =y 7 (4) y =x 1/7 2) If the graph of y =6 x is reflected

More information

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.

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

More information

High School Algebra I Scope and Sequence by Timothy D. Kanold

High School Algebra I Scope and Sequence by Timothy D. Kanold High School Algebra I Scope and Sequence by Timothy D. Kanold First Semester 77 Instructional days Unit 1: Understanding Quantities and Expressions (10 Instructional days) N-Q Quantities Reason quantitatively

More information

Write each expression as a sum or difference of logarithms. All variables are positive. 4) log ( ) 843 6) Solve for x: 8 2x+3 = 467

Write each expression as a sum or difference of logarithms. All variables are positive. 4) log ( ) 843 6) Solve for x: 8 2x+3 = 467 Write each expression as a single logarithm: 10 Name Period 1) 2 log 6 - ½ log 9 + log 5 2) 4 ln 2 - ¾ ln 16 Write each expression as a sum or difference of logarithms. All variables are positive. 3) ln

More information

2.4 Solve a system of linear equations by graphing, substitution or elimination.

2.4 Solve a system of linear equations by graphing, substitution or elimination. lgebra 1 Oklahoma cademic tandards for athematics P PRCC odel Content Frameworks Current ajor Curriculum Topics Name.REI.05 olve systems of equations. Prove that, given a system of two equations in two

More information

Algebra II. Slide 1 / 261. Slide 2 / 261. Slide 3 / 261. Linear, Exponential and Logarithmic Functions. Table of Contents

Algebra II. Slide 1 / 261. Slide 2 / 261. Slide 3 / 261. Linear, Exponential and Logarithmic Functions. Table of Contents Slide 1 / 261 Algebra II Slide 2 / 261 Linear, Exponential and 2015-04-21 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 261 Linear Functions Exponential Functions Properties

More information

graphs, Equations, and inequalities 2

graphs, Equations, and inequalities 2 graphs, Equations, and inequalities You might think that New York or Los Angeles or Chicago has the busiest airport in the U.S., but actually it s Hartsfield-Jackson Airport in Atlanta, Georgia. In 010,

More information

ALGEBRA I. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. (N-RN2)

ALGEBRA I. 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents. (N-RN2) ALGEBRA I The Algebra I course builds on foundational mathematical content learned by students in Grades K-8 by expanding mathematics understanding to provide students with a strong mathematics education.

More information

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

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

More information

Big Ideas Chapter 6: Exponential Functions and Sequences

Big Ideas Chapter 6: Exponential Functions and Sequences Big Ideas Chapter 6: Exponential Functions and Sequences We are in the middle of the year, having finished work with linear equations. The work that follows this chapter involves polynomials and work with

More information

Unit 2 Modeling with Exponential and Logarithmic Functions

Unit 2 Modeling with Exponential and Logarithmic Functions Name: Period: Unit 2 Modeling with Exponential and Logarithmic Functions 1 2 Investigation : Exponential Growth & Decay Materials Needed: Graphing Calculator (to serve as a random number generator) To

More information

ISPS MATHEMATICS Grade 8 Standards and Benchmarks

ISPS MATHEMATICS Grade 8 Standards and Benchmarks GRADE 8 ISPS MATHEMATICS Grade 8 Strands 1. The Number System 2. Expressions and Equations 3. Functions 4. Geometry 5. Statistics and Probability Strand 1 The Number System Standard 1: Know that there

More information

Chapter 3 Exponential and Logarithmic Functions

Chapter 3 Exponential and Logarithmic Functions Chapter 3 Exponential and Logarithmic Functions Overview: 3.1 Exponential Functions and Their Graphs 3.2 Logarithmic Functions and Their Graphs 3.3 Properties of Logarithms 3.4 Solving Exponential and

More information

Please allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry

Please allow yourself one to two hours to complete the following sections of the packet. College Integrated Geometry Honors Integrated Geometry Incoming Integrated Geometry Summer Work Dear Incoming Integrated Geometry Students, To better prepare for your high school mathematics entry process, summer work is assigned to ensure an easier transition

More information