Algebra 1 EOC Bellringer Review

Transcription

1 Class: Date: Version: A Algebra EOC Bellringer Review Multiple Choice Identify the choice that best completes the statement or answers the question.. What must be done to the graph of f(x)= x to obtain the graph of the function g(x) = 0.25 x a. horizontal shift 3 units left; vertical shift 8 units down and vertical compression by factor of.25 b. horizontal shift 3 units right; vertical shift 8 units down and vertical compression by factor of.25 c. Vertical shift 3 units up; horizontal shift 8 units down and vertical compression by factor of.25 d. horizontal shift.25 units left; vertical shift 8 units down and vertical compression by factor of 3 2. Jasmine is saving to buy a bicycle. The amount she has saved is shown in the table. What is the function that describes the amount A, in dollars, Jasmine has saved after t weeks? Weeks Amount $30 2 $45 3 $60 4 $75 5 $90 6 $05 a. Quadratic c. Square root b. Exponential d. Linearr

2 3. The data for the distance d, in miles remaining for a boat to travel to its destination t hours after it departs a pier are shown in the scatter plot. Which of the following functions best fits the data? a. d(t) = 50t c. d(t) = -50t b. d(t) = 50t d. d(t) = -50t 4. Which of the following residual plots indicate a good fit for a linear model? I II III a. I c. III b. II d. Not enough information to determine 2

3 5. Weather data were recorded for a sample of 25 American cities in one year. Variables measured included January high temperature (in degrees Fahrenheit), January low temperature (in degrees Fahrenheit), annual precipitation (in inches), and annual snow accumulation. The relationships for three pairs of variables are shown in the graphs below (Jan. Low Temperature-Graph A; Precipitation-Graph B; Annual Snow Accumulation-Graph C). Graph A Graph B Graph C Which graph would have a correlation coefficient closest to 0? Explain your choice. a. Graph A c. Graph C b. Graph B d. Not enough information to determine 6. Which scatterplot shows the relationship between money earned and hours skating at a fundraiser if the skater was raising money at an hourly rate? a. a c. c b. b d. d 7. The function A(d) = 0.65d + 95 models the amount A, in dollars, that Thomas s company pays him based on round trip distance d, in miles, that Thomas travels to a job site. How much does Thomas s pay increase for every mile of travel? a. $95 c. $200 b. $95.65 d. $0.65 3

4 8. A biologist put some living cells into a petri dish. After 3 hours, she noticed that the number of cells had increased by a factor of 27. After 6 hours, the number of cells had increased by a factor of 729. The number of cells after h hours is described by the expression c 27 where c is the original number of cells in the petri dish. By what factor does the sample grow in a hour period? a. 3 c. 27 b. 9 d. 8 h 3 9. Bruno started a Biology experiment with 500 cells and 5% of the cells were dying every minute. This experiment be modeled with which function. a. Linear c. Exponential Decay b. Exponential Growth d. Quadratic 0. Which is the equation for this graph a. f(n) = n c. f(n) = ( ) n b. f(n) = 2 n d. f(n) = ( 2) n 4

5 . Jeremy shows that 9 = 9 2 Part of his work is shown. 2 9 = 3 = = 3 = _ = 9 Which expression or equation can be placed in the blank to correctly complete Jeremy s work? a. Ê 3 2 Ë Á ˆ b c d = ( 3 3) 2 = ( 3 3) A local supermarket sells shrimp $9.49/lb and beef for $5.99/lb. Todd buys s pounds of shrimp and b pounds of beef. Which of the following inequalities represents Todd s purchase is he only has $65 to spend? a. 9.49s 65 c. s + b 65 b. 5.99b 65 d. 9.49s b What two properties are used in the following solution to 5x 7 = 23? 5x 7 = 23 5x = x = 30 5x/5 = 30/5 x = 6 a. Addition and division properties of equality b. Subtraction and addition properties of equality c. Multiplication property of equality and distributive property d. Subtraction property of equality and zero product property 4. Which of the following operations will solve Ohm s law, V = IR, for I? a. Subtract R from both sides c. Subtract V from both sides b. Divide both sides by R d. Divide both sides by I 5

6 5. Describe the graph that represents the solutions of the inequality y<3x+4 a. All point that lie above the line y = 3x + 4 b. All point that lie on and above the line y = 3x + 4 c. All points that lie below the line y = 3x + 4 d. All point that lie on and below the line y = 3x Which points are included in the solution set for this system of inequalities? a. A only c. A, B and D b. A and B only d. A and C 7. Which of the following systems of equations has the same solutions as the given system. Ï Ô 2x + 2y = 2Ô Ì ÓÔ 3x y = 9 Ô Ï 2x + 2y = 2 a. Ô Ô Ì ÓÔ x + y = Ô Ï 2x + 2y = 2 b. Ô Ô Ì ÓÔ 6x 2y = 8 Ô c. d. Ï Ô4x + 4y = 4Ô Ì ÓÔ 3x y = 9 Ô Ï Ô 3x 7y = 3Ô Ì ÓÔ 3x y = 9 Ô 6

7 8. a. The domain is {0.25, 0.5,, 2, 4, 8} and the range is {-3, -2, -, 0,, 2} b. The domain is {-3, -2, -, 0,, 2} and the range is {0.25, 0.5,, 2, 4, 8} c. The domain is all real numbers between -3 and 2, and the range is all real numbers between 0.25 and 8 d. The domain is all real numbers between 0.25 and 8, and the range is all real numbers between -3 and 2 9. Ms. Jones is taking the Drama Club on a field trip to see the musical Phantom of the Opera. The school treasurer asked Ms. Jones for the group s total ticket cost. He wrote the following cost function for the school treasurer: Total Cost = 53 (40 + 4) Which of the following statements best describes this cost function? a. A total of 53 people, which included 40 students and 4 teachers, will attend the field trip. b. The bus fits 53 people, including 40 students and 4 teachers. c. Tickets cost $53 each, and there are 40 students and 4 teachers going on the field trip. d. The school will buy 53 tickets for the musical. Tickets cost $40 for each student and $4 for each teacher. 7

8 20. If a, b, c, and d are integers. Then a b + c d will: a. Always produce a rational number b. Never produce a rational number. c. Sometimes produce a rational number d. Do not have enough information to determine 2. If y = -4, what is equivalent to the value of y 2 y a. c. 3 3 b. -5 d The Freshman Spirit Club took a trip to the state fair. There were 59 Students and 6 chaperones, and the total admission cost for the groups was $508. Student tickets cost $2 more than chaperone tickets. Write and solve an equation to find the cost of a student ticket. a. $6 c. $8 b. $4 d. $2 Multiple Response Identify one or more choices that best complete the statement or answer the question. 23. Determine whether the correlation in each situation below implies causation. Select all that apply. a. As you age, the amount of money you earn increases. c. As the amount of time listening to music increases, the probability of hearing loss increases. b. As a person s income increases, the amount they pay in taxes increases d. the more ore a person types, the more likely the person is to experience carpal tunnel syndrome. 8

9 24. Which of the following ar equivalent to f(x) = 8 x a x d x + b. 53,44 8 x 3 e x 2 c. 9 9 x 25. Which statement is true about the graph of the exponential function f(x). Select all that apply. a. The domain is all real numbers d. There is no x-intercetp b. The range is all real numbers e. As x increases f(x) approaches but never reaches 2 c. The f(x) intercept is The function a(t) = 53,000(.032) t models Janice s annual earnings a, in dollars, t years after she starts her job. Which of the following statements are true about Janice s salary? Select all that apply. a. Janice initially earns $53,000 per year. d. Janice s salary increases by 3.2% per year. b. Janice initially earns $54,696 per year. e. Janice s salary increases by 03.2% per year. c. Janice s salary increases by.032% per year. 9

10 27. Tammy is reviewing for her Algebra test. She made this graph representing a system of inequalities. Choose the ordered pairs below that represent solutions to the system of inequalities. Select all that apply. a. (-8, 3) e. (-3, 8) b. (-, 9) f. (0, 0) c. (-4, 9) g. (9, 6) d. (0, 9) h. (2, 7) 28. The domain of the function f(x) is the set of integers greater than -3. Which of the following values represent elements of the range of f? Select all that apply. a. f(3. 8) e. f(/2) b. f(-2) f. f(0) c. f(-5) g. f(4) d. f(8) h. f(-8) 0

11 Completion Complete each statement. 29. Describe the property used to convert the equation from one line to the next: x( x) + 2x 4 = 8x 24 x 2 x x 2 + 2x 4 = 8x 24 x 2 x + 2x 4 = 8x 24 _ 3x 4 = 8x 24 3x + 20 = 8x 20 = 5x _ 4 = x In each of the steps above, we applied a property of real numbers and/or equations to create a new equation. Short Answer 30. Given h(x) = x Describe how to obtain the graph of h from the graph of a(x) = x using transformations.

12 3. The table shows the height of a Oak tree at each of two ages. What was the tree s average rate of growth during this time period? Age (years) Height(meters) Determine whether the rate of change is constant. If it is, find the rate of change and explain what it represents. Time (Minutes) Number of Words Typed What is the rate of change of the line pictured below? What does it represent? 2

13 34. Stephanie s annual salary S, in dollars, after working at the same company for t years is given by the functions s(t) = 45, ,000t. Complete the table showing Stephanie s salary after each year for the first five years. Time, t (years) Salary, S (Dollars) That table shows the population of two cities. Which city s population is changing at a constant rate per year? Year City A City B , , , , , , , , The function h(t) = -,00t + 20,000 models the height, h, in feet of an airplane t minutes after it starts descending in order for it to land. What is the height of the airplane when it begins to descend? Explain. 3

14 37. Read each statement, then determine whether there is a positive, negative, or no correlation. I II III The mileage on a car and its resale value The length of a woman s hair and her height A child s age and their weight 38. What is the equation of the following line? 39. You would like to open a savings account deposit $2500. Bank A offers a rate of 2% compounded annually and Bank B offers a rate of.5% compounded monthly. Which bank would you choose to earn the greatest interest over 5 years? Justify your answer. Ê 40. Graph f(x) = 3( ˆ Ë Á 2 x Identify the intercept and end behavior of the graph. 4

15 4. Find a bank account balance if the account starts with $00, has an annual rate of 4% compounded quarterly, and the money left in the account for 2 year. Is this an exponential growth or decay model? 42. Each year the local country club sponsors a tennis tournament. Play starts with 28 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds? Is this an exponential growth or decay? 43. Jessica started a chain letter by . She sent it to four of her friends and asked them to each send it to four of their friends. Assume that no one breaks the chain and that no person receives the twice. How many s will be sent during the 5 th generation? (Treat Jessica s s as the st generation of the letter.) 44. Write the recursive rule and explicit rule for geometric sequence where the first term is -6 and the common ratio is 2? 45. Jessica started a chain letter by . She sent it to four of her friends and asked them to each send it to four of their friends. Assume that no one breaks the chain and that no person receives the twice. How many s will be sent during the 5 th generation? (Treat Jessica s s as the st generation of the letter.) 46. Write the explicit formula for the sequence: 4, 24, 44, 864, 47. The population of Town A and the population of Town B t years after 2000 is described in the table. Determine which function is exponential. Use the table of values to justify your choice. Time,t (years) Town A populations, A(t) Town B population, B(t)

16 48. Decide which situation is linear and which is exponential. a) Charles borrows $200 from his friend and each month he pays him half of the remaining balance. b) Sue s scarf was only 8 inches long. Her grandmother took it and each day she knitted 75% of its original length. 49. Money on Mark s bank account grows according to the formula A = 350(.07) 6. What is the initial investment? How long is the money invested for? What is the interest rate? Ê 50. Rewrite 49 Ë Á 3 ˆÊ Ë Á 3 7 ˆ as a single power of 7 5. Rewrite as a single power of Let c and d be real numbers. If c = 35 + d is true, then which is greater: c or d or are you not able to tell? Explain how you know your choice is correct. 53. Mike and Brad have $30 to spend making model cars. Since wheels cost $0.50 each, they decide they will be able to make more cars if they use three wheels instead of four. The car body and other materials cost $.25 per car. How many cars will they be able to make? 54. The formula for Kinetic Energy is K = 2 mv 2, were K is kinetic energy, m is mass and v is velocity. Solve this formula for mass. 55. Solve the following equation for x, in terms of a and b. ax = 5 + bx 6

17 56. If the perimeter of the pentagon is 39, what is the value of x? 57. Gabriel has already read 200 pages of his 530-page summer reading book. If he reads at an average rate of 55 pages per hour, how long will he need to finish the book? Write and solve an equation to find the answer. Show your work. 58. Solve and graph the inequality 5-7x < 33 7

18 59. The figure shows the graphs of the systems of equations: Ï Ô y = f(x) Ô Ì ÓÔ y = g(x) Ô The four indicated points, A, B, C, and D all have integer coordinates. Part A: Identify the slope-intercept forms of f(x) and g(x). Part B: If f(x) = kg(x), what is the value of k? Part C: What is the solution to the system? 60. Solve the system of equations, write your answer ans an ordered pair. 2x - 3y = 7 4x + y = Stephen and Shane are twins. They came up with a math puzzle. Stephen says he is (5x+4) years old, and Shane says he is (0x-3) years old. What is the value of x? What are their ages? 62. In which quadrant is the solution to this system of equations? 5x + 2y = 7 4x - 3y = 24 8

19 63. Next weekend Maria want to attend either carnival A or carnival B. Carnival A charges $6 for admission and an additional $.50 per ride. Carnival B charges $2.50 for admission and an additional $2.00 per ride. Determine the number of rides Maria can go on such that the total cost of attending each carnival is the same. 64. Graph the solution set of the system. Ï y Ô 2 x + 2 Ô Ì y < 2 ÓÔ 3 x 4 Ô 65. Graph the system of inequalities 66. Functions f and g are graphed below. Use the graph to find the solution(s) of the equation f(x)=g(x). Explain how you found the solution(s). 9

20 67. Ethan s Towing Company charges $35 to hook a vehicle to the truck and $2.30 for each mile the vehicle is towed. Write an equation that best represents the relationship between the number of miles towed, m, and the total charges, c? 68. Catherine is planting green beans and peppers. She has 50 acres of farmland and wants to plant no less than 30 acres of each crop. Determine if each of the following inequalities are meaningful constraints on whether Catherine can plant g acres of green beans and p acres of peppers. a. g 30 yes no b. p < 30 yes no c. g + p 50 yes no d. g + p 50 yes no e. 50 g 20 yes no 69. Daniella has two jobs. She earns $7 per hour babysitting her neighbor s children and she earns $2 per hour working at the coffee shop. Part A: Write an inequality to represent the number of hours, x, babysitting and the number of hours, y, working at the coffee shop that Daniella will need to work to earn a minimum of $200. Part B: Daniella worked 4 hours at the coffee shop. Use the inequality to find the number of full hours she must babysit to reach her goal of $ Daniella worked 4 hours at the coffee shop. Use the inequality to find the number of full hours she must babysit to reach her goal of $ Catherine has a movie rental card worth $85. After she rents the first movie, the card s value is $ After she rents the second movie, its value is $ After she rents the third movie, the card is worth $ Assuming the pattern continues, write an equation to define A(n), the amount of money on the rental card after n rentals. Catherine rents a movie every Friday night. How many weeks in a row can she afford to rent a movie using her rental card only? Explain how you arrived to your answer. 20

21 72. Yolanda is conditioning all summer so she can try out for her high school s varsity softball team. She is incorporating walking planks to her daily workout routine. Everyday, she will complete 6 more walking planks than the day before. Part A: If sse starts with seven planks on the first day, how many walking planks will she do on the 2th day. Part B; Write an explicit rule to find the number of planks walked on any given day. 73. The production cost of g graphing calculators is C(g) = 45g. Evaluate the function at g = 6. What does the value of the function at g = 6 represent? 74. Tammy is printing a report. There are 50 sheets of paper in the printer, and the number of sheets p left after t minutes of printing is given by the function p(t) = -2t How long would it take the printer to use all 00 sheets of paper? Explain how you found your answers. 75. The graph of y = f(x) is shown below. Which point could be used to find f(-2)? 2

22 76. What are the values of the x- and y-intercepts for the graph of 4x - 5y = In 203, the United States Postal Service charged $0.46 to mail a letter weighing up to oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c, of mailing a letter weighing z ounces where z is an integer greater than? 78. Mary runs a computer repair business. She charges a flat rate of $50 plus $25 per hour of service. Write an equation to represent the cost, C, of h hours of service. 79. The function f has a domain of {2, 4, 6, 8} and a range of {, 3, 5}. Could f be represented by {(2, ), (4, 3), {6, 5), (8, )}? Justify your answer. 80. S is an example of a sequence defined recursively. S() = 27 S(n) = S(n-) 5 for all n 2. Write out the first five terms of this sequence by completing the table. n s(n) 2. Explain why this sequence is a function. 3. Describe the domain of S. 8. John designs computer labs for a community college. The college has 5 computers and receives 26 additional computers each year. What expression can Sue use to determine the number of computers the college will have in n years? 22

23 82. Kaye want to make trail mix made up of almonds, walnuts, and raisins. She wants to mix one part almonds, three parts walnuts, and four parts raisins. Almonds cost $0 per pound, walnuts cost $2 per pound, and raisins cost $6 per pound. Kaye has $25 to spend on the trail mix. Determine how many pounds of trail mix she can make. 83. A rectangular garden measuring 5 meter by 2 meters is to have a walkway installed around it with a width of x meters, as shown in the diagram below. Together, the walkway and the garden have an area of 378 square meters. Write an equation that can be used to find x, the width of the walkway. 84. Is the result of the following operation a rational or irrational number?

24 ID: A Algebra EOC Bellringer Review Answer Section MULTIPLE CHOICE. ANS: A 2. ANS: D 3. ANS: C 4. ANS: B 5. ANS: B 6. ANS: B 7. ANS: D 8. ANS: A 9. ANS: C 0. ANS: B. ANS: C 2. ANS: D 3. ANS: A 4. ANS: B 5. ANS: C 6. ANS: B 7. ANS: B 8. ANS: B 9. ANS: C 20. ANS: A 2. ANS: B 22. ANS: C MULTIPLE RESPONSE 23. ANS: B, D 24. ANS: B, D 25. ANS: A, C, D, E 26. ANS: A, D 27. ANS: B, C, D, E, H 28. ANS: A, B, D, E, F, G

25 ID: A COMPLETION 29. ANS: Distributive property Addition property of equality Combine like terms Addition property of equality Subtraction property of equlaity Division property of equality SHORT ANSWER 30. ANS: Horizontal shift 2 units left. Vertical shift 3 units down 3. ANS: 0.25 meters per year 32. ANS: Yes, 30 words per minute. This is the amount of words someone can type in a minute. 33. ANS: -2/3 Sample Answer: As y decreases by 2, x increases by ANS: Time, t (years) Salary, S (Dollars) 35. ANS: City B 36. ANS: 20,000 ft 37. ANS: I Negative II None III Positive 38. ANS: y =

26 ID: A 39. ANS: Bank B would earn more interest. Bank A: 2500( +.2) 5 = 4,406 Bank B :2500( )5 2 = 4, ANS: The y-intercept is 3. The end behavior is as x approaches negative infinity f(x) approaches positive infinity and as x approaches positive infinity f(x) approaches ANS: y = Ê ˆ Ë Á 4 The balance is $6.22 This is an exponential growth model. 42. ANS: y = 28( 0.5) 5 = 4 There are 4 players. This is an exponential decay. 43. ANS: Situation is a geometric sequence. Use the explicit formula for 5th generation f(n) = 4(4) n f(5) = 4(4) 5 =, ANS: Recursive f() = 6 f(n) = f(n ) 2 n 2 Explicit f(n) = 6(2) n 3

27 ID: A 45. ANS: solve recursively f() = 4, r = ,024 solve using explicit formula f(5) = 4(4) 5 f(5) =, ANS: f(n) = 4(6) n 47. ANS: Town B. common ratio is about ANS: a - exponential b - linear 49. ANS: Initial investment is : $350 Money in the account for: 6 years Interest rate is: 7% 50. ANS: ANS: 6 2 or ANS: C must be greater because c is always 35 more than d 53. ANS: They can make 0 cars. 20 >= 0.50(30) +.25(0) 20 >= ANS: m = 2k v ANS: x = 5 a b 4

28 ID: A 56. ANS: kdsfj 57. ANS: ( )/55 = 330/55 = 6 It will take him 6 hours to finish the book. 58. ANS: x > 27/7 59. ANS: Part A: f(x) - -6x + 9; g(x) = 2x - 3 Part B: k = -3 Part C: Solution is (.5, 0) 60. ANS: (-, -3) 6. ANS: 5x+ 4 = 0x - 3 x = 7 5 Each boy is years old 62. ANS: Quadrant IV, since the solution is (3, -4) 5

29 ID: A 63. ANS: y =.50x + 6 y = 2.00x x = 7 rides 64. ANS: 65. ANS: 66. ANS: (-2,0) and (3, 5) 6

30 ID: A 67. ANS: $35 represents a fixed amount $2.30 represents how much is charged for each additional mile. c = 2.30m ANS: a. Yes b. No c. No d Yes e. No 69. ANS: Part A 7x + 2y 200 Part B 5 hours 70. ANS: x < x 7. ANS: A(n) = 2.75n + 85 She can afford to rent movies for 67 weeks in a row 72. ANS: Part A 73 Part B f(n) = 7 + 6(n - ) 73. ANS: C(6) = 45(6) = 720 The value 720 represents how much it would cost to produce 6 graphing calculators. 74. ANS: 0 = -2t = -2t 2.5 = t It would take 2.5 minutes to use all 50 sheets of paper. 75. ANS: c 7

31 ID: A 76. ANS: x int = 0; y int = ANS: There is a fixed fee of $0.46 for mailing a letter weighing up to oz. For each ounce more it will cost $0.20 for each ounce over oz. c = z 78. ANS: C(h) = 25h ANS: Yes, because each element of the domain goes to exactly one element of the range. 80. ANS: n s(n) The sequence is a function because for every value of n there is one value of S(n). The domain are all positive integers 8. ANS: Start with 5 computers. Receive 26 additional each year. n = number of years 26n + 5 8

32 ID: A 82. ANS: Let x = pounds of an ingredient almonds: 3 walnuts: 4 raisins :3:4 x + 3x + 4x = 8x pounds of mix 0(x) + 2(3x) + 6(4x) = 25 70x = 25 x = 25/70 = 5/4 8(5/4) =????????? Let x = pounds of an ingredient almonds: 3 walnuts: 4 raisins :3:4 x + 3x + 4x = 8x pounds of mix 0(x) + 2(3x) + 6(4x) = 25 70x = 25 x = 25/70 = 5/4 8(5/4) =????????? Kaye can make????????? lbs of trail mix. 83. ANS: x = width of walkway One side of the garden including walkway = 2x+2 Other side of the garden including walkway = 2x +5 Area is 378 Length x Width = Area (2x + 2)(2x +5) = 378 9

33 ID: A 84. ANS: When you add a rational and an irrational number the resulting number will be irrational. 0