Algebra 2 Unit 1 Practice

Transcription

1 Algebra Unit Practice Lesson - Use this information for Items. Aaron has $ to rent a bike in the cit. It costs $ per hour to rent a bike. The additional fee for a helmet is $ for the entire ride.. Write an equation that can be used to find h, the number of hours Aaron can rent the bike. Lesson - Use this information for Items 0. Susan plans to rent a bike in New Orleans to tour the cit. The cost of the rental is $0 per da. The cost of a helmet is $7 for as long as Susan needs the bike.. Make a table that shows the cost of the rental for,,,, and das.. Solve our equation from Item, and interpret the solution.. Aaron would like to rent the bike for hours. How much more mone will Aaron need? Eplain.. Aaron and Zell want to rent a tandem bike so that the can ride together. The rental for a tandem bike is $8.0 per hour plus $ for each helmet. Aaron and Zell have $80 to spend on the bike rental. Which equation can be used to find h, the number of hours the can rent a tandem bike? 7. Write a linear equation in two variables that models the situation. Tell what each variable in the equation represents. 8. Graph the equation. Be sure to include titles, and use an appropriate scale on each ais. A h B h C. 80 h 8.0 D. 80 h 8.0. Make sense of problems. Eliza bought a da pass to rent a bike in the cit. The da pass costs $0 from 9 a.m. to 7 p.m. There is an additional fee of $ per quarter hour if she returns the bike after 7 p.m. Eliza has $0 and plans to return the bike at 8: p.m. a. Does Eliza have enough mone? Eplain using an equation. b. When should she return the bike? 9. Which of the following statements describes what the slope and -intercept represent in the situation? A. The slope represents the cost of the rental. The -intercept represents the cost of the helmet. B. The slope represents the cost of the helmet per da. The -intercept represents the cost of the helmet at da 0. C. The slope represents the cost of the bike per da. The -intercept represents the cost of the helmet for the entire time of the rental. D. The slope represents the rise of a hill in New Orleans. The -intercept represents rise of the slope. 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

2 0. Construct viable arguments. Barbara has $0 to rent a bike for das. Does Barbara have enough mone? Eplain. Lesson -. Solve each absolute value equation. Graph the solutions on the number line. a b c d If the speed of a car on the highwa detected b a radar gun is within 7 mph of the speed limit, a police officer will not issue a ticket to a car for driving too fast or too slow. What is the acceptable range of speeds in a -mph speed zone?. Solve each absolute value inequalit. Graph the solutions on the number line. a., b. $ College Board. All rights reserved. SpringBoard Algebra, Unit Practice

3 c. # d Which number line shows the solutions of the inequalit,? A B C D Model with mathematics. The weight of a pen manufactured at the PEN factor is 8 g. The actual weight can var b as much as g. Write and solve an inequalit to represent all acceptable weights for a pen at this factor. Graph the inequalit College Board. All rights reserved. SpringBoard Algebra, Unit Practice

4 Lesson -. Write the equation of a line with a -intercept of and a slope of. Graph the equation. 9. Graph the function using appropriate scales on the aes. 0. Reason quantitativel. What would Julian s sales have to be for him to earn $000 in one month? Eplain how ou determined our answer. Lesson -. a. Graph the inequalit,. 7. Which is the equation of the line that passes through the point (, ) and has a slope of? A. B. 8 C. D. Use the following information for Items 8 0. Julian works as a sales representative for a home improvement store. He earns $00 plus 9 % commission on sales each month. 8. Write the equation of the function f (e) that represents Julian s monthl earnings, where e represents the amount of monthl sales. b. Did ou use a solid or dashed line for the boundar line? Eplain our choice. c. Did ou shade above or below the boundar line? Eplain our choice. 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

5 . Graph the following inequalities on the same grid and shade the solution region that is common to all of the inequalities. a., b. # c. $. Model with mathematics. Write a sstem of inequalities for the graph Which ordered pair lies in the solution region that is common to all of the inequalities in Item? A. (, ) B. (0, 0) C. (, 0) D. (, ). a. Identif two ordered pairs that do not satisf the constraints in Item. Lesson -. Solve each sstem b graphing. a. b. Reason abstractl. For each ordered pair from part a, identif the constraint or constraints that it fails to meet. 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

6 b. d. c. 7. Solve each sstem b substitution. a. 8 b. c. d. 7 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

7 8. Solve each sstem b elimination. a. b. 9 Lesson -. Solve each sstem b substitution. z 0 z 8 a. z b. z z 8 z c. 7 0 d. c. z 7 z z d. z 9 z 8 z 9. Reason abstractl. Eplain how ou would eliminate one of the variables in this sstem Solve each sstem using Gaussian elimination. 0. Persevere in solving problems. Noah s Café sells special blends of coffee mitures. Noah wants to create a 0-pound miture with coffee that sells for $9.0 per pound and coffee that sells for $.0 per pound. How man pounds of each miture should he blend to create coffee that sells for $.98 per pound? a. z z 9 z b. z 8 z 8 z A. 8 pounds of the $.0-per-pound coffee, pounds of the $9.9-per-pound coffee B. 0 pounds of the $.0-per-pound coffee, 0 pounds of the $9.9-per-pound coffee c. z z z 0 d. z z z C. pounds of the $.0-per-pound coffee, 8 pounds of the $9.0-per-pound coffee D. pounds of the $.0-per-pound coffee, pounds of the $9.0-per-pound coffee 7 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

8 . Use the table for parts a and b. Time Period Classic No. of cups sold Smoothie Sales Fruit No. of cups sold Veggie No. of cups sold Sales 8:00 :00 0 $0.0 :00 :00 8 $.0 :00 8:00 8 $0.00 a. Write a sstem of equations that can be used to determine c, f, and v, the price in dollars of a classic, fruit, and veggie smoothie. b. Solve our sstem and eplain what the solution means in the contet of the situation.. A food store makes a 0-pound miture of peanuts, cashews, and raisins. The miture has twice as man peanuts as cashews. Peanuts cost $ per pound, cashews cost $ per pound, and raisins cost $ per pound. The total cost of the miture is $. How much of each ingredient did the store use to make the miture?. Make sense of problems. A compan placed $00,000 in three different investment plans. The compan placed some mone into short-term notes paing.% per ear. The placed three times as much into government bonds paing % per ear. The placed the rest in utilit bonds paing.% per ear. The income for one ear was $,000. How much more mone did the compan place in government bonds than in utilit bonds? A. $00,000 B. $00,000 C. $00,000 D. $00, College Board. All rights reserved. SpringBoard Algebra, Unit Practice

9 9 Name class date 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice Lesson -. Which entr corresponds to the address c for the following matri? C 0 A. B. C. D A is a matri. B is a matri. What are the dimensions of the matri product, AB? 8. Find the sum or difference. a A 8 B 9 7 C a. A B b. A B c. B C d. C B 9. Find the product. D E 0 F 0 a. DE b. DF c. EF d. FD 0. Make use of structure. Use the following matrices for parts a and b. G H a. Can ou add or subtract the matrices? Eplain. b. Can ou multipl the matrices, GH? Eplain. Lesson -. Which of the following is the inverse of 0? A. 0 B. 0 C. 0 D. 0

10 . Model with mathematics. Write a matri equation to model each sstem. Then use the matri equation to solve the sstem. a. 0 0 b. Write a matri equation that can be used to solve the sstem. c. Use the matri equation to solve the sstem. b. z z 8 z d. Eplain the meaning of the solution.. Lori bought cheeses for a part. The cheddar cost $7.9 per pound, and the Swiss cost $9.0 per pound. Lori bought pounds of cheese for a total of $7.0. a. Write a sstem of equations that can be used to determine how man pounds of each tpe of cheese Lori bought. Let be the number of pounds of cheddar cheese, and let be the number of pounds of Swiss cheese.. The local bookstore had a sale. The table shows the number of items sold over three das. Da Sales Da Paperback Hardcover e-book Amount of Sales Monda 7 $970 Tuesda 0 $ Wednesda 8 9 $9 a. Write a matri equation that can be used to find the price of each item. b. Solve the equation to find the solution of the sstem and eplain the meaning of the solution. 0 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

11 . Mari has coins consisting of nickels, dimes, and quarters. The total value of the coins is $9.. The number of dimes is one less than three times the number of nickels. How man of each tpe of coin does Mari have? b. f( ) if, if. f () Lesson -. The domain of a function is all real numbers greater than or equal to and less than. Write the domain using an inequalit, interval notation, and set notation. 7. The range of a function is (`, ]. Which of the following shows this range using set notation? A. # B. {,, } C., D. {, # } 8. Graph each piecewise function. Then write its domain and range using inequalities, interval notation, and set notation. a. f( ) if # if. c. f( ) if # 0 if. 0 f () f () 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

12 d. f( ) if, if. b. Graph the piecewise function. f () c. Wh are the slopes of each piece of the function different? Eplain. 9. Evaluate the piecewise function for,, and 0. d. On average, a famil of four consumes 7. gallons of water per da. Calculate the quarterl water bill for a famil of four. Eplain how ou determined our answer. 8 if, h ( ) if, # if,,` 0. Model with mathematics. A water compan charges residential customers a quarterl flat fee of $ for up to 000 gallons of water. The compan charges $0 per thousand for the first 0,000 gallons of water after the minimum allowance. The net 0,000 gallons is $ per thousand. All other consumption over,000 gallons is $.0 per thousand. a. Write a piecewise function w() that can be used to determine a customer s quarterl bill for using gallons of water. Lesson -. A step function, known as the greatest integer function or the floor function, is written as f the largest integer not greater than. ( ) a. Graph this step function. Floor function f ( ) f() b. Find f (.), f (0.0), and f (.). 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

13 . Use the absolute value function h() for parts a d. a. Graph h(). b. Graph the function. h() c. Evaluate the function for hour 0 minutes and for hours minutes. b. What are the domain and range of the function? d. Chance hired the tutor to help him prepare for his calculus eam. The tutor and Chance worked together from : p.m. until : p.m. How much did the tutor charge Chance for the session? A. $80 B. $ C. $80 D. $70. Use the step function h() for parts a and b. c. What are the coordinates of the verte of the function s graph? d. Write the equation for the function using piecewise notation. 0 if 0,, h ( ) if,, if. a. Graph the function. h(). Model with mathematics. A tutor charges $ for each hour or for an fraction of an hour. a. Write a function t() to represent this situation using the ceiling function, the smallest integer greater than or equal to. b. Evaluate the function for 0.,,., and College Board. All rights reserved. SpringBoard Algebra, Unit Practice

14 . Maura gets $8 per hour for the first 0 hours she works in a week. She gets. times her hourl rate for ever hour she works over 0 hours per week. Maura worked hours last week. How much did Maura earn last week? Is this a step function? Eplain. Lesson -. Write the equation g () of each transformation of the parent graph f () described below. a. reflection over the -ais b. stretched horizontall b a factor of 8. Write the equation for the transformation of f () as shown in the graph f() c. translated right units d. stretched verticall b a factor of, translated up units e. stretched verticall b a factor of, reflected over the -ais, translated left unit and down units 9. Make use of structure. Find the coordinates of the verte of g (). A. (, ) B. (, ) C. (, ) D. (, ) 0. Graph g( ) as a transformation of f (). Then identif the transformation. g() 7. What is the domain and range of g ()? 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

15 Lesson -. For parts a d, use the following functions. f () g () Find each function and simplif the function rule. Note an values that must be ecluded from the domain. a. ( f g)() b. ( f g)() c. Add the functions m() and p() to find (m p)(). Then simplif the function rule. d. What does (m p)(0,000) represent in this situation? Find (m p)(0,000). e. How could ou use (m p)() in this situation? c. ( f? g)() d. ( f g) (). Given g () ( ) and h (), which of the following is ( g? h)()? A. B. 8 C. D.. Make use of structure. Given h (), for what values of is h () 8? Eplain.. Shanti has a vegetable garden that is 8 ft long and ft wide. She wants to increase both the length and the width of the garden b number of feet. a. Write a function to represent the new area. b. What is the new area if she increases both the length and width b ft? Lesson -. Given the functions () and (z) z, write the equation for the composition function ((z)) and evaluate it for z.. Mart Besson is a salesperson who earns $,000 per ear plus 8% commission on sales. His wife Phllis is also a salesperson. She earns $0,000 per ear plus % commission on sales. Last ear, Mart and Phllis each made sales of $0,000. a. Write a function m() to represent Mart s annual earnings, and a function p() to represent Phllis s annual earnings. b. What does the function (m p)() represent in this situation? 7. The notation j (k(l )) represents a composite function. The domain of j (l ) is all real numbers, and the range is all real numbers greater than or equal to. What is the domain of the composite function? 8. Model with mathematics. Tom s in-home computer service charges a flat fee of $ plus $7 per hour to service a computer in a home. a. Write a function c (h) for the cost of servicing a computer or computers for h hours at one location. 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

16 b. What are the units of the domain and range of this function? Lesson - 7. Use the tables of values to evaluate each epression. c. What is the slope of this function? Interpret the slope as a rate of change. f f ( ) 9 g g ( ) It takes about minutes for one of Tom s technicians to service one computer. a. Write a function h() for the hours needed to service computers. a. f () b. g () c. f ( g()) d. g ( f ()) 7. For parts a h, use these three functions to evaluate each composite function. f () g () h () a. ( f g)() b. ( g f )() b. Write a function c (h()) to represent the cost of servicing computers in one location. c. ( f h)() d. ( g h)() e. (h f )() f. (h g)() c. Which is the value of c (h())? A. $0. B. $8.7 C. $8.7 D. $.7 g. ( f f )() h. (h g h)() 70. Will the cost be the same to service three computers in one location or one computer in each of three different locations? Eplain. 7. Given that a() and b(), write each composite function in terms of. a. (a b)() b. (b a)() 7. Make use of structure. Given that j(n) n and k(n) n, for which value(s) of n is ( j k)(n)? A. B. C. or D. or 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

17 7. Marion wants to bu a laptop at the computer store. Laptops are on sale for % off. The sales ta is 7%. Use this information for parts a and b. a. Write a function s(p) that gives the sale price of a laptop regularl priced at p dollars. a 79. The function k( a) gives the map distance in centimeters between two points on a map that are actuall a kilometers apart. Use this information for parts a c. a. What is k()? What does k() represent? b. Write a function t(p) that gives the total cost including ta for a laptop priced at p dollars. b. What is the inverse of k(a)? What does the inverse represent? c. Determine the cost of a laptop regularl priced at $0. c. Evaluate k (). What does k () represent? Lesson - 7. If h and j are inverse functions, what is h( j())? 80. Make use of structure. Given f () 8, what is f (8)? 77. Find the inverse of each function. a. f () b. g( ) ( ) c. h ( ) d. j ( ) Lesson - 8. Make use of structure. Find the inverse of each function. Then use the definition of inverse functions to prove that the functions are inverses. Show our work. a. f () b. g( ) 78. Which is the inverse of the function a(d) d? d A. a ( d)d B. a ( d) a d d C. ( ) D. a ( d) d 8. h() and j() are inverse functions. Which of the following statements is NOT true? A. h( j()) B. The domain of j() is the range of h(). C. The slopes of h() and j() are reciprocals. D. The graphs of h() and j() are reciprocals. 7 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice

18 8. In parts a and b, graph the inverse of each function shown on the coordinate planes. a f() b f() Write the inverse of the function defined b the table. Epress our answer tabularl or smbolicall. 0 8 f ( ) 7 8. Graph each function and its inverse on the same coordinate plane. a. f () b. f () 8 0 College Board. All rights reserved. SpringBoard Algebra, Unit Practice