Lesson 3.1 Recursive Sequences

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1 Lesson 3.1 Recursive Sequences 1) 1. Evaluae he epression 2(3 for each value of. a. 9 b. 2 c. 1 d Consider he sequence of figures made from riangles. Figure 1 Figure 2 Figure 3 Figure a. Complee he able for five figures. b. Wrie a recursive rouine o find he perimeer of each figure. c. Find he perimeer of Figure 10. d. Which figure has a perimeer of 1? Figure # Perimeer Lis he firs si values generaed by he following recursive rouine: 27. ENTER Ans 9.2 ENTER, ENTER,.... Wrie a recursive rouine o generae each sequence. Then use your rouine o find he 10h erm of your sequence. a. 7., 3.6, 0.6,.,... b. 9.2, 6., 3., 1.1,... c. 1, 3, 9, 27,... d. 36, 12,, 1.3,.... Ben s school is 3 mile, or 3960 fee, away from his house. A 3:00, Ben walks sraigh home a 330 fee per minue. a. On your calculaor, ener a recursive rouine ha calculaes how far Ben is from home each minue afer 3:00. b. How far is he from home a 3:0? c. A wha ime does Ben arrive home? 2007 Key Curriculum Press Discovering Algebra More Pracice Your Skills 21

2 Lesson 3.2 Linear Plos 1. Solve each equaion. a. ( 3) 9 2 b. 16 ( ) 6 c ( ) d. 3( 9) Lis he erms of each number sequence of y-coordinaes for he poins shown on each graph. Then wrie a recursive rouine for each sequence. a. y b. y c. y d. y Plo he firs five poins represened by each recursive rouine on separae graphs. a. {0, } ENTER {Ans(1) 1, Ans(2) 3} ENTER, ENTER,... b. {2, 6} ENTER {Ans(1) 1, Ans(2) 0.2} ENTER, ENTER,... c. {, 1} ENTER {Ans(1) 1, Ans(2) 2} ENTER, ENTER,.... Consider he following epression: ( ) 3 a. Use he order of operaions o find he value of he epression if 1 and if. b. Se he epression equal o 12. Creae an undoing able and solve by undoing he order of operaions you used in a.. One hundred meersicks are used o ouline a recangle. Wrie a recursive rouine ha generaes a sequence of ordered pairs (l, w) ha liss all possible recangles. 22 Discovering Algebra More Pracice Your Skills 2007 Key Curriculum Press

3 Lesson 3.3 Time-Disance Relaionships 1. Consider he following ables: a. Time (s) Disance (m) b Time (s) Disance (m) i. Describe he walk shown in each able. Include where he walker sared and how quickly and in wha direcion he walker moved. ii. Wrie a recursive rouine for each able. 2. Walker A sars a he 0. m mark and walks away from he sensor a a consan rae of 1.7 m/s for 6 s. Walker B sars a he m mark and walks oward he sensor a a consan rae of 0.3 m/s for 6 s. a. Make a able of values for each walker. b. Wrie a recursive calculaor rouine for each walk and use i o check your able enries. 3. Look a he ables in 1a and b. Assume ha boh walkers sar a he same ime and are walking along he same roue. a. Make one graph showing boh walks. b. Wha do you noice abou he wo lines? Eplain he significance of your observaion.. Describe he walk shown in each graph. Include where he walker sared, how quickly and in wha direcion he walker moved, and how long he walk lased. The unis for are seconds and for y are meers. a. y b y Disance (m) 6 2 Disance (m) Time (s) Time (s) 2007 Key Curriculum Press Discovering Algebra More Pracice Your Skills 23

4 Lesson 3. Linear Equaions and he Inercep Form 1. Mach he answer rouine in he firs column wih he equaion in he second column. a. 2 ENTER i. y Ans 0.7 ENTER, ENTER,... b. 0.7 ENTER ii. y Ans 2 ENTER, ENTER,... c. 0.7 ENTER iii. y Ans 2 ENTER, ENTER,... d. 2 ENTER iv. y Ans 0.7 ENTER, ENTER, A sore could use he equaion P w o calculae he price P i charges o mail merchandise ha weighs w lb. (1 lb 16 oz) a. Find he price of mailing a 3 lb package. b. Find he cos of mailing a 9 lb oz package. c. Wha is he real-world meaning of 6.7? d. Wha is he real-world meaning of 1.20? e. A cusomer sen $20.00 o he sore o cover he cos of mailing. He received he merchandise plus $6.6 change. How much did his parcel weigh? 3. You can use he equaion d 10 3 o model a walk in which he disance d is measured in miles and he ime is measured in hours. Graph he equaion and use he race funcion o find he approimae disance for each ime value given in 3a and b. a. 2.2 h b. h c. Wha is he real-world meaning of 10? d. Wha is he real-world meaning of 3?. Undo he order of operaions o find he -value in each equaion. a ( ) 2 b. 1 ( 6) 2.2. The equaion y gives he disance in miles ha a rucker is from Flin afer hours. a. How far is he rucker from Flin afer 2 hours and 1 minues? b. How long will i ake unil he rucker is 10 miles from Flin? Give he answer in hours and minues. 2 Discovering Algebra More Pracice Your Skills 2007 Key Curriculum Press

5 Lesson 3. Linear Equaions and Rae of Change 1. Complee he able of oupu values for each equaion. a. y 2 3 b. L2 0.7 L1 Inpu Oupu y Inpu lis L Oupu lis L2 2. Use he equaion d o approimae he disance in miles and ime in hours of a pilo from her desinaion. a. Find he disance d for. h. b. Find he ime for a disance of 770 mi. 3. Tell wheher each graph is a possible model for a person s disance from a ree. If i is a possible model, describe he rae of change shown in he graph. If i is no a possible model, eplain why no. a. d b. d c. d d. d. Each able shows a differen inpu-oupu relaionship. i. Inpu Oupu ii. Inpu Oupu iii Inpu Oupu a. Find he rae of change, or slope, for each able. b. For each able, find he oupu value ha corresponds o an inpu value of 0. Wha is his oupu value called? c. Use your resuls from a and b o wrie an equaion in slope inercep form for each able. d. Use calculaor liss o verify ha your equaions acually produce he able values Key Curriculum Press Discovering Algebra More Pracice Your Skills 2

6 Lesson 3.6 Solving Equaions Using he Balancing Mehod 1. Give he equaion ha each picure models and solve for. a b c. 1 1 d Wrie each equaion in inercep form, y a b. a. y 2 1 b. y 9 2 c y 3. Solve each equaion using he balancing mehod. Give he acion aken for each sep. a. 2a 1 b. b 20 c. 6 c 3c 10. Give he muliplicaive inverse of each number. a. 7 b. 0.2 c. d. 36. Give he addiive inverse of each number. a. 0.2 b. c. 36 d. 2z 6. Solve each equaion using he mehod of your choice. Then use anoher mehod o verify your answer. a. 12 9w 30 b. 3v 1 c. 3 m 9 d. n 2 e. ( 3.2) f. 2 (3 y) Discovering Algebra More Pracice Your Skills 2007 Key Curriculum Press