Fair Game Review. Chapter 6. Evaluate the expression. 3. ( ) 7. Find ± Find Find Find the side length s of the square.

Transcription

1 Name Date Chapter 6 Evaluate the epreion. Fair Game Review ( 8) ( 6 8) ( ) 5. Find Find Find ± Find the ide length of the quare. Area 9 ft Copyright Big Idea Learning, LLC Big Idea Math Algebra 133

2 Name Date Chapter 6 Fair Game Review (continued) Write an equation for the nth term of the arithmetic equence. 9. 1, 5, 9, 13, 10. 1, 11, 3, 35, , 1, 6, 0, 1., 15, 6, 3, 13. Your family i driving on the highway. The amount of ga in the tank after 1 hour, hour, and 3 hour i 19.5 gallon, 17 gallon, and 1.5 gallon, repectively. a. Write an equation for the amount of ga left after the nth hour of driving. b. How much ga will be left in the tank after 8 hour? 13 Big Idea Math Algebra Copyright Big Idea Learning, LLC

3 Name Date 6.1 Propertie of Square Root For ue with Activity 6.1 Eential Quetion How can you multiply and divide quare root? Recall that when you multiply a number by itelf, you quare the number. Symbol for quaring i nd power. 16 quared i 16. To undo thi, take the quare root of the number. Symbol for quare root i a radical ign. 16 The quare root of 16 i. 1 ACTIVITY: Finding Square Root Work with a partner. Ue a quare root ymbol to write the ide length of the quare. Then find the quare root. Check your anwer by multiplying. a. 81 Check: Area 81 ft The ide length of the quare i. b. Area 11 yd c. Area 3 cm d. Area 361 mi Copyright Big Idea Learning, LLC Big Idea Math Algebra 135

4 Name Date 6.1 Propertie of Square Root (continued) e. Area.89 in. f. Area 6.5 m g. Area ft 16 5 ACTIVITY: Operation with Square Root Work with a partner. When you have an epreion that involve two operation, you need to know whether you obtain the ame reult regardle of the order in which you perform the operation. In each of the following, compare the reult obtained by the two order. What can you conclude? a. Square Root and Addition I equal to ? In general, i a + b equal to a + b? Eplain your reaoning. b. Square Root and Multiplication I 9 equal to 9? In general, i a b equal to a b? Eplain your reaoning. 136 Big Idea Math Algebra Copyright Big Idea Learning, LLC

5 Name Date 6.1 Propertie of Square Root (continued) c. Square Root and Subtraction I 6 36 equal to 6 36? In general, i a b equal to a b? Eplain your reaoning. d. Square Root and Diviion I equal to? a a In general, i equal to? b b Eplain your reaoning. What I Your Anwer? 3. IN YOUR OWN WORDS How can you multiply and divide quare root? Write a rule for: a. The product of quare root b. The quotient of quare root Copyright Big Idea Learning, LLC Big Idea Math Algebra 137

6 Name Date 6.1 Practice For ue after Leon 6.1 Simplify the epreion Simplify the epreion. Aume all variable are poitive y yz 9. A trampoline ha an area of 9π quare feet. What i the diameter of the trampoline? 138 Big Idea Math Algebra Copyright Big Idea Learning, LLC

7 Name Date Etenion 6.1 Real Number Operation For ue with Etenion 6.1 A et of number i cloed under an operation when the operation performed on any two number in the et reult in a number that i alo in that et. For eample, the et of integer i cloed under addition, ubtraction, and multiplication. Thi mean that if a and b are two integer, then a + b, a b, and ab are alo integer. 1 ACTIVITY: Sum and Product of Rational Number The table how everal um and product of rational number. Complete the table. Sum or Product Anwer Rational or Irrational? Copyright Big Idea Learning, LLC Big Idea Math Algebra 139

8 Name Date Etenion 6.1 Real Number Operation (continued) ACTIVITY: Sum of Rational and Irrational Number The table how everal um of rational and irrational number. Complete the table. Sum Anwer Rational or Irrational? π Practice 1. Uing the reult in Activity 1, do you think the et of rational number i cloed under addition? under multiplication? Eplain your reaoning.. Uing the reult in Activity, what do you notice about the um of a rational number and an irrational number? 10 Big Idea Math Algebra Copyright Big Idea Learning, LLC

9 Name Date Etenion 6.1 Real Number Operation (continued) 3 ACTIVITY: Product of Rational and Irrational Number The table how everal product of rational and irrational number. Complete the table. Product Anwer Rational or Irrational? 6 1 π ACTIVITY: Sum and Product of Irrational Number The table how everal um and product of irrational number. Complete the table. Sum or Product Anwer Rational or Irrational? π π + π π 7 5 π 3 Copyright Big Idea Learning, LLC 3 3 Big Idea Math Algebra 11

10 Name Date Etenion 6.1 Real Number Operation (continued) Practice 3. Uing the reult in Activity 3, i the product of a rational number and an irrational number alway irrational? Eplain.. Uing the reult in Activity, do you think the et of irrational number i cloed under addition? under multiplication? Eplain your reaoning. 5. CRITICAL THINKING I the et of irrational number cloed under diviion? If not, find a countereample. (A countereample i an eample that how that a tatement i fale.) 6. STRUCTURE The et of integer i cloed under addition and multiplication. Ue thi information to how that the um and product of two rational number are alway rational number. 1 Big Idea Math Algebra Copyright Big Idea Learning, LLC

11 Name Date 6. Propertie of Eponent For ue with Activity 6. Eential Quetion How can you ue inductive reaoning to oberve pattern and write general rule involving propertie of eponent? 1 ACTIVITY: Writing a Rule for Product of Power Work with a partner. Write the product of the two power a a ingle power. Then, write a general rule for finding the product of two power with the ame bae. 3 a. ( 3 )( 3 ) 3 b. ( )( ) 1 5 c. ( )( ) 3 5 d. ( 5 )( 5 ) 6 e. ( )( ) ACTIVITY: Writing a Rule for Quotient of Power Work with a partner. Write the quotient of the two power a a ingle power. Then, write a general rule for finding the quotient of two power with the ame bae. a. 3 3 b. c. d e. 3 3 Copyright Big Idea Learning, LLC Big Idea Math Algebra 13

12 Name Date 6. Propertie of Eponent (continued) 3 ACTIVITY: Writing a Rule for Power of Power Work with a partner. Write the epreion a a ingle power. Then, write a general rule for finding a power of a power. a. ( 3 ) 3 b. ( ) 3 c. ( 7 ) 3 d. ( y ) 3 e. ( ) ACTIVITY: Writing a Rule for Power of Product Work with a partner. Write the epreion a the product of two power. Then, write a general rule for finding a power of a product. a. ( 3) 3 b. ( 5) c. ( 5 ) 3 d. ( 6a ) e. ( 3 ) 1 Big Idea Math Algebra Copyright Big Idea Learning, LLC

13 Name Date 6. Propertie of Eponent (continued) 5 ACTIVITY: Writing a Rule for Power of Quotient Work with a partner. Write the epreion a the quotient of two power. Then, write a general rule for finding a power of a quotient. a. b. c. d. e a b What I Your Anwer? 6. IN YOUR OWN WORDS How can you ue inductive reaoning to oberve pattern and write general rule involving propertie of eponent? 7. There are 3 3 mall cube in the cube below. Write an epreion for the number of mall cube in the large cube at the right. Copyright Big Idea Learning, LLC Big Idea Math Algebra 15

14 Name Date 6. Practice For ue after Leon 6. Simplify. Write your anwer uing only poitive eponent. m m. t t h h 3 3. ( ) 5. ( p ) 6. y a 5 8. ( w) 7 9. Write an epreion uing only poitive eponent for the width w of the rectangle. y 3 w Area 7 7 y 16 Big Idea Math Algebra Copyright Big Idea Learning, LLC

15 Name Date 6.3 Radical and Rational Eponent For ue with Activity 6.3 Eential Quetion How can you write and evaluate an nth root of a number? Recall that you cube a number a follow. Symbol for cubing i 3rd power. 3 8 cubed i 8. To undo thi, take the cube root of the number. Symbol for cube root i The cube root of 8 i. 1 ACTIVITY: Finding Cube Root Work with a partner. Ue a cube root ymbol to write the ide length of the cube. Then find the cube root. Check your anwer by multiplying. Which cube i the larget? Which two are the ame ize? Eplain your reaoning. a. Volume 7 ft 3 b. Volume 15 cm 3 c. Volume 3375 in. 3 Cube are not drawn to cale. Copyright Big Idea Learning, LLC Big Idea Math Algebra 17

16 Name Date Radical and Rational Eponent (continued) d. Volume m 3 e. Volume 1 yd 3 f. 15 Volume mm 8 3 Cube are not drawn to cale. ACTIVITY: Etimating nth Root Work with a partner. When you raie an nth root of a number to the nth power, you get the original number. ( n a) n a Sample: The th root of 16 i becaue Check: Match the nth root with the point on the number line on the following page. Jutify your anwer. a. 5 b. 0.5 c. 5.5 d e f. 6 0, Big Idea Math Algebra Copyright Big Idea Learning, LLC

17 Name Date 6.3 Radical and Rational Eponent (continued) A. B. C. D. E. F What I Your Anwer? 3. IN YOUR OWN WORDS How can you write and evaluate the nth root of a number?. The body ma m (in kilogram) of a dinoaur that walked on two feet can be modeled by m.73 ( ) C where C i the circumference (in millimeter) of the dinoaur femur. The ma of a Tyrannoauru re wa 000 kilogram. What wa the circumference of it femur? Copyright Big Idea Learning, LLC Big Idea Math Algebra 19

18 Name Date 6.3 Practice For ue after Leon 6.3 Simplify the epreion The radiu r of the bae of a cylinder i given by 1 V the equation r, where V i the volume π h of the cylinder and h i the height of the cylinder. Find the radiu of the cylinder to the nearet inch. Ue 3.1 for π. 6 in. r Volume 170 in Big Idea Math Algebra Copyright Big Idea Learning, LLC

19 Name Date 6. Eponential Function For ue with Activity 6. Eential Quetion What are the characteritic of an eponential function? 1 ACTIVITY: Decribing an Eponential Function Work with a partner. The graph below how etimate of the population of Earth from 5000 B.C. through 1500 A.D. at 500-year interval. a. Decribe the pattern. b. Did Earth population increae by the ame amount or the ame percent for each 500-year period? Eplain. c. Aume the pattern continued. Etimate Earth population in 000. d. Ue the Internet to find Earth population in 000. Did the pattern continue? If not, why did the pattern change? Population of Earth Million of people B.C. 000 B.C B.C. 000 B.C B.C A.D. 000 A.D. Year Copyright Big Idea Learning, LLC Big Idea Math Algebra 151

20 Name Date 6. Eponential Function (continued) ACTIVITY: Modeling an Eponential Function Work with a partner. Ue the following eponential function to complete the table. Compare the reult with the data in Activity 1. P 15( 1.06) t 500 Year t Population from Activity 1 P 5000 B.C B.C B.C B.C B.C B.C B.C B.C B.C B.C B.C A.D A.D A.D Big Idea Math Algebra Copyright Big Idea Learning, LLC

21 Name Date 6. Eponential Function (continued) What I Your Anwer? 3. IN YOUR OWN WORDS What are the characteritic of an eponential function?. Sketch the graph of each eponential function. Doe the function match the characteritic you decribed in Quetion 3? Eplain. a. y y O b. y 3 () y O c. y 31.5 ( ) y O Copyright Big Idea Learning, LLC Big Idea Math Algebra 153

22 Name Date 6. Practice For ue after Leon 6. Evaluate the function for the given value of.. f( ) ( ) 1. y ;.5 10 ; 1 ; 5 3. f( ) ( ). y ( ) 7 ; 3 Graph the function. Decribe the domain and range. 5. f( ) y () 3 3 y y O O 7. The number of viit y to a new webite quadruple every day. The function y 1( ) repreent the number of viit, where i the day.. a. Graph the function. Decribe the domain and range. b. How many viitor did the webite have on the 3rd day? y 15,000 1,000 9,000 6,000 3, Big Idea Math Algebra Copyright Big Idea Learning, LLC

23 Name Date Etenion 6. Practice For ue after Etenion 6. Solve the equation. Check your olution, if poible Copyright Big Idea Learning, LLC Big Idea Math Algebra 155

24 Name Date Etenion 6. Practice (continued) Ue a graphing calculator to olve the equation Retaurant A open acro the treet from retaurant B. Retaurant A begin gaining cutomer and retaurant B begin loing cutomer. The equation and 9 A B repreent the daily number of cutomer that eat at the repective retaurant. a. When do the retaurant have the ame number of cutomer? b. Check your anwer. 156 Big Idea Math Algebra Copyright Big Idea Learning, LLC

25 Name Date 6.5 Eponential Growth For ue with Activity 6.5 Eential Quetion What are the characteritic of eponential growth? 1 ACTIVITY: Comparing Type of Growth Work with a partner. Decribe the pattern of growth for each equence and graph. How many of the pattern repreent eponential growth? Eplain your reaoning. a. 1,, 7, 10, 13, 16, 19,, 5, b. 1.0, 1.,.0,.7, 3.8, 5., 7.5, 8, , 1.8, 0.7, 8.9 y y c. 1.0, 1.3,.3,.0, 6.3, 9.3, 13.0, d. 1.0, 1.6, 3.,.,.7, 6., 8.7, 17.3,.3, 8.0, , 15.3, 0., 6.6 y y Copyright Big Idea Learning, LLC Big Idea Math Algebra 157

26 Name Date 6.5 Eponential Growth (continued) ACTIVITY: Decribing a Growth Pattern Work with a partner. It i etimated that in 178 there were about 100,000 neting pair of bald eagle in the United State. By the 1960, thi number had dropped to about 500 neting pair. Thi decline wa attributed to lo of habitat, lo of prey, hunting, and the ue of the peticide DDT. The 190 Bald Eagle Protection Act prohibited the trapping and killing of the bird. In 1967, the bald eagle wa declared an endangered pecie in the United State. With protection, the neting pair population began to increae, a hown in the graph. Finally, in 007, the bald eagle wa removed from the lit of endangered and threatened pecie. Decribe the growth pattern hown in the graph. I it eponential growth? Aume the pattern continue. When will the population return to the level of the late 1700? Eplain your reaoning. Bald Eagle Neting Pair in Lower 8 State Number of neting pair y 11,000 10, Year 158 Big Idea Math Algebra Copyright Big Idea Learning, LLC

27 Name Date 6.5 Eponential Growth (continued) What I Your Anwer? 3. IN YOUR OWN WORDS What are the characteritic of eponential growth? How can you ditinguih eponential growth from other growth pattern?. Which of the following are eample of eponential growth? Eplain. a. Growth of the balance of a aving account b. Speed of the moon in orbit around Earth c. Height of a ball that i dropped from a height of 100 feet Copyright Big Idea Learning, LLC Big Idea Math Algebra 159

28 Name Date 6.5 Practice For ue after Leon 6.5 Identify the initial amount a and the rate of growth r (a a percent) of the eponential function. Evaluate the function when t. Round your anwer to the nearet tenth. 1. y 50( 1.01) t. f() t ( ) t 3. f() t.( 1.9) t. y ( ) t 5. Credit card debt of $1100 increae by 8% each year. Write and graph a function that repreent thi ituation. y 6. You depoit $675 in an account that earn 3.% annual interet compounded twice a year. a. Write a function that repreent thi ituation. t b. Find the balance in the account after.5 year. 160 Big Idea Math Algebra Copyright Big Idea Learning, LLC

29 Name Date 6.6 Eponential Decay For ue with Activity 6.6 Eential Quetion What are the characteritic of eponential decay? 1 ACTIVITY: Comparing Type of Decay Work with a partner. Decribe the pattern of decay for each equence and graph. How many of the pattern repreent eponential decay? Eplain your reaoning. a. 30.0,.3, 19., 1.7, 10.8, 7.5,.8, b. 30, 7,, 1, 18, 15, 1, 9,.7, 1., 0.3, 0.0 6, 3, 0 y y c. 30.0,.0, 19., 15., 1.3, d. 30.0, 9.7, 8.8, 7.3, 5.,.5, 9.8, 7.9, 6.3, 5.0,.0, , 15.3, 10.8, 5.7, 0.0 y y Copyright Big Idea Learning, LLC Big Idea Math Algebra 161

30 Name Date 6.6 Eponential Decay (continued) ACTIVITY: Decribing a Decay Pattern Work with a partner. Newton Law of Cooling tate that when an object at one temperature i epoed to air of another temperature, the difference in the two temperature drop by the ame percent each hour. A forenic pathologit wa called to etimate the time of death of a peron. At midnight, the body temperature wa 80.5 F and the room temperature wa 60 F. One hour later, the body temperature wa 78.5 F. a. By what percent did the difference between the body temperature and the room temperature drop during the hour? b. Aume that the original body temperature wa 98.6 F. Ue the percent decreae found in part (a) to make a table howing the decreae in body temperature. Ue the table to etimate the time of death. Time Temperature ( F) Big Idea Math Algebra Copyright Big Idea Learning, LLC

31 Name Date 6.6 Eponential Decay (continued) What I Your Anwer? 3. IN YOUR OWN WORDS What are the characteritic of eponential decay? How can you ditinguih eponential decay from other decay pattern?. Sketch a graph of the data from the table in Activity. Do the data repreent eponential decay? Eplain your reaoning. T t 5. Suppoe the pathologit arrived at 5:30 A.M. What wa the body temperature at 6 A.M.? Copyright Big Idea Learning, LLC Big Idea Math Algebra 163

32 Name Date 6.6 Practice For ue after Leon 6.6 Determine whether the table repreent an eponential growth function, an eponential decay function, or neither y y y y Write the rate of decay of the function a a percent. 5. f() t 0( 0.78) t 6. y t The ma of a radioactive element i 35 milligram. The ma of the element decreae by 1.9% every year. a. Write a function that repreent thi ituation. b. Predict the ma of the element in year. Round your anwer to the nearet tenth. 16 Big Idea Math Algebra Copyright Big Idea Learning, LLC

33 Name Date 6.7 Geometric Sequence For ue with Activity 6.7 Eential Quetion How are geometric equence ued to decribe pattern? 1 ACTIVITY: Decribing Calculator Pattern Work with a partner. Enter the keytroke on a calculator and record the reult in the table. Decribe the pattern. a. Step 1 Step Step 3 Step Step 5 % ME M M+ CE OFF ON/C Step Calculator Diplay b. Step 1 Step Step 3 Step Step Step Calculator Diplay Copyright Big Idea Learning, LLC Big Idea Math Algebra 165

34 Name Date 6.7 Geometric Sequence (continued) c. Ue a calculator to make your own equence. Start with any number and multiply by 3 each time. Record your reult in the table. Step Calculator Diplay ACTIVITY: Folding a Sheet of Paper Work with a partner. A heet of paper i about 0.1 mm thick. a. How thick would it be if you folded it in half once? b. How thick would it be if you folded it in half a econd time? c. How thick would it be if you folded it in half 6 time? d. What i the greatet number of time you can fold a heet of paper in half? How thick i the reult? e. Do you agree with the tatement below? Eplain your reaoning. If it were poible to fold the paper 15 time, it would be taller than you. 166 Big Idea Math Algebra Copyright Big Idea Learning, LLC

35 Name Date 6.7 Geometric Sequence (continued) 3 ACTIVITY: Writing a Story The King and the Beggar A king offered a beggar fabulou meal for one week. Intead, the beggar aked for a ingle grain of rice the firt day, grain the econd day, and double the amount each day after for one month. The king agreed. But, a the month progreed, he realized that he would loe hi entire kingdom. Work with a partner. Why doe the king think he will loe hi entire kingdom? Write your own tory about doubling or tripling a mall object many time. Draw picture for your tory. Include a table to organize the amount. Write your tory o that one of the character i urpried by the ize of the final number. What I Your Anwer?. IN YOUR OWN WORDS How are geometric equence ued to decribe pattern? Give an eample from real life. Copyright Big Idea Learning, LLC Big Idea Math Algebra 167

36 Name Date 6.7 Practice For ue after Leon 6.7 Find the common ratio of the geometric equence. 1. 5, 15, 5, 135,. 8, 11, 8, 7, 3. 0., 1.6, 1.8, 10., Write the net three term of the geometric equence. Then graph the equence ,, 3, 1, , 65, 15, 5, Tell whether the equence i arithmetic, geometric, or neither. 6. 6, 13, 0, 7, 7. 1,, 8, 8, 8. 1,,,, 3 9. In art cla, you are creating a deign that ue 1 gla bead in the firt row, 3 gla bead in the econd row, and 9 gla bead in the third row. a. Decribe the pattern of the deign. b. Write the net three term of the equence. c. I the equence arithmetic, geometric, or neither? Eplain. 168 Big Idea Math Algebra Copyright Big Idea Learning, LLC

37 Name Date Etenion 6.7 Practice For ue after Etenion 6.7 Write the firt i term of the equence. Then graph the equence. 1 a 1, a a + 6. a1 6, an an n n 1 a 5, a 3a. a1 0, an an n n 1 Write a recurive rule for the equence. 5., 31, 38, 5, 5, 6. 5, 30, 180, 1080, 680, 7. Write a recurive rule for the inect population over time. Week 1 3 Inect Population Copyright Big Idea Learning, LLC Big Idea Math Algebra 169

38 Name Date Etenion 6.7 Practice (continued) Write an eplicit equation for the recurive rule. 1 a 5, a a 9. a1 0, an an n n 1 Write a recurive rule for the eplicit equation. 10. a 5n 85 n ( ) a n n 1 Write a recurive rule for the equence. Then write the net 3 term of the equence. 1. 3, 8, 11, 19, 30, 13. 1,, 1, 1,, 1, 1,, Ue a pattern in the product of conecutive term to write a recurive rule for the equence. Then write the net term of the equence ,, 5, 0, 100, 15. 3,, 6, 1, 7, 170 Big Idea Math Algebra Copyright Big Idea Learning, LLC