14 DAY 1 CHAPTER FIVE Wht fscinting mthemtics is now on our gend? We will review the pst four chpters little bit ech dy becuse mthemtics builds. Ech concept is foundtion for nother ide. We will hve grph of the dy ech dy to reinforce wht we know bout grphing. The min focus of chpter five, however, is reviewing how to rewrite polynomils using the lws of exponents properly. In order to be successful, you hve to know nd understnd the lws of exponents nd how to use them properly. Wht is n exponent? An exponent is number tht tells how mny times to use nother number (or vrible) s fctor. And fctor implies to multiply. 5 x mens to use x s fctor five times, or ( ) b mens to use ( b) ( b) ( b) ( b) ( b) 5 x x x x x x s fctor three times, or 4 ( c ) mens to use c s fctor four times, or But, Tht is, 4 ( c) ( c)( c)( c)( c) 4 c mens to use c s fctor four times nd multiply by ONE fctor of, 4 c c c c c Recll tht in the expression 4 c : is clled the coefficient c is clled the bse 4 is clled the power or exponent Your techer will provide you with some prctice using exponents properly. If you cn imgine it, you cn chieve it. If you cn drem it, you cn become it. - Anonymous
15 Opportunities To Lern DAY 1 REVIEW BLOCK 1. ) clssify ABC b) with protrctor, find m ABC d) find m CBD c) clssify CBD. List t lest four fcts tht you know bout slope of line.. Wht words re represented with the cronym URESC? 4. Grph Of The Dy For the Grphs of the Dy : put them on the sme sheet of grph pper. Entitle the pge CHAPTER 5: GRAPHS OF THE DAY. Lbel ech grph with the dy number. Cll tody s DAY 1. Drw ONE pir of xes tht re 8 units in ech direction. Through the given points, drw nd lbel the lines with the given slope. Line ) through ( -, 5 ) with slope = Line b) through ( 4, 0 ) with slope = Line c) through ( -1, - 5 ) with slope = 0
16 5. Mke FLASH CARDS: EXPONENTS FRONT OF FLASH CARD BACK OF FLASH CARD 4 6 5 ( ) ( ) 9 ( ) ( ) 6 6 4 6 4 4 6 4 6 4 6 4 6 4 ( ) 5 5 5 5 5 5 5 5 5 10 4 4 8 4 4 6 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4 4 4 6. Prctice the EXPONENTS flsh crds few times s we hve been doing. Redo the missed ones s necessry nd lern from them. 7. Correct the test on Chpter 4 to turn in tomorrow. DAY Opportunities To Lern DAY REVIEW BLOCK 1. 1
17. Use the URESC method to solve the following. Show ech step clerly. The mesure of one ngle is 0 degrees less thn hlf the mesure of the other ngle. If the two ngles re complementry, find the mesure of ech ngle.. Solve for y in terms of x: x y = 4. Grph Of The Dy For the Grphs of the Dy : put this on the sme sheet of grph pper s you did DAY 1. Lbel this grph with the dy number. Cll tody s DAY. Drw ONE pir of xes tht re 8 units in ech direction. For ech pir of points: i. Plot the two points ii. Find the slope of the line tht contins these two points grphiclly. Show your work. iii. Using the slope formul, lgebriclly find the slope of the line. Show your work on your grph pper. ) ( - 1, 5 ) (, ) b) ( - 4, - 5 ) ( -, - 1 ) 5. Prctice the EXPONENTS flsh crds few times s we hve been doing. Redo the missed ones s necessry nd lern from them. 6. If there re ny problems tht you think you should dd to the flsh crds, do so t ANY time. 7. Copy the problem nd rewrite in simplest form. 7. 8. 9. 10. x x x x y y y y 4 4 4 4 4 4 11. 1. ( ) 1. 14. 7 8 z z z z z 15. 7 8 16. b b 17. b ( b ) 18. 4c 4c 6 6 6 6 19. 4c 4c 0. ( n ) 1. n n. n n 8. Generlize. Copy the problem nd rewrite in simplest form.. x x 4. x x 5. x x 6. x x c d c d e f 7. ( x ) 8. ( x ) 5
18 9 8. Copy the problem, expnd s necessry, then simplify. 4 4 5 9. ( x y )( x y) 0. ( x y )( xy ) 1. ( b )( b) 4. ( b )( b ). ( 6 c d)(6 c d) 4. ( 5 c d )(5 c d ) 5. 6c d 6c d 6. 5c d 5c d 7. ( x y ) 8. ( x y ) 4 5 9. ) Look t problem. b) Are you being sked to dd, subtrct, multiply or divide in this problem? c) Look t problem 5. d) Are you being sked to dd, subtrct, multiply or divide in this problem? e) Explin in couple of sentences how these two problems re different nd yet similr. Include HOW these problems re done differently lso. DAY TERMINOLOGY A TERM is number, vrible, or the PRODUCT of number nd vrible(s). 4 Ech of the following is single term: -6 x 4x y z 5(+b) Since ech of the bove hs just ONE term, ech is clled MONOMIAL. An expression with TWO terms is clled BINOMIAL. The following re binomils: 4 7 x xy c 45d An expression with THREE terms is clled TRINOMIAL. The following re trinomils: 4 5 4 x x 1 45 y y 16x y 40x y 5y SIMILAR TERMS re terms with the exct sme vrible(s) nd exct sme exponent(s). b BIG RULE, HUGE RULE: You cn ONLY dd or subtrct terms tht re similr terms! EX b b b b b b b b.1 4 ( 6 ) 10 [4 10 ] [ 6 ] 6 b ( 5 b) 6 b 5 b NOTE: These two terms cnnot be combined They don t hve the sme exponents!
19 When multiplying, multiply the coefficients, keep the sme bses nd dd the exponents EX x y x y x x y y 4 4. ( )(5 ) ( 5)( )( ) 4 1 ( 15)( x )( y ) 15xy 7 When rising power to power, keep the bse the sme nd multiply the exponents EX. ( y ) y 4 4 y 1 If minus sign ( ) is in front of prentheses, remove the prentheses nd tke the opposite of ech term EX x x x x x x x x.4 ( 5) ( 4 1) 5 4 1 [ x x ] [ x 4 x] [ 5 1] x x 5 4 A shortcut is often the quickest wy to some plce tht you weren t going. - Anonymous Opportunities To Lern DAY REVIEW BLOCK 1. 10 =? Deciml =? Percent. Solve nd show tht your solution does, in fct, check: 7 1. 14 =
140 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of y x 4 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. Go bck nd rered the definition of TERM. Stte how mny terms in ech of the following: ) x b) n n 5 c) 6 b c d 4 5 d e y y y f c d ) ) 7 ) ( ) 6. Using f in exercise five bove: ) Rewrite the ones tht re monomils b) Rewrite the ones tht re binomils c) Rewrite the ones tht re trinomils 7. Prctice the EXPONENTS flsh crds few times s we hve been doing. Redo the missed ones s necessry nd lern from them. 8. If there re ny problems tht you think you should dd to the flsh crds, do so t ANY time. 9. Copy nd simplify. Show your work netly. Use proper form. 4 4 9. y y y y 5 y y y 5y 1 4 4 10. w w 5w w 5 w w w 5w 1 11. (6 7) ( 5) 1. (7c 4) (c c 1) 1. ( xy y x y) ( xy y 4 x y) 14. ( b b ) ( b 4 b )
141 15. ( xy y x y) ( xy y 4 x y) 16. ( b b ) ( b 4 b ) 17. x x 18. y y 19. x x 0. y y 4 4 4 4 1. ( x ). ( y ). z z 4. 4 4 5 5 4 4 5. z ( z ) 6. ( ) 7. ( z ) 8. ( ) 5 5 4 4 5 5 4 4 4 5 4 5 6 9. ( x y )( xy ) 0. ( 4 xy )(x y ) 1. ( x x 5) ( x 4x 5). (x x 7) ( x 5x ). Hortio sid tht ( x 4) x 16. But Alger sid tht ( x 4) x 8x 16. To see who is correct, STOre 5 into X in your clcultor nd: ) Evlute ( x 4) x 16 8x 16 b) Evlute c) Evlute x d) Who is correct nd why? e) Copy nd complete: ( x 4) DAY 4 THE DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION AND SUBTRACTION Ex. 1 Rewrite using the distributive property (expnd nd simplify): (x 5) (x 5) x 5 6x 15 IN GENERAL: ( b c) b c ( b c) b c Ex. Expnd nd Simplify: x( x x 5) This is clled monomil X trinomil x( x x 5) [ x x ] [ x x] [ x 5] 1 11 x [ 6 x ] 10x x 6x 10x The severity of n itch is inversely proportionl to the rech. - Anonymous
14 Ex. Expnd nd Simplify: (5)( 8) This is clled multiplying binomils ( 5)( 8) ( 8) 5( 8) [ ] [ 8] [5 ] [5 8] 16 5 40 11 40 Alterntive solution: FOIL First Outside Inside Lst F O I L ( 5)( 8) [ ] [ 8] [5 ] [5 8] 16 5 40 11 40 Ex. 4 Expnd nd Simplify: (n 8) This is clled squring binomil (n 8) (n 8)(n 8) Now use FOIL! [n n] [n 8] [ 8 n] [ 8 8] 9n 4n 4n 64 9n 48n 64 Plese notice tht when you squre binomil, your nswer hs THREE TERMS!!! Ex. 5 Expnd nd Simplify: ( 4 ) 5 5 5 5 ( 4 x y ) ( 4 x y )( 4 x y )( 4 x y ) 5 xy This is clled cubing monomil 5 5 5 [ 4 4 4] [ x x x ] [ y y y ] 64xy 6 15 BIG QUESTION: Why didn t we use the distributive property in exmple 5? A friend is present you give yourself. - Robert Louis Stevenson
14 Opportunities To Lern DAY 4 REVIEW BLOCK 1. 1 7 8. Point D is the midpoint of CE. CD (x 5) cm DE (5x 7) cm Find CD, DE, CE.. Find the slope nd y-intercept of: x y =. 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of y b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. Wht is the complete nme of the property illustrted here: ( b c) b c ( b c) b c 6. Using the method shown in Exmple, expnd nd simplify: (y4)( y 1). Show ech step. 7. Wht words does the cronym FOIL represent? 8. Use FOIL to expnd nd simplify: ( x8)( x ). 9. Using the method shown in Exmple 4, expnd nd simplify: step. 10. Using the method shown in Exmple 5, expnd nd simplify: ech step. (4n ). Show ech ( 5 xy) 4. Show 11. Prctice the EXPONENTS flsh crds few times s we hve been doing. Redo the missed ones s necessry nd lern from them. 1. If there re ny problems tht you think you should dd to the flsh crds, do so t ANY time.
144 1 6. Copy the problem. Expnd nd simplify. Show ny necessry steps using the proper form. 1. x y(4x xy y ) 14. x y( x xy y ) 15. ( n 6)( n 8) 16. ( n 5)( n 4) 17. ( y 7) 18. ( y 5) 4 5 19. ( b) 0. ( b ) 1. (n )( n 5). (n 5)( n 4). b ( b b b ) 4. 4 b ( 4 b b b ) 5. (4 ) 6. ( 5 x y x y) 7. C.Y.O.P. ) Mke up your own problem of squring binomil. b) Expnd nd simplify. c) Be prepred to shre this problem tomorrow in clss. 8. C.Y.O.P. ) Mke up your own problem of squring monomil. b) Expnd nd simplify. c) Be prepred to shre this problem tomorrow in clss. DAY 5 Opportunities To Lern DAY 5 REVIEW BLOCK 1. 7 7. How mny sides does decgon hve?
145. ) Copy this problem onto your pper b) Point out where the error(s) occur c) Redo the problem correctly 6 4 1 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of x b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. Prctice the EXPONENTS flsh crds few times s we hve been doing. Redo the missed ones s necessry nd lern from them. 6. If there re ny problems tht you think you should dd to the flsh crds, do so t ANY time. 7 6. Copy the problem nd perform the indicted opertions. Write your nswer in simplest form. Show ll necessry steps netly nd using the proper form. 7. x x 8. x x 9. x x 10. x x 4 4 4 4 11. ( x ) 1. ( x ) 1. y y 14. y y 4 4 4 15. y y 16. y y 17. ( y ) 18. ( y ) 4 4 4 4 4 19. ( b )( b ) 0. ( 4 b )( b ) 1. ( x y z). ( xy z ) 4 5. xy ( x x y xy y ) 4. x y( x x y xy y ) 5. ( x 4)( x 5) 6. ( x 6)( x 7) 7. ( y7) 8. ( y8)
146 9. ( 5 8) ( 6 1) 0. ( 7 5) ( 4) 1. ( 5 8) ( 6 1). ( 7 5) ( 4). ( b c) 4. ( bc ) 5 4 5. (n7) 6. (n5) DAY 6 MORE RULES WITH EXPONENTS?! OH NO!!! Oh, yes. Your techer will supply you with some exmples. Opportunities To Lern DAY 6 REVIEW BLOCK 1. 5. A type of thinking when you observe something specific hppen over nd over gin, nd then you mke generl conclusion bout it, is clled.. Copy the figure onto your pper netly using strightedge: j k m 58 Find the mesure of ech numbered ngle. 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of xy b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir).
147 5. Write few sentences to explin how you would simplify ech of these two frctions. Then do them: x ) b) x x x 6 6 6. Mke dditionl flsh crds using the lws of exponents just reviewed tody: Front of flsh crd 6 6 Bck of flsh crd 1 1 6 6 5 8 8 4 4 4 4 4 1 8 8 4 8 8 6 5 5 1 7 7 1 5 7. Prctice the new EXPONENTS flsh crds couple of times until you feel tht you know the rules for division pretty well.
148 8. Prctice the old EXPONENTS flsh crds couple of times until you feel tht you know them pretty well. 9 4. Copy the problem nd simplify. No negtive exponents in your nswers. 4 b c d 9. 10. 11. 1. 4 b c d e f g h 1. 14. 15. 16. e f g h 6 8 8 6 i j k m 17. 18. 19. 0. i j k m 1 1 4 1 4 1 5 4 16 0b 16c 6d 1... 4. 4b 6c 7d 8 10 DAY 7 DIVIDING A POLYNOMIAL BY A MONOMIAL EX. 1 Divide the polynomil by the monomil nd simplify: 10 8 5 10 8 5 4x 0x 10x 8x 4x 0x 10x 8x 4x 4x 4x 4x 4x 5 1 x 5 x x x 8 6 5 x 5x x x 10 8 5
149 EX. Divide the polynomil by the monomil nd simplify: x y 10x y x y xy x y 10x y x y xy xy xy xy xy xy 5 8 4 6 5 8 4 6 4 6 4 x y x y xy 10 1 ***Don t forget this 1! EX. Divide the polynomil by the monomil nd simplify: 1 9 8 6 4 1 9 8 6 4 18 b 1 b 6 b 18 b 1 b 6 b 6 b 6 b 6 b 6 b 8 6 4 b b 1 4 4 4 4 ***Don t forget this 1! One tody is worth two tomorrows. - Benjmin Frnklin Opportunities To Lern DAY 7 REVIEW BLOCK 1. Simplify: 8 1. If the perimeter of this tringle is in., find the length of ech side.. COPY nd complete: A tringle with t lest two sides equl in length is clled.
150 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of y x b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. Prctice the new EXPONENTS flsh crds couple of times until you feel tht you know the rules for division pretty well. 6. Prctice the old EXPONENTS flsh crds couple of times until you feel tht you know them pretty well. 7 18. Divide the following polynomils by the monomils indicted nd simplify. Show ll steps using the proper form: 0y 4y 6y y 18z 6z z z 7. 8. y z 1 10 6 4 1 9 6 8x 4x x 9y 5y y 9. 10. x y 5 4 6 5 6 11 1 7 11. 1. b xy 5 4 4 5 4 b b b x y x y x y 5 b 5 b 10 b 54 p q 6 p q 1 p q 1. 14. 4 5 b 6p q 15. 10 1 8 6 1 10 8 4 4 8 4 7 6x y 10x y 4x y 1 b 1 b b 16. 5 5 4x y b 5 8 7 6 5 4x 18x x 6x 4 18 6 17. 18. 6 7 5 4 7 5 4 19. C.Y.O.P. Crete problem similr to one like #7 through 18 bove. Simplify the problem nd be prepred to shre this in clss tomorrow. There re times when silence hs the loudest voice. - Leroy Brownlow
151 DAY 8 DIVIDING A POLYNOMIAL BY A BINOMIAL EX. 1 Divide nd check: x x5 x 1 x 1 x x 5 Think : Divide the first term by the first term : x x x 1 x x 5 Multiply using the distributive property ( ) x x Subtrct by tking the opposite of ech term nd then dding x x x x x x 1 5 x x Simplify nd then 4x 5 " bring down" the next term x 4 x x x 1 5 4x : 4 x x x Agin divide the first term by the first term 4x 5 ( 4x 4) Next tke the opposite nd dd x 4 x x x 1 5 x x 4x 5 4x 4 1 This is the reminder Therefore: x x 5 1 x 4 x1 x1
15 To check division problem: multiply the quotient by the divisor nd dd the reminder. The result should be the dividend (tht is, wht you divided into ). Check: ( x 1)( x 4) ( 1) x 4x x 4 1 x x 5 it checks!! EX. Divide nd check. Show ech step using the proper form: x x x 4 4 x EX. Divide nd check. Show ech step using the proper form: y 9 y 4 Opportunities To Lern DAY 8 REVIEW BLOCK 1. Copy the following nd fill in the blnks to complete the pttern: 1,, 4, 8, 16,, ) b). Evlute this expression using clcultor nd round your finl nswer to the nerest thousndth. 4. Grph Of The Dy.1 b 5 b b b ) On its own pir of xes, netly drw the grph of x 4y 0 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 4 5. Prctice the new EXPONENTS flsh crds couple of times until you feel tht you know the rules for division pretty well. 6. Prctice the old EXPONENTS flsh crds couple of times until you feel tht you know them pretty well.
15 7 14. Divide ech polynomil by the binomil. Show ech step netly using the proper form. Show tht your nswer does, in fct, check. n 6n 7 y 9y 10 7. 8. n1 y1 5 b 5b 9. 10. 1 b1 x 4x x 6 y 5y y 4 11. 1. x y z 16 t 9 1. 14. z t 15 18. Copy the problem nd simplify using the proper form: 15. b b 16. b ( b ) 17. ( b ) 5 18. ( 4 x y )( xy )
154 DAY 9 NEGATIVE EXPONENTS AND ZERO AS AN EXPONENT Investigte, investigte, investigte, nd DISCOVER! Copy the following tble onto your pper. Use your grphing clcultor to evlute. You re to write the nswers in two forms: deciml nd frction (using the MATH Frc key). Number 1 1 1 4 1 5 1 6 Evluted s DECIMAL Evluted s FRACTION Conjecture. Copy onto your pper nd rewrite ech s frction: 7 ; 8 1 1 Are you redy to generlize? Discuss with your prtner: s n eqution. 1 x? Write your nswer Copy the following tble onto your pper. Use your grphing clcultor to evlute. You re to write the nswers in just one form: frction (using the MATH Frc key). Number 4 1 1 5 9 1 1 1 4 1 Evluted s FRACTION
155 Conjecture. Copy onto your pper nd rewrite ech s frction. Verify with clcultor s necessry. Number 6 7 1 5 1 1 4 9 1 8 1 5 1 1 Evluted s FRACTION Are you redy to generlize? Discuss with your prtner: nswer s n eqution. n d 1? Write your Now summrize in words nd symbols. Rising number or expression to the negtive one power mens to tke its reciprocl, or n d 1 d n nd 1 1 x, n 0, d 0, x 0 x INVESTIGATE one more time! Copy the following tble onto your pper. Use your grphing clcultor to simplify. Expression 0 4 ( 7) 7 0 0 0 41 16 Simplified
156 Conjecture. Copy onto your pper nd simplify. Verify with clcultor s necessry. Expression 0 8 ( ) 0 6 11 0 95.7 0 Simplified Are you redy to generlize? Discuss with your prtner: 0 B? Before we jump to wrong conclusion, we need to investigte one specil cse: 0 0 Enter 0 0 into your clcultor nd discuss the result with your prtner. Now summrize in words nd symbols. Opportunities To Lern DAY 9 REVIEW BLOCK Wht ppers to be the end my relly be new beginning. - Anonymous 1. ) Nme the hypotenuse b) Nme the legs. Lines nd b re prllel. Lines nd c re perpendiculr. If the slope of line is, then find the slope for: ) line b b) line c. First solve the eqution for b. Then substitute to find the vlue for b. 1 A b h ; A 161 sq. ft. h 7 ft.
157 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of y6 0 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. Mureen sid tht ny number rised to the zero power is equl to one. Justin disgreed with Mureen. Who is correct? Explin why. 6. Copy nd complete: Rising number or expression to the negtive one power is equivlent to. 7 6. Copy the problem onto your pper nd simplify. Assume no vribles hve vlue of zero. No clcultors here. 7. 6 8. 1 9. 7 10. 11 0 0 1 1 1 1 1 11. 1. 1. ( 17) 14. ( 105) 5 1 1 0 0 0 41 15 c p 15. 16. 17. 18. 9 17 d q 1 1 1 1 x b 5c 19. 0. 1.. y 4 4 1 1 1 1 x y 1. 4. 5. 6. 4 4 z bc 5 7. Copy onto your pper nd simplify. Show ll necessry steps using the proper form. 7. ( 5) ( 5) 8. (x 5)( x ) 9. ( y 8) 0. ( c d )( cd) ( c d)( 5 c d ) 1. 1. ( 1) 1 1 0
158 DAY 10 Investigte, investigte, investigte, nd DISCOVER AGAIN!! Copy the following tble onto your pper. Use your grphing clcultor to evlute. You re to write the nswers in one form: exct frction (using the MATH Frc key). Number 4 5 Evluted s FRACTION Conjecture. Copy onto your pper nd rewrite ech s frction: 6 ; 8 Are you redy to generlize? Discuss with your prtner: s n eqution. x? Write your nswer Copy the following tble onto your pper. Use your grphing clcultor to evlute. You re to write the nswers in one form: exct frction (using the MATH Frc key). Number 4 Evluted s FRACTION Conjecture. Copy onto your pper nd rewrite ech s frction: 5
159 Are you redy to generlize? Discuss with your prtner: s n eqution. x? Write your nswer Copy the following tble onto your pper. Use your grphing clcultor to evlute. You re to write the nswers in one form: frction (using the MATH Frc key). Number 5 6 8 7 1 6 Evluted s FRACTION Conjecture. Copy onto your pper nd rewrite ech s frction: 7 ; 4 5 Are you redy to generlize? Discuss with your prtner: nswer s n eqution. n d? Write your Discuss with your prtner if you think similr reltionship will hold true for frction rised to the negtive three power. Investigte nd then mke conjecture. Now summrize in words nd symbols. If frction is rised to negtive integer power, tke the reciprocl of the frction nd then rise tht nswer to the power without the negtive sign. Or, in symbols, k k n d for n 0, d 0 d n
160 EX. 1 Rewrite without negtive exponents in simplest form: x y x y y x y y x x y x y 6 9x 11 EX. Rewrite without negtive exponents in simplest form: 4 5 bc 5 4 bc 5 5 5 bc bc bc 4 4 4 11 1 555 b c 4 4 4 7b c 7b c 7b c or or 1 1 1 8 8 8 15 15 15 Either nswer is cceptble. bc 4 5 Opportunities To Lern DAY 10 REVIEW BLOCK 1. Copy nd simplify showing ech step: 5 4 x. If 4x y, then? y
161. SR = (6x 7) in QR = in. If the perimeter of PQRS is 5 in.: ) Find the vlue for x b) Find the dimensions of the rectngle. 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of x 0 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5 6. Copy the sttement nd complete: 5. A negtive one exponent mens to. 6. A negtive two exponent first mens to nd then rise tht result to the power. 7 6. Copy the problem onto your pper nd rewrite the expression without negtive exponents. Simplify s necessry. 1 1 7 9 8 7. 8. 9. 10. 5 9 4 5 11 1 1 11. 1. 1. 14. 8 7 4 4 4 5 x c d f 15. 16. 17. 18. y b e gh
16 4 5 4 5 b 11x 5c d 19. 0. 1.. 1c 14yz e 4b c 4 0 4 0. 7x y z 4. 8 b c 5. 6. 5 x x y y Wht we ll tend to complin bout most in other people re those things we don t like bout ourselves. - Willim Whrton DAY 11 Exponents when do we need them? Answer: Scientific nottion. 1 For numbers between 1000 nd, or 0.001, regulr or stndrd nottion is fine. 1000 However, for extremely lrge numbers nd extremely smll numbers, we need different nottion scientific nottion. One exmple of n extremely lrge number would be the number of miles from the erth to the sun:,700,000,000 miles, which is red three billion, seven hundred million miles. In order to write numbers this lrge (nd lrger) nd to be ble to perform mthemticl clcultions on these numbers, it would be dvntgeous to hve better nottion: 9,700,000,000.7 10 The number on the left is in stndrd nottion, the number on the right is in scientific nottion. One exmple of n extremely smll number would be n Angstrom, which is used to 1 mesure the wve length of light. An Angstrom is defined to be 100,000,000 of centimeter. Using scientific nottion: 1 100,000,000 1 10 8 The number on the left is in stndrd nottion, the number on the right is in scientific nottion. As you cn see, we use positive powers of ten to represent lrge numbers nd negtive powers of ten to represent tiny numbers.
16 Before we go ny further, let s discuss some powers of ten: 5 5 1 1 1 1 1 1 1 10 mens or 0.00001 10 10 10 10 10 10 100,000 Copy nd complete the following tble: Power of 10 Mening Whole number Frction Deciml 10 10 1 10 0 10 10 10 10 1 All right now, so wht exctly IS scientific nottion? Scientific nottion is wy of representing numbers s the product of number between one nd 10, nd power of ten. Tht is, scientific nottion is in the form: N 10 p where 1 N 10 nd p is n integer. NOTE: The number of digits in the number, N, is clled the number of significnt digits. Our gol is for you to be ble to tke number tht is in stndrd nottion nd to rewrite it in scientific nottion nd the reverse of tht. EX. 1 Rewrite the following in scientific nottion with the suggested number of significnt digits: 45,00,000 ) three significnt digits b) two significnt digits c) one significnt digit ) three significnt digits: 45,00,000 b) two significnt digits: 45,00,000 c) one significnt digit: 45,00,000 7 4.5 10 7 4.5 10 7 5 10
164 EX. Rewrite the following in scientific nottion with the suggested number of significnt digits: 0.000000051 ) three significnt digits b) two significnt digits c) one significnt digit ) three significnt digits: 0.000000051 b) two significnt digits: 0.000000051 c) one significnt digit: 0.000000051.5 10 8.4 10 8 10 8 EX. Rewrite the following in stndrd form: ) 4.710 b).004 10 8 5 8 ) 4.7 10 mens to multiply by 10,000,000 which will mke the number lrger by moving the deciml point to the right 8 plces, the sme number s the number of zeros. 8 4.710 47,000,000 b).004 10 by moving the deciml point to the left 5 plces. 5.00410 0.0000004 5 mens to multiply by 0.00001 which will mke the number smller Opportunities To Lern DAY 11 REVIEW BLOCK x x 1. Solve nd show tht your solution does check: 9 15. Copy the problem nd simplify (mentlly if possible): ) b) 4 4. SR = (6x 7) cm RQ = cm If the re of rectngle SPQR is 51 sq cm,: ) Find the vlue for x b) Find the dimensions of the rectngle
165 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of 4x y 0 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 5. A number tht is written in scientific nottion is in the form N 10 p ) Wht must be true bout the vlues used for N? b) Wht kind of numbers must be used for p? 6. ) For numbers written in scientific nottion, positive exponent mens to move the deciml point in which direction? b) For numbers written in scientific nottion, negtive exponent mens to move the deciml point in which direction? 7 18. Rewrite the number in scientific nottion using the number of significnt digits requested. 7. 48,000,000 using significnt digits 8. 9,600,000 using significnt digits 9. 0.000061 using significnt digits 10. 0.0005 using significnt digits 11. 1,760,000,000 ) significnt digits b) significnt digits c) 4 significnt digits 1. 1,400,000,000 ) significnt digits b) significnt digits c) 4 significnt digits 1. 0.00000000041 ) significnt digits b) 1 significnt digit c) significnt digits 14. 0.00000000001 ) significnt digits b) 1 significnt digit c) significnt digits 15. 80,000,000,000,000 ) significnt digits b) 1 significnt digit 16. 7,000,000,000,000 ) significnt digits b) 1 significnt digit 17. 0.00000005 ) significnt digits b) significnt digits c) 1 significnt digit 18. 0.0000000408 ) significnt digits b) significnt digits c) 1 significnt digit
166 19 6. ) Copy the problem nd rewrite in stndrd form b) Stte the number of significnt digits 19. 4.710 0..810 1. 4.10..5610 5 6 7 8. 6.010 4. 7.9110 5. 10 6..010 1 10 5 7 Diplomcy is the rt of letting someone else hve your wy. - Anonymous DAY 1 Using Scientific Nottion on the TI-8 On your clcultor, press the <MODE> key. Hve your clcultor in NORMAL nd FLOAT mode. Clcultor nottion EX. 1 To enter 7.61 10 on the TI-8, type:.61 < nd > <comm> (EE) <7> <ENTER> The clcultor should show:.61 E 7 6,100,000 This is the clcultor s version of This is stndrd nottion. scientific nottion. EX. To enter 5. 10 5 on the TI-8, type: 5. < nd > <comm> (EE) < -5> <ENTER> The clcultor should show: 5. E -5 5. E -5 This is the clcultor s version of The clcultor will not put this in Scientific nottion. stndrd nottion unless the negtive exponent is -, -, or -1.
167 EX. <MODE> SCI FLOAT Enter into clcultor: 56000 The clcultor should show: Enter into clcultor: 0.0000471 The clcultor should show: Press <ENTER> 5.6 E 4 which mens Press <ENTER> 4.71 E -5 which mens 4 5.6 10 4.71 10 5 EX. 4 <MODE> NORMAL FLOAT Simplify:.610 4 1.7510 4.9710 8 ) Answer in scientific nottion with three significnt digits b) Answer in stndrd nottion with three significnt digits ) 14.99 10 b) 99,000,000,000,000 NOTE: In order to write n nswer in stndrd nottion with so mny significnt digits, you must FIRST write the nswer in scientific nottion with tht number of significnt digits. EX. 5 Simplify: 5 5.17 10 ) Answer in scientific nottion with three significnt digits b) Answer in stndrd nottion with three significnt digits ) 1 7.19 10 b) 7,190,000,000,000 EX. 6 The distnce from New York City to Los Angeles is pproximtely 000 miles. How mny inches is tht? ) Exct nswer b) In scientific nottion with three significnt digits c) In stndrd nottion with three significnt digits ) 190,080,000 inches 8 b) 1.90 10 inches (pproximtely) c) 190,000,000 inches (pproximtely)
168 EX. 7 Put ech of the following in order from lest to gretest: ) b) 6 5 6.710, 4.510,.99 10 5.10, 6.10, 7.04 10 7 8 8 Answers: ) b) 5 6 6 4.510,.9910,.7 10 6.10, 7.0410, 5. 10 8 8 7 Opportunities To Lern DAY 1 REVIEW BLOCK 1. Copy nd complete: 0.75 =? Frction =? Percent. Copy nd simplify: 1 1 ) b) 1 1. The rtio of the mesures of two supplementry ngles is 4:11. Find the mesure of ech. Show ech step using the URESC method. 4. Grph Of The Dy ) On its own pir of xes, netly drw the grph of xy 8 b) Stte the slope c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir).
169 5. The following nswers ppered on the screen of Mx s TI-8 clcultor. Copy the clcultor nswer nd write wht tht number is: i) s number in scientific nottion ii) s number in stndrd nottion ) 5.4 E 7 b).041 E -6 c) -4.005 E 6 d) -.0 E -5 6. The clcultor displys one E with its nswers on the screen but hs two E s (EE) in gold on the clcultor itself, bove the comm key. Do you find tht confusing? Also bove the division symbol there is lower cse e tht mens something ltogether different. Is this confusing to you? 7 16. Plce your clcultor into MODE SCI FLOAT. Perform the clcultions. ) Write your nswer in scientific nottion using significnt digits. b) Write your nswer in stndrd nottion using significnt digits. 11 6 1 9 7. 4.91 10.07 10 8..5 10 1.7 10 9..7410 10. 9.110 16 6 17 1 10 410 5 810 6 14 6 7 910 10 10 710 7 9 6 6 4 4.6110 7.0510 19 6 6 17 6.110 7.4510.1710.510 11. 1. 1. 8.71 10 14..65 10 15. 16. 17. The distnce between two cities is 500 miles. How mny inches is tht: ) exctly b) in scientific nottion with significnt digits c) in stndrd nottion with significnt digits 18. The distnce between two cities is 4500 miles. How mny inches is tht: ) exctly b) in scientific nottion with significnt digits c) in stndrd nottion with significnt digits
170 19. If your mth techer is exctly 75 yers old, how mny seconds hs your mth techer lived: (use 1 yer = 65 dys) ) exctly b) in scientific nottion with significnt digits c) in stndrd nottion with significnt digits 0. If your English techer is exctly 80 yers old, how mny seconds hs your English techer lived: (use 1 yer = 65 dys) ) exctly b) in scientific nottion with significnt digits c) in stndrd nottion with significnt digits 1. Put in order from lest to gretest: 1.. 8 7 7.810, 4.0110,.9 10 4 4 5 10, 710, 4 10 4. Put in order from lrgest to smllest:. 4. 4.10, 4.110, 4. 10 9 8 9 9.710, 5.10, 4.0 10 5 4 5 5 0. Quick Review. Simplify (positive exponents only): 8 8 8 x 5. x x 6. x 7. x x 8 x x 9 8. 9. x x 0. Divide : 8 x x 5
171 CHAPTER 5 REVIEW 1 6. Grph Of The Dy ) On its own pir of xes, netly drw the grph of the eqution. b) Stte the slope. c) Stte the coordintes of the y-intercept (s n ordered pir). d) Stte the coordintes of the x-intercept (s n ordered pir). 1. y. x 4. x y 0 4. x y 0 5. x 4y 8 6. x 5y 5 7 8. How mny terms in ech of the following: 7. ) 5 b) x yz c) 4c d cd d 1 4 8. ) y y 8 b) 4 9 z c) (x 4) 9. A polynomil with one term is clled (n). 10. A polynomil with two terms is clled (n). 11 56. Copy the problem nd simplify. (No zero or negtive exponents in nswers). 11. z z 1. x x 1. z z 14. x x 4 4 4 4 4 5 4 5 15. y 16. z 17. y y 18. z z 19. y y 0. z z 1. 6 6. 4x 4x 4 5 5 5 5 5 4 5 x x c c d b b 4 5 b xy y y y y n n n n. 6 6 4. 4 4 5. 4 6. 7. 8. 4 9. 5 4 1 0. 4 6 5 6 1. 4x xy y 5x xy 6y. 7 7b b 8b b 4 4 4 4. ( ) 4. c ( c ) 5. 6. c 7. 8. c c 4 4 5 4 5 4 9. 4 40. 4 x y x x y y b b b
17 z z x 41. 7 5 4. 8 10 4. 6 4 5 y x y z b c 44. 4 45. 46. x y y 47. 48. 49. x y y 10 1 4 1 7 8 x 6 8 50. 51. 5. x 4 10 1 9 16 1 4 15y 18y 1y 40x 16x x 5. 54. 4 y 8x 8 6 10 4 50 5 5 55. 56. 5 4 4xy 5x y 8 4 7 5 7 6 4 x y x y x y x y x y x y 57 58. Divide nd check: y y 5 x 4x 6 57. 58. y1 x 59 76. Simplify. Rewrite with no zero or negtive exponents. 0 0 1 1 59. 8 60. 7 61. 8 6. 7 1 1 1 1 7 8 6. 64. 65. 66. 5 9 1 1 1 9 5 67. 68. 69. 70. 4 8 4 7 4 5 c d b 71. 7. 7. 74. 4 e c 4 1 18x y 75. 76. 15bc 11z
17 77 8. Write in scientific nottion using the number of significnt digits requested: 77. 40,000,000 ) significnt digits b) significnt digits c) 1 significnt digit 78. 580,000,000,000 ) significnt digits b) significnt digits c) 1 significnt digit 79. 0.00000000007061 ) significnt digits b) significnt digits c) 1 significnt digit 80. 0.000000005807 ) significnt digits b) significnt digits c) 1 significnt digit 81. 17,480,000,000,000 ) significnt digits b) significnt digits c) 1 significnt digit 8. 04,900,000 ) significnt digits b) significnt digits c) 1 significnt digit 8 88. Use clcultor to compute your nswer in scientific nottion to three significnt digits. 15 4 1 9 8. 4.7610 8.0910 84..1110 7.1610 17 6.8710.610 7 18 11 5 4.610.10.710 4.10 85. 86. 87..710 88. 4.910 5 16 89. The distnce between two cities is 8000 miles. How mny inches is tht? ) scientific nottion to two significnt digits b) stndrd nottion to two significnt digits 90. The distnce between two cities is 6500 miles. How mny inches is tht? ) scientific nottion to two significnt digits b) stndrd nottion to two significnt digits 91. Your socil studies techer is exctly 6 yers old. How mny seconds is tht? ) scientific nottion to two significnt digits b) stndrd nottion to two significnt digits 9. Your guidnce counselor is exctly 100 yers old. How mny seconds is tht? ) scientific nottion to two significnt digits b) stndrd nottion to two significnt digits 9 94. Write in stndrd form: 7 7 6 9. ).0610 b) 4.0110 c).910 d) 5.E 04 6 5 4 94. ) 7.1410 b).610 c) 9.0710 d) 7.E 0 95 96. Put in order from lest to gretest: 6 7 6 95. 7.610, 4.9510, 4. 10 96. 10 11 10 5.410,.10, 4.99 10