Unit 4 PacketMPLG
onalExponents(Chapter7)Name:Teacher:Period:1
Unit 4 Radical Expressions and Rational Exponents (chapter 7)Learning Targets:Properties ofExponentsSimplifying RadicalExpressionsMultiplying andDividingMajor OperationsRational ExponentsSolving RadicalEquationsGraphing Radicals1. I can use properties of exponents to simplify expressions.2. I can simplify radical algebraic expressions.3. I can multiply radical expressions.4. I can divide radical expressions (and rationalize a denominator).5. I can add and subtract radical expressions.6. I can multiply and rationalize binomial radical expressions.7. I can convert from rational exponents to radical expressions (and vice versa).8. I can simplify numbers with rational exponents.9. I can solve equations with roots.10. I can solve equations with rational exponents.11. I can graph radical expressions & identify domain and range of radical n17- ‐027- ‐13,47- ‐25,67- ‐37,87- ‐49,107- ‐5117- ‐82
dpractice,Iwillbeableto use properties of exponents to simplify expressions.(LT1)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- )A)( 3) 52 35 B) 3 3 3 56 C) 4 5 2 14 Example2:Simplify 2 3 3
sinyoursolution. 3 r 2 B) 4 c A)w5 w 8 w616m5 n 4C)2n 6(xD)43y 3 )x3 y ponentsinyoursolution. 52 2w 3 B) 4 m 2A)( 4x )( 2x )(12m n )C)2 68m4 n725 2(3x )D)y32 x 4 y 7FINALCHECK:(calcallowed)LT 1. I can use properties of exponents to simplify veexponentsinyoursolution.(x y )4a.( 5x )(2x y )( 6x y )6 4 34b.( 3x 5 y) 2c. 3x0 y244
PracticeAssignment(LT1) LT1. I can use properties of exponents to simplify expressions.oBOOK7.0page368LT 1 MORE PRACTICE #1 (Yay!!!!) 26)xy 5 7)(xy)- ‐53)(- ‐4x)- ‐3 8)2x1)92)4x 3 4 2 9)(2x)- ‐45)10 2 10)2 21)1814) 1497)4) 73)164 x36)xy515 5x y 3 28)2x49)116x42)10)4x35)110013365
LT 1 More Practice xponents&somedon’t!a)5x- ‐1d)- ‐2x3g)5y3x- ‐2i)(5b3)- ‐21)2x- ‐5b)2- ‐52)2- ‐3c)(- ‐2)33)- ‐2x44)(- ‐2)4 e)(- ‐2)- ‐35)(- ‐2)- ‐4 f)5x2y- ‐3 6)7a5b- ‐10 7)- ‐10a2b- ‐3c- ‐4h)52ab- ‐38)(a5b2)- ‐39)(4x5)- ‐2j)(- ‐2a2b4)310)(- ‐5x4)- ‐3l)(7a)2b- ‐3m)4x- ‐2yz- ‐1n)k)(5x)- ‐2y38x 6y 10z 35 24520x y zLT 1 MorePractice#311)(- ‐2)2(- ‐2)312)[- ‐32]313)(32x2y)214)5 515)(2- ‐3)216)m7 5 18) 4 19) 3x2y0z 4 5 317)83 858931m46
5x 4 y3 3x 3y520) 8x 56y421)23)2x 6y46x 3 4x 2 y312y522)x 7 y 3 z 2 1 4xy z 5x 3 yz15y 10z0 2 x 9 y 2 z 4 a 7 b 3 c 24) 0 10 2 4 3 5a bc x y z 7
lessonandpractice,Iwillbeableto simplify radical algebraic expressions.(LT2)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- anumberorexpression(i.e.16 42).a.4!49b.10!xc.6 8!144x ySince52 25,5isasquarerootof25.Since54 ,5isarootof.Since53 ,5isarootof.Since55 lfourthroot(s)of- ‐16?.Whataretherealcuberoot(s)of- rootsof- ‐1000and!27B)Thefourthrootsof1,- ‐0.0001,and16!6258
otoftheradicand.Example2:Findeachreal- ‐numberroot.A)3 8B) 100C)4 tivenumbera,!n an ?!A)4x 6B) 3 a 3b6C)4 x 4 y 8D)4x 2 y 4E) 3 27c6F)4 x 8 y12G)3 40x 8 y12H) 4 112ac 6I)4 tonwillholdthree- ulaw ces.Cartonscanonlybeorderedinwhole- inerthegrowershouldorder?FINALCHECK:I can simplify radical algebraic expressions. ennecessary.a.144a6b20b.3 125x 12 y 6c.464x18 y129
LT 2 PracticeAssignment I can simplify radical algebraic expressions.(LT2).o Worksheet(Practice7.1)(below)Practice7- ‐1RootsandRadicalExpressionsFindeachreal- ‐numberroot.1.5.41442. 253.0.00816.37.273 0.014. 9.21610. 34311. r.13.40014. chnumber.17. on.Useabsolutevaluesymbolswhenneeded.21.25.581x 422.121y10243x5 y1526.3 ( x 9)323.27.38g 624.3125x925( x 2)428.364 x9343Findthetworeal- ‐numbersolutionsofeachequation.29.x2 430.x4 8131.x2 0.1632.x2 164933.AcubehasvolumeV tcanbefoundusingtheformulav2 tyoftheobjectaftera10- bjectfalls20feetratherthan10feet?10
LT2MorePractice#1:7.1BookPage37211
uebarswhenneeded.1)45 2) 125 3)20 5)3 27 4)5 64 56)3 81 7) 4 16 8)4 32 539)16x16 10)8x 9 ,wemust“ ”.11)x 5 12)3x 8 3 313)9x 20 14)3 24x13 y6 15)4 11 3 8a b c 16)2xy 32x 6y2z 9 12
n:Afterthislessonandpractice,Iwillbeableto multiply radical expressions.(LT3) divide radical expressions (and rationalize a denominator).(LT4)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- mplifiedexpression).A)5! 50xB)38! rty1:MultiplyingRadicalExpressions–If!n aand!n b arerealnumbers,then!n a n b ablesarepositive.A)! 2 8B)!3 5 3 25C)3 25xy 8 3 5x 4 y variablesarepositive.A)3 27B)!3 3 3 9C)3 54x 2 y 3 3 5x 3 y 4!13
adicalExpressions–If!n aand!n b arerealnumbersand!b 0 ,thennan! b lesarepositive.3 8133192x Assumeallvariablesarepositive.4243162x 533x 21024x 15A)B)44x! youmightobtainasolutionin2theformx 3 sumeallvariablesarepositive.3A)5!x3B)5xy!2C)3! 3x14
.Assumeallvariablesarepositive.A)2x 310xy3B)34! 6x3C)34525x2FINALCHECK:LT3- ‐4I can multiply radical expressions. (LT3)I can divide radical expressions (and rationalize a denominator) rwork.a.c.490a5bb.d.3 35a5 14a269a539a2PracticeAssignmentLT3,4 Icanmultiplyradicalexpressions.(LT3)o BOOK7.2page377- ‐378#2- ‐8even,18- ‐22even Icandivide radical expressions (and rationalize a denominator)(LT4)o BOOK7.2page377- ‐378#24- ‐34evenPracticeboth:BOOK7.2page377#38- ‐54even15
LT3,4BookPage37716
LT3,4MorePractice#1:Worksheet7.2Practice7- 4 64.4 2 x 3 8 x32.9 x 2 9 y 53.50 x 2 z 5 3 15 y3 z5.xy 4 xy6.9 2 3 ssumethatallvariablesarepositive.13.16.34 2514.81 3615. 3 3 917.3x 6 x318.Simplify.Assumethatallvariablesarepositive.3 2732 xy 2 3 4 x 2 y 736x320.3 125y 2 z 421. 18k 619.22.3 16a1223.x 2 y10 z24.4 256s 7t1225.3216x 4 y326.75r 327.4 625u .328.31.4x 26x29. 3x3x(2 x) 2(5 y ) 432.318 y 23 12 y30.33.4243k 33k 7162a6a 3434.ThevolumeofasphereofradiusrisV π r 3 ofaspherewithvolume100in3.17
LT3,4MorePractice#2:Simplify.(Multiply)2)23 5 4 73)74) 2 11 7 35)2 4 3 5 4 36)3 2 58)5 3 9 6 3 39)11)2 3 51)2 3 5 7()()5 10 2()()27)4 5( )33210)(8x 7 y)()6x 5 y 3 )2 6 117)17 1219)20)3318)8 30 2 515)3 18643 353223251021)4822)5m410m323)3 4 2a246a318
fterthislessonandpractice,Iwillbeableto addandsubtractradicalexpressions.(LT5) LT6)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- me.LIKERADICALSORNOT?!A)!6 3 11 ,2 3 11B)!6 3 11 ,2 11C)!5 7 ,3 7D)!5 7 ,3 2Example1:Addorsubtract,ifpossible.A)!5 3 x 3 3 xB)!4 2 4 :Simplify!6 18 4 8 3 72 .A)6 3 5 3B)!2 3 8 32C)!3 24 5 3 3D)! 50 75 98 2719
Multiplyandsimplify.()()()2A)3 2 5 2 4 5B)2 adicalconjugates.()()Example5:Multiplyandsimplify 3 7 3 thedenominatorofeachexpression.3 56 15A)B)1 54 ominatorsifnecessary.()(()()A)2 7 1 3 7)C)4 2 3 4 2 3B)!3 54 3 162 3D)4 3!20
FINALCHECK:LT5- ‐6I can add and subtract radical expressions. (LT 5)I can multiply and rationalize binomial radical expressions. (LT .Showyourwork.a.c. 3 125 40 6 20()27 2b.d.(1 7 6 )(5 2 6 )4 53 5LT5,6PracticeAssignment Icanaddandsubtractradicalexpressions.(LT5) ns.(LT6)o WorksheetPractice7.3(below)Practice7- njugates.1.(3)()2 9 3 2 92.(1 7 )(1 7 )3.(5)()3 2 5 3 2Addorsubtractifpossible.4.9 3 2 35.5 2 2 36.3 7 7 3 x7.14 3 xy 33 2 3 49.52 310.1 51 511.2 125 12Simplify.12.3 32 2 5013.200 7214.3 81 33 315.2 4 48 3 4 24321
Multiply.()(())(16.1 5 2 5)()17.1 4 10 2 10219.4 2 320.(2)()((2 7)18.1 3 7 4 3 7)221.2 3 3 variablesarepositive22.28 4 63 2 723.6 40 2 90 3 16024.3 12 7 75 5425.4 3 81 2 3 72 3 3 2426.3 225 x 5 144 x27.6 45 y 2 4 20 y 2()()28.3 y 5 2 y 5 53 105 230.29.31.(x 32 147 2)()x 332.2 3 2
LT5,6MorePractice#1:Book7- ‐3Page38223
)6 34)2 5 39)a 3 5 3 3 2 3 4 3)25)4 3 5 13 7 56)a ab3 7ab ab8)d2 16d5 8 d13443 8 32b5 a 25a b2 49b 50 10)2)5 3 440 5 907)3 2475 98 27Simplify.(Multiplying)11)3 2 6 5()12)3 214)16)()8 2 3 5 1213)()26 5 2(34 3)(2 33 4 3)2Simplify(Rationalize)15)3 5 72 71 51 2 524
RationalExponents eto ndviceversa).(LT7) simplifynumberswithrationalexponents.(LT8)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- mPBRBPOR R BP !125 3B)!5 2 5 2C)!10 3 25 2!25 arealnumberandmisaninteger,then:1m!a n !a n- ‐Thedenominatorbecomestheoftheradical.- d.25
onsinradicalform.3 1.5a.b.c.!x 4! nentialform.a.( )5!x9b.4! 3r!a 14( ioninradicalform,andviceversa.4A)!(5x) 3B)!w 0.4C)!3 c 4D)( Simplifyeachnumbercompletely. 53A)!( 32) 5B)!36 sare.(Example6:Write 27x 6!)23insimplifiedexponentialform.26
Writeanswersinsimplifiedexponentialform.(A) 8x 15!) 13 h6 p9 B) 3 1000m ! 23 3! 32a 5 5c)# 10 20 &"b c storadicalexpressions(andviceversa).51.Writex 7inradicalform.2.Write10 ionalexponents. 33.Evaluatewithoutacalculator:64 wer.Showyourwork.a.(81a1 80 32 0 4b c ) 2b." a12c 18 % 6 ''# b&3LT7,8PracticeAssignment ns(andviceversa).(LT7) Icansimplifynumberswithrationalexponents.(LT8)o WorksheetPractice7.4(nextpage)27
Practice7- thatallvariablesarepositive.14.(2564 ) 4112. 814 13. 32 5 5.706.8 3227.( 1) 518.( 27) 3115411.27 39.16 41110.x 2 x 312.(82 ) 311.2y 2 y113.3.6016.8 27 315. 8 12117. 3 x 2 4 x 3 018.3822.y y1 6220. y 3 2 121. a 3 b 2 x 7423. 2 x 3 124. 2a 4 32126. 2 x 5 6 x 4 125.81 212 y 34y2 921 119. 3a 2 b 3 252 1 414. 16 27.9x 4 y 2(12)Writeeachexpressioninradicalform.1429.x 330.(2 y ) 3131.a1.5232.b 533.z 335.m2.436.t 72134.(ab) 437.a 1.6 Writeeachexpressioninexponentialform.ANSWERS:x 339.3 m40. 5y38.41.32y 242.3( 4 b )43. 644.5(6a)445.n 446. 4 (5ab)328
LT7,8MorePractice#1:Book7.4page38829
a n118)a 4220)a 3 x 6 117)a 2 m19)a n sitive.22)324)7 x 21y49 Simplify.Useabsolutevaluebarswhenneeded.62326)( 27 x ) 49 23)4 x12 25)x 4 y8z14 122327)( 64 y ) 128)(8x115 3)! 27b 9 329)# 6 &" 8a % 1! 16c8 430)#16 &" 81d %30
andpractice,Iwillbeableto solveequationswithroots(orradicals).(LT9) solveequationswithrationalexponents.(LT10)- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐WarmUp:Solvebyfactoring.!x 2 5x onent).RADICALEQUATIONORNOT?!A)! x 3 12B)! 3 2x 10C)!x 2 6
Unit 4 Radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. I can use properties of exponents to simplify expressions. Simplifying Radical Expressions 2. I can simplify radical algebraic expressions. Multiplying and Dividing 3. I can multiply radical expressions. 4.
Trigonometry Unit 4 Unit 4 WB Unit 4 Unit 4 5 Free Particle Interactions: Weight and Friction Unit 5 Unit 5 ZA-Chapter 3 pp. 39-57 pp. 103-106 WB Unit 5 Unit 5 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and ZA-Chapter 3 pp. 57-72 WB Unit 6 Parts C&B 6 Constant Force Particle: Acceleration Unit 6 Unit 6 and WB Unit 6 Unit 6
ice cream Unit 9: ice cream ka bio Unit 3: say it again kaa Unit 10: car kakra Unit 3: a little Kofi Unit 5: a name (boy born on Fri.) Koforidua Unit 4: Koforidua kↄ Unit 9: go Kↄ so Unit 7: Go ahead. kↄↄp Unit 9: cup kube Unit 10: coconut Kumase Unit 4: Kumasi Labadi Beach Unit 10: Labadi Beach
CAPE Management of Business Specimen Papers: Unit 1 Paper 01 60 Unit 1 Paper 02 68 Unit 1 Paper 03/2 74 Unit 2 Paper 01 78 Unit 2 Paper 02 86 Unit 2 Paper 03/2 90 CAPE Management of Business Mark Schemes: Unit 1 Paper 01 93 Unit 1 Paper 02 95 Unit 1 Paper 03/2 110 Unit 2 Paper 01 117 Unit 2 Paper 02 119 Unit 2 Paper 03/2 134
BASIC WIRING TABLE OF CONTENTS Unit I: Occupational Introduction 1 Unit II: General Safety 15 Unit III: Electrical Safety 71 Unit IV: Hand Tools 101 Unit V: Specialty Tools and Equipment 195 Unit VI: Using Trade Information 307 Unit VII: Basic Equipment 343 Unit VIII: Basic Theory 415 Unit IX: DC Circuits 469 Unit X: AC Circuits 533 Unit XI: Wiring Methods 641 Unit XII: Conductors 685
CONTENTS Page Thank you page 3 About the book 4 UNIT 1: About Academic IELTS Task 1 6 UNIT 2: Line Graphs – Language of Change 8 UNIT 3: Introducing a graph 20 UNIT 4: Grouping Information 26 UNIT 5: A More Complicated Line Graph 29 UNI T 6: Describing Bar Charts 36 UNIT 7: Describing Pie Charts 44 UNIT 8: Describing Tables 49
Unit 39: Adventure Tourism 378 Unit 40: Special Interest Tourism 386 Unit 41: Tourist Resort Management 393 Unit 42: Cruise Management 401 Unit 43: International Tourism Planning and Policy 408 Unit 44: Organisational Behaviour 415 Unit 45: Sales Management 421 Unit 46: Pitching and Negotiation Skills 427 Unit 47: Strategic Human Resource Management 433 Unit 48: Launching a New Venture 440 .
Unit 1: Science and fiction 3 Unit 2: A model career 6 Unit 3: On the farm 7 Unit 4: Crime scene investigations 8 Materials and their properties 9 Unit 5: Building for the future 9 Unit 6: Sculpture park 10 Unit 7: Cleaning up 12 Unit 8: Flying materials 13 Physical processes 14 Unit 9: Buying energy 14 Unit 10: Satellites and space 15
Organizations have to face many challenges in modern era. The same is the position in schools and collages as they are also organizations. To meet the challenges like competition, efficient and economical uses of sources and maximum output, knowledge of management and theories of management is basic requirement. Among Management Theories, Classical Management Theories are very important as .
