H SERIES. Algebra Basics. Algebra Basics. Curriculum Ready.

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1 H SERIES Curriulum Rey

2 Copyright 009 P Lerning. All rights reserve. First eition printe 009 in Austrli. A tlogue reor for this ook is ville from P Lerning Lt. ISBN Ownership of ontent The mterils in this resoure inluing without limittion ll informtion text grphis vertisements nmes logos n tre mrks (Content) re protete y opyright tre mrk n other intelletul property lws unless expressly inite otherwise. You must not moify opy reproue repulish or istriute this Content in ny wy exept s expressly provie for in these Generl Conitions or with our express prior written onsent. Copyright Copyright in this resoure is owne or liense y us. Other thn for the purposes of n sujet to the onitions presrie uner the Copyright At 968 (Cth) n similr legisltion whih pplies in your lotion n exept s expressly uthorise y these Generl Conitions you my not in ny form or y ny mens: pt reproue store istriute print isply perform pulish or rete erivtive works from ny prt of this resoure; or ommerilise ny informtion prouts or servies otine from ny prt of this resoure. Where opyright legisltion in lotion inlues remunerte sheme to permit eutionl institutions to opy or print ny prt of the resoure we will lim for remunertion uner tht sheme where worksheets re printe or photoopie y tehers for use y stuents n where tehers iret stuents to print or photoopy worksheets for use y stuents t shool. A worksheet is pge of lerning esigne for stuent to write on using n ink pen or penil. This my le to n inrese in the fees for eutionl institutions to prtiipte in the relevnt sheme. Pulishe P Lerning Lt For more opies of this ook ontt us t: Designe P Lerning Lt Although every preution hs een tken in the preprtion of this ook the pulisher n uthors ssume no responsiility for errors or omissions. Neither is ny liility ssume for mges resulting from the use of this informtion ontine herein.

3 Fill in the spes with nything you lrey know out Alger Creer Opportunities: Arhitets eletriins plumers et. use it to o importnt lultions. Give this go! Q Tringles hve een stke to form n inresing numer pttern elow:... 7 tringles tringles 7 tringles How mny smll tringles woul e neee to mke the 5 th piture in this pttern? Work through the ook for gret wy to solve this Mthletis P Lerning Lt H SERIES TOPIC

4 How oes it work? Wors n symols Alger uses letters or symols lle vriles. Eh prt in n lgeri expression is lle term. Look t the lgeri expression 4 4 Constnt term (Cn't hnge) Vrile term (Cn hnge) if is the outome is If is 8 the outome is 4 Let's look t nother similr expression. m 9 + m + 9 Vrile term (Cn hnge) Constnt term (Cn't hnge) If m is the outome is If m is 4 the outome is 5 Algeri expressions with n equls sign = re lle equtions. 4+ x = 7 4+ x = 7 The equl sign mens 4 + x hs the sme vlue s 7 Constnt Vrile Constnt To mke this orret x must e Here's nother one. m = m = The equl sign mens m - 5 hs the sme vlue s 9 Vrile Constnt Constnt To mke this orret m must e 4 H SERIES TOPIC Mthletis P Lerning Lt

5 How oes it work? Your Turn Wors n symols Write own the vrile in eh of the following mthemtil sttements: + m + WORDS AND.../.../0... S Y M B O L S 7 # k + + Cirle eh of the lgeri expressions elow in whih the vrile n e ny vlue: + x = 5 # w = 0 x' x = # g = # = 6 00' s = 5 # x + 6 = Mth up eh of the lgeri expressions with the orret outome using the given vrile vlue: x if x = 4 4# m if m = 5 7 ' if = + # z if z = Write own the vlue of the vrile tht mkes these equtions equl on oth sies: + = 0 4 h = = h = k ' = 6 # y = 7 k = y = Mthletis P Lerning Lt H SERIES TOPIC

6 How oes it work? Multiplition x = Inste of writing Alwys put the numer first. Simplify # # n 5 # mor # we simply write 5 m or to men the ext sme thing! # # n = 6 # n Multiply the numers together = 6n If multiplying y o not write in front of the vrile. Simplify # y # y = y ^not yh The is hien # is just. The sme rule pplies when multiplying vrile y Write multiplie vriles in lphetil orer. Simplify # p# 5 # r# q # p # 5 # r # q = # 5 # p # r# q Re-orer with numers first = = 0 # p # r # q 0pqr Multiply the numers first Put vriles in lphetil orer Use powers to simplify multiplitions of the sme vrile. Simplify # # # # = # = Just like 4 # 4is 4 # is = x Doing the opposite of these exmples is lle expning. Write in expne form ` = # # Simplifie form Expne form 4 H SERIES TOPIC Mthletis P Lerning Lt

7 How oes it work? Your Turn Multiplition Multiplition ABBREVIATIONS * ABBREVIATIONS * Simplify: (psst: rememer the rules!).../.../0... # 7 # k u # 5 # r# p n # m # m e 6# # # f 4# j # l # # k Expn eh of these 4pq 4 m n It's omo time! Clulte the vlue of these expressions using the vrile in the squre rkets. x+ 6 x = 4@ 5 6 = 6@ # 5g 6 g 4m 6 m COMBO TIME * COMBO TIME * COMBO TIME *.../.../0... Mthletis P Lerning Lt H SERIES TOPIC 5

8 How oes it work? Division ' = When iviing two lgeri terms it sometimes helps to write the ivision s frtion first. Simplify h 8 ' h ' 8 Numertor Denomintor ` h ' 8 = h 8 Awys write frtions in simplest form. Simplify 4x ' 4x ' Numertor ` 4x ' = = Denomintor 4x x 4 = when simplifie Brkets re not neessry for simple ivisions written in frtion form. Simplify ( + m) ' n ( + m) ' n { Numertor Denomintor ` ^ + mh' n = + m rkets re hien in frtion form n When oing the reverse n there is more thn one term rkets must e put in. ` y y' ( 4 x) 4 + x = + rkets or (prentheses) 6 H SERIES TOPIC Mthletis P Lerning Lt

9 How oes it work? Your Turn Division Simplify y writing without using ivision sign: Division.../.../0... ABBREVIATIONS * ABBREVIATIONS * ' ' 5' ^r + h ^y+ zh' z Re-write these expressions using ivision sign: (psst: some my nee rkets) w x y x + v+ w Re-write these expressions using ivision sign: (psst: simplify the frtions first) 6 6 5x 0y 4 ^m+ nh p Mthletis P Lerning Lt H SERIES TOPIC 7

10 How oes it work? Your Turn Mixe simplifying onepts COMBO TIME * COMBO TIME * COMBO TIME * It's omo time! Simplify these y writing without multiplition or ivision signs:.../.../ # ' 4 # m' ^4+ nh n # m'^ # # h ^8# ph' ^ # qh e x# x' ^y+ xh f # f# ' ^ + f # eh Expn these y re-writing with multiplition/ivision signs n grouping symols: + 4 q r 9q l e 5 f 7xyz j k + x+ 7y 8 H SERIES TOPIC Mthletis P Lerning Lt

11 How oes it work? Phrses s lgeri expressions To solve prolems with lger we use vriles to turn the prolem into n lgeri rule (or reltionship). Use vrile Write rule for: the sum of numer n 5 plus Give the numer vrile. Let the numer e n `The sum of numer n 5 is: n + 5 Write rule for: the ifferene etween numer n minus Let the numer e n ` n - The orer of the wors in sentene mkes ifferene to whih opertion is one first. Write rule for: the ifferene etween oule numer n minus multiply y Let the numer e n ` n - ` numer oule minus Write rule for: oule the ifferene etween numer n multiply y minus Let the numer e n ` ( n - ) Brkets use euse n is lulte first ` oule the ifferene etween numer n Write rule for: the quotient of 4 times numer n ivie Let the numer e n numertor enomintor ` 4n 4n ws first in the sentene so it is the numertor Mthletis P Lerning Lt H SERIES TOPIC 9

12 How oes it work? Your Turn Phrses s lgeri expressions Write these phrses s lgeri expressions (let the numer e n ) The sum of numer n 7: Phrses s Algeri Expressions.../.../0... ALGEBRA BASICS * ALGEBRA BASICS * n + 7 The ifferene etween 9 n numer: The sum of 6 times numer n : The prout (#) of numer n 4: e The quotient (') of two more thn numer n : f The ifferene etween numer squre n 6: g The prout of numer minus 5 n : h 8 less thn twie numer: i 0 e to numer hlve: j A numer multiplie y 5 more thn itself: 0 H SERIES TOPIC Mthletis P Lerning Lt

13 How oes it work? Your Turn Phrses s lgeri expressions Cirle whether the lgeri expression is orret or inorret for eh phrse. A numer multiplie y 4 e to 7: Corret Inorret 4n + 7 The ifferene etween numer n 4: Corret Inorret 4 - n The sum of 6 n the prout of n numer: Corret Inorret n + 6 The quotient of 4 plus numer n 9: Corret Inorret 4' ( n + 9) e A numer ivie y 5 n e to the numer: Corret Inorret nn- ( ) n f A numer times the ifferene etween the numer n one: Corret Inorret g The sum of numer n three minus the numer hlve: Corret Inorret n - n + h The prout of 6 more thn twie numer n 4: Corret Inorret 4(n + 6) i The prout of numer squre n : Corret Inorret ( n) j The quotient of 5 less thn numer n the numer: Corret Inorret n 5 n Mthletis P Lerning Lt H SERIES TOPIC

14 How oes it work? Aition n sutrtion + & If the vrile prts re extly the sme the terms re lle like terms. Like terms: x Like terms - x y - 5y Like terms Like terms Not Like terms: p p x Not like terms Not like terms Not like terms - 5y Only like terms n e e or sutrte. Simplify + + Vrile prts re the sme (like terms) ` + = Simplify 8x- x 8x- x like terms ` 8x- x = 5x Simplify like terms = 7+ 6 This nnot e simplifie ny further Why on t we or sutrt unlike terms? Goo Question! Let s look t prolem the lst exmple oul represent. At pini for pets eh og gets 7 trets n eh t gets 6 trets. Numer of trets neee is: (7 trets # numer of ogs) + (6 trets # numer of ts) = (7 # ) + (6# ) the numer of ogs the numer of ts Simplifie: = 7+ 6 n represent two ifferent nimls so it oes not mke sense to them together. Therefore 7+ 6 is the simplest expression for this prolem. H SERIES TOPIC Mthletis P Lerning Lt

15 SIMPLIFYING * SIMPLIFYING * SIMPLIFYING * How oes it work? Your Turn Aition n sutrtion Simplify: + 9 u+ 5u Aition n Sutrtion.../.../0... 4r- 9r 4g- 7g e 6m- 8m f - x+ x g 7y+ y+ 4y h 0p- 5p- 0p Simplify: (psst: look for the like terms!) m+ 9n+ m x+ 9y+ 5y 9-5- e 7e+ e+ f g- 5g- 4h Mthletis P Lerning Lt H SERIES TOPIC

16 How oes it work? Grouping like terms Terms n hve the sme vrile letter ut still not e like terms. Sme hrter ut not like Simplify is ifferent to so they re not like terms. Like terms ` = Grouping the like terms Like terms = 8+ 5 Eh term of n expression inlues the sign in front of it. Simplify 9j- k+ 5j+ 8k no sign in front men + 9j- k+ 5j+ 8k = 9j - k + 5j + 8k = 9j+ 5j - k+ 8k Grouping the like terms = 4j- k Simplify It s helpful to irle the like terms with similr shpes inluing the sign in front. - Here re two more exmples tht omine two simplifying onepts. Simplify n write in frtion form: ( ) ' ( )' = (+ 4) ' Simplify the rket = + 4 Write ivision s frtion Simplify eh rket n write in frtion form: ( x- x + 8x) ' ( x + 8x - 5x) ( x - x + 8x )'( x + 8x - 5x) = ( 9x- x )'( x - 5x) Simplify the rket = 9x- x x - 5x Write ivision s frtion 4 H SERIES TOPIC Mthletis P Lerning Lt

17 How oes it work? Your Turn Grouping like terms Simplify: (psst: look for the like terms!) p + p+ 9p+ 7p ROUPING LIKE TERMS *.../.../0... GGROUPING LIKE TERMS * n- m- n- m y- 5x+ y- 8x e 9p- 4q+ p+ q f Como time! Simplify n write in frtion form: y' ( y+ x- y) ' ( 7p - 5p- 8p ) Simplify eh rket n write in frtion form: ( x- y+ x) ' ^4x+ x- yh ^# 4+ # h' ( # # + ) Mthletis P Lerning Lt H SERIES TOPIC 5

18 ESCAPE FROM ALGEBRA ISLAND * ESCAPE FROM ALGEBRA ISLAND * How oes it work? Your Turn Espe from lger isln puzzle.../.../0... Espe from Alger Isln puzzle Squre steps = multiply Cirle steps = ivie Trpezium steps = Pentgon steps = sutrt } Rememer like terms only! One pth hs een foun for you! 6 ^6^4x + 4x h- h ' x@ # = x Strting with vlue of 4x trvel long the lines from step to step until you get to the outer ege. Eh step ffets your vlue. If you hve extly x left when you reh one of the shpes t the outer ege then you hve espe! Goo luk. How mny pths n you fin to get wy from Alger Isln? How mny steps is the longest pth you n fin? 6 H SERIES TOPIC Mthletis P Lerning Lt

19 How oes it work? Bringing ll the previous onepts together These exmples omine the ifferent simplifying onepts together. Clulte the vlue of 4 ' when = 6 When = 6 4 = 4# 6 not 46! 4 ' = 4# 6' or 4 ' = 4 = 6 = = = 6 4 ' 8 = = = 4# This is useful in questions with multiple vriles. The fny nme given to oing this sort of thing in Mthemtis is sustitution. Clulte the vlue of 5x+ y when x = n y = 6 5x+ y = 5 # + # 6 Sustitute the vlue of the vriles. = 0 + = x = y = 6 Where possile simplify the expression first efore sustituting in the vrile vlues. Evlute 4m+ n- m+ 5n when m = 6 n n =- Simplify: 4m + n - m + 5n = 4m- m + n+ 5n Ientify the like terms n their sign Group the like terms = m+ 8n Simplify Evlute: m+ 8n = # 6+ 8# - Sustitute in the vrile vlues "fin the vlue of" m = 6 = - 4 =- n =- Mthletis P Lerning Lt H SERIES TOPIC 7

20 How oes it work? The sme vrile vlue n e sustitute into unlike terms. Evlute p + 8p- p - p when p = Simplify: p + 8p - p - p = p - p + 8p- p Ientify the like terms n their sign Group the like terms = p + 5p Simplify y omining the like terms Evlute: p + 5p = # + 5# p = p = = # 4+ 5 # = 8+ 0 = 8 Sustitute in the vrile vlue Chekout these two extr exmples... x+ y Evlute when x = n y = x Rememer: numertor enomintor x = y = x+ y = # + x # x = = = 8 ( 8 ' 9) 9 = Sustitute in the vrile vlues Simplify the numertor n enomintor Simplify the frtion Evlute mn when m = n n = 7 Evlute: mn= # m # n Expne form # m # n = # # 7 Sustitute in the vrile vlues = = m = n = 7 # 4# 7 56 Multiply terms together 8 H SERIES TOPIC Mthletis P Lerning Lt

21 SIMPLIFYING: BRINGING ALL THE CONCEPTS TOGETHER * How oes it work? Your Turn Bringing ll the previous onepts together Clulte the vlue of these expressions when v 4 = 4v + 4 ' v.../.../ v 4 v Clulte the vlue of these expressions when =- n = Evlute these expressions when = 6 = ^ - + h # ^ h Mthletis P Lerning Lt H SERIES TOPIC 9

22 How oes it work? Your Turn Bringing ll the previous onepts together & Give these three vrile questions go! 4 Evlute these expressions when x = 6 y = n z =-8 x+ y+ z z+ xy x - yz 4y x+ z Ern n Awesome pssport stmp with these questions: 5 Evlute ( + ) ( - ) when = =-4 * AWESOME *.../.../0... * AWESOME * 6 ( x- y) Evlute e o when x =- y =-5 ( y- x) 0 H SERIES TOPIC Mthletis P Lerning Lt

23 Where oes it work? Tles of vlues These re use to show how one vrile hnges when nother vrile in given rule is hnge. Complete the tle of vlues using the rule: = Sustitute eh vlue of into the rule to fin = 0 = = = = 4 = 5 ` = 0+ ` = + ` = + ` = + ` = 4 + ` = 5 + = = 4 = 5 = 6 = 7 = 8 Complete the tle of vlues using the rule: y = x x y x = x = 6 x = 9 x = x = 5 x = 8 ` y = ' ` y = 6 ' ` y = 9 ' ` y = ' ` y = 5 ' ` y = 8 ' = y = y = y = 4 y = 5 y = 6 Complete the tle of vlues using the rule: m = n- n m n = 0 n = n = n = n = 4 n = 5 ` m = # 0- ` m = # - ` m = # - ` m = # - ` m = # 4 - ` m = # 5 - =- = = 5 = 8 = = 4 Mthletis P Lerning Lt H SERIES TOPIC

24 TABLE OF VALUES * TABLE OF VALUES * Where oes it work? Your Turn Tle of vlues T A B L E Complete eh tle of vlues using the given rule..../.../0... u = v+ = v 0 4 u 0 4 g = 4h y = x + h 4 5 g x y Drw lines to mth eh tle of vlues with the orret mthing rule = + = + 4 = = 5-4 Hve go t figuring out the rule use for eh tle of vlues elow n fill in the gps. Rule: Rule: x 0 4 m 0 4 y n 0 4 Rule: p 0 4 Rule: 5 6 q H SERIES TOPIC Mthletis P Lerning Lt

25 Where oes it work? Numer ptterns There re lot of ptterns in the worl n it is useful skill to e le to work them out.... t the en mens the igrms ontinue to hnge following the sme pttern. Look t the following ptterns of riks li y uiler over three minute perio: st minute n minute r minute... (i) Desrie the numer pttern of riks li y the uiler every minute: Pttern: The uiler ly s three riks in the first minute n then nother every minute therefter (ii) Write numer pttern for the totl numer of riks li fter every minute: Numer Pttern: The numer pttern forme n e isplye using tle of vlues: Look t the inresing rrow sign pttern elow: st sign n sign r sign... (i) Desrie the numer pttern forme y the rrow signs: Pttern: The first sign hs three rrows then eh following sign inreses y two rrows (ii) Complete tle of vlues for the first three rrow signs: Sign numer Numer of rrows 5 7 Numer pttern for the rrows use in eh sign inreses y two rrows eh time. (iii) How mny rrows woul e in the 6 th sign of the pttern? First six vlues in the numer pttern re: ` there woul e rrows in the 6 th sign Mthletis P Lerning Lt H SERIES TOPIC

26 Where oes it work? Your Turn Numer ptterns For eh of these pttern igrms: (i) Desrie the numer pttern forme y the shpes (ii) Write numer pttern for the totl numer of shpes use to mke the first five igrms... (i) (ii) (i) (ii) * NUMBER PATTERNS /.../0... * NUMBER PATTERNS (i) (ii)... 4 H SERIES TOPIC Mthletis P Lerning Lt

27 Where oes it work? Your Turn Numer ptterns For eh of these pttern igrms: (i) Complete tle of vlues for the first 4 igrms (ii) Write own how mny shpes re neee for the 7 th igrm... st n r (i) Digrm numer 4 Numer of herts (ii) Numer of herts neee for the 7 th igrm =... st n r (i) Digrm numer 4 Numer of hexgons (ii) Numer of hexgons neee for the 7 th igrm =... st n r (i) Digrm numer 4 Numer of mthstiks (ii) Numer of mthstiks neee for the 7 th igrm = Mthletis P Lerning Lt H SERIES TOPIC 5

28 Where oes it work? Moelling numer ptterns m=t + Moelling numer pttern is the fny wy Mthemtiins sy: fin the lger rule for the pttern. These exmples use the numer of shpes n mthstiks in eh pttern to fin the rule. Fin the lgeri rule for the mthstik pttern elow: Numer of tringles (t): Numer of mthstiks (m): Pttern: Strting with mthstiks the numer of mthstiks goes up y with eh tringle e on ` The numer of mthstiks in eh igrm equls x the numer of tringles in the igrm Using lger this is: m = t The generl rule Completing tle of vlues n help to fin the generl rule: Numer of tringles (t) Numer of mthstiks (m) 6 9 Numer of mthstiks (m) equls the numer of tringles (t) multiplie y the onstnt inrese Fin the generl rule for this pttern forme using mthstiks... Numer of tringles (t): Numer of mthstiks (m): Pttern: Strting with 5 mthstiks the mthstiks inrese y for eh extr tringle e on Numer of tringles (t) 4 Numer of mthstiks (m) Cheking with the first shpe this time we nee to put + into the rule to get the orret numer of mthstiks ` m = t+ The generl rule Multiply t y : ` m = t 6 H SERIES TOPIC Mthletis P Lerning Lt

29 Where oes it work? Your Turn MODELLING NUMBER PATTERNS * MODELLING NUMBER PATTERNS * Moelling numer ptterns Write own the generl rule for eh of the following mthstik numer ptterns:.../.../ Let s e the numer of squres n m the numer of mthstiks Numer of squres (s) Numer of mthstiks (m) Generl rule: m = # s+... Let t e the numer of tringles n m the numer of mthstiks Numer of tringles (t) Numer of mthstiks (m) Generl rule: m t = +... Let r e the numer of grey rings n the numer of irles rwn Numer of grey rings (r) Generl rule: Numer of irles rwn () r = Let p e the numer of pentgonl shpes n t the numer of tringles use Numer of pentgonl shpes (p) Generl rule: Numer of tringles (t) t = p Mthletis P Lerning Lt H SERIES TOPIC 7

30 Where oes it work? More numer pttern moelling The igrm numer (n th igrm) n the numer of shpes in eh igrm is use for these questions. Fin the generl rule for this pttern forme using pentgons... n th igrm (n) Pentgons (p) use: st n r 4 th Pttern: Strting with pentgons the numer of pentgons goes up y for eh following igrm Digrm numer (n) 4 Numer of pentgons (p) 5 8 Cheking with the first shpe we nee to put into the rule to get the orret numer of pentgons Multiply n y : ` p = n ` p = n- The generl rule This metho lso works for mthstik ptterns. Fin the generl rule for this pttern forme using mthstiks... n th igrm (n) mthstiks (m) use: st n r Pttern: Strting with 4 mthstiks the numer of mthstiks goes up y 6 for eh following igrm Digrm numer (n) Numer of mthstiks (m) Cheking with the first pttern we nee to put into the rule to get the orret numer of mthstiks 6 6 Multiply n y 6: ` m = 6n ` m = 6n- The generl rule 8 H SERIES TOPIC Mthletis P Lerning Lt

31 Where oes it work? Your Turn More numer pttern moelling Write own the generl rule for eh of the following mthstik numer ptterns:.../.../0... * MORE NUMBER PATTERN MODELLING... st n r Let n e the igrm numer n m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) Generl rule: m = # n+... st n r Let n e the igrm numer n m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) Generl rule: m n = +... st n Let n e the igrm numer n m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) r Generl rule: m n = +... st n r Let n e the igrm numer n m the numer of mthstiks Digrm numer (n) Generl rule: Numer of mthstiks (m) m = n Mthletis P Lerning Lt H SERIES TOPIC 9

32 Where oes it work? Your Turn More numer pttern moelling Write own the generl rule for eh of the following numer ptterns:... st n r Let s e the numer of snow flkes n n the n th igrm Digrm numer (n) Numer of snow flkes (s) Generl rule: s = # n... st n r Let t e the numer of tyres n n the n th igrm Digrm numer (n) Numer of tyres (t) Generl rule: t n = -... st n r Let e the numer of ots n n the n th igrm Digrm numer (n) Numer of ots () Generl rule: = # st Let t e the numer of tringles forme n n the n th igrm Digrm numer (n) n # Numer of tringles (t) = r Generl rule:... There re tully two numer ptterns here the other involves the numer of mthstiks use. See if you n work it out! 0 H SERIES TOPIC Mthletis P Lerning Lt

33 Wht else n you o? Using the generl rule Sustitution into the generl rule is use to nswer questions out the n th igrm in pttern. Fin the generl rule for the prllelogrm pttern:... Let p e the numer of prllelogrms n n the n th igrm n p 4 6 ` p = n generl rule How mny prllelogrms re there in the 0 th igrm of the pttern ove? ` p = # 0 Sustitute n = 0 into the generl rule = 40 prllelogrms Fin the generl rule for the mthstik numer pttern:... Let m e the numer of mthstiks n n the n th igrm n m How mny mthstiks re there in the 8 th igrm? ` m = 5n- generl rule ` m = 5# 8- Sustitute n = 8 into the generl rule = 8 mthstiks Fin the generl rule for the mzing stik gymnst pttern:... Let g e the numer of gymnsts n n the n th igrm n g 5 8 How mny gymnsts re there in the 0 th pttern? ` g = n- generl rule ` g = # 0- Sustitute n = 0 into the generl rule = 89 gymnsts Mthletis P Lerning Lt H SERIES TOPIC

34 Wht else n you o? Your Turn USING THE GENERAL RULE * USING THE GENERAL RULE * Using the generl rule Every time Nimh kike gol (g) the tem sore (s) inrese y. The generl rule for this is given y: s = g.../.../0... How mny points i Nimh sore fter kiking g = 8 gols? If the totl numer of hikens () tht rosse the ro fter eh minute (m) is given y the generl rule: = 5m- How mny hikens h rosse the ro when m = 7 minutes? The totl numer of shirts (s) trie on y ustomers () in store is represente y the generl rule: s = + How mny shirts h een trie on when there were = ustomers? The totl numer of vegetrin mels (v) orere (on verge) in resturnt y iners () is given y the generl rule: v = How mny vegetrin mels were orere on night with = 6 iners? H SERIES TOPIC Mthletis P Lerning Lt

35 Wht else n you o? Your Turn Using the generl rule The stke tyres elow form numer pttern. Fin the generl rule n then lulte how mny tyres re in the th stk.... st stk n stk r stk Let t e the numer of tyres n n the n th stk of tyres. n t Generl rule: Tyres in the th stk: New leves re ppering on tree eh y forming numer pttern. Fin the generl rule n lulte how mny leves there re on the 0 th y.... Dy Dy Dy Let l e the numer of leves n n the n th y. n l Generl rule: Leves on the 0 th y: 4 The sketlls represent the numer of goo shots uring eh trining session. The goo shots re inresing y the sme mount eh time. How mny goo shots re me uring the 8 th session?... Session Session Session Let s e the numer of goo shots n n the n th trining session. n s Generl rule: Goo shots in the 8 th session: Mthletis P Lerning Lt H SERIES TOPIC

36 Wht else n you o? Your Turn Using the generl rule 5 A tiler is lying out some otgonl tiles in the following numer pttern:... st igrm n igrm r igrm How mny tiles will e li in the th igrm? let t e the numer of tiles li n n the n th igrm. n t Generl rule: Tiles li in the th igrm: 6 Tringles hve een stke to form n inresing numer pttern:... Rememer me? 7 tringles tringles 7 tringles Fin the generl rule n lulte the numer of tringles neee for the 5 th shpe. Let t e the numer of trngles n n the n th shpe. n t Generl rule: Tringles in the 5 th shpe: 4 H SERIES TOPIC Mthletis P Lerning Lt

37 ADD * MORE THAN * PLUS * AND * SUM * PRODUCT * LOTS OF * MULTIPLY * TIMES * SUBTRACTION * DIFFERENCE * LESS THAN * TAKE AWAY * Chet Sheet Here is summry of the importnt things to rememer for lger sis Wors n symols Alger uses letters or symols lle vriles. Eh prt in n lgeri expression is lle term. Vrile term (n hnge) x 6 + x + 6= 0 Constnt term (n't hnge) equl sign '=' mens x + 6 hs the sme vlue s 0 The equl sign mkes this n eqution. The vlue of x must e 4 to e orret Multiplition Multiplitions n e: Simplifie 6# n= 6n x # y= xy Expne 6n= 6 # n xy = x # y Division It sometimes helps to write ivisions s frtion first when simplifying: ' = y Brkets n e hien when writing ivision s frtion: y' ^4 + xh = 4 + x When oing the reverse rkets must e put in: - m 6 = ^- mh' 6 Phrses s lgeri expressions To solve prolems with lger we use vriles to turn the prolem into n lgeri rule (or reltionship). DIVIDE * QUOTIENT * * INTO GOES Aition n sutrtion Only Like terms n e e or sutrte. Like terms: x Like terms - x Like terms y - 5y Like terms Not Like terms: Not Like terms p p Not Like terms x - 5y Not Like terms Mthletis P Lerning Lt H SERIES TOPIC 5

38 Chet Sheet Tle of vlues These show how one vrile hnges when nother vrile in given rule is hnge Rule: y = x+ x y x = `y = # + = 4 x = ` y = # + = 6 x = ` y = # + = 8 Moelling numer ptterns This is fny wy Mthemtiins sy "fin the lger rule for the pttern" The rule n e foun using two methos:. Compring the igrm numer with the numer of shpes in it.. Compring the numer of shpes with the numer of ojets use to mke eh igrm. Tles of vlues help with oth methos n s This mens 'n' is multiplie y in the rule After looking t the first vlues of n = n s = 4 the rule must e: s = n+ Using the generl rule The numer of shpes/ojets in prtiulr prt of the pttern is foun y sustituting into the generl rule. How mny Squres (s) re there in the 0 th pttern if s = n+? when n = 0 s = # 0+ = 4 squres. 6 H SERIES TOPIC Mthletis P Lerning Lt

39 Answers Wors n symols Mixe simplifying onepts. The vrile is The vrile is m. # ' ( + 4 )' The vrile is k The vrile is ( q- r) ' ( 9 # q) l # l' ( j- k). + x = x' x = # g = # x + 6 = e f 5 # # ' ( # + # ) 7 # x# y# z' ( x+ 7 # y) Phrses s lgeri expressions. 4 - k if x = 4 4 m if m = 5 7 if = + 7 z if z = e n n 6# n+ = 6n+ 4# n = 4n n + f n = 8 h = k = 8 y = 6 g i ( n - 5) 0 + n h j n - 8 nn ( + 5) Multiplition. Corret Inorret Corret. 4k u 5pr jkl Inorret e Inorret f Corret e 8 f jkl g Inorret h Corret i Inorret. 4 # p # q 4 # # # m # m # n j Corret Aition n sutrtion 0 8u 5r -g Division e -m f -9x g y h 5p. 5 y+ z r + z. 5m+ 9n 4+ 6x+ 4y. w ' 4 ' ^ + h 6-5 e 8e+ f -g-4h 6' ^x + h ^x- yh' ^v+ wh Grouping like terms. ' ' p + p -m x' 4y ^m+ nh ' p 4y- x e p+ 8q f Mixe simplifying onepts. y y+ x -p -5p p 9q e m 4+ n x y+ x f mn f + ef. 4x- y 7x- y Mthletis P Lerning Lt H SERIES TOPIC 7

40 Answers Espe from Alger Isln Puzzle Tles of Vlues x. v x 8x 0 x x x x x x 5 x 7 8 4x 7x 8x x x x x 5 x 7 6 5x 0 5 x 8x 7 x 4x x x Alger Isln 5 5 5x x 6x 7 x 7 5 x 4x 5 8x x 5x 5 x 7 x x7 x 8x x x 7 6x 7 x x x. u h 4 5 g x y = + Bringing ll the previous onepts together = = = x y m n p 0 4 q H SERIES TOPIC Mthletis P Lerning Lt

41 Answers Numer ptterns More numer pttern moelling. (i) Strting with one smiley fe in the first igrm smiley fes re e to eh igrm every time. (ii) m = # n+ m = 4 n + (i) Strting with three rrows in the first igrm 4 rrows re e to eh igrm every time m m = 4 n + 5 = 9 n - 5 (ii) (i) Strting with 6 tringles to form the first igrm 6 tringles re e to eh igrm every time.. s = t # n = 5 n - (ii) = 4 # n +. (i) Digrm numer 4 Numer of herts 5 8 t = # n + (ii) 0 Using the generl rule (i) Digrm numer 4 Numer of hexgons points 5 shirts hikens vegetrion mels (ii) (i) Digrm numer Numer of mthstiks (ii) Moelling Numer Ptterns. m = # s+ m = t+ = r+ t = 7 p Mthletis P Lerning Lt H SERIES TOPIC 9

42 Notes 40 H SERIES TOPIC Mthletis P Lerning Lt

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44 H SERIES