Curriulum Redy ACMNA: 33 75 76 77 79 www.mthletis.om
Fill in the spes with nything you lredy know out Alger Creer Opportunities: Arhitets eletriins plumers et. use it to do importnt lultions. Give this go! Q Tringles hve een stked to form n inresing numer pttern elow:... 7 tringles tringles 7 tringles How mny smll tringles would e needed to mke the 5 th piture in this pttern? Work through the ook for gret wy to solve this H SERIES TOPIC
How does it work? Words nd symols Alger uses letters or symols lled vriles. Eh prt in n lgeri expression is lled term. Look t the lgeri expression 4 4 Constnt term (Cn't hnge) Vrile term (Cn hnge) if is the outome is 3 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 3 the outome is If m is 4 the outome is 5 Algeri expressions with n equls sign = re lled 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 3 Here's nother one. m 5 9 - = m 5 9 - = 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
How does it work? Your Turn Words nd symols Write down the vrile in eh of the following mthemtil sttements: + 3 m + WORDS AND.../.../0... S Y M B O L S 7 # k + 3 d + 3 Cirle eh of the lgeri expressions elow in whih the vrile n e ny vlue: 3 + x = 5 # w = 30 x ' x = # g = 3 # d = 6 00 ' s = 5 3 # x + 6 = 3 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 = 3 + 3 # z if z = 3 0 0 9 7 4 Write down the vlue of the vrile tht mkes these equtions equl on oth sides: + = 0 4 h = = h = k ' 3 = 6 d # y = 7 k = y = H SERIES TOPIC 3
How does it work? Multiplition x = Insted of writing Alwys put the numer first. Simplify 3 # # n 5 # m or # we simply write 5 m or to men the ext sme thing! 3 # # n = 6 # n Multiply the numers together = 6n If multiplying y do not write in front of the vrile. Simplify # y # y = y ^not yh The is hidden # is just. The sme rule pplies when multiplying vrile y Write multiplied vriles in lphetil order. Simplify # p # 5 # r # q # p # 5 # r # q = # 5 # p # r # q = 0 # p # r # q = 0pqr Re-order with numers first Multiply the numers first Put vriles in lphetil order Use powers to simplify multiplitions of the sme vrile. Simplify # # # # = # = Just like 4 # 4 is 4 # is = x Doing the opposite of these exmples is lled expnding. Write in expnded form ` = # # Simplified form Expnded form 4 H SERIES TOPIC
How does it work? Your Turn Multiplition Multiplition ABBREVIATIONS * ABBREVIATIONS * Simplify: (psst: rememer the rules!).../.../0... # 7 # k u # 5 # r # p d n # m # m e 6 # # 3 # f 4 # j # l # 3 # k Expnd eh of these 4pq 4 3m n 3 It's omo time! Clulte the vlue of these expressions using the vrile in the squre rkets. 3x + 6 x = 4@ 5 6 = 6@ 3 # 5g 6 g = @ d 4m 6 m = 3@ COMBO TIME * COMBO TIME * COMBO TIME *.../.../0... H SERIES TOPIC 5
How does it work? Division ' = When dividing two lgeri terms it sometimes helps to write the division s frtion first. Simplify h 8 ' h ' 8 Numertor Denomintor ` h ' 8 = h 8 Awys write frtions in simplest form. Simplify 4x ' 4x ' Numertor Denomintor ` 4x ' = 4x = x 3 4 = when simplified 3 Brkets re not neessry for simple divisions written in frtion form. Simplify (3 + m) ' n ( 3 + m) ' n { Numertor Denomintor ` ^3 + mh ' n = 3 + m rkets re hidden in frtion form n When doing the reverse nd there is more thn one term rkets must e put in. ` y y ' ( 4 x) 4 + x = + rkets or (prentheses) 6 H SERIES TOPIC
How does it work? Your Turn Division Simplify y writing without using division sign: Division.../.../0... ABBREVIATIONS * ABBREVIATIONS * ' d ' 5 ' ^r + 3h d ^y + zh ' z Re-write these expressions using division sign: (psst: some my need rkets) w 4 3 + 6 x y d 3x + v + w 3 Re-write these expressions using division sign: (psst: simplify the frtions first) 6 6 5x 0y d 4 ^m + nh p H SERIES TOPIC 7
How does it work? Your Turn Mixed simplifying onepts COMBO TIME * COMBO TIME * COMBO TIME * It's omo time! Simplify these y writing without multiplition or division signs:.../.../0... 5 # ' 4 # m ' ^4 + nh n # m '^ # # h d ^8 # ph ' ^3 # 3qh e x # x ' ^y + xh f d # f # d ' ^ + f # eh Expnd these y re-writing with multiplition/division signs nd grouping symols: d + 4 3 q r 9q d l e 5 f 7xyz j k + x + 7y 8 H SERIES TOPIC
How does 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 nd 5 plus Give the numer vrile. Let the numer e n `The sum of numer nd 5 is: n + 5 Write rule for: the differene etween numer nd 3 minus Let the numer e n ` n - 3 The order of the words in sentene mkes differene to whih opertion is done first. Write rule for: the differene etween doule numer nd 3 minus multiply y Let the numer e n ` n - 3 ` numer douled minus 3 Write rule for: doule the differene etween numer nd 3 multiply y minus Let the numer e n ` ( n - 3) Brkets used euse n 3 is lulted first ` doule the differene etween numer nd 3 Write rule for: the quotient of 4 times numer nd 3 divide Let the numer e n numertor denomintor ` 4n 3 4n ws first in the sentene so it is the numertor H SERIES TOPIC 9
How does it work? Your Turn Phrses s lgeri expressions Write these phrses s lgeri expressions (let the numer e n ) The sum of numer nd 7: Phrses s Algeri Expressions.../.../0... ALGEBRA BASICS * ALGEBRA BASICS * n + 7 The differene etween 9 nd numer: The sum of 6 times numer nd : d The produt (#) of numer nd 4: e The quotient (') of two more thn numer nd 3: f The differene etween numer squred nd 6: g The produt of numer minus 5 nd : h 8 less thn twie numer: i 0 dded to numer hlved: j A numer multiplied y 5 more thn itself: 0 H SERIES TOPIC
How does it work? Your Turn Phrses s lgeri expressions Cirle whether the lgeri expression is orret or inorret for eh phrse. A numer multiplied y 4 dded to 7: Corret Inorret 4n + 7 The differene etween numer nd 4: Corret Inorret 4 - n The sum of 6 nd the produt of 3 nd numer: Corret Inorret 3n + 6 d The quotient of 4 plus numer nd 9: Corret Inorret 4 ' ( n + 9) e A numer divided y 5 nd dded to the numer: Corret Inorret n + 5 5 f A numer times the differene etween the numer nd one: Corret Inorret n( n - ) g The sum of numer nd three minus the numer hlved: Corret Inorret n 3 - n + h The produt of 6 more thn twie numer nd 4: Corret Inorret 4(n + 6) i The produt of numer squred nd 3: Corret Inorret (3 n) j The quotient of 5 less thn numer nd the numer: Corret Inorret n 5 n H SERIES TOPIC
How does it work? Addition nd sutrtion + & If the vrile prts re extly the sme the terms re lled like terms. Like terms: x Like terms -x 3 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 dded or sutrted. Simplify + + Vrile prts re the sme (like terms) ` + = 3 Simplify 8x - 3x 8x - 3x like terms ` 8x - 3x = 5x Simplify 3d + 4d + 6 d d 3 4 6 + + like terms 3d + 4d + 6 = 7d + 6 This nnot e simplified ny further Why don t we dd or sutrt unlike terms? Good Question! Let s look t prolem the lst exmple ould represent. At pini for pets eh dog gets 7 trets nd eh t gets 6 trets. Numer of trets needed is: (7 trets # numer of dogs) + (6 trets # numer of ts) = (7 # d) + (6 # ) the numer of dogs the numer of ts Simplified: = 7d + 6 d nd represent two different nimls so it does not mke sense to dd them together. Therefore 7d + 6 is the simplest expression for this prolem. H SERIES TOPIC
SIMPLIFYING * SIMPLIFYING * SIMPLIFYING * How does it work? Your Turn Addition nd sutrtion Simplify: + 9 3u + 5u Addition nd Sutrtion.../.../0... 4r - 9r d 4g - 7g e 6m - 8m f - x + x g 7y + y + 4y h 30p - 5p - 0p Simplify: (psst: look for the like terms!) 3m + 9n + m 4 + + 0 6x + 9y + 5y d 9d - 5-3d e 7e + e + f 3g - 5g - 4h H SERIES TOPIC 3
How does it work? Grouping like terms Terms n hve the sme vrile letter ut still not e like terms. Sme hrter ut not like Simplify 7 + 3 + + is different to so they re not like terms. Like terms ` 7 + 3 + + = 7 + + 3 + Grouping the like terms Like terms = 8 + 5 Eh term of n expression inludes 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 - 3k Simplify It s helpful to irle the like terms with similr shpes inluding the sign in front. -3 Here re two more exmples tht omine two simplifying onepts. Simplify nd write in frtion form: ( 5 + 4 - ) ' 3 ( 5 + 4 - ) ' 3 = (3 + 4 ) ' 3 = 3 + 4 3 Simplify the rket Write division s frtion Simplify eh rket nd write in frtion form: ( x - x + 8x) ' ( 3x + 8x - 5x) ( x - x + 8x ) ' ( 3x + 8x - 5x) = ( 9x - x ) ' ( x - 5x) Simplify the rket = 9x - x x - 5x Write division s frtion 4 H SERIES TOPIC
How does it work? Your Turn Grouping like terms Simplify: (psst: look for the like terms!) 9 + 3 + + 4 4p + 3p + 9p + 7p ROUPING LIKE TERMS *.../.../0... GGROUPING LIKE TERMS * n - m - n - m d 3y - 5x + y - 8x e 9p - 4q + 3p + q f 4 + 4-3 + Como time! Simplify nd write in frtion form: y ' ( y + x - y) ' ( 7p - 5p - 8p ) 3 Simplify eh rket nd write in frtion form: ( x - 3y + x) ' ^4x + 3x - yh ^ # 4 + 3 # h ' (3 # # + ) H SERIES TOPIC 5
ESCAPE FROM ALGEBRA ISLAND * ESCAPE FROM ALGEBRA ISLAND * How does it work? Your Turn Espe from lger islnd puzzle.../.../0... Espe from Alger Islnd puzzle Squre steps = multiply Cirle steps = divide Trpezium steps = dd Pentgon steps = sutrt } Rememer like terms only! One pth hs een found for you! 6 ^6^4x + 4x h- 5x @ ' h ' 3x@ # = x Strting with vlue of 4x trvel long the lines from step to step until you get to the outer edge. Eh step ffets your vlue. If you hve extly x left when you reh one of the shpes t the outer edge then you hve esped! Good luk. How mny pths n you find to get wy from Alger Islnd? How mny steps is the longest pth you n find? 6 H SERIES TOPIC
How does it work? Bringing ll the previous onepts together These exmples omine the different simplifying onepts together. Clulte the vlue of 4 ' 3 when = 6 When = 6 4 = 4 # 6 not 46! 4 ' 3 = 4 # 6 ' 3 or 4 ' 3 = 4 3 = 6 = 6 = 4 ' 3 = 8 4 # = 6 3 = 4 3 = 8 This is useful in questions with multiple vriles. The fny nme given to doing this sort of thing in Mthemtis is sustitution. Clulte the vlue of 5x + y when x = nd 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 + 3n - m + 5n when m = 6 nd n = -3 Simplify: 4m + 3n - m + 5n = 4m - m + 3n + 5n Identify the like terms nd their sign Group the like terms = m + 8n Simplify Evlute: m + 8n = # 6 + 8 #-3 Sustitute in the vrile vlues "find the vlue of" m = 6 = - 4 = - n = -3 H SERIES TOPIC 7
How does it work? The sme vrile vlue n e sustituted into unlike terms. Evlute 3p + 8p - p - 3p when p = Simplify: 3p + 8p - p - 3p = 3p - p + 8p - 3p Identify the like terms nd 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 = 3 nd y = 3x Rememer: numertor denomintor x = 3 y = x + y = # 3 + 3x 3 # 3 x = 3 = 6 + 9 = 8 ( 8 ' 9) 9 = Sustitute in the vrile vlues Simplify the numertor nd denomintor Simplify the frtion Evlute m n when m = nd n = 7 Evlute: m n = # m # n Expnded form # m # n = # # 7 Sustitute in the vrile vlues m = n = 7 = # 4 # 7 = 56 Multiply terms together 8 H SERIES TOPIC
SIMPLIFYING: BRINGING ALL THE CONCEPTS TOGETHER * How does it work? Your Turn Bringing ll the previous onepts together Clulte the vlue of these expressions when v 4 = 4v + 4 ' v.../.../0... 0 v 4 d v + 6 7 Clulte the vlue of these expressions when =- nd = 5 + 3-6 4 + d 4 3 Evlute these expressions when = 6 d = 9 + d + + 3d + d + 3 d d d d - ^ - + d h # ^ d h H SERIES TOPIC 9
How does it work? Your Turn Bringing ll the previous onepts together & Give these three vrile questions go! 4 Evlute these expressions when x = 6 y = 3 nd z =- 8 x + y + z 3 z + xy x - yz d 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
Where does it work? Tles of vlues These re used to show how one vrile hnges when nother vrile in given rule is hnged. Complete the tle of vlues using the rule: 3 = + 0 3 4 5 Sustitute eh vlue of into the rule to find 0 3 4 5 3 4 5 6 7 8 = 0 = = = 3 = 4 = 5 ` = 0 + 3 ` = + 3 ` = + 3 ` = 3 + 3 ` = 4 + 3 ` = 5 + 3 = 3 = 4 = 5 = 6 = 7 = 8 Complete the tle of vlues using the rule: y = x 3 x 3 6 9 5 8 y 3 4 5 6 x = 3 x = 6 x = 9 x = x = 5 x = 8 ` y = 3 ' 3 ` y = 6 ' 3 ` y = 9 ' 3 ` y = ' 3 ` y = 5 ' 3 ` y = 8 ' 3 = y = y = 3 y = 4 y = 5 y = 6 Complete the tle of vlues using the rule: m = 3n - n 0 3 4 5 m - 5 8 4 n = 0 n = n = n = 3 n = 4 n = 5 ` m = 3 # 0 - ` m = 3 # - ` m = 3 # - ` m = 3 # 3 - ` m = 3 # 4 - ` m = 3 # 5 - =- = = 5 = 8 = = 4 H SERIES TOPIC
TABLE OF VALUES * TABLE OF VALUES * Where does it work? Your Turn Tle of vlues T A B L E Complete eh tle of vlues using the given rule..../.../0... u = v + = d v 0 3 4 u d 0 3 4 g = 4h 3 d y = x + h 3 4 5 g x 4 6 8 0 y Drw lines to mth eh tle of vlues with the orret mthing rule. 0 4 6 8 3 4 5 6 3 4 5 6 6 0 3 4 0 3 6 9 0 3 4 3 5 7 9 = + 3 = + 4 = 3 = 5-4 3 Hve go t figuring out the rule used for eh tle of vlues elow nd fill in the gps. Rule: Rule: x 0 3 4 m 0 3 4 y 5 6 9 n 0 4 Rule: p 0 3 4 d Rule: 5 6 q -3 - d -5-3 9 H SERIES TOPIC
Where does it work? Numer ptterns There re lot of ptterns in the world nd it is useful skill to e le to work them out.... t the end mens the digrms ontinue to hnge following the sme pttern. Look t the following ptterns of riks lid y uilder over three minute period: st minute nd minute 3 rd minute... (i) Desrie the numer pttern of riks lid y the uilder every minute: Pttern: The uilder ly s three riks in the first minute nd then nother 3 every minute therefter (ii) Write numer pttern for the totl numer of riks lid fter every minute: Numer Pttern: 3 6 9... The numer pttern formed n e displyed using tle of vlues: Look t the inresing rrow sign pttern elow: st sign nd sign 3 rd sign... (i) Desrie the numer pttern formed 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 3 Numer of rrows 3 5 7 Numer pttern for the rrows used in eh sign inreses y two rrows eh time. (iii) How mny rrows would e in the 6 th sign of the pttern? First six vlues in the numer pttern re: 3 5 7 9 3 ` there would e 3 rrows in the 6 th sign H SERIES TOPIC 3
Where does it work? Your Turn Numer ptterns For eh of these pttern digrms: (i) Desrie the numer pttern formed y the shpes (ii) Write numer pttern for the totl numer of shpes used to mke the first five digrms... (i) (ii)...... (i) (ii)...... * NUMBER PATTERNS 4 6....../.../0... * NUMBER PATTERNS (i) (ii)... 4 H SERIES TOPIC
Where does it work? Your Turn Numer ptterns For eh of these pttern digrms: (i) Complete tle of vlues for the first 4 digrms (ii) Write down how mny shpes re needed for the 7 th digrm... st nd 3 rd (i) Digrm numer 3 4 Numer of herts (ii) Numer of herts needed for the 7 th digrm =... st nd 3 rd (i) Digrm numer 3 4 Numer of hexgons (ii) Numer of hexgons needed for the 7 th digrm =... st nd 3 rd (i) Digrm numer 3 4 Numer of mthstiks (ii) Numer of mthstiks needed for the 7 th digrm = H SERIES TOPIC 5
Where does it work? Modelling numer ptterns m=t + Modelling numer pttern is the fny wy Mthemtiins sy: find the lger rule for the pttern. These exmples use the numer of shpes nd mthstiks in eh pttern to find the rule. Find the lgeri rule for the mthstik pttern elow: Numer of tringles (t): Numer of mthstiks (m): 3 3 6 9......... Pttern: Strting with 3 mthstiks the numer of mthstiks goes up y 3 with eh tringle dded on ` The numer of mthstiks in eh digrm equls 3 x the numer of tringles in the digrm Using lger this is: m = 3t The generl rule Completing tle of vlues n help to find the generl rule: Numer of tringles (t) 3 Numer of mthstiks (m) 3 6 9 Numer of mthstiks (m) equls the numer of tringles (t) multiplied y the onstnt inrese 3 3 Find the generl rule for this pttern formed using mthstiks... Numer of tringles (t): Numer of mthstiks (m): 3 4 5 7 9 Pttern: Strting with 5 mthstiks the mthstiks inrese y for eh extr tringle dded on Numer of tringles (t) 3 4 Numer of mthstiks (m) 5 7 9 Cheking with the first shpe this time we need 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
Where does it work? Your Turn MODELLING NUMBER PATTERNS * MODELLING NUMBER PATTERNS * Modelling numer ptterns Write down the generl rule for eh of the following mthstik numer ptterns:.../.../0...... Let s e the numer of squres nd m the numer of mthstiks Numer of squres (s) Numer of mthstiks (m) Generl rule: m = # s +... Let t e the numer of tringles nd m the numer of mthstiks Numer of tringles (t) Numer of mthstiks (m) Generl rule: m t = + 3... Let r e the numer of grey rings nd the numer of irles drwn Numer of grey rings (r) Generl rule: Numer of irles drwn () r = + 4... Let p e the numer of pentgonl shpes nd t the numer of tringles used Numer of pentgonl shpes (p) Generl rule: Numer of tringles (t) t = p H SERIES TOPIC 7
Where does it work? More numer pttern modelling The digrm numer (n th digrm) nd the numer of shpes in eh digrm is used for these questions. Find the generl rule for this pttern formed using pentgons... n th digrm (n) Pentgons (p) used: st nd 3 rd 4 th 5 8...... Pttern: Strting with pentgons the numer of pentgons goes up y 3 for eh following digrm Digrm numer (n) 3 4 Numer of pentgons (p) 5 8 3 3 3 Cheking with the first shpe we need to put into the rule to get the orret numer of pentgons Multiply n y 3: ` p = 3n ` p = 3n - The generl rule This method lso works for mthstik ptterns. Find the generl rule for this pttern formed using mthstiks... n th digrm (n) mthstiks (m) used: st nd 3 rd 4 0 6...... Pttern: Strting with 4 mthstiks the numer of mthstiks goes up y 6 for eh following digrm Digrm numer (n) 3 Numer of mthstiks (m) 4 0 6 Cheking with the first pttern we need 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
Where does it work? Your Turn More numer pttern modelling Write down the generl rule for eh of the following mthstik numer ptterns:.../.../0... * MORE NUMBER PATTERN MODELLING... st nd 3 rd Let n e the digrm numer nd m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) Generl rule: m = # n +... st nd 3 rd Let n e the digrm numer nd m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) Generl rule: m n = +... st nd Let n e the digrm numer nd m the numer of mthstiks Digrm numer (n) Numer of mthstiks (m) 3 rd Generl rule: m n = + d... st nd 3 rd Let n e the digrm numer nd m the numer of mthstiks Digrm numer (n) Generl rule: Numer of mthstiks (m) m = n H SERIES TOPIC 9
Where does it work? Your Turn More numer pttern modelling Write down the generl rule for eh of the following numer ptterns:... st nd 3 rd Let s e the numer of snow flkes nd n the n th digrm Digrm numer (n) Numer of snow flkes (s) Generl rule: s = # n... st nd 3 rd Let t e the numer of tyres nd n the n th digrm Digrm numer (n) Numer of tyres (t) Generl rule: t n = -... st nd 3 rd Let d e the numer of dots nd n the n th digrm Digrm numer (n) Numer of dots (d) Generl rule: d = # d st Let t e the numer of tringles formed nd n the n th digrm Digrm numer (n) nd # Numer of tringles (t) = 3 rd Generl rule:... There re tully two numer ptterns here the other involves the numer of mthstiks used. See if you n work it out! 30 H SERIES TOPIC
Wht else n you do? Using the generl rule Sustitution into the generl rule is used to nswer questions out the n th digrm in pttern. Find the generl rule for the prllelogrm pttern:... Let p e the numer of prllelogrms nd n the n th digrm n 3 p 4 6 ` p = n generl rule How mny prllelogrms re there in the 0 th digrm of the pttern ove? ` p = # 0 Sustitute n = 0 into the generl rule = 40 prllelogrms Find the generl rule for the mthstik numer pttern:... Let m e the numer of mthstiks nd n the n th digrm n 3 m 3 8 3 5 5 How mny mthstiks re there in the 8 th digrm? ` m = 5n - generl rule ` m = 5 # 8 - Sustitute n = 8 into the generl rule = 38 mthstiks Find the generl rule for the mzing stik gymnst pttern:... Let g e the numer of gymnsts nd n the n th digrm n 3 g 5 8 3 3 How mny gymnsts re there in the 30 th pttern? ` g = 3n - generl rule ` g = 3 # 30 - Sustitute n = 30 into the generl rule = 89 gymnsts H SERIES TOPIC 3
Wht else n you do? Your Turn USING THE GENERAL RULE * USING THE GENERAL RULE * Using the generl rule Every time Nimh kiked gol (g) the tem sore (s) inresed y. The generl rule for this is given y: s = g.../.../0... How mny points did Nimh sore fter kiking g = 8 gols? If the totl numer of hikens () tht rossed the rod fter eh minute (m) is given y the generl rule: = 5m - 3 How mny hikens hd rossed the rod when m = 7 minutes? The totl numer of shirts (s) tried on y ustomers () in store is represented y the generl rule: s = + How mny shirts hd een tried on when there were = ustomers? d The totl numer of vegetrin mels (v) ordered (on verge) in resturnt y diners (d) is given y the generl rule:: v = d 3 How mny vegetrin mels were ordered on night with d = 36 diners? 3 H SERIES TOPIC
Wht else n you do? Your Turn Using the generl rule The stked tyres elow form numer pttern. Find the generl rule nd then lulte how mny tyres re in the th stk.... st stk nd stk 3 rd stk Let t e the numer of tyres nd n the n th stk of tyres. n t Generl rule: Tyres in the th stk: 3 New leves re ppering on tree eh dy forming numer pttern. Find the generl rule nd lulte how mny leves there re on the 0 th dy.... Dy Dy Dy 3 Let l e the numer of leves nd n the n th dy. n l Generl rule: Leves on the 0 th dy: 4 The sketlls represent the numer of good shots during eh trining session. The good shots re inresing y the sme mount eh time. How mny good shots re mde during the 8 th session?... Session Session Session 3 Let s e the numer of good shots nd n the n th trining session. n s Generl rule: Good shots in the 8 th session: H SERIES TOPIC 33
Wht else n you do? Your Turn Using the generl rule 5 A tiler is lying out some otgonl tiles in the following numer pttern:... st digrm nd digrm 3 rd digrm How mny tiles will e lid in the th digrm? let t e the numer of tiles lid nd n the n th digrm. n t Generl rule: Tiles lid in the th digrm: 6 Tringles hve een stked to form n inresing numer pttern:... Rememer me? 7 tringles tringles 7 tringles Find the generl rule nd lulte the numer of tringles needed for the 5 th shpe. Let t e the numer of trngles nd n the n th shpe. n t Generl rule: Tringles in the 5 th shpe: 34 H SERIES TOPIC
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 Words nd symols Alger uses letters or symols lled vriles. Eh prt in n lgeri expression is lled 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: Simplified 6 # n = 6n x # y = xy Expnded 6n = 6 # n xy = x # y Division It sometimes helps to write divisions s frtion first when simplifying: ' = y Brkets n e hidden when writing division s frtion: y ' ^4 + xh = 4 + x When doing the reverse rkets must e put in: 3 - m = ^ 3 - m h ' 6 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 Addition nd sutrtion Only Like terms n e dded or sutrted. Like terms: x Like terms -x 3 Like terms y -5y Like terms Not Like terms: Not Like terms p p Not Like terms x -5y Not Like terms H SERIES TOPIC 35
Chet Sheet Tle of vlues These show how one vrile hnges when nother vrile in given rule is hnged Rule: y = x + x 3 y 4 6 8 x = `y = # + = 4 x = ` y = # + = 6 x = 3 ` y = # 3 + = 8 Modelling numer ptterns This is fny wy Mthemtiins sy "find the lger rule for the pttern" The rule n e found using two methods:. Compring the digrm numer with the numer of shpes in it.. Compring the numer of shpes with the numer of ojets used to mke eh digrm. Tles of vlues help with oth methods n 3 s 4 6 8 + + This mens 'n' is multiplied y in the rule After looking t the first vlues of n = nd s = 4 the rule must e: s = n + Using the generl rule The numer of shpes/ojets in prtiulr prt of the pttern is found 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. 36 H SERIES TOPIC
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