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

Transcription

1 Alger Bsis H SERIES Alger Bsis 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 How oes it work? Alger Bsis Pge questions Wors n symols The vrile is The vrile is m The vrile is k The vrile is + x 5 # w 0 x' x # g # 6 00' s 5 # x + 6 x if x 0 # m if 7 ' if m 5 + # z if z h k 8 y 6 Pge 5 questions Multiplition # 7 # k # k u # u k 5# r # p 5pr n # m # m m n e 6 # # # 6 # # # 8 # 8 f # j # l # # k # # j # l # k # j # k # l jkl Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC

4 How oes it work? Alger Bsis Pge 5 questions pq # p# q # # mn # m # m # n Como Time! x + # # # 5g # 5 # 0 m # # 9 6 Pge 7 questions Division ' ' 5 r 5 y z ' ^ + h ^y+ zh' z + r + z w w ' ' + ^ + h 6 6' x x + ^ + h x - y ^ x - y h ' ^ v + w h v+ w 6 ' 6 ' 5x 0y x y x' y ^m+ nh p m+ n p ^m+ nh ' p H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

5 How oes it work? Alger Bsis Pge 8 questions Mixe simplifying onepts 5 # ' 5' 5 # m' ^+ nh m' ^+ nh m + n n # m' ( # # ) mn ' mn (8 # ) p '( # q) 6p' 9q 6p 9q e x# x' ( y+ x) x '( y+ ) x x y + x f # f# ' ( + f # e) f' ( + ef) f + ef ' # ' + ( + ) ' q- r ( q - r) ' 9q 9q ( q- r) ' (9 # q) l l ' ( j k) j- k - l # l' ( j- k) e 5 5 ( ) ' # # ' ( # + # ) 7xyz f 7xyz ' ( x+ 7y) x+ 7y 7 # x# y# z' ( x+ 7 # y) Pge 0 questions Phrses s lgeri expressions n n 6# n+ 6n+ # n n Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC

6 How oes it work? Alger Bsis Pge 0 questions e ( n + ) ' n + f n - 6 g ( n- 5) # ( n- 5) h # n- 8 n- 8 i 0 + n ' 0 + n j n # ( n+ 5) nn ( + 5) Pge questions Corret Inorret Corret Inorret expression shoul e: n - Corret Inorret Corret Inorret expression shoul e: ( + n) ' 9 or + n 9 e Corret Inorret expression shoul e: ( n' 5) + n or n n 5 + f Corret Inorret g Corret Inorret expression shoul e: n + ( - n ) h Corret Inorret i Corret Inorret expression shoul e: n n # j Corret Inorret H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

7 How oes it work? Alger Bsis Pge questions Aition n sutrtion u+ 5u 8u 0 r- 9r 5r g- 7g -g e 6m- 8m -m f - x+ x -9x g 7y+ y+ y y h 0p- 5p- 0p 5p m + 9n + m m+ m+ 9n m+ 9n Like terms 6x + 9y + 5y 6x+ y Like terms 6-5 e 7e + e + 8e+ f g - 5g - h -g- h Like terms Like terms Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC 5

8 How oes it work? Alger Bsis Pge 5 questions Grouping like terms p + p + 9p + 7p p + 7p + p+ 9p Like terms p + p n - m - n - m n- n - m- m -m y - 5x + y - 8x y+ y - 5x- 8x y- x e 9p - q + p + q 9p+ p - q+ q p+ 8q e Como time! y' ( y + x - y ) y' ( y+ x) y y + x ( 7p - 5p - 8 p )' (- p - 5) p ' p 5p H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

9 How oes it work? Alger Bsis Pge 5 questions ( x - y + x )'( x + x - ) y (x- ) y '(7x- ) y Like x- y terms 7x- y ( # + # ) '( # # + ) (8+ 6) '( + ) ( 8+ 6) ' Like terms Pge 6 questions Espe from Alger Isln Puzzle x 5 7 x 8x 0 x x x x x x 5 x 7 8 x 7x 8x x x 5 x 7 6 5x 0 5 x x x x x Alger Isln 5 5x x 6x 7 x 7 5 x x 5 8x x 5x 5 x 7 x x7 x 50 8x x 5 x 7 6x 7 x x x x x 8x 7 5 Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC 7

10 How oes it work? Alger Bsis Pge 9 questions Bringing ll the previous onepts together v + # + 8 ' v ' ( # ) ' v v + 6 ( v + 6) ' 7 7 ( # + 6) ' 7 ' # # 5-6 #(- ) 5 - (- ) 7 ' ( ) + + ' (- + 5) ' 8 ' # ((- ) 5) ' ( # 5) ' 0 ' # 6+ # # 6 0 ( ) ( ) - - ' - - ( # 9-6) ' (9-6) ' ( - ) #( - ) ( - ) #( - ) ( 6-9) # ( # 6-9) (- ) # -9 8 H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

11 How oes it work? Alger Bsis Pge 0 questions x+ y+ z # 6+ + (- 8) z- xy #(- 8) + 6# x - yz 6 - ( # (- 8)) 6 - (- ) 60 y y' ( x z) x+ z + # ' (6 + (- 8)) # (- ) -6 5 ( + ) ( - ) ( + ) ' ( - ) when, - #( + #(- )) ' (- - ) # (- 6) ' (- 6) # 6' 6 6 ( x- y) e ( y- x) o ^( x- y) ' ( y- x) h when x -, y -5 ( 6 ' 6) () ^( - - (- 5) h ' ^-5- (- )) h ^( - + 5) ' (- 5+ ) h ^ ' (- ) h Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC 9

12 Where oes it work? Alger Bsis Pge questions Tles of Vlues u v + v 0 u g h- h 5 g y x + x y Rule: y x 5 + Rule: n # m or n m x 0 m 0 y n Rule: q p - Rule: - 5 p q H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

13 Where oes it work? Alger Bsis Pge questions Numer ptterns, (i) Strting with one smiley fe in the first igrm, smiley fes re e to eh igrm every time (ii) Numer pttern for first five smiley igrms:,, 5, 7, 9,... (i) Strting with three rrows in the first igrm, rrows re e to eh igrm every time (ii) Numer pttern for first five rrow igrms:, 7,, 5, 9,... (i) Strting with 6 tringles to form the first igrm, 6 tringles re e to eh igrm every time. (ii) Numer pttern for first five rrow igrms: 6,, 8,, 0,... Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC

14 Where oes it work? Alger Bsis Pge 5 questions Numer ptterns st n r (i) Digrm numer Numer of herts 5 8 (ii) Numer of herts neee for the 7 th igrm 0 st n r (i) Digrm numer Numer of hexgons 8 8 (ii) Numer of hexgons neee for the 7 th igrm st n r (i) Digrm numer Numer of mthstiks 7 5 (ii) Numer of mthstiks neee for the 7 th igrm 7 H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

15 Where oes it work? Alger Bsis Pge 7 questions Moelling Numer Ptterns Numer of squres (s) Numer of mthstiks (m) 7 0 m # s+ Numer of tringles (t) 5 Numer of mthstiks (m) 7 9 m t+ Numer of grey rings (r) Numer of irle rwn () r+ Numer of pentgonl shpes (p) Numer of tringles (t) 7 t 7 p Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC

16 Where oes it work? Alger Bsis Pge 9 questions More numer pttern moelling st n r Digrm numer (n) Numer of mthstiks (m) 7 0 m # n+ st n r Digrm numer (n) Numer of mthstiks (m) 5 9 m n + st n r Digrm numer (n) Numer of mthstiks (m) 9 7 m n + 5 st n r Digrm numer (n) Numer of mthstiks (m) m 9 n - 5 H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

17 Where oes it work? Alger Bsis Pge 0 questions More numer pttern moelling st n r Digrm numer (n) Numer of snow flkes (s) 6 s # n st n r Digrm numer (n) Numer of tyres (t) 9 5 t n - st n r Digrm numer (n) Numer of ots () 5 9 # n + st n r Digrm numer (n) Numer of tringles (t) 5 7 # t n + Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC 5

18 Wht else n you o? Alger Bsis Pge questions Using the generl rule s g Nimh sore: s # 8 6 points 5m- The numer of hikens tht h rosse the ro: 5 # 7- hikens s + The numer of shirts trie on: s # + 5 shirts v The numer of vegetrin mels orere: v 6 vegetrin mels Pge questions,... st stk n stk r stk n t 8 Tyres in the th stk: t 5n- t 5 # - 58,... Dy Dy Dy n l 7 l n- Leves on the 0 th y: l # H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

19 Wht else n you o? Alger Bsis Pge questions,... Session Session Session n s 0 7 s 7n- Goo shots in the 8 th session: s 7 # 8-5 Pge questions 5,... st igrm n igrm r igrm n t 0 6 t 6n- Tiles li in the th igrm: t 6# - 70 Rememer me? 6,... 7 tringles tringles 7 tringles n t 7 7 t 5n+ Tringles in the 5 th shpe: t 5 # Alger Bsis Mthletis P Lerning Lt H SERIES TOPIC 7

20 Alger Bsis Notes 8 H Alger Bsis SERIES TOPIC Mthletis P Lerning Lt

21

22 Alger Bsis H SERIES