basic math again

Upload: jaded-jade

Post on 02-Jun-2018

218 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/10/2019 basic math again

    1/21

    BASIC MATHEMATICS

    COURSE WORKPOLYAS MODEL

    STUDENTS NAME : ZAHIDAH BINTI MD YUSSOF

    I/C NUMBER : 900407-06-!"4

    INDE# NUMBER :$00%$!$"!0046

    &ROUP : PPISMP MATHEMATIS COHORT '(ULY0% INTAKE)

    SEMESTER : TWO

    LECTURERS NAME : PN NOOR KHALIZA BINTI MOHD KHAIRUDDIN

  • 8/10/2019 basic math again

    2/21

    ACKNOWLED&EMENT

    F*+, . 112 I 3.15 1* . 8 . &.5 ;, I 8+.1? +=+5*= . Polyas Model,;;,,11@ A+ 112 I

    ?= . **,8 ,;8 * 5**;1 ,

    I 1,. 3.15 1* . 8 . ?@ ,*; ?8?*; 1;++2 P K81* 38.

    =1*. . 8*, , N. .+=. ?@ 1.

    ??+,2 F+82 N*882H, 5 (,?* I 1,. 3 . 8 . ?@

    ,*.+ 8 13@, 81> ? 5 ?@ =+.> ??+, * .+5+ . **,8 8*, , 5

    =* >1*. 18.=8 8@ 1,. 8.>1 38. + *

  • 8/10/2019 basic math again

    3/21

    CHAPTER !: INTRODUCTION

    C.?>1 ?8?*;1 ,, ,;8 , >+.1? ,.1+.>.+**, . 5 8*=8+ .+5+ ?8?*;1 >+.;,,,

    ,;8 , +>+,*.2 ,+;*.2 5 =+1**. A ,;**= ,>; .

    8? 8.=8 *, 8 *1*@ . =+1* +.? ,>;**; >+*;, 5 . .+?

    3 5 ?.+ ,+; ;.;>, T8 P+*;*>1, 5 S5+5, .+ S;8..1

    M8?*;, 'N*.1 C.;*1 . T;8+, . M8?*;,2 $000) ;11, .+

    *,+;*.1 >+.=+?, 8 ?>8,* >+.1? ,.1*=

    ,5, 5 ,.>8*,*;*. 3*8 ?8?*;1 >+.;,,, ,;8 ,

    +>+,*.2 ?8?*;1 +,.*=2 ,+;*.2 5 =+1**. I =.,

    . . >+.;1*? 8 ,5, ,8.15 5 *;+,5 ,.>8*,*;*. 3*8?8?*;1 >+.;,,,2 ,>;*11@ >+.1? ,.1+,*.2 5

    +,.*=2 5 8*+ *;+,5 *1*@ . +1; . 5 ?.*.+ 8*+ 3.+ ,8.15

    15 . =++ ,+;*. 5 ;>*1*@ .+ =+1**. T8,2 8 *1*@ .

    =+1* *, 8 +,1 . ;+* ?8?*;1 >+*;, 5 *, *?>.+

    ;.?>. . ?8?*;1 *1*@ T8 5? . 8*, *1*@ *, .;*1 >+.1?-,.1 * 8*+ *1**, . .+?1 >+.1?,

    ,>..,1@2 8*+ 1**1*@ * 5 ?=?2 5 8*+ *1*@ . ,+;

    5 =+1* T8+ *, 1,. ?>*+*;1 +,;8..1 1

  • 8/10/2019 basic math again

    4/21

    CHAPTER $: LITERATURE REIEW

    A 311-.3 >+.1?-,.1+.+.1?-,.1+.+?; . .8,*, . 8+*,*;

    ,*11, 38*1 *=.+*= J?=+*1 ,*11, ;,,+@ . +=1 ., ;*1*=2

    *?>1?*=2 5 1..*= ; 3+ +1115 , .+**.2 .+=**.2

    ;*.2 5 ;*+8,*. ,+=*,2

    1@,*, . *.+?*.2 ***1 5 ,, +>+,*.2 5 ,,,,? .

    11*=2 5 1.;1 >1*= E;*. ++, . +=1*. .

    81, I *;15, >+.+?; . 1.;1 ;*.,2

    ?.*.+*= >+.=+,, 5 ;.,*,;@ . 1.;1 >1,2 5 +5-. 5;*,*.,

    ',>5

  • 8/10/2019 basic math again

    5/21

    ;8+;+*,*;, 8 ?@ *1; >+.+?; T, +.;,, F.+

    ?>12 *5*+.+?;

    F*11@2 ,+=@ +8,*.2 .+=**=2 ;*= >1,2 5 ;8;*= 5

    +*;1+ .; .

    ,, ;*., A,+;*. *, >+.;,, 8 .;;+, 38 8 ,;

    .;,, *. . ,>;**; >+.>+*, . =*+.>+*, * *,.1*. +.? 8 .+*=*1 T8*, ?*=8 5. . 5+,5

    8 ,,; . ;+* >8.? 5 . 1+ >>1@ 8 ,? 8.+@ . .8+

    >>1*;1 ;,,

    E+1@ +,+;8 . =+1**. .;,5 . 1?+@ ,;8..1 ;8*15+,

    *1**, . =+1* ?+ ;.;>, 'D+.;,, . =+1**.

    ?.= ?8?*;, 5;*. +,+;8+, * 8 .+?+ S.

  • 8/10/2019 basic math again

    6/21

    Shapiro'!96) 3+. 8 ?.= ?8?*;11@ =*5 ,5,2 8

    5? . =+1**., .;;+, +.? 8 *+, ?>1,2 8 ***1

    ,=, . 1+*= T+,+ * 8 =+1 .+? *, 1?., ?+=5 * *? 3*8

    =+1**. 5 *, ;;.?>1*,85 *??5*1@ .+ 38.1 ;1,, . >+.1?, .

    ,*=1 @> ?.= 1,, ;>1 ,5, =+1**., +*> =+511@ 5

    + ?*,5 1+ ,=, .+ 8@ 5. . 5 11

    Krutetskii'!976) 1@5 8 =+1**. *1*@ . .8 J.+?1J 5

    J;>1J '=*5) ,5, * ,+*, . >+*?, H 8@>.8,*5 8

    J,5, 3*8 5*+ *1**, + ;8+;+*5 @ 5*+;, * 5=+ .

    5? . .8 8 *1*@ . =+1* ?8?*;1 ?+*1 5 8

    *1*@ . +??+ =+1**.,J K+,** ,5*5 !9 ,5, 3*8 +*?, 3*8 8 !9 ,5,2 K+,**

    ;.;155 8 ?.+ J;>1J '=*5) ,5, 3+ 1 . .+? ?8?*;1

    =+1**., +>*51@ 5 +.51@ H .5 8 8, J;>1J ,5, 3+

    1 . 5*,;+ 8 =+1 ,+;+ . 8 >+.1?, .+ 8@ ,.11J ,5, *+5 >..+1@ * 8*, , I .+5+ .+,5, . .+?1 =+1**., ;.++;1@2 8@ 85 . ,+; +.? 8

    ,>;**; ;. 5 ,*=1 . ,*?*1+**,2 ,+;+,2 5 +1*. ,8*>,

    M., . 8 *, 1*++ . 8 >+.;,, . =+1**. *, * 8

    ;. . ?+ ;.;>,2 +*8?*;2 5 1=+ T8+ *, 1; . +,+;8 .

    =+1**. * 8 ;. . 8*=8+ .+5+ ?8?*;1 >+.;,,, ,;8 ,

    >+.1? ,.1+.1?-,.1

  • 8/10/2019 basic math again

    7/21

    CHAPTER ": METHODOLO&Y

    A, >+ . 8*, 3.+ . >+.1? ,.1 >+.1?-

    ,.1+.;,,, 38*;8 + 5+,5 8 >+.1?2 512 ;++@ . 8 >1

    5 1.. ;

    1. Understand the prole!" #See$

    M@ ,5, + .+.1? A 8*, >.* =+.>

    5*,;,,*. *, *;*1 T8 ,*., 8 ?@ 81> . 5+,5 8 >+.1?

    +:

    W8 + @. ,5 . *5 . .+ ,8.3

    C @. 5+3 >*;+ .+ 5*=+? . 81> @. 5+,5 8 >+.1?

    C @. +, 8 >+.1? * @.+ .3 3.+5,

    C @. 3.+ . ,.? ?+*;1 ?>1, 8 3.15 81> ? 8

    >+.1? ;1++

    %. Devise a plan" #Plan$

    T8 >1 *, ,11@ ;115 ,+=@ T8 .11.3*= 1*, . ,+=*,2 18.=8 .

    8,*+.1?, 5 5+?* * 8 ,? ;8* ;

    >>1*5 E?* ,*?>1+ .+ ,>;*1 ;, . 8 >+.1? . =* *,*=8 *. 8

    ,.1*. . 8 .+*=*1 >+.1?

    M 1

    M 5*=+?

    W+* *.

    U, =,, 5 ;8;

  • 8/10/2019 basic math again

    8/21

    W.+ ;3+5

    I5*@ , =.1

    &. arry out the plan" #Do$

    C++@*= . 8 >1 *, ,11@ ,*+ 8 51 H.3* 5 5+,5 8 ?., >+.1?, + . ,.1 I >1 5., . 3.+ *??5*1@2 >+,*, 5 5. .

    1 @.+,1 = 5*,;.+=5 I . ,+=@ *, 3.+*=2 +@ 5*+ . *1

    8 ,.1*. *, .*5

    (. Look ack" #heck$T8*, *, ,*?>1@ ;8;*= 11 ,>, 5 ;1;1*., I ,.? ;,,2 8*, 3*11 +*+

    >+.. I+>+ 8 ,.1*. * +?, . 8 .+*=*1 >+.1? D., @.+ ,3+

    ? ,, I, * +,.1 T82 5+?* 388+ 8+ *, .8+ ?8.5

    . *5*= 8 ,.1*. I >.,,*12 5+?* .8+ +15 .+ ?.+ =+1

    >+.1?, .+ 38*;8 8 ;8*, 3*11 3.+

    T8, 5 .8+ =+1 ?8?*;, >+.1?-,.1+.1? ,.1

  • 8/10/2019 basic math again

    9/21

    L.+ L .. 8, ,+5 . 31 .+ +;*, S8 315 ! ?*1 8 *+, 32

    ?*1, 8 ,;.5 32 9 ?*1, 8 8*+5 32 !" ?*1, 8 .+8 32 5

    !7 ?*1, 8 *8 3 I ,8 ;.*, . *;+, 8+ 31*= 5*,; 8*,

    3@2 * 38*;8 3 3*11 L.+ *+, 31 "7 ?*1,

    By using the Polyas Model, we choose the IDENTIFYING PTTE!N as

    our strategy to sol"e the Pro#le$ %.

    Step 1" Understand the prole!

    C1, / I.+?*. ',*= ,*.)

    L.+ 8, ,+5 . 31

    ! ?*1 8 *+, 3

    ?*1, 8 ,;.5 3

    9 ?*1, 8 8*+5 3

    !" ?*1, 8 .+8 3

    !7 ?*1, 8 *8 3

    Step %" Devise a plan

    L.. .+ >+

    M 1 . 8 3, 5 8 ?+ . ?*1, 315 ;8 . 8

    *+, .+ 3,

    Step &" Do the plan

    WEEK MILES WALKED

  • 8/10/2019 basic math again

    10/21

    !

    $

    "

    4

    !

    9

    !"

    H.3 ?@ ?.+ ?*1, 5*5 L.+ 31 * W $ 8 * W !

    ' ! 4 ?.+ ?*1,)

    H.3 ?@ ?*1, 5*5 L.+ 31 * W " 8 * W $

    '9 4 ?.+ ?*1,)

    H.3 ?@ ?*1, 5*5 L.+ 31 * W 4 8 * W "

    '!" 9 4 ?.+ ?*1,)

    WEEK MILES WALKED

    6

    7

    %

    9

    !0

    !" 4 !7

    !7 4 $!

    $! 4 $

    $ 4 $9

    $9 4 ""

    "" 4 "7

    L.+ 3*11 *+, 31 "7 ?*1, * 8 8 3

  • 8/10/2019 basic math again

    11/21

    Y. ?@ +1* 8 @. 5*5 8 . 8 8

    3 . ,.1+.1? N.*; 82 8 ?+ . *?, 8 @. 55 4 ?*1,

    *, . 1,, 8 8 3 ?+

    W $: ! 4 4 55**.1 ?*1,

    W ": $ 4 % 55**.1 ?*1,

    W 4: " 4 !$ 55**.1 ?*1,

    I 8 3 8 L.+ *+, 31, "7 ?*1,2 ,8 8, 555 "6 ?*1, . 8 .+*=*1

    5*,; . ! ?*1 B;, 8+ + "6 Q 4 9 =+.>, . 4 * "62 * ?, 8

    8 32 ,*; 8 3 ?+ *, . ?.+ 8 8 ?+ . =+.>, . 4

    ?*1, 555

    Step (" heck your ans)er

    S.1+.1? @ .,++, * 3. 5*+ 3@,2 5 =*= 8

    ,? ,3+2 >+.

  • 8/10/2019 basic math again

    12/21

    S@+* 3 . 8 ?+ 38+ 8 .=8 3. ,;, . =..5, 5 ;8 ,;

    3, 815 .. ;?1 S@+* 5 8 >.*, 8>*1@ 11 8

    3@2 38*1 8 ,;.5 ;?1 +.*= ,1.31@ 3*8 85 *. 8

    3+ 3*8 8 ,;, . 8*, ; , 8 3, *+5 5 8,52 5 .11.35 @

    8 ;?1 W8*1 * 8 >.52 8 ,;.5 ;?1 3, 3.5+*= 38@ 8 ,;, .

    ,*?*1+ ,*2 38@ 8*, ,;, 3, 85 8>>*1@ 11 8 3@ 8.?2 8 ,3 8 *+, ;?1 ,+==1 3*8 8*,

    ,>, 5 . 8 8

  • 8/10/2019 basic math again

    13/21

    Step %" Devise a plan

    T8 ;*

  • 8/10/2019 basic math again

    14/21

    (++@ 3, ?.3*= 8*, 13 38 8 .*;5 C8+*,@ 3, ,. ?.3*= 8+ 13

    5..+ T8@ ,.>>5 . 1 5 (++@ 1+5 8 C8+*,@ ?.3, 8+ 13

    .;

  • 8/10/2019 basic math again

    15/21

    Step &" Do the plan

    M T1:

    C8+*,@ % 5@, !6 5@, 24 days "$ 5@,

    (++@ 6 5@, !$ 5@, !% 5@, 24 days

    Step (" heck the *ns)er

    T8 5*+; @ C8+*,@ ?.3, 8+ 13, .+ *+, % 5@ *, %2 38*1 (++@

    ?.3, 8+ 13, .+ *+, 6 5@ *, 6

    W8 3 5*5 8 ?1*>1 . 6 5 %2 3 ; = 8 ,? 5@, 8

    C8+*,@ 5 (++@ 3*11 ?.3 .=8+ 5@, . $4

    W8 ?*= 8 12 3 ; ;.;15 8 (++@ 5 C8+*,@ 3*11 ?.3*=

    8*+ 13, .=8+ =* * $4 5@,

  • 8/10/2019 basic math again

    16/21

    +- /S+ -00-2+ S+3*+-G4"

    I 85 ,5*5 11 8 ,+=*, * >+.1? ,.1+ *, 8 , 3@ . ,.1+.1? T8*, *, ;, 8*, @> . ,+=*,

    ; ? ? , 8 1.=*;1 8**= . ,.1+.1? 8 I 85

    F+8+?.+2 ,*= 8, ,+=*, ; ;8 ? . ? ,?+ 5;*,*.

    F+.? 82 I 85 5,*= 3 >+.1? . ,8.3 8 ,*= 8*, ,+=*, *, 8

    ,*, 3@ 5 ?.+ *;* . = ?.+ 1.=*;1 ,3+

    DESI&NED PROBLEM

    L, @+2 C+ C+ *+@ T8*,

    @+2 ,8 *

  • 8/10/2019 basic math again

    17/21

    Step &" Do the plan

    F*5 8 *;+, * 8 ?+ . ;8*15+ *

  • 8/10/2019 basic math again

    18/21

    CHAPTER : CONCLUSION

    W ; ;.;15 8 8+ + ?@ @> . >+.1? ,.1+ , ,+=*, . ,.1+.1? W *5 8 8*, ,+=*, *,

    8 ,*, 3@ . ,.1+.1?, T8*, *, ;,2 3 ,5 8 5 8 3

    ; = +.? 8 >+*; 5 3 ; ? ,?+ =,, +.? 8 >+

    8 .+?5 +.? 8 >+*; B;, . 82 3 8* 8 8*, ,+=*, *,

    8 , * .+5+ . ? ,?+ =,, 5 . ,.1+.1? H;2 3 85

    ;+5 .8+ >+.1? 5 ,.1+.1? 8 3 ; ; , 8*,

    ,+=*, . ,.1++ 8*, ?8.5 , +*11*

    ,+=@ . ,.1+.1?,

    I PROBLEM "2 3 85 =*+.1? 8 ,.1+.1? 8

    3 85 5 , . ;.,+; 1 I .2 3 ; . 5. 8*, @> . ,+=@

    B;, . 82 3 8* 8 8*, ,+=@ *, . ,*1 . , * ?*=

    ,?+ =,,

    I ;.;1,*.2 3 +1* 8 8+ + ?@ @> . ,+=*, ;

    ,5 . ,.1+.1? I 5>5, . , . ;8.., 38 @> . ?8.5 8 3

    3 . , 5 ?8.5 8 3 8* *, 8 ,*, 3@

  • 8/10/2019 basic math again

    19/21

  • 8/10/2019 basic math again

    20/21

    APPENDICES

    &EOR&E POLYA

    THE RANDOM WALKS OF &EOR&E POLYA

  • 8/10/2019 basic math again

    21/21