!"#$%&'()*+,%-!%./0%*1%2%3%"4''*51(46%7819:;*'3<*6)(*6%0=>?30=>@%
!
Q3.%W6%K*'F*%8*%9(8(*+%'C:51(466*8%D:6F%8G:9B4+8*%M%DC5:61*'L%M%8G:(D*%DG+6%*614664('%M%8(J+(D*N%W6%:X4+1*%(5(%
>=% 9A% DGC1S*'% D(C1S;8(J+*% Y9*F+'C% M% 8GCB'4+K*11*% T':D+C*Z% D:6F% 8G:9B4+8*% M% DC5:61*'L% M% 8G:(D*% DG+6%
*614664('%M%8(J+(D*N%W6%H4+5S*%8G:9B4+8*L%46%8:%'*14+'6*%*1%46%DCT:)*%K*'F%+6%*6D'4(1%(6455+BCN%W6%:T(1*%
8G:9B4+8*% *1% 46% DCT:)*% 'CT+8(P'*9*61N% A*F% F48+1CF% F*% B:'1:T*61% :84'F% *61'*% 8*F% D*+,% BS:F*F% F*846% 8*+'%
:EE(6(1C%:K*5%8*F%F48K:61FN%O+:6D%(8%6G;%:%B8+F%D*%DCT:):T*L%46%'*B4F*%8G:9B4+8*L%46%*68PK*%8*%H4+5S46%*1%46%
8:(FF*%DC5:61*'%Q%8*F%D*+,%BS:F*F%F*%FCB:'*61N!%
%
$5(L% 8:% BS:F*%4'T:6(J+*% *F1% 8:% BS:F*%F+BC'(*+'*% 5:'% 8:%
D*6F(1C% D*% 8GC1S*'% D(C1S;8(J+*% Y=L@=Z% *F1% (6EC'(*+'*% M%
5*88*% D*% 8G*:+% Y>L==ZN% W6% 'C5+BP'*% D465% DG:H4'D% 8:%
BS:F*% :J+*+F*% Y5461*6:61% 8*F% (46F% H*6)4:1*% *1% 8*F%
(46F% S;D'4,;D*% D:6F% 8G*:+Z% D:6F% +6% *'8*69*;*'% *6%
4+K':61% 8*% '4H(6*1L% B+(F% 8:% BS:F*% 4'T:6(J+*%
Y5461*6:61% 8G:85448% H*6);8(J+*% D:6F% 8GC1S*'%
D(C1S;8(J+*Z%D:6F%+6%:+1'*%*'8*69*;*'N%
!
Remarques)de)bonnes)manipulations):)
» "/+.#&!3,#&3#+$#7#&!/+/0/%3!14(&!&-.(1-&#&!3,/+0-8&%3/0-!9(!$/3/#(!&-%.0/4++#36!
» :0/3/2#&!(+!#+04++4/&!;!3/'(/9#!34&2!9(!&#$13/22%8#!9,(+#!%$14(3#!;!9-.%+0#&!1#&$#0!;!3,%$14(3#!9#!
#&!5#&$-0/'(#!(+#!<4/2!=4(.5-#6!
» >4(?4(&2!@-&/</#&!'(#!3#!&4=/+#0!9#!3,%$14(3#!#20!<#&$-!%@%+0!9#!.4$$#+.#&!;!3%!&#$13/&!A!
» :+#!<4/2!'(#!3,%$14(3#!#20!(&+-#B!+#!CDEDFG!�/&#&!2%!$%/+!9(!=4(.54+!A!
» :+!243@%+0!H4&8%+/'(#H!#20!04(0!243@%+0!%(0&#!'(#!3,#%(6!I%!15%2#!H%'(#(2#H!#20!.#33#!94+0!3#!243@%+0!
#20!3,#%(6!
» J4(&! &#.4++%K0&#! 3%! 142/0/4+! 9#2! 15%2#2! 9%+2! 3,%$14(3#! ;! 9-.%+0#&B! 4+! .4$1%&#! 3%! 9#+2/0-! 9#! 3%!
15%2#!4&8%+/'(#!;!.#33#!9#!3,#%(6!G/!#33#!#20!13(2!<%/=3#!'(#!LB!.,#20!3%!15%2#!2(1-&/#(&#B!2/+4+B!.,#20!3%!
15%2#!/+<-&/#(!
%
Q4.%W6%:X4+1*%>[%T%D*%T8:5*%B(8C*%*1%+6%H:''*:+%:(9:61C%D:6F%8G*'8*69*;*'%5461*6:61%8:%BS:F*%:J+*+F*L%
B+(F%46%8*%E(,*%D:6F%+6%5'(F1:88(F4('%DG*:+%T8:5C*L%:+3D*FF+F%DG+6%:T(1:1*+'%9:T6C1(J+*N%W6%B'C8PK*%D:6F%+6%
HC5S*'% >=% 9A% DG:5(D*% 5S84'S;D'(J+*% 5465*61'C% :+% D(FB4F*+'N% W6% :X4+1*% T4+11*3M3T4+11*% 8G:5(D*% D:6F%
8G*'8*69*;*'%M% 8G:(D*%DG+6*%B(B*11*%*6%B8:F1(J+*N%W6%4HF*'K*%8:% E4'9:1(46% DG+6% F48(D*%Q% 8G:5(D*%H*6)4IJ+*L%
E:(H8*9*61%F48+H8*%D:6F%8G*:+N%W6%5461'\8*%8*%B<%*1%46%FG:'']1*%84'FJ+G(8%*F1%F+EE(F:99*61%:5(D*%YB<%^%2ZN%
%
!4+'%(F48*'%8G:5(D*%H*6)4IJ+*%F48(D*%D*%8:%BS:F*%:J+*+F*%YDCF4'9:(F%:5(D*ZL%46%*EE*51+*%+6%*FF4':T*%F4+F%
K(D*N%%
W6% E(,*% +6*% E(48*% M% K(D*% F+'% +6% F+BB4'1% M% 8G:(D*% DG+6*% B(65*% 23D4(T1FL% B+(F% 46% B8:5*% +6% X4(61% 546(J+*% *1%
8G*614664('%&_5S6*'N%W6%;%B8:5*%+6%E(81'*%'46DL%J+*% 8G46%S+9(D(E(*%:K*5%J+*8J+*F%T4+11*F%D+%F48K:61%D*%8:%
BS:F*%M%E(81'*'%Y(5(%D*%8G*:+%D(F1(88C*ZL%:E(6%D*%E:('*%:DSC'*'%8*%E(81'*%:+%&_5S6*'N%W6%H':65S*%8*%1+;:+%'*8(C%M%
+6*%1'49B*%M%*:+%4+%M%+6*%B49B*N%W6%K*'F*%8*%5461*6+%D*%8G*'8*69*;*'%D:6F%8G*614664('%&_5S6*'%B+(F%46%
:88+9*%8:%B49B*%Y4+%46%4+K'*%8*% '4H(6*1%*6%T':6D%F(% 5G*F1%+6*%1'49B*%M%*:+ZN%`6*%E4(F% J+*%8*% F48(D*%*F1%
*FF4'CL%46%54+B*% 8*%K(D*L%B+(F%46%C1*(61%8:%B49B*%Y4+% 46%E*'9*% 8*%'4H(6*1ZN%W6%:X4+1*%+6%B*+%D*%F48K:61%
E'4(D% Y(5(% D*% 8G*:+% D(F1(88C*% E'4(D*ZL% 46% 1'(1+'*% 8*% F48(D*% :K*5% +6*% H:T+*11*% *6% K*''*% Y4+% *6% B8:F1(J+*Z% B4+'%
8:K*'% 8*% F48(D*L% B+(F% 46% ':88+9*% 8:% B49B*N% W6% 8:(FF*% *FF4'*'% X+FJ+GM% 5*% J+G:+5+6% 8(J+(D*% 6*% 54+8*% B:'%
8G*614664('N%A*%B'4D+(1%4H1*6+%*F1%+6%F48(D*%H8:65N%W6%8*%B8:5*%D:6F%+6*%54+B*88*%B'C:8:H8*9*61%1:'C*%*1%46%
8:%9*1%M%8GC1+K*%B4+'%B4+'F+(K'*%8*%FC5S:T*N%