DS3 – FONCTIONS – STATISTIQUES – 2NDE I – 21/11/2016 La

DS3$–$FONCTIONS$–$STATISTIQUES$–$2NDE$I$–$21/11/2016$
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EXERCICE$1$:$
!"#$%&'"'(#)*#&+",('+"#f#-./#
!
##0*/#
!!f x
( )
=−x2−x−2
( )
1−2x
( )
−7x−15
#1#
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!
Cf
#)*#,+./32#/20/%-2"(*('42#$2#f#$*"-#."#/205/2#6.2),+"6.21#
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!f x
( )
1#
2. 8+"(/2/#6.2#0+./#(+.(#/%2)#x9#
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( )
=x−6
( )
2
−49
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!f x
( )
#
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!!f x
( )
=x+1
( )
x−13
( )
#@#
D#)*#&+/;2#$%42)+00%2#$2#f#2-(#$+""%2#0*/#
!!f x
( )
=x2−12x−13
#@##
D#)*#&+/;2#$'(2#,*"+"'6.2#$2#f#2-(#$+""%2#0*/#
!!f x
( )
=x−6
( )
2
−49
1#
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Montrer#votre#écran#au#professeur#!#
b.#O%-+.$/2#
!!f x
( )
=51
1#
7. QO%-+.$/2#)I%6.*('+"#
!!f x
( )
=−6x−22
1#
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EXERCICE$2$:#
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-+"(#$+""%-#$*"-#)2#(*3)2*.#-.'4*"(#C#
#
Nombre de tirs
dans la cible
Nombre de
concurrents
Fréq.
ECC
ECD
fCC
fCD
0
2
1
6
2
20
3
24
4
12
5
16
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&/%6.2",2-#,.;.)%2-#,/+'--*"(2-#2(#$%,/+'--*"(2-1#!"#=*/$2/*#F#,L'&&/2-#*0/5-#)*#4'/=.)21#
b.#V*'/2#."2#0L/*-2#0+./#2J0)'6.2/#,2#6.2#/20/%-2"(2#)I:<<#0+./#F#('/-#$*"-#)*#,'3)2#W,*-2#AX#2(#
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2. a.$7%(2/;'"2/#)*#;%$'*"2# $2#,2((2#-%/'29#*'"-'#6.2#)2-#6.*/(')2-# #2(# #2"#2J0)'6.*"(#)2-#
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b.$V*'/2#(/+'-#0L/*-2-#2J0)'6.*"(#,2#6.2#,L*,."2#$2-#(/+'-#;2-./2-# /20/%-2"(21#
c.$7+""2/#)I'"(2/4*))2#'"(2/6.*/(')2#2(#0/%,'-2/#,2#6.I')#/20/%-2"(21#
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Me
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EXERCICE$3$:$
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c. 7+""2/#)2#6.*/(')2#
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EXERCICE$4$:$
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a. 7*"-#)I2"(/20/'-2#K#0*/#/*00+/(#S#)I2"(/20/'-2#Z9#)2-#&2;;2-#-+"(#;'2.J#0*`%2-#2(#)2-#L+;;2-#
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b. R*#;+'('%#$2-#-*)*/'%-#$2#)I2"(/20/'-2#Z#(+.,L2#2"(/2#EPUUd#2(#?UUUd1$
c. B).-#$2#)*#;+'('%#$2-#-*)*/'%-#$2#)I2"(/20/'-2#K#(+.,L2#?UUUd#+.#;+'"-1$
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e. 8+'"-#$I."#6.*/(#$2-#-*)*/'%-#$2-#$2.J#2"(/20/'-2-#(+.,L2"(#0).-#$2#FUUUd1$
f. :"#;+`2""29#)2-#-*)*/'%-#$2#)I2"(/20/'-2#Z#-+"(#;'2.J#0*`%-#6.2#,2.J#$2#)I2"(/20/'-2#K1#
g. Q7*"-#)I2"(/20/'-2#Z9#)*#A2#02/-+""2#)*#;'2.J#0*`%2#(+.,L2#FUUUd1$
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EXERCICE$BONUS$:$
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DS3$–$FONCTIONS$–$STATISTIQUES$–$CORRECTION$
$
EXERCICE$1$:$
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1.$B+./#(+.(#x#/%2)#C#
!!
f x
( )
=−x2−x−2x2−2+4x
( )
−7x−15
=−x2− −2x2+5x−2
( )
−7x−15
=−x2+2x2−5x+2−7x−15
=x2−12x−13
#
2.$
x−6
( )
2
−49 =x2−12x+36 −49
!!=x2−12x−13
$
3.$
!!f x
( )
=x−6
( )
2
−49
=x−6−7
( )
x−6+7
( )
$
!!=x−13
( )
x+1
( )
$
4.$
!!f−2
( )
=15
$@
!!f6
( )
=−49
#@
!!
f2
( )
=−11 −12 2
#
5a.$
!!f x
( )
=−13
$ $
!!f x
( )
=−49
$
!!
x2−12x−13 =−13
x2−12x=0
x x −12
( )
=0
x=0!ou!x=12
S=0;12
{ }
#
!!
x−6
( )
2
−49 =−49
x−6
( )
2
=0
x−6=0
x=6
#
5b.$
!!f x
( )
=0
$
!!
x−13
( )
x+1
( )
=0
x=13!ou!x=−1
S=13;−1
{ }
#
6a.$a)#&*))*'(#*$*0(2/#)*#&2"M(/2#*&'"#6.2#)I+"#0.'--2#4+'/#)2-#2#
*"(%,%$2"(-#$2#PE#0*/#f1#
6b.$
!!f x
( )
=51
$
x−6
( )
2
−49 =51
x−6
( )
2
−100 =0
x−6−10
( )
x−6+10
( )
=0
x−16
( )
x+4
( )
=0
x=16(ou(x=−4
S=16;−4
{ }
#
7.$
!!x2−12x−13 =−6x−22
$
⇔x2+6x+9=0⇔x+3
( )
2
=0⇔x+3=0⇔x=−3
$
$
EXERCICE$2$:$
1.$
Nombre'de'tirs'
Effectif'
Fréq.'
ECC'
ECD'
fCC'
fCD'
0'
2'
0,025'
2'
80'
0,025'
1'
1'
6'
0,075'
8'
78'
0,1'
0,975'
2'
20'
0,25'
28'
72'
0,35'
0,9'
3'
24'
0,3'
52'
52'
0,65'
0,65'
4'
12'
0,15'
64'
28'
0,8'
0,35'
5'
16'
0,2'
80'
16'
1'
0,2'
$
1b.$P?#,+",.//2"(-#+"(#2.#."2#-,+/2#'"&%/'2./#+.#%=*)#S#F1#
He9Pi#$2-#,+",.//2"(-#+"(#;*/6.%#*.#;+'"-#."#0+'"(1#
2a.$TUj?kGU1#R*#;%$'*"2#2-(#$+",#)*#;+`2""2#$2#)*#GU2#2(#)*#
GE2#4*)2./1#7I*0/5-#)2-#:<<9#
!!Me=3
1#
!80/4 =20:
!!Q1
2-(#$+",#)*#?U2#4*)2./#C#
!!Q1=2
#
!80×0,75 =60:
!!Q3
2-(#)*#AU2#4*)2./#C#
!!Q3=4
#
2b.$PUi#$2-#,+",.//2"(-#+"(#;*/6.%#*.#;+'"-#W+.#*.#0).-X#
F#0+'"(-1#
!25%
#$2-#,+",.//2"(-#+"(#;*/6.%-#*.#0).-#F#0+'"(-1#
!75%
#$2-#,+",.//2"(-#+"#;*/6.%-#*.#0).-#G#0+'"(-1#
2c.$
!2;4
⎡
⎣⎤ ⎦
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0+'"(-1#
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EXERCICE$3$:$
1a.$PPi#$2-#%)542-#+"(#2.#."2#"+(2#'"&%/'2./2#+.#%=*)2#S#EU1#
1b.$FUi#$2-#%)542-l#
1c.$
!!Q1=7
$:$?Pi#$2-#%)542-#+"(#2.#."2#"+(2#'"&%/'2./2#+.#
%=*)2#S#e1#
2.$
!!Q3=16
$C#ePi#$2-#%)542-#$2#)*#?"$2#Z#+"(#2.#."2#"+(2#
'"&%/'2./2#+.#%=*)2#S#EA1#
3.$!"#,L2/,L2#)I*3-,'--2#$2#)*#,+./32#*`*"(#0+./#+/$+""%2#
PUi9#-+'(#2"(/2#6#2(#71#
4.$
Note'
0
'
2
'
4
'
6
'
8
'
10
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12
'
14
'
16
'
18
'
20'
Fréq.'
0'
0,1'
0,15'
0,2'
0,15'
0,15'
0,1'
0,1'
0,05'
0'
0'
5.$7I*0/5-#)2#=/*0L'6.2#$2#)*#?"$2#Z9#+"#0.(#4+'/#6.2#)2-#
2&&2,('&-#$2-#"+(2-#&*'3)2-#-+"(#'"&%/'2./-#*.J#*.(/2-#,)*--2-#
W,+./32#2"#$2--+.-#$2-#*.(/2-X#*)+/-#6.2#)2-#2&&2,('&-#$2-#
"+(2-#%)24%2-#-+"(#0).-#';0+/(*"(-#W,+./32#,/+'--*"(#0).-#
4'(2#6.2#)2-#*.(/2-9#APi#-.0%/'2./-#S#E?X1#R*#;2'))2./2#
,)*--2-#2-(#-*"-#,+"(2-(2#)*#2nde$B1#
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EXERCICE$4$:$
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a.$VRAI$:$)2-#-*)*'/2-#$2-#$2.J#=/+.02-#-+"(#0).-#%)24%-#
$I*0/5-#)2#(*3)2*.J1#
b.$FAUX$:$RI'"(2/4*))2#2"(/2#
!!Q1
#2(#
!Me
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?Pi#$2-#-*)*/'%-#(+.,L2"(#2"(/2#EPUU#2(#?UUU#2./+-1#
c.$VRAI$:$
!!Me <2000
$$+",#0).-#$2#)*#;+'('%#$2-#-*)*/'%-#
(+.,L2"(#;+'"-#$2#?UUU#2./+-1#
d.$VRAI$:$)2-#6.*/(')2-#
!!Q1
$2-#$2.J#2"(/20/'-2-#-+"(#
'"&%/'2./2-#+.#%=*.J#S#EGUU#2./+-1#
e.$VRAI$:$)2-#$2.J#6.*/(')2-#
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6.2#)*#;+`2""2#$2-#-*)*'/2-#$2#Z#2-(#$2#?EPA#2./+-#WS#
,*),.)2/X1#
g.$On$ne$peut$pas$savoir$:$
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/%&%/2",2#*.#6.*/(')2#
!!Q3
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h.$VRAI$:$
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EXERCICE$BONUS$:$
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;+`2""2#2-(#%=*)2#S#H9H9#+"#-*'(#6.2#)*#-+;;2#$2-#"+(2-#2-(#
%=*)2#S#
!9,9×35
1##
b+'(#x#)*#"+(2#$2#)*#FA2#,+0'21#!"#/%-+.(#C#

9,9 ×35+x
36
≥10 ⇔346,5 +x≥360
!!⇔x≥13,5
#