Intermedio maio 2011

Teste Intermédio de Matemática

Versão 1

TI de Matemática – Versão 1 ! Página 1/ 12

Teste Intermédio

Matemática

Versão 1

Duração do Teste: 90 minutos | 11.05.2011

8.º Ano de Escolaridade

Decreto-Lei n.º 6/2001, de 18 de Janeiro

!"#$%&'()*(+),)-#$%#.*$)*/0+1)*"#*,#2302%)2.*)*4#,250*"0*%#2%#*67*08*9:*)*;8#*,#230$"#2<

=%&+&>)*)3#$)2*()$#%)*08*#2/#,0?,@'()*"#*%&$%)*&$"#+A4#+.*)>8+*08*3,#%)<

B50* A* 3#,-&%&"0* 0* 820* "#* (0,,#(%0,<* C#-3,#* ;8#* 3,#(&2),#2* "#* )+%#,),* 08* "#* )$8+),* 8-)*

,#2302%).*,&2()*"#*/0,-)*(+),)*0*;8#*3,#%#$"#2*;8#*';8#*2#-*#/#&%0<

D2(,#4#*"#* /0,-)* +#?E4#+*)*$8-#,)F50*"02* &%#$2.*G#-*(0-0*)2* ,#23#(%&4)2* ,#2302%)2<*H2*

,#2302%)2*&+#?E4#&2*250*(+)22&'()")2*(0-*>#,0*30$%02<

I),)*()")*&%#-.*)3,#2#$%)*)3#$)2*8-)*,#2302%)<*C#*)3,#2#$%),#2*-)&2*"0*;8#*8-)*,#2302%)*

)*8-*&%#-.*2J*)*3,&-#&,)*A*(+)22&'()")<

I0"#2*8%&+&>),*)*-@;8&$)*"#*()+(8+),*(0-*;8#*1)G&%8)+-#$%#*%,)G)+1)2<

I),)*,#230$"#,#2*)02*&%#$2*"#*#2(0+1)*-K+%&3+).*#2(,#4#.*$)*/0+1)*"#*,#2302%)2L

!" 0*$K-#,0*"0*&%#-M

!" )*+#%,)*;8#*&"#$%&'()*)*03F50*#2(0+1&")<

H2*(0%)FN#2*"02*&%#$2*#$(0$%,)-O2#*$0*'$)+*"0*#$8$(&)"0*"0*%#2%#<

P*%#2%#*&$(+8&.*$)*3@?&$)*9.*8-*/0,-8+@,&0<


Formulário

Números

Valor aproximado de ! (pi):!!3,14159

Geometria

Perímetro do círculo: 2!r, sendo r o raio do círculo

Áreas

Paralelogramo: Base # Altura

Losango: Diagonal maior Diagonal menor!

!

Trapézio: Base maior Base menor

Altura+

×!

Círculo: !r!, sendo r o raio do círculo

Volumes

Prisma e cilindro: Área da base # Altura

Pirâmide e cone: 1— 3

#"Área da base # Altura


1. H2*+#%,)2*P.*Q e R*"#2&?$)-*02*%,Q2*()$"&")%02*$8-)*#+#&F50*$02*D2%)"02*=$&"02*")*H-A,&()<*

H*R)G#+)*7*)3,#2#$%)*)2*"&2%,&G8&FN#2*")2*3#,(#$%)?#$2*"#*40%02*$#22#2*()$"&")%02<

D-*()")*+&$1)*#2%@*)3,#2#$%)")*)*"&2%,&G8&F50*")2*3#,(#$%)?#$2*"#*8-)*(#,%)*3038+)F50M*30,*#S#-3+0.*$)*

3,&-#&,)*+&$1)*#2%@*)*"&2%,&G8&F50*")2*3#,(#$%)?#$2*"#*40%02*")*3038+)F50*"#*10-#$2*"02*D2%)"02*=$&"02*

")*H-A,&()<

Tabela 1

PERCENTAGEM DE VOTOS

Candidatos

PopulaçõesP Q R

Homens 41 38 21

T8+1#,#2 46 37 17

U,)$(02 39 41 20

B#?,02 82 11 7

V&23W$&(02 61 25 14

H2&@%&(02 29 55 16

X8)+*"02*?,@'(02*2#?8&$%#2*,#3,#2#$%)*)*"&2%,&G8&F50*")2*3#,(#$%)?#$2*"#*40%02.*3#+02*()$"&")%02*P.*Q e R.*

")*3038+)F50*"#*$#?,02Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) (B)

P

R

Q

P

R

Q

(C) (D)

R

P

Q

P

R

Q


2. Z#4&$*[08$?.*)%+#%)*$0,%#O)-#,&()$0*"02*\]]*-#%,02*G),,#&,)2.*(0,,#8*"#>*3,04)2*"#2%)*-0")+&")"#*#-*

H?02%0*"#*7^^9<

B)*R)G#+)*9.*)3,#2#$%)-O2#*02*,#28+%)"02*0G%&"02*#-*$04#*"#22)2*3,04)2<

B)*3,04)*,#)+&>)")*$0*"&)*_*"#*H?02%0.*Z#4&$*[08$?*#2%)G#+#(#8*8-*$040*,#(0,"#*-8$"&)+<

Tabela 2

Local DataTempo obtido(em segundos)

U),(#+0$) `*"#*H?02%0 48,76

U),(#+0$) a*"#*H?02%0 47,63

U),(#+0$) _*"#*H?02%0 (*)

TJ$)(0 77*"#*H?02%0 47,60

C1#/'#+" 7\*"#*H?02%0 47,67

b0+J$&) 7_*"#*H?02%0 47,42

c8,&;8# 7^*"#*H?02%0 47,40

U#,+&- 97*"#*H?02%0 47,81

b03#$1)?) 9a*"#*H?02%0 48,57

U,8S#+)2 9d*"#*H?02%0 47,70

6e:*f#(0,"#*-8$"&)+<

C)G#O2#*;8#*)*-A"&)*"02*%,Q2*-#+10,#2*%#-302*0G%&"02*30,*Z#4&$*[08$?*$)2*"#>*3,04)2*A*47,20*2#?8$"02<

g#%#,-&$)*0*%#-30.*#-*2#?8$"02.*0G%&"0*30,*Z#4&$*[08$?*$)*3,04)*,#)+&>)")*$0*"&)*_*"#*H?02%0<

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<


3. B)*i&?8,)*7.*#2%50*,#3,#2#$%)"02*02*%,Q2*3,&-#&,02*%#,-02*"#*8-)*2#;8Q$(&)*"#*(0$j8$%02*"#*G0+)2*;8#*

2#?8#*)*+#&*"#*/0,-)F50*28?#,&")*$)*'?8,)<

1.º termo 2.º termo 3.º termo

Figura 1

3.1. X8)$%)2*G0+)2*250*$#(#22@,&)2*3),)*(0$2%,8&,*0*7.º*%#,-0*")*2#;8Q$(&)Y

3.2. V@*8-*%#,-0*")*2#;8Q$(&)*;8#*%#-*8-*%0%)+*"#*108*G0+)2<

X8)$%)2*G0+)2*3,#%)2*%#-*#22#*%#,-0Y

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<

4. X8)+*"02*$K-#,02*2#?8&$%#2*A*&?8)+*)0*$K-#,0*125

1*Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) 5

1"$

(B) 5 "$ (C) 5

125

(D) 525

5. B8-*+)G0,)%J,&0*"#*G&0+0?&).*250*8%&+&>)"02*"0&2*2&$)&2*+8-&$0202L*0*2&$)+*A .*;8#*3&2()*"#*105 em 105*2#?8$"02.*

#*0*2&$)+*B .*;8#*3&2()*"#*195 em 195*2#?8$"02<

P2*"0&2*2&$)&2*3&2()-*2&-8+%)$#)-#$%#*$0*&$2%)$%#*#-*;8#*2#*&$&(&)*8-)*(#,%)*#S3#,&Q$(&)*$0*+)G0,)%J,&0<

H0*'-*"#*;8)$%02*2#?8$"02*A*;8#*02*"0&2*2&$)&2*40+%)-*)*3&2(),*2&-8+%)$#)-#$%#Y

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<


6. X8)+*"02*$K-#,02*2#?8&$%#2*A*&?8)+*)*100 10050 2# Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) 100100 (B) 10052 (C) 002 100 (D) 002 52

7. P*I#",0*2)&8*"#*()2)*3),)*"),*8-*3)22#&0*"#*G&(&(+#%)<

k*&").*-)$%#4#*8-)*4#+0(&")"#*(0$2%)$%#<

B0*,#?,#220.*-)$%#4#*%)-GA-*8-)*4#+0(&")"#*(0$2%)$%#.*-)2*"#2+0(08O2#*-)&2*rapidamente*"0*;8#

h*&")<

X8)+*"02*?,@'(02*2#?8&$%#2*30"#*,#3,#2#$%),*)*distância percorrida*3#+0*I#",0.*$0*2#8*3)22#&0.*#-*

/8$F50*"0*%#-30*;8#*"#(0,,#8*"#30&2*"#*#+#*2)&,*"#*()2)Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

tempo

dis

tância

perc

orr

ida

tempo

dis

tância

perc

orr

ida

tempo

dis

tância

perc

orr

ida

tempo

dis

tância

perc

orr

ida

(A) (B)

(C) (D)


8. H*/8$F50*f* A*8-)*/8$F50*"#*3,030,(&0$)+&")"#*"&,#(%)<*C)G#O2#*;8#* f 2 6%_ i

X8)+*")2*&?8)+")"#2*2#?8&$%#2*"#'$#*)*/8$F50*f*Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) f xx3

%_ i

(B) f x x3%_ i

(C) f x x 4= +_ i

(D) f x x 4= −_ i

9. f#20+4#*)*#;8)F50*2#?8&$%#<

2x x2 4

3 2− =

−_ i

H3,#2#$%)*02*(@+(8+02*;8#*#/#(%8),#2<

10. B)*K+%&-)*)8+)*"0*%#,(#&,0*3#,E0"0.*)*%8,-)*")*T),?),&")*0/#,#(#8*h*3,0/#220,)*"#*T)%#-@%&()*8-*,)-0*

(0$2%&%8E"0*30,*%K+&3)2*4#,-#+1)2*#*%K+&3)2*G,)$()2<

P*,)-0.*/0,-)"0*30,*18*%K+&3)2.*%&$1)*-)&2*4*%K+&3)2*4#,-#+1)2*"0*;8#*G,)$()2<

X8)$%)2*%K+&3)2*G,)$()2*%&$1)*0*,)-0*;8#*)*%8,-)*")*T),?),&")*0/#,#(#8*h*3,0/#220,)Y

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<


11. H*V#+#$)*(0$2%,8&8.*3),)*)*"&2(&3+&$)*"#*D"8()F50*l&28)+.*4@,&02*-0"#+02*"#*2J+&"02*#-*#2/#,04&%#<

R0"02*02*-0"#+02*250*3,&2-)2*,#(%02*"#*G)2#*;8)",)")<

H2*G)2#2*"02*-0"#+02*250*%0")2*&?8)&2*#*)2*)+%8,)2*250*%0")2*"&/#,#$%#2<

11.1. B)*i&?8,)*9.*#2%50*,#3,#2#$%)"02*%,Q2*"02*-0"#+02*/#&%02*3#+)*V#+#$)<

Figura 2

H*V#+#$)*4)&*/0,,),*#2%#2*%,Q2*-0"#+02*(0-*3)3#+*)8%0(0+)$%#<

C)G#O2#*;8#L

!" 0*40+8-#*"0*-0"#+0*-)&0,*A*&?8)+*h*20-)*"02*40+8-#2*"02*"0&2*-0"#+02*-#$0,#2M

!" *3),)* /0,,),*02*"0&2*-0"#+02*-#$0,#2.*?)2%)-O2#*-)&2*50 cm2*"#*3)3#+*"0*;8#*3),)* /0,,),*0*

-0"#+0*-)&0,<

g#%#,-&$).*#-*(#$%E-#%,02.*)*-#"&")*")*),#2%)*")*G)2#*"02*-0"#+02<*

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<

11.2. H*"#23#2)*(0-*)*(0$2%,8F50*"#*()")*-0"#+0*"#3#$"#*")*)+%8,)*"#22#*-0"#+0<

P*?,@'(0*2#?8&$%#*,#3,#2#$%)*)*,#+)F50*#$%,#*)*)+%8,)*"02*-0"#+02.*#-*-&+E-#%,02.*#*)*"#23#2).*

#-*(Q$%&-02<

altura

despesa

10

20

30

40

50

60

0 10 30 40 50 60 7020

H*"#23#2)*(0-*)*(0$2%,8F50*"#*8-*"02*-0"#+02*/0&*50*(Q$%&-02<

X8)+*A*)*)+%8,).*#-*-&+E-#%,02.*"#22#*-0"#+0Y


12. B)*i&?8,)*`.*#2%@*,#3,#2#$%)"0*8-*,#(%W$?8+0*[ABCD ]<*H*'?8,)*$50*#2%@*"#2#$1)")*h*#2()+)<

A B

C

G

D

EF

Figura 3

3,5

5 3

C)G#O2#*;8#L

!" 02*30$%02*E e G* 3#,%#$(#-*)02*+)"02*[AD ] e [BC ].*,#23#(%&4)-#$%#M

!" 0*2#?-#$%0*[EG ]*A*3),)+#+0*)0*2#?-#$%0*[AB ]

!" 0*2#?-#$%0*[BD ]*&$%#,2#(%)*0*2#?-#$%0*[EG ]*$0*30$%0*F

!" EF 5%

!" FG 3%

!" 3,ED 5%

12.1. H"-&%#*;8#*DFE 35o

%t

X8)+*A*)*)-3+&%8"#.*#-*?,)82.*"0*W$?8+0*FBG*Y

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<

12.2. P2*%,&W$?8+02*[EFD ] e [GFB ]*250*2#-#+1)$%#2<

Determina BG

T02%,)*(0-0*(1#?)2%#*h*%8)*,#2302%)<

13. g#*8-*%,&W$?8+0*[PQR ]*2)G#O2#*;8#L

!" 5PQ %

!" 11QR %

X8)+*"02*2#?8&$%#2*4)+0,#2*30"#*2#,*0*4)+0,*"#*PR *Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) 4 (B) 12 (C) 18 (D) 24


gPC*gP!C*!RDBC*CDm=!BRDC.*14.A. E 14.B.*fDCPnlD*HIDBHC*=T.*gD*HbPfgP*bPT*HC*!BCRf=opDC*

X=D*RDBVHC*fDbDU!gP<

14.A. B)*i&?8,)*\.*#2%@*,#3,#2#$%)"0*8-*%,&W$?8+0*,#(%W$?8+0*[ABC ]<*H*'?8,)*$50*#2%@*"#2#$1)")*h*#2()+)<

A

B C

Figura 4

B8-)*")2*03FN#2*2#?8&$%#2*#2%50*&$"&()")2*)2*-#"&")2*"02*+)"02*"#2%#*%,&W$?8+0<

D-*;8)+*"#+)2Y

H22&$)+)*)*03F50*(0,,#(%)<

(A) AB

BC

AC

4

11

12

%

%

%

(B) AB

BC

AC

5

12

13

%

%

%

(C) AB

BC

AC

6

13

14

%

%

%

(D) AB

BC

AC

7

14

15

%

%

%


14.B. B)*i&?8,)*a.*#2%@*,#3,#2#$%)")*8-)*(0-302&F50*?#0-A%,&()*"#*0,&?#-*&2+W-&()<

A B

C D

1 2

43

i&?8,)*a

B#2%)* '?8,).* #2%50* ,#3,#2#$%)"02.* )* 20-G,#)"0.* ;8)%,0* 30+E?0$02*?#0-#%,&()-#$%#* &?8)&2.* (0-*)*

/0,-)*"#*8-)*2#%)<*D22#2*30+E?0$02*#2%50*"#2&?$)"02*3#+02*)+?),&2-02*1.*2.*3 e 4

P2*30$%02*A.*B.*C e D.* )22&$)+)"02*$)*'?8,).*250*4A,%&(#2*"02*,#/#,&"02*30+E?0$02<

P*30+E?0$0*3*30"#*2#,*0G%&"0*(0-0*&-)?#-*"0*30+E?0$0*1*30,*-#&0*")*%,)$2+)F50*)220(&)")*)*8-*"02*

4#(%0,#2*2#?8&$%#2<*H*;8)+*"#+#2Y

R,)$2(,#4#*)*+#%,)*")*03F50*(0,,#(%)<

(A) AC CB&

(B) AC CA&

(C) AB BD&

(D) AB BC&

FIM


COTAÇÕES

1. ...........................................................................................................* a*30$%02

2. ...........................................................................................................* a*30$%02

3.

3.1. ..................................................................................................* \*30$%02

3.2. ..................................................................................................* q*30$%02

4. ...........................................................................................................* a*30$%02

5. ...........................................................................................................* q*30$%02

6. ...........................................................................................................* a*30$%02

7. ...........................................................................................................* a*30$%02

8. ...........................................................................................................* a*30$%02

9. ...........................................................................................................* ^*30$%02

10. ..........................................................................................................* d*30$%02

11.

11.1. .................................................................................................* _*30$%02

11.2. .................................................................................................* \*30$%02

12.

12.1. .................................................................................................* q*30$%02

12.2. .................................................................................................* d*30$%02

13. ..........................................................................................................* a*30$%02

14. ..........................................................................................................* a*30$%02

TOTAL ......................................... 100 pontos

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