1. Teste Intermédio de Matemática
Versão 1
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
,GHQWL¿FD FODUDPHQWH QD IROKD GH UHVSRVWDV D YHUVmR GR WHVWH RX

2. D TXH UHVSRQGHV
8WLOL]D DSHQDV FDQHWD RX HVIHURJUi¿FD GH WLQWD LQGHOpYHO D]XO RX SUHWD
1mR p SHUPLWLGR R XVR GH FRUUHFWRU 6HPSUH TXH SUHFLVDUHV GH DOWHUDU RX GH DQXODU XPD
UHVSRVWD ULVFD GH IRUPD FODUD R TXH SUHWHQGHV TXH ¿TXH VHP HIHLWR
(VFUHYH GH IRUPD OHJtYHO D QXPHUDomR GRV LWHQV EHP FRPR DV UHVSHFWLYDV UHVSRVWDV $V
UHVSRVWDV LOHJtYHLV VmR FODVVL¿FDGDV FRP ]HUR SRQWRV
3DUD FDGD LWHP DSUHVHQWD DSHQDV XPD UHVSRVWD 6H DSUHVHQWDUHV PDLV GR TXH XPD UHVSRVWD
D XP LWHP Vy D SULPHLUD p FODVVL¿FDGD
3RGHV XWLOL]DU D PiTXLQD GH FDOFXODU FRP TXH KDELWXDOPHQWH WUDEDOKDV
3DUD UHVSRQGHUHV DRV LWHQV GH HVFROKD P~OWLSOD HVFUHYH QD IROKD GH UHVSRVWDV
x R Q~PHUR GR LWHP
x D OHWUD TXH LGHQWL¿FD D RSomR HVFROKLGD
$V FRWDo}HV GRV LWHQV HQFRQWUDPVH QR ¿QDO GR HQXQFLDGR GR WHVWH
2 WHVWH LQFOXL QD SiJLQD XP IRUPXOiULR
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3. Formulário
Números
Valor aproximado de Q (pi): 3,14159
Geometria
Perímetro do círculo: 2Qr, sendo r o raio do círculo
Áreas
Paralelogramo: Base u Altura
Diagonal maior u Diagonal menor
Losango:
Base maior + Base menor
Trapézio: × Altura
Círculo: Qr , sendo r o raio do círculo
Volumes
Prisma e cilindro: Área da base u Altura
1
Pirâmide e cone: — u Área da base u Altura
3
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4. 1. $V OHWUDV P Q e R GHVLJQDP RV WUrV FDQGLGDWRV QXPD HOHLomR QRV (VWDGRV 8QLGRV GD $PpULFD
$ 7DEHOD DSUHVHQWD DV GLVWULEXLo}HV GDV SHUFHQWDJHQV GH YRWRV QHVVHV FDQGLGDWRV
(P FDGD OLQKD HVWi DSUHVHQWDGD D GLVWULEXLomR GDV SHUFHQWDJHQV GH XPD FHUWD SRSXODomR SRU H[HPSOR QD
SULPHLUD OLQKD HVWi D GLVWULEXLomR GDV SHUFHQWDJHQV GH YRWRV GD SRSXODomR GH KRPHQV GRV (VWDGRV 8QLGRV
GD $PpULFD
Tabela 1
PERCENTAGEM DE VOTOS
Candidatos
P Q R
Populações
Homens 41 38 21
0XOKHUHV 46 37 17
%UDQFRV 39 41 20
1HJURV 82 11 7
+LVSkQLFRV 61 25 14
$VLiWLFRV 29 55 16
4XDO GRV JUi¿FRV VHJXLQWHV UHSUHVHQWD D GLVWULEXLomR GDV SHUFHQWDJHQV GH YRWRV SHORV FDQGLGDWRV P Q e R
GD SRSXODomR GH QHJURV
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) (B)
P P
R
R
Q Q
(C) (D)
P P
R R
Q Q
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5. 2. .HYLQ RXQJ DWOHWD QRUWHDPHULFDQR GRV PHWURV EDUUHLUDV FRUUHX GH] SURYDV GHVWD PRGDOLGDGH HP
$JRVWR GH
1D 7DEHOD DSUHVHQWDPVH RV UHVXOWDGRV REWLGRV HP QRYH GHVVDV SURYDV
1D SURYD UHDOL]DGD QR GLD GH $JRVWR .HYLQ RXQJ HVWDEHOHFHX XP QRYR UHFRUGH PXQGLDO
Tabela 2
Tempo obtido
Local Data
(em segundos)
%DUFHORQD GH $JRVWR 48,76
%DUFHORQD GH $JRVWR 47,63
%DUFHORQD GH $JRVWR (*)
0yQDFR GH $JRVWR 47,60
6KHI¿HOG GH $JRVWR 47,67
ROyQLD GH $JRVWR 47,42
=XULTXH GH $JRVWR 47,40
%HUOLP GH $JRVWR 47,81
RSHQKDJD GH $JRVWR 48,57
%UX[HODV GH $JRVWR 47,70

6. 5HFRUGH PXQGLDO
6DEHVH TXH D PpGLD GRV WUrV PHOKRUHV WHPSRV REWLGRV SRU .HYLQ RXQJ QDV GH] SURYDV p 47,20 VHJXQGRV
'HWHUPLQD R WHPSR HP VHJXQGRV REWLGR SRU .HYLQ RXQJ QD SURYD UHDOL]DGD QR GLD GH $JRVWR
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
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7. 3. 1D )LJXUD HVWmR UHSUHVHQWDGRV RV WUrV SULPHLURV WHUPRV GH XPD VHTXrQFLD GH FRQMXQWRV GH ERODV TXH
VHJXH D OHL GH IRUPDomR VXJHULGD QD ¿JXUD
1.º termo 2.º termo 3.º termo
Figura 1
3.1. 4XDQWDV ERODV VmR QHFHVViULDV SDUD FRQVWUXLU R 7.º WHUPR GD VHTXrQFLD
3.2. +i XP WHUPR GD VHTXrQFLD TXH WHP XP WRWDO GH 108 ERODV
4XDQWDV ERODV SUHWDV WHP HVVH WHUPR
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
1
4. 4XDO GRV Q~PHURV VHJXLQWHV p LJXDO DR Q~PHUR
125
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) 1 (B) 5 (C) 1 (D) 525
5 525
5. 1XP ODERUDWyULR GH ELRORJLD VmR XWLOL]DGRV GRLV VLQDLV OXPLQRVRV R VLQDO A TXH SLVFD GH 105 em 105 VHJXQGRV
H R VLQDO B TXH SLVFD GH 195 em 195 VHJXQGRV
2V GRLV VLQDLV SLVFDP VLPXOWDQHDPHQWH QR LQVWDQWH HP TXH VH LQLFLD XPD FHUWD H[SHULrQFLD QR ODERUDWyULR
$R ¿P GH TXDQWRV VHJXQGRV p TXH RV GRLV VLQDLV YROWDP D SLVFDU VLPXOWDQHDPHQWH
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
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8. 6. 4XDO GRV Q~PHURV VHJXLQWHV p LJXDO D 10050 # 1002
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) 100100 (B) 10052 (C) 200100 (D) 20052
7. 2 3HGUR VDLX GH FDVD SDUD GDU XP SDVVHLR GH ELFLFOHWD
¬ LGD PDQWHYH XPD YHORFLGDGH FRQVWDQWH
1R UHJUHVVR PDQWHYH WDPEpP XPD YHORFLGDGH FRQVWDQWH PDV GHVORFRXVH PDLV rapidamente GR TXH
j LGD
4XDO GRV JUi¿FRV VHJXLQWHV SRGH UHSUHVHQWDU D distância percorrida SHOR 3HGUR QR VHX SDVVHLR HP
IXQomR GR WHPSR TXH GHFRUUHX GHSRLV GH HOH VDLU GH FDVD
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) (B)
distância percorrida
distância percorrida
tempo tempo
(C) (D)
distância percorrida
distância percorrida
tempo tempo
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9. 8. $ IXQomR f p XPD IXQomR GH SURSRUFLRQDOLGDGH GLUHFWD 6DEHVH TXH f _2 i 6
4XDO GDV LJXDOGDGHV VHJXLQWHV GH¿QH D IXQomR f
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
x
(A) f _x i
3
(B) f _x i 3x
(C) f _x i = x + 4
(D) f _x i = x − 4
9. 5HVROYH D HTXDomR VHJXLQWH
x 3 _2 − x i
−2 =
2 4
$SUHVHQWD RV FiOFXORV TXH HIHFWXDUHV
10. 1D ~OWLPD DXOD GR WHUFHLUR SHUtRGR D WXUPD GD 0DUJDULGD RIHUHFHX j SURIHVVRUD GH 0DWHPiWLFD XP UDPR
FRQVWLWXtGR SRU W~OLSDV YHUPHOKDV H W~OLSDV EUDQFDV
2 UDPR IRUPDGR SRU 18 W~OLSDV WLQKD PDLV 4 W~OLSDV YHUPHOKDV GR TXH EUDQFDV
4XDQWDV W~OLSDV EUDQFDV WLQKD R UDPR TXH D WXUPD GD 0DUJDULGD RIHUHFHX j SURIHVVRUD
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
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10. 11. $ +HOHQD FRQVWUXLX SDUD D GLVFLSOLQD GH (GXFDomR 9LVXDO YiULRV PRGHORV GH VyOLGRV HP HVIHURYLWH
7RGRV RV PRGHORV VmR SULVPDV UHFWRV GH EDVH TXDGUDGD
$V EDVHV GRV PRGHORV VmR WRGDV LJXDLV H DV DOWXUDV VmR WRGDV GLIHUHQWHV
11.1. 1D )LJXUD HVWmR UHSUHVHQWDGRV WUrV GRV PRGHORV IHLWRV SHOD +HOHQD
Figura 2
$ +HOHQD YDL IRUUDU HVWHV WUrV PRGHORV FRP SDSHO DXWRFRODQWH
6DEHVH TXH
x R YROXPH GR PRGHOR PDLRU p LJXDO j VRPD GRV YROXPHV GRV GRLV PRGHORV PHQRUHV
x SDUD IRUUDU RV GRLV PRGHORV PHQRUHV JDVWDPVH PDLV 50 cm2 GH SDSHO GR TXH SDUD IRUUDU R
PRGHOR PDLRU
'HWHUPLQD HP FHQWtPHWURV D PHGLGD GD DUHVWD GD EDVH GRV PRGHORV
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
11.2. $ GHVSHVD FRP D FRQVWUXomR GH FDGD PRGHOR GHSHQGH GD DOWXUD GHVVH PRGHOR
2 JUi¿FR VHJXLQWH UHSUHVHQWD D UHODomR HQWUH D DOWXUD GRV PRGHORV HP PLOtPHWURV H D GHVSHVD
HP FrQWLPRV
despesa
60
50
40
30
20
10
0 10 20 30 40 50 60 70
altura
$ GHVSHVD FRP D FRQVWUXomR GH XP GRV PRGHORV IRL 50 FrQWLPRV
4XDO p D DOWXUD HP PLOtPHWURV GHVVH PRGHOR
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11. 12. 1D )LJXUD HVWi UHSUHVHQWDGR XP UHFWkQJXOR [ABCD ] $ ¿JXUD QmR HVWi GHVHQKDGD j HVFDOD
D C
3,5
F
E G
5 3
A B
Figura 3
6DEHVH TXH
x RV SRQWRV E e G SHUWHQFHP DRV ODGRV [AD ] e [BC ] UHVSHFWLYDPHQWH
x R VHJPHQWR [EG ] p SDUDOHOR DR VHJPHQWR [AB ]
x R VHJPHQWR [BD ] LQWHUVHFWD R VHJPHQWR [EG ] QR SRQWR F
x EF 5
x FG 3
x ED 3, 5
t
12.1. $GPLWH TXH DFE 35 o
4XDO p D DPSOLWXGH HP JUDXV GR kQJXOR FBG
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
12.2. 2V WULkQJXORV [EFD ] e [GFB ] VmR VHPHOKDQWHV
Determina BG
0RVWUD FRPR FKHJDVWH j WXD UHVSRVWD
13. 'H XP WULkQJXOR [PQR ] VDEHVH TXH
x PQ 5
x QR 11
4XDO GRV VHJXLQWHV YDORUHV SRGH VHU R YDORU GH PR
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) 4 (B) 12 (C) 18 (D) 24
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12. '26 '2,6 ,7(16 6(*8,17(6 14.A. E 14.B 5(62/9( $3(1$6 80 '( $25'2 20 $6 ,16758d®(6
48( 7(1+$6 5((%,'2
14.A. 1D )LJXUD HVWi UHSUHVHQWDGR XP WULkQJXOR UHFWkQJXOR [ABC ] $ ¿JXUD QmR HVWi GHVHQKDGD j HVFDOD
A
B C
Figura 4
1XPD GDV RSo}HV VHJXLQWHV HVWmR LQGLFDGDV DV PHGLGDV GRV ODGRV GHVWH WULkQJXOR
(P TXDO GHODV
$VVLQDOD D RSomR FRUUHFWD
(A) AB 4
BC 11
AC 12
(B) AB 5
BC 12
AC 13
(C) AB 6
BC 13
AC 14
(D) AB 7
BC 14
AC 15
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13. 14.B. 1D )LJXUD HVWi UHSUHVHQWDGD XPD FRPSRVLomR JHRPpWULFD GH RULJHP LVOkPLFD
1 2
A B
3 4
C D
)LJXUD
1HVWD ¿JXUD HVWmR UHSUHVHQWDGRV D VRPEUHDGR TXDWUR SROtJRQRV JHRPHWULFDPHQWH LJXDLV FRP D
IRUPD GH XPD VHWD (VVHV SROtJRQRV HVWmR GHVLJQDGRV SHORV DOJDULVPRV 1 2 3 e 4
2V SRQWRV A B C e D DVVLQDODGRV QD ¿JXUD VmR YpUWLFHV GRV UHIHULGRV SROtJRQRV
2 SROtJRQR 3 SRGH VHU REWLGR FRPR LPDJHP GR SROtJRQR 1 SRU PHLR GD WUDQVODomR DVVRFLDGD D XP GRV
YHFWRUHV VHJXLQWHV $ TXDO GHOHV
7UDQVFUHYH D OHWUD GD RSomR FRUUHFWD
(A) AC CB
(B) AC CA
(C) AB BD
(D) AB BC
FIM
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14. COTAÇÕES
1. ........................................................................................................... SRQWRV
2. ........................................................................................................... SRQWRV
3.
3.1. .................................................................................................. SRQWRV
3.2. .................................................................................................. SRQWRV
4. ........................................................................................................... SRQWRV
5. ........................................................................................................... SRQWRV
6. ........................................................................................................... SRQWRV
7. ........................................................................................................... SRQWRV
8. ........................................................................................................... SRQWRV
9. ........................................................................................................... SRQWRV
10. .......................................................................................................... SRQWRV
11.
11.1. ................................................................................................. SRQWRV
11.2. ................................................................................................. SRQWRV
12.
12.1. ................................................................................................. SRQWRV
12.2. ................................................................................................. SRQWRV
13. .......................................................................................................... SRQWRV
14. .......................................................................................................... SRQWRV
TOTAL ......................................... 100 pontos
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