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ENCCEJA 2017 Prova Matemática e suas tecnologias ENSINO MÉDIO 4 Tarde

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Ensino Médio
Prova IV - Tarde
Matemática e suas Tecnologias
a
C C
C
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X XX
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++
*BMR175AMMT1*
2 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 31
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A ��ƒ
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D ���ƒ
*BMR175AMMT2*
3Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 32
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A I.
B II.
C III.
D IV.
*BMR175AMMT3*
4 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 33
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*BMR175AMMT4*
5Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 34
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$QGDU�QR�PDU�FRP�iJXD�QDV�FDQHODV 140
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SUHSDUDGRU�ItVLFR"
A ���
B 220
C ���
D 356
*BMR175AMMT5*
6 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 35
(P�XPD�FRUULGD��D�TXDWUR�YROWDV�GR�¿QDO��UHJLVWURX�VH�HP�XP�TXDGUR�DV�GLVWkQFLDV�HQWUH�
RV�GRLV�SULPHLURV�FRPSHWLGRUHV��QRV�LQVWDQWHV�HP�TXH�R�SULPHLUR�GHOHV�FRPSOHWDYD�FDGD�YROWD�
Número de voltas restantes para o 
�ƒ�FRPSHWLGRU�FKHJDU�DR�¿QDO��v) 4 3 2 1 0
Distância entre os dois primeiros 
competidores (D) ����P ����P ����P ����P ����P
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A D = 150v
B D = 200v
C D� �������� v��� 800
D D = 800 ��������� v�
*BMR175AMMT6*
�Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 36
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WDQWR�� XP�PRGHOR� GH� XQLIRUPH� IRL� HVFROKLGR� H� RUoDPHQWRV� IRUDP� WRPDGRV� HP� TXDWUR� ORMDV��
FRQIRUPH�GHVFULWR�QD�WDEHOD�
Loja Camisa (R$) Calção (R$) Par de meiões (R$)
1 26,00 14,00 9,00
2 29,00 13,00 8,00
3 31,00 13,00 5,00
4 32,00 10,00 ����
$V�ORMDV�Vy�YHQGHP�XQLIRUPHV�FRPSOHWRV��FDPLVDV��FDOo}HV�H�SDUHV�GH�PHL}HV��2�JUXSR�
YDL� VH� UHXQLU� SDUD� HVFROKHU� WUrV� GDV� SURSRVWDV� PDLV� DGHTXDGDV� SDUD� WHQWDU� XPD� VHJXQGD�
QHJRFLDomR�GH�SUHoRV��HOLPLQDQGR�D�ORMD�TXH�DSUHVHQWDU�R�RUoDPHQWR�PDLV�FDUR�SDUD�D�FRPSUD�
GH�XP�XQLIRUPH�FRPSOHWR�
4XDO�GHVVDV�ORMDV�WHUi�VHX�RUoDPHQWR�HOLPLQDGR"
A 1
B 2
C 3
D 4
*BMR175AMMT7*
8 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 37
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GH�VXD�DOWXUD��HP�PHWUR���RX�VHMD�� IMC = Massa
(Altura)2
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IMC Categoria
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25,1 a 30 6REUHSHVR
30,1 a 40 Obeso
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PHWD�SURSRVWD�SHOR�PpGLFR�p
A 38,0.
B �����
C 22,0.
D 12,0.
QUESTÃO 38
$�VDIUD�GH�JUmRV�QR�%UDVLO�HP������DWLQJLX�������PLOK}HV�GH�WRQHODGDV��UHVXOWDGR�VXSHULRU�
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(P�TXDQWRV�PLOK}HV�GH�WRQHODGDV�D�SURGXomR�GH�JUmRV�GH������VXSHURX�D�GH�����"
A 23,2
B 23,8
C 24,2
D 24,8
*BMR175AMMT8*
9Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 39
8PD�IiEULFD�GH�SDUDIXVRV�WHP�XPD�SUHRFXSDomR�HVSHFLDO�FRP�DV�DUHVWDV�GH�VHXV�SURGXWRV��
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PDQXDOPHQWH�WRGDV�DV�DUHVWDV�GRV�SDUDIXVRV�SURGX]LGRV��$�¿JXUD�UHSUHVHQWD�XP�WLSR�GHVVHV�
SDUDIXVRV�SURGX]LGRV��FRQKHFLGR�FRPR�VH[WDYDGR��TXH�SRVVXL�D�FDEHoD�QD�IRUPD�GH�XP�SULVPD�
UHJXODU�KH[DJRQDO�
2�Q~PHUR�GH�DUHVWDV�QD�FDEHoD�GH�XP�SDUDIXVR�VH[WDYDGR�TXH�GHYHP�VHU�OL[DGDV�p
A 6.
B 12.
C 18.
D 24.
QUESTÃO 40
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'LVSRQtYHO�HP��ZZZ�LVWRH�FRP�EU��$FHVVR�HP����DJR�������
6HJXQGR�HVVDV�LQIRUPDo}HV��R�Q~PHUR�GH�SDVVDJHLURV�PHQFLRQDGRV�HTXLYDOH�D
A GH]HVVHLV�PLOK}HV�H�VHWH��
B GH]HVVHLV�PLOK}HV�H�VHWH�PLO�
C GH]HVVHLV�PLOK}HV�H�VHWHQWD�PLO�
D GH]HVVHLV�PLOK}HV�H�VHWHFHQWRV�PLO�
*BMR175AMMT9*
10 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 41
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FRPSUD�GHVVHV�SURGXWRV�p� IHLWD�HP�SHoDV� LQWHLUDV�GH���NJ��([LVWHP�TXDWUR�HVWDEHOHFLPHQWRV�
IRUQHFHGRUHV��,��,,��,,,�H�,9��FXMRV�SUHoRV�SUDWLFDGRV�VmR�LQGLFDGRV�D�VHJXLU�
I. ��NJ�GH�TXHLMR��±��5������������NJ�GH�SUHVXQWR��±��5��������
II. ��NJ�GH�TXHLMR��±��5������������NJ�GH�SUHVXQWR��±��5��������
III. ��NJ�GH�TXHLMR��±��5������������NJ�GH�SUHVXQWR��±��5��������
IV. ��NJ�GH�TXHLMR��±��5������������NJ�GH�SUHVXQWR��±��5��������
3RU�UD]}HV�RSHUDFLRQDLV��R�DGPLQLVWUDGRU�GD�ODQFKRQHWH�RSWD�SRU�FRPSUDU�RV�GRLV�SURGXWRV�
HP�XP�Vy�HVWDEHOHFLPHQWR��$QWHV�GH� UHDOL]DU�D�FRPSUD��YHUL¿FD�TXH�QD� ODQFKRQWH�Ki�����NJ�
GH�TXHLMR� H� ����J� GH�SUHVXQWR� D� VHUHP�XWLOL]DGRV��(OH� GHVHMD� FRPSUDU� RV� GRLV� SURGXWRV� HP�
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1HVVDV� FRQGLo}HV�� HP� TXDO� HVWDEHOHFLPHQWR� GHYHUi� VHU� UHDOL]DGD� D� FRPSUD� GR� TXHLMR� H� GR�
SUHVXQWR"
A I
B II
C III
D IV
QUESTÃO 42
$�WDEHOD�DSUHVHQWD�D�H[SHFWDWLYD�GH�YLGD��HP�DQR��QR�%UDVLO�H�VXDV�UHJL}HV��QRV�DQRV������
e 2000.
País e regiões 1950 2000
%UDVLO 43,3 ����
Norte 44,3 69,5
Nordeste 35,9 ����
6XGHVWH 48,0 ����
6XO ���� ����
&HQWUR�2HVWH 50,3 ����
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'H�DFRUGR�FRP�D�WDEHOD��QR�DQR�������D�UHJLmR�HP�TXH�D�H[SHFWDWLYD�GH�YLGD�WHYH�YDORU�PDLV�
SUy[LPR�GD�H[SHFWDWLYD�GH�YLGD�GR�SDtV�IRL�D�UHJLmR
A 6XO�
B Norte.
C Nordeste.
D &HQWUR�2HVWH�
*BMR175AMMT10*
11Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 43
8P�UHVHUYDWyULR�FRP�FDSDFLGDGH�GH�������OLWURV�SRVVXL�����OLWURV�GH�iJXD�HP�VHX�LQWHULRU��
3DUD� HQFKHU� HVVH� UHVHUYDWyULR�� XPD�SHVVRD�XWLOL]D� XPD�ERPED� FRP�YD]mR� �TXDQWLGDGH�GH�
OLWURV�TXH�HQWUDP�QR� UHVHUYDWyULR�HP� UHODomR�DR� WHPSR� WUDQVFRUULGR��GH�x� OLWURV�SRU�PLQXWR��
/RJR�DSyV�R�LQtFLR�GR�HQFKLPHQWR�GR�UHVHUYDWyULR��D�ERPED�IRL�GHVOLJDGD�SRU����PLQXWRV��$R�
VHU�UHOLJDGD��FRPSOHWRX�R�HQFKLPHQWR�GR�UHVHUYDWyULR��(QTXDQWR�HVWHYH�IXQFLRQDQGR��D�ERPED�
WUDEDOKRX�VHPSUH�QD�PHVPD�YD]mR�H�KRXYH�VRPHQWH�HVVD�HQWUDGD�GH�iJXD�QR�UHVHUYDWyULR�H�
QmR�KRXYH�VDtGD�
$�H[SUHVVmR�TXH�UHSUHVHQWD�R�WHPSR�GH�HQFKLPHQWR�GR�UHVHUYDWyULR��HP�PLQXWR��HP�IXQomR�GD�
TXDQWLGDGH�x�GH�iJXD��HP�OLWUR��p�LJXDO�D
A
2 760
x + 10
B
3 000
x + 10
C
2 760
x
+ 10
D
3 000
x
+ 10
QUESTÃO 44
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��ERODV�YHUPHOKDV����ERODV�D]XLV����ERODV�DPDUHODV�H���ERODV�EUDQFDV��2�IXQFLRQiULR�GR�PrV�
GHYH�UHWLUDU�XPD�EROD�DR�DFDVR�H�VHX�SUrPLR�VHUi�GHWHUPLQDGR�GH�DFRUGR�FRP�D�FRU�GD�EROD��D�
EROD�YHUPHOKD�FRUUHVSRQGH�D�XP�WHOHYLVRU��D�EROD�D]XO��D�XPD�ELFLFOHWD��D�EROD�DPDUHOD��D�XP�
YHQWLODGRU��H�D�EROD�EUDQFD��D�XP�PLFUR�RQGDV�
4XDO�p�D�SUREDELOLGDGH�GH�R�IXQFLRQiULR�GR�PrV�JDQKDU�XP�WHOHYLVRU"
A
1
3
B
1
4
C
3
20
D
1
20
*BMR175AMMT11*
12 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 45
3DUD� D� SURGXomR� GH� XP� SURGXWR� GH� PDVVD� ���� NJ�� XPD� LQG~VWULD� XWLOL]D� ���� NJ� GD�
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FDOFXODGR�DFUHVFHQWDQGR�VH�����DR�YDORU�GH�FXVWR�WRWDO�GHVVDV�GXDV�PDWpULDV�SULPDV�
$�SDUWLU�GR�SUy[LPR�PrV��R�SUHoR�GH�FXVWR�SRU�TXLORJUDPD�GD�PDWpULD�SULPD�$�VRIUHUi�XP�
DXPHQWR� GH�5�������� �(QWUHWDQWR�� GHVHMD�VH�PDQWHU� D�PHVPD�FRPSRVLomR�QD�SURGXomR�H� R�
PHVPR� YDORU� GH� YHQGD� GR� SURGXWR�� 3DUD� LVVR�� D� LQG~VWULD� DQDOLVD� TXH� QHFHVVLWDUi� UHGX]LU� R�
SHUFHQWXDO�GH�DFUpVFLPR�DSOLFDGR�VREUH�R�YDORU�GH�FXVWR�SDUD�FDOFXODU�R�VHX�YDORU�GH�YHQGD�
3DUD�DWHQGHU�D�HVVDV�FRQGLo}HV��R�QRYR�SHUFHQWXDO�DSOLFDGR�VREUH�R�YDORU�GH�FXVWR�GHYH�VHU�GH
A ������
B ������
C ������
D ������
*BMR175AMMT12*
13Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 46
1R�SODQHMDPHQWR�GH�XPD�YLDJHP�HQWUH�GXDV�FLGDGHV��IRUDP�DYDOLDGRV�GRLV�GLVWLQWRV�WUDMHWRV��
$V�RSo}HV�HVWXGDGDV�HQYROYHP�D�GLVWkQFLD�WRWDO�D�VHU�SHUFRUULGD�H�R�FXVWR�FRP�SHGiJLR�QRV�
UHVSHFWLYRV�WUDMHWRV�
Trajeto A
'LVWkQFLD�WRWDO� �����NP
&XVWR�GR�SHGiJLR� �5�������
Trajeto B
'LVWkQFLD�WRWDO� �����NP
&XVWR�GR�SHGiJLR� �5������
2�FDUUR�D�VHU�XWLOL]DGR�QD�YLDJHP�SHUFRUUH����NP�SRU�OLWUR��2�SUHoR�GR�FRPEXVWtYHO�XWLOL]DGR�
p�VHPSUH�LJXDO�D�5�������SRU�OLWUR�
$�GLIHUHQoD�SRVLWLYD�HQWUH�RV�FXVWRV�GD�YLDJHP��VHJXQGR�R�SODQHMDPHQWR�DSUHVHQWDGR��UHIHUHQWH�
DRV�WUDMHWRV�DYDOLDGRV�p�LJXDO�D
A 5�������
B 5��������
C 5��������
D 5��������
*BMR175AMMT13*
14 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 47
2�HVTXHPD�PRVWUD�R�SHUFXUVR�GH�XP�EDUFR�DR�ORQJR�GH�WRGR�R�VHX�WUDMHWR��
2� EDUFR� PDQWpP�VH� VHPSUH� QD� PHVPD� GLUHomR�� SHUSHQGLFXODU� j� FRUUHQWH]D��
3RUpP��GHYLGR�j�DomR�GHVWD�� VXD� WUDMHWyULD�p�GLUHFLRQDGD�SDUD�R�SRQWR�C�� QR�RXWUR� ODGR�GD�
PDUJHP��D�����PHWURV�GR�SRQWR�LQLFLDO�GH�GHVWLQR�B��6DEH�VH�WDPEpP�TXH�R�kQJXOR�IRUPDGR�
HQWUH�R�QRYR�WUDMHWR�H�D�GLUHomR�SHUSHQGLFXODU�j�PDUJHP��QR�SRQWR�A��p�GH���ž�
$�GLVWkQFLD��HP�PHWUR��SHUFRUULGD�SHOR�EDUFR�p�GH�
A
100¥3
3
B
200¥3
3
C 100¥3
D 200
*BMR175AMMT14*
15Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 48
$�FiSVXOD�TXH� UHWLURX�RV�PLQHLURV�TXH�SHUPDQHFHUDP�SUHVRV�GXUDQWH�YiULRV�GLDV�VRE�D�
WHUUD�QR�QRUWH�GR�&KLOH��HP�������¿FDUi�H[SRVWD�HP�/RQGUHV��$�¿JXUD� UHSUHVHQWD�D�)rQL[����
FRPR�IRL�FKDPDGD�D�FiSVXOD��XPD�MDXOD�PHWiOLFD�GH�TXDVH�����FHQWtPHWURV�GH�FRPSULPHQWR�H�
���FHQWtPHWURV�GH�GLkPHWUR�
'LVSRQtYHO�HP��KWWS���J��JORER�FRP��$FHVVR�HP�����MXO��������DGDSWDGR��
$V�PHGLGDV�GR�FRPSULPHQWR�H�GR�GLkPHWUR��HP�PHWUR��GD�)rQL[���VmR��UHVSHFWLYDPHQWH�
A 0,004 e 0,00053.
B 0,04 e 0,0053.
C 0,4 e 0,053.
D 4 e 0,53.
QUESTÃO 49
8P�UHODWyULR�GR�XVR�GD�LQWHUQHW�QR�VHJXQGR�VHPHVWUH�GH������PRVWURX�TXH�D�YHORFLGDGH�
PpGLD�GDV�FRQH[}HV�IHLWDV�QR�%UDVLO�HUD�GH���0ESV��(VVD�YHORFLGDGH�PpGLD�HVWi�EHP�DEDL[R�GDV�
PpGLDV�LQWHUQDFLRQDLV��FRPR�PRVWUD�R�TXDGUR�
País Velocidade
&KLOH 19
(TXDGRU 15
(8$ 26
&DQDGi 25
-DSmR 39
5RPrQLD 38
'LVSRQtYHO�HP��KWWS���PHLRELW�FRP��$FHVVR�HP�����MXO��������DGDSWDGR�
&RQVLGHUH�TXH�D�PHWD�QR�%UDVLO�VHMD�FRQVHJXLU�TXH�D�YHORFLGDGH�PpGLD�GDV�FRQH[}HV�¿TXH�
LJXDO�j�PpGLD�GHVVHV�SDtVHV��8PD�GDV�Do}HV�GDV�HPSUHVDV�TXH�IRUQHFHP�RV�VHUYLoRV�GH�LQWHUQHW�
SDUD�DWLQJLU�HVVD�PHWD�VHUi�WURFDU�R�VLVWHPD�GH�¿DomR�H[LVWHQWH�SHOR�VLVWHPD�GH�¿EUD�yWLFD�
3DUD�DWLQJLU�HVVD�PHWD��R�SHUFHQWXDO�GD�YHORFLGDGH�GH�FRQH[mR�GHYH�DXPHQWDU�HP
A �������
B �������
C �������
D �������
*BMR175AMMT15*
16 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 50
3DUD�REWHU�XPD�PHOKRUD�PDLV�UiSLGD��TXDQGR�GD�LQWHUQDomR�GH�XP�SDFLHQWH��DOJXQV�WLSRV�
GH�PHGLFDPHQWRV�VmR�DGPLQLVWUDGRV�SRU�YLD�YHQRVD��4XDQGR�R�SDFLHQWH�UHFHEH�DOWD�KRVSLWDODU��
R�PpGLFR� SUHVFUHYH� XP� UHPpGLR�� FRP� IyUPXOD� VLPLODU�� SDUD� VHU� LQJHULGR� SRU� YLD� RUDO�� GDQGR�
FRQWLQXLGDGH�DR�WUDWDPHQWR��&RQVLGHUH�TXH�XP�SDFLHQWH�SDVVRX�SRU�HVVD�VLWXDomR�H�HQTXDQWR�
HVWDYD�LQWHUQDGR�WRPDYD��QD�YHLD������PJ�GH�PHGLFDPHQWR��$R�DYDOLDU�D�FRUUHVSRQGrQFLD�HQWUH�
RV�PHGLFDPHQWRV�SUHVFULWRV�SRU�YLDV�GLVWLQWDV��R�PpGLFR�HODERURX�XP�JUi¿FR�UHWLOtQHR�1 200
1 000
800
600
400
200
0
25 100
Remédio via oral (mg)
Correspondência entre medicamentos via venosa u via oral
R
em
éd
io
 v
ia
 v
en
os
a 
(m
g)
175 250
4XDO� p� D� GRVDJHP�� HP� PLOLJUDPD�� GR� PHGLFDPHQWR� SUHVFULWR� SHOR� PpGLFR� SRU� YLD� RUDO�
FRUUHVSRQGHQWH�j�GRVDJHP�GR�PHGLFDPHQWR�TXH�R�SDFLHQWH�WRPDYD�HQTXDQWR�HVWDYD�LQWHUQDGR"
A 1 200 
B 300
C ���
D 25
QUESTÃO 51
8P� FRUUHWRU� GHVHMD� SXEOLFDU� HP� MRUQDO� XP� DQ~QFLR� UHIHUHQWH� D� XP� HPSUHHQGLPHQWR�
TXH� HOH� HVWi� YHQGHQGR�� 2� HPSUHHQGLPHQWR� WHP� IRUPDWR� UHWDQJXODU�� GH� GLPHQV}HV�
����P�u�����P��H�R�HVSDoR�GLVSRQtYHO�SDUD�R�DQ~QFLR�QR�MRUQDO�p�WDPEpP�GH�IRUPDWR�UHWDQJXODU��GH�
���FP�u���FP��(OH�SUHWHQGH�XWLOL]DU�WRGR�R�HVSDoR�GH�TXH�GLVS}H�H��SDUD�LVVR��GHYH�GHWHUPLQDU�
D�HVFDOD�DGHTXDGD�
$�HVFDOD�D�VHU�XWLOL]DGD�VHUi
A �������
B ��������
C ��������
D ����������
*BMR175AMMT16*
��Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 52
8PD�HPSUHVD�TXH�UHDOL]D�VHUYLoRV�JUi¿FRV�SRVVXL���IXQFLRQiULRV�TXH�WUDEDOKDP�HP�XPD�
MRUQDGD�GH����KRUDV�GLiULDV�QR�VHWRU�GH�FySLDV��$�¿P�GH�HYLWDU�R�SDJDPHQWR�GH�KRUDV�H[WUDV�H�
RXWURV�HQFDUJRV�WUDEDOKLVWDV��R�JHUHQWH�GREURX�R�Q~PHUR�GH�IXQFLRQiULRV�TXH�WUDEDOKDP�QHVVH�
VHWRU�H� UHGX]LX�D� MRUQDGD�GH� WUDEDOKR�SDUD���KRUDV�GLiULDV��9HUL¿FRX�DLQGD�TXH��QD�VXD�QRYD�
HTXLSH��FDGD�IXQFLRQiULR�SURGX]�����FySLDV�SRU�KRUD�WUDEDOKDGD�
1HVVDV�FRQGLo}HV��R�Q~PHUR�WRWDO�GH�FySLDV�SURGX]LGDV�HP�XP�GLD�SHOD�QRYD�HTXLSH�SDVVDUi�D�
VHU�LJXDO�D
A 3 600.
B ������
C 36 000.
D 43 200.
QUESTÃO 53
2�GRQR�GH�XPD�SDSHODULD�SUHFLVD�FRPSUDU�������UHVPDV�GH�SDSHO�QR�IRUPDWR�$���SDUD�UHSRU�
VHX�HVWRTXH��$SyV�XPD�SHVTXLVD�GH�SUHoRV��HVFROKH�UHDOL]DU�D�FRPSUD�HP�XPD�ORMD�DWDFDGLVWD�
TXH� YHQGH� FDGD� UHVPD�DR�SUHoR�GH�5��������&RQVWDWRX�� WDPEpP��TXH�5���������p� R� YDORU�
PDLV� EDUDWR� D� VHU� SDJR� � SHOR� WUDQVSRUWH� GHVVDV� UHVPDV��6DEH�VH� TXH�� QHVVD� SDSHODULD�� HOH�
YHQGH�HVVH�SURGXWR�FRP�OXFUR�GH������VREUH�VHX�FXVWR�WRWDO��6DEH�VH�DLQGD�TXH�HOH�GHVHMD�
PDQWHU�VXD�PDUJHP�GH�OXFUR�H�YHQGHU�HVVDV�UHVPDV�SRU��QR�Pi[LPR��5��������FDGD��3DUD�WDQWR��
SUHFLVDUi�FRQVHJXLU�XP�GHVFRQWR�QR�SUHoR�GH�FRPSUD�GDV�UHVPDV��XPD�YH]�TXH�R�YDORU�GR�IUHWH��
QmR�SRGHUi�VHU�QHJRFLDGR�
3DUD�DWLQJLU�VHXV�REMHWLYRV��TXDO�GHYHU�VHU�R�YDORU�PDLV�SUy[LPR�GR�PHQRU�GHVFRQWR�TXH�R�GRQR�
GD�SDSHODULD�SUHFLVD�REWHU�QR�YDORU�GH�FRPSUD�GHVVDV�UHVPDV"
A �����
B �����
C �����
D ������
*BMR175AMMT17*
18 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 54
8PD�SHVTXLVD�UHDOL]DGD�HP�XPD�FLGDGH�DSUHVHQWRX�R�Q~PHUR�GH�FDVRV�GH�GHQJXH�TXH�
IRUDP�FRQ¿UPDGRV�QR�SHUtRGR�GH������D�������2�JUi¿FR�DSUHVHQWD�R�Q~PHUR�GH�FDVRV�SRU�DQR�
2010 2011 2012 2013
450
425
400
375
350
325
300
275
250
225
200
175
150
125
100
75
50
25
0
N
úm
er
o 
de
 c
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os
 d
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de
ng
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$� PpGLD� DULWPpWLFD� DQXDO� GR� Q~PHUR� GH� FDVRV� GH� GHQJXH� FRQ¿UPDGRV�� QR� SHUtRGR� GH�
�����D�������IRL�LJXDO�D
A 262,5.
B 300,0.
C 325,0.
D ������
QUESTÃO 55
$V� PiTXLQDV� GH� XPD� ODYDQGHULD� FRQVRPHP�� TXDQGR� HP� IXQFLRQDPHQWR�� �� ���� OLWURV�
GH�iJXD�SRU�KRUD��GH� IRUPD�FRQVWDQWH��(ODV� IXQFLRQDP�GDV���K�jV����K�H�GDV����K�jV����K��
$� FDL[D�G¶iJXD� TXH� DEDVWHFH� HVVDV�PiTXLQDV� WHP� FDSDFLGDGH� GH� ��� ���� OLWURV�� (OD� p� FRQWLQXDPHQWH�
DOLPHQWDGD�SRU�XPD�WXEXODomR�FRP�YD]mR�FRQVWDQWH�GH�������OLWURV�SRU�KRUD�H�SRVVXL�VLVWHPD�
GH�FRQWUROH�GH�YROXPH��ERLD��
&RQVLGHUH�XP�GLD�HP�TXH�KRXYH� LQWHUUXSomR�GR� IRUQHFLPHQWR�GH�iJXD�QD� IDL[D�KRUiULD�
HQWUH���K�H����K�
*BMR175AMMT18*
19Matemática e suas Tecnologias – ENCCEJA 2017
2�JUi¿FR�TXH� UHSUHVHQWD�R� YROXPH�GH�iJXD��HP� OLWUR�� H[LVWHQWH�QD�FDL[D��QD� IDL[D�
KRUiULD�HQWUH���K�H����K�GHVVH�GLD�p
A
18 000
15 000
12 000
9 000
6 000
3 000
0 2 4 6 8 10 12 14 16 18
Vo
lu
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de
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a 
(L
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Horário (h)
B
18 000
15 000
12 000
9 000
6 000
3 000
0 2 4 6 8 10 12 14 16 18
Vo
lu
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de
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a 
(L
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Horário (h)
C
18 000
15 000
12 000
9 000
6 000
3 000
0 2 4 6 8 10 12 14 16 18
Vo
lu
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(L
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Horário (h)
D
18 000
15 000
12 000
9 000
6 000
3 000
0 2 4 6 8 10 12 14 16 18
Vo
lu
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de
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(L
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Horário (h)
*BMR175AMMT19*
20 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 56
'H�DFRUGR�FRP�D�2UJDQL]DomR�GDV�1Do}HV�8QLGDV��218���FDGD�SHVVRD�QHFHVVLWD�GH�FHUFD�
GH����� OLWURV�GH�iJXD�SRU�GLD�SDUD�DWHQGHU�jV�VXDV�QHFHVVLGDGHV�GH�FRQVXPR�H�KLJLHQH��1R�
HQWDQWR��QR�%UDVLO��R�FRQVXPR�SRU�SHVVRD�XOWUDSDVVD�HVVH�YDORU��
'LVSRQtYHO�HP��KWWS���VLWH�VDEHVS�FRP�EU��$FHVVR�HP����VHW��������DGDSWDGR��
$�SUHIHLWXUD�GH�XPD�FLGDGH�GHVHQYROYHX�XPD�FDPSDQKD�SDUD�TXH�FDGD�PRUDGRU�FXPSUD��
GLDULDPHQWH�� R� HTXLYDOHQWH� D� ���� GDTXLOR� TXH� p� LQGLFDGR� SHOD� 218�� 8P� PRUDGRU� XWLOL]D��
GLDULDPHQWH������OLWURV�GH�iJXD�
3DUD�FXPSULU�D�PHWD�GD�SUHIHLWXUD��HVVH�PRUDGRU�GHYH�UHGX]LU�VHX�FRQVXPR�GLiULR�GH�iJXD�HP
A ���
B ���
C ���
D ���
QUESTÃO 57
8PD� FRQVWUXWRUD� VROLFLWD� DR� VHX� IDEULFDQWH� GH� SUp�PROGDGRV� TXH� DOWHUH� DV� GLPHQV}HV�
GRV� EORFRV� UHWDQJXODUHV� XWLOL]DGRV� QD� FRQVWUXomR� GH� SDUHGHV�� )RL� VROLFLWDGR� TXH� FDGD� EORFR�
WHQKD�FRPSULPHQWR�H[WHUQR�GH�����FP�H�ODUJXUD�H[WHUQD�GH����FP��2�IDEULFDQWH�FDOFXORX�TXH�D�
HVSHVVXUD�GD�SDUHGH�GR�EORFR�VHUi�GH���FP�SDUD�VXSRUWDU�R�SHVR�QR�HPSLOKDPHQWR�GRV�EORFRV��
VHQGR�QHFHVViULR�GLPHQVLRQDU�D�DOWXUD�GR�EORFR�GH�IRUPD�D�XWLOL]DU�XP�YROXPH�GH�FRQFUHWR�GH�
�������FP3�QD�SURGXomR�GH�FDGD�EORFR��FRQIRUPH�LOXVWUD�D�¿JXUD�
1HVVDV�FLUFXQVWkQFLDV��TXDO�GHYH�VHU�D�DOWXUD�GR�EORFR��HP�FHQWtPHWUR"
A 13
B 26
C ��
D 60
*BMR175AMMT20*
21Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 58
2�JHUHQWH�GH�XPD�FRQFHVVLRQiULD��FRP�D�¿QDOLGDGH�GH�PRVWUDU�R�ERP�GHVHPSHQKR�GH�
VXD�HTXLSH�� WUDoRX�XP�SODQR�GH�DomR�SDUD�VHXV�YHQGHGRUHV�EDVHDGR�QR�Q~PHUR�GH�YHQGDV�
GH� YHtFXORV� GR� DQR� DQWHULRU�� (OH� DSUHVHQWRX� D� TXDQWLGDGH� GH� YHtFXORV� YHQGLGRV�� GLVWULEXtGD�
PHQVDOPHQWH��FRQIRUPH�R�JUi¿FR�
0
Jan Fev Mar Abr Maio Jun Jul Ago Set Out Nov Dez
50
100
100
150
200
250
N
úm
er
o 
de
 v
eí
cu
lo
s 
ve
nd
id
os
130 130
160
180
200
40
30 26
90
20
25
6HX� SODQR� SDUD� R� SUy[LPR� DQR� p� HVWDEHOHFHU�� FRPR�PHWD� GH� YHQGDV�PHQVDLV�� D�PpGLD�
DULWPpWLFD� GRV� VHLV� PHVHV� FRP�PDLRUHV� TXDQWLGDGHV� GH� YHtFXORV� YHQGLGRV� DSUHVHQWDGRV� QR�
JUi¿FR�
4XDO�p�R�Q~PHUR�PtQLPR�GH�YHtFXORV�TXH�GHYHUmR�VHU�YHQGLGRV�SDUD�VH�FXPSULU�D�PHWD�SURMHWDGD�
SHOR�JHUHQWH"
A 130
B 145
C 150
D 154
*BMR175AMMT21*
22 Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 59
8P�FRQVWUXWRU� SUHWHQGH� FREULU� XP� WHOKDGR��1R�PHUFDGR�H[LVWHP�GLIHUHQWHV�PHGLGDV� GH�
FRPSULPHQWR�GH�WHOKDV�GH�PHVPD�ODUJXUD��1D�MXQomR��DV�WHOKDV�VH�VREUHS}HP�HP����FP�H�QD�
H[WUHPLGDGH�LQIHULRU�GHYHP�XOWUDSDVVDU�D�SDUHGH��FRQIRUPH�LOXVWUD�D�¿JXUD��
Inclinação
do telhado
3 m
4 m
2V�WLSRV�GH�WHOKD�VmR�
Telha tipo A Telha tipo B Telha tipo C
&RPSULPHQWR������P
3UHoR�SRU�XQLGDGH�5�������
&RPSULPHQWR������P
3UHoR�SRU�XQLGDGH�5�������
&RPSULPHQWR������P
3UHoR�SRU�XQLGDGH�5�������
3DUD�FREULU�WRGD�D�FDVD��IRUDP�FRQVLGHUDGDV�DOJXPDV�SRVVLELOLGDGHV�
I. 7RGR�R�WHOKDGR�FRP�WHOKDV�GR�WLSR�$�
II. &RPELQDU�WHOKDV�GR�WLSR�$�FRP�WHOKDV�GR�WLSR�%��
III. &RPELQDU�WHOKDV�GR�WLSR�$�FRP�WHOKDV�GR�WLSR�&�
IV. &RPELQDU�WHOKDV�GR�WLSR�%�FRP�WHOKDV�GR�WLSR�&�
$�SRVVLELOLGDGH�TXH�UHVXOWRX�QR�PHQRU�FXVWR�QD�FRPSUD�GDV�WHOKDV�p�D
A I.
B II.
C III.
D IV.
*BMR175AMMT22*
23Matemática e suas Tecnologias – ENCCEJA 2017
QUESTÃO 60
8PD�SHVVRD�WHP�GXDV�GtYLGDV�SDUFHODGDV��XPD�QR�YDORU�GH�5���������PHQVDLV��IDOWDQGR�
���SDUFHODV�SDUD�TXLWDU��H�RXWUD��QR�YDORU�GH�5���������PHQVDLV��IDOWDQGR����SDUFHODV�SDUD�TXLWDU��8PD�¿QDQFHLUD��DR�HQWUDU�HP�FRQWDWR�FRP�HVVD�SHVVRD��SURS}H�OKH�TXLWDU�DV�GXDV�GtYLGDV�VH�HOD�
¿]HU�XP�¿QDQFLDPHQWR�SDJDQGR����SDUFHODV�GH�56��������H�UHFHEHQGR�GH�UHWRUQR�XP�YDORU�GH�
5�����������
6H�D�SHVVRD�DFHLWDU�R�¿QDQFLDPHQWR�RIHUHFLGR�SRU�HVVD�¿QDQFHLUD��TXDQWR�HOD�SDJDUi�D�PDLV�SRU�
VXDV�GtYLGDV�DWXDLV"
A 5����������
B 5����������
C 5����������
D 5����������
*BMR175AMMT23*
*BMR175AMMT24*

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