pobrano z www.sqlmedia.pl

(1)

pobrano z www.sqlmedia.pl pobrano z www.sqlmedia.pl

1

Matematyka Klucz punktowania

Zadania wyboru wielokrotnego

Numer zadania 2. 3. 4. 6. 8. 14. 17.

Poprawna

RGSRZLHGě B C A D A C B

Zasady przyznawania punktów:

SNWļNDĝGDSRSUDZQDRGSRZLHGě

SNWļEïÚGQDRGSRZLHGěOXEEUDNRGSRZLHG]L

3R]RVWDïH]DGDQLD UWAGA:

=DNDĝGHSRSUDZQHUR]ZLÈ]DQLH]DGDQLDRWZDUWHJRLQQHQLĝSU]HGVWDZLRQHSU]\]QDMHVLÚPDNV\PDO- QÈOLF]EÚSXQNWöZ

-HĂOL XF]Hñ QD GRZROQ\P HWDSLH UR]ZLÈ]\ZDQLD ]DGDQLD SRSHïQLï MHGHQ OXE ZLÚFHM EïÚGöZ UDFKXQ- NRZ\FK MHGQDN ]DVWRVRZDQH PHWRG\ E\ï\ SRSUDZQH ZöZF]DV RFHQÚ FDïHJR UR]ZLÈ]DQLD REQLĝD VLÚ

RSXQNW

Numer

zadania 3RSUDZQDRGSRZLHGě Liczba

punktów Zasady przyznawania punktów 1. 1.1. F

1.2. P 1.3. F

0–2 SNWļWU]\SRSUDZQHRGSRZLHG]L

SNWļGZLHSRSUDZQHRGSRZLHG]L

SNWļMHGQDSRSUDZQDRGSRZLHGě

OXEZV]\VWNLHRGSRZLHG]L

QLHSRSUDZQHOXEEUDNRGSR- ZLHG]L

5. 5.1. P 5.2. P

0–1 SNWļGZLHSRSUDZQHRGSRZLHG]L

OXEZV]\VWNLHRGSRZLHG]L

QLHSRSUDZQHOXEEUDNRGSR- ZLHG]L

7. 7.1. B 7.2. C 7.3. F

SNWļQLHSRSUDZQHRGSRZLHG]LOXE

EUDNRGSRZLHG]L 9. 9.1. P

9.2. F

OXEQLHSRSUDZQHRGSRZLH- G]LOXEEUDNRGSRZLHG]L

pobrano z www.sqlmedia.pl

(2)

2

Numer

punktów Zasady przyznawania punktów 10. 3URSR]\FMHUR]ZLÈ]DQLD

]ZïDVQRĂFLNÈWöZSU]\OHJï\FK

·CAB180n135n n45

]WZLHUG]HQLDRVXPLHPLDUNÈWöZZH- ZQÚWU]Q\FKZWUöMNÈFLH

·ABC180n 45n n 90

180n135n n45

2GSRZLHGě2WU]\PDOLĂP\WUöMNÈW

SURVWRNÈWQ\RNÈWDFKRVWU\FKUöZQ\FK

n

45 7UöMNÈWWDNLQD]\ZDP\SURVWRNÈW- Q\PUöZQRUDPLHQQ\P

0–3 SNWļSHïQHUR]ZLÈ]DQLHļREOLF]H- QLHPLDUNÈWöZCAB i ABC RUD]SRSUDZQH]DSLVDQLH

ZQLRVNX

SNWļSRSUDZQHZ\]QDF]HQLH

PLDU\GZöFKNÈWöZ

OXE ]DSLVDQLHOXE]D]QDF]HQLHQD

U\VXQNXĝH·ABC n45

i ·CAB n45DOHEUDN

ZQLRVNX

SNWļZ\NRQDQLHW\ONRMHGQHJR

HWDSXUR]ZLÈ]DQLD]DGDQLD

REOLF]HQLHPLDU\NÈWDCAB

SNWļQLHSRSUDZQHUR]ZLÈ]DQLH

SU]\SDGNRZHG]LDïDQLD

LQLHSRSUDZQHREOLF]HQLDOXE

EUDNUR]ZLÈ]DQLD 11. 11.1. P

11.2. F

OXEEUDNRGSRZLHG]L 12. 3URSR]\FMDUR]ZLÈ]DQLD

REOLF]HQLHSRZLHU]FKQLG]LDïNL

¸ ² ²

P P P FP REOLF]HQLHLORĂFLREMÚWRĂFLĂQLHJXNWöU\

VSDGïQDG]LDïNÚ

V_¥ FP FP FP²¸ ³ REOLF]HQLHREMÚWRĂFLĂQLHJX]Xĝ\WHJRGR

XOHSLHQLDEDïZDQD

¸ x ¸ ¸

3 3 3

3

4 50 30 20

3

4 4

FP

3 3

Vb Q

Q

REOLF]HQLHLOHSURFHQWĂQLHJX]G]LDïNL

G]LHFLZ\NRU]\VWDï\GRXOHSLHQLDEDïZDQD

¸ 640000 ¸

100% 100% 2%

32000000

b Ă

V V

2GSRZLHGě']LHFLGRXOHSLHQLDEDïZDQD

Z\NRU]\VWDï\ĂQLHJX]G]LDïNL

0–4 SNWļSHïQHUR]ZLÈ]DQLHļSRSUDZ- QHREOLF]HQLHLOHSURFHQW

ĂQLHJX]G]LDïNLZ\NRU]\VWDï\

G]LHFLGRXOHSLHQLDEDïZDQD 3 pkt – SRSUDZQ\VSRVöEREOLF]HQLD

LOHSURFHQWĂQLHJX]G]LDïNL

Z\NRU]\VWDï\G]LHFLGRXOH- SLHQLDEDïZDQDDOHSRSHïQLH- QLHEïÚGöZUDFKXQNRZ\FK OXE

QLHGRSURZDG]HQLHREOLF]Hñ

GRNRñFD

SNWļREOLF]HQLHREMÚWRĂFLĂQLH- JXQDG]LDïFHLREOLF]HQLH

REMÚWRĂFLĂQLHJX]Xĝ\WHJRGR

XOHSLHQLDEDïZDQD

SNWļUR]ZLÈ]DQLHW\ONRMHGQHJR

HWDSX REOLF]HQLHREMÚWRĂFL

ĂQLHJXQDG]LDïFH OXE REOLF]HQLHREMÚWRĂFLĂQLH- JX]Xĝ\WHJRGRXOHSLHQLD

EDïZDQD

LQLHSRSUDZQHREOLF]HQLDOXE

EUDNUR]ZLÈ]DQLD

pobrano z www.sqlmedia.pl

(3)

3

Numer

punktów Zasady przyznawania punktów 13. 3URSR]\FMDUR]ZLÈ]DQLD

x – OLF]ED]MD]GöZ$GDPDxļOLF]ED

QDWXUDOQD

y –OLF]ED]MD]GöZ0DFLHMDy ļOLF]ED

QDWXUDOQD

¸

x

16 x

y

3U]\EOLĝHQLH]QLHGRPLDUHP x 16

y

2GSRZLHGě$GDPL0DFLHMPRJÈZ\NR- QDÊQDMZLÚFHMSR]MD]GöZ

0–3 SNWļSHïQHUR]ZLÈ]DQLHļZ\]QD- F]HQLHPDNV\PDOQHMOLF]E\

]MD]GöZZ\NRQDQ\FKSU]H]

FKïRSFöZ

SNWļSRSUDZQH]DSLVDQLHLUR]ZLÈ- ]DQLHREXUöZQDñDOHEUDN

SU]\EOLĝHQLDOXEQLHSR- SUDZQHSU]\EOLĝHQLHOLF]E\

]MD]GöZ0DFLHMD

OXE SRSUDZQ\VSRVöEREOLF]H- QLDOLF]E\]MD]GöZNDĝGHJR

]FKïRSFöZ]JRGQLH]ZDUXQ- NDPL]DGDQLDDOHSRSHïQLH- QLHEïÚGöZUDFKXQNRZ\FK

OXE

QLHGRSURZDG]HQLHREOLF]Hñ

GRNRñFD

SNWļSRSUDZQH]DSLVDQLHREX

UöZQDñ

OXE SRSUDZQH]DSLVDQLHLUR]ZLÈ- ]DQLHMHGQHJR]UöZQDñ

LQLHSRSUDZQHREOLF]HQLD OXEEUDNUR]ZLÈ]DQLD 15. GRSXV]F]DOQHOXE

15.2. 2

SNWļQLHSRSUDZQHRGSRZLHG]LOXE

EUDNRGSRZLHG]L 16. 3URSR]\FMDUR]ZLÈ]DQLD

RFHQDSLHUZV]HJRVNRNX

¹⁰²^{95 2}

^¸⁶⁰⁷⁴

RFHQDGUXJLHJRVNRNX

⁹⁷^{95 2}

^¸⁶⁰⁶⁴

ïÈF]QDQRWD]DRGOHJïRĂÊ

74 64 138

2GSRZLHGě.DPLO6WRFKZREXVNRNDFK

X]\VNDïïÈF]QLHSXQNWöZ]DRGOH- JïRĂÊ

0–2 SNWļSHïQHUR]ZLÈ]DQLHļREOLF]H- QLHïÈF]QHMOLF]E\SXQNWöZ

NWöUH.DPLO6WRFKX]\VNDï

ZREXVNRNDFK]DRGOHJïRĂÊ

SNWļSRSUDZQHRGF]\WDQLH

]WHNVWXL]WDEHOLZV]\VWNLFK

ZDUWRĂFLDOHSRSHïQLHQLH

EïÚGöZUDFKXQNRZ\FK

LQLHSRSUDZQHREOLF]HQLD OXEEUDNUR]ZLÈ]DQLD