| Te Āhuahanga Taumata 7
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| Ngā Whāinga Paetae
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| Te torotoro āhuahanga taunga
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 1. ki te kimi i te tawhiti i waenganui i ētahi taunga e 2 i runga i tētahi tukutuku;
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co-ordinates; plane |
| 2. ki te kimi i te rōnaki o tētahi rārangi tika ahu&;2, mai i tētahi whārite ;
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gradient |
| 3. ki te tuhi, ki te whakamahi whārite
rārangi ahu&;2, mehemea kei te mōhiotia ngā kōrero
e hiahiatia ana (arā, ko te pūwāhi me te whārite o tētahi
rārangi whakarara, rārangi hāngai kē rānei );
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2-dimensional linear equations
point
perpendicular |
| 4. ki te kimi mai i ngā taunga o te tutakitanga o tētahi rārangi tōtika ki tētahi ānau , mehemea e mōhiotia ana ngā whārite ;
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co-ordinate; curve |
| 5. ki te whakawhitiwhiti i waenganui i ngā taunga kauwhata me ngā taunga pākoki ahu&;2.
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convert; rectangular co-ordinates; polar co-ordinates |
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Te torotoro rauara
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 6. ki te kōwhiri i te rauara tika
hei whakarite, hei whakaatu raraunga mārama ai te kitea atu;
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network |
| 7. ki te whakamahi rauara ki te āta kimi
mai, ki te tatari i ngā whakaotinga tino tika.
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evaluate; optimal solution |
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He Tauira Horopaki
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- NGA PĀ MAIORO&;Whakamahia
te ture rōnaki ki te kimi mai i te rōnaki o te maioro o tētahi
pa kua whakaritea hei tirotiro.
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- NGA TAUNGA IKA&;Kimihia ngā taunga ika ki te tikanga pākoki .
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- NGA HIKOI O NEHE RA&;Tuhia ngā arā i hikoi ai ngā tira haere o mua. (Hei whakatauira, ko ngā haere Mā runga pae maunga.)
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- NGĀ arā
KARERE RETA &;Mahia mai he rauara e kitea mai ai ngā
huarahi pai hei kawe reta. (Hei whakatauira, me whakaatu ngā pokatata
me ngā hononga e tere oti ai te mahi a te karere.)
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- TE UTU WHARE&;Whakamahia
ngā putahitanga o ngā rārangi tōtika hei kimi mai
ite utu-ā-mārama mō te whare.
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| He Tauira Mahi
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| Te torotoro āhuahanga taunga
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| Anei ētahi tauira mahi e taea ai ngā whāinga paetae o tenei taumata te whakatutuki:
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| 1. Me mōhio te ākonga ki te kimi i te tawhiti i waenganui i ētahi pūwāhi e 2 i runga i tētahi tukutuku;
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| 2. Me mōhio te ākonga ki te kimi i te rōnaki o tētahi rārangi tika ahu&;2, mai i tētahi whārite ;
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- he whakamahi i ngā kupu me ngā tikanga ahuahanga taunga hei hōpara , hei whakaahua, hei kimi mai i ngā āhuatanga o ngā āhua ahu-2, ahu-3 rānei (me whakamahi ngā pumanawa rorohiko i ngā wahi e tika ana);
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- he whakaoti rapanga whaitake e whai wahi mai ana ngā āhuatanga rārangi , tawhiti, koki rānei .
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| 3. Me mōhio te ākonga ki te tuhi, ki te whakamahi
whārite rārangi ahu&;2, mehemeakei te mōhiotia ngā
kōrero e hiahiatia ana (arā, ko te pūwāhi me te whārite
o tētahi rārangi whakarara, rārangi hāngai ke rānei
);
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| 4. Me mōhio te ākonga ki te kimi mai i ngā taunga o te tutakitanga o tētahi rārangi tōtika ki tētahi ānau , mehemea e mōhiotia ana ngā whārite ;
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- he hōpara i te tutakitanga o ētahi rārangi torotika
e rua, o tētahi rārangi rānei ki tētahi ānau
(tae atu hoki ki te porohita kei te (0,0), y=ax2,
y = a/x tōna punga), me te whakamahi anō i ngā tikanga
taurangi, kauwhata rānei .
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| 5. Me mōhio te ākonga ki te whakawhitiwhiti i waenganui i ngā taunga kauwhata me ngā taunga pākoki ahu&;2;
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- he whakamahi hangarau hei torotoro pūnaha taunga, tae atu hoki ki ngā
tauritenga i waenganui i ngā taunga kauwhata me ngā taunga
pākoki .
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| Te torotoro rauara
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| Anei ētahi tauira mahi e taea ai ngā whāinga
paetae o tēnei taumata te whakatutuki:
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| 6. Me mōhio te ākonga ki te kōwhiri i te rauara
tika hei whakarite, hei whakaatu raraunga mārama ai te kitea atu;
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| 7. Me mōhio te ākonga ki te whakamahi rauara ki te
ata kimi mai, ki te tātari i ngā whakaotinga tino tika;
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- he hōpara i te nui o te waea e hiahiatia ana hei tuhonohono haere
i ētahi wāhi noho ki te pūnaha waea o te taone;
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- he torotoro mehemea e ahei ana te tangata ki te katoa o ngā arā
kua tohua ki te maheretera pea kei te aukatihia ētahi . Me whai
whakaaro atu anō ki ngā karere reta, ki ngā arawhiti
rānei o Konigsberg;
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- he whakamahi rauara hei whakatauira, hei hōpara āhuatanga
pēnei i te tukanga hanga taonga māmā, i te whakahaere
kaupapa māmā, i te whakahaere hōtaka rānei . Hei
whakatauira, ko te mahi poke parāoa, ko te whakahaere i tētahi
hui whiriwhiri kaupapa hauora i te marae.
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| He Tauira Aro Matawai
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| He tauira noa ēnei hei awhina i te kaiwhakaako:
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- He whakahangai tikanga āhuahanga taunga ki ngā horopaki ahutatai.
Hei whakatauira:
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mena e mōhiotia ana ngā taunga o ngā akitu o tētahi
tapatoru (ngā whārite rānei o ētahi tapa e toru),
me kimi mai ngā taunga o te pū porohita raroto rānei
, ka whakamātau ai i ngā otinga.
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Mā tenei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
| Āhua 7/1 | Āhua 7/2 |
Āhua 7/3 |
WA-6 |
WR-3 |
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- He hōpara , he whakatakoto pūrongo e pā ana ki te whakahāngaitia
o ngā tikanga āhuahanga taunga ki te mahi whakaoti rapanga.
Hei whakatauira, ka hōpara , ka whakatakoto pūrongo te ākonga
e whakaatu ana i te tokomaha o ngā ākonga māori kua puta
te ihu i ngā whakamātauranga kura tuarua o te motu i ngā
tau ka hori ake nei.
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Mā tenei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
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- He mahi mai, he tatari rānei i tētahi momo tauwhainga kopapa e whai
wāhi mai ana ngā taunga kauwhata me ngā taunga pākoki
, ka tuhi pūrongo ai e whakaatu ana i ngā otinga.
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Mā tenei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
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Mā tenei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
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