| Te Taurangi Taumata 7
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| Ngā Whāinga Paetae
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| Te torotoro tauira, pānga
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 1. ki te whakamahi raupapa, tapeke raupapa hei whakatauira rapanga tūturu , ka whakamāori ai i ngā otinga;
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sequence; series
real |
| 2. ki te whakaahua, ki te whakamahi raupapa
tāpiri, whakarea, tapeke raupapa tapiri, whakarea
rānei , i roto i ngā pūāhua o ia rangi;
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arithmetic or geometric sequence or series |
| 3. ki te whakatauira pūāhua
huhua ki te kauwhata;
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situation |
| 4. ki te tuhi kauwhata, ki te hōpara
kauwhata pānga . Me whakamahi tātaitai, me tuhi rānei ngā
puwāhi i ngā wāhi e hiahiatia ana;
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function
points |
| 5. ki te whakamahi tikanga kauwhata
hei hōpara tauira i roto i ngā raraunga, ki te kimi i tōna
āhua taurangi i ngā wāhi e tika ana;
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graphing techniques
data |
| 6. ki te kimi&;ā&;kanohi,
ki te whakamāori tihi, whāruarua, wāhi tupa,
rārangi patata, aputa hoki i roto i ngā kauwhata kua whakaritea
hei tirotiro;
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find by inspection; maximum; point of inflection
asymptote |
| 7. ki te whakaahua hononga panoni i
waenganui i ngā whānau anau.
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transformation; curve |
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Te torotoro whārite, kīanga
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 8. ki te tuhi whārite, torite
rānei hei whakaahua pūāhua whaitake;
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inequation |
| 9. ki te kōwhiri rautaki (kauwhata,
tau, taurangi, pākoki) e kitea mai ai ngā otinga whārite,
torite rānei , ka whakamāori ai i ngā otinga;
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strategy; trigonometric
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| 10. ki te whawhe, ki te whakaruna
kīanga taurangi.
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manipulate; simplify |
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He Tauira Horopaki
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- NGĀ KAPA
HAKA&;He kimi mai i te kaha o te haruru o ngā rōpū
whakataetae i a rātou e mahi ana i ngā mahi. (Me whakaatu
ngā otinga ki te anau aho).
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- NGĀ RĀKAU
O TE WAO-NUI-Ā-TĀNE&;He aha te pānga o te
teitei ki te pakeke o te rākau? (Me pānga taupū.)
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exponential function |
- TE UTU WHAKAKORE
MAHI&;He kimi mai i te pānga i waenganui i te roa o
te wā i mahia me te nui o te utu whakakore mahi ka whakawhiwhia
atu. (Me pānga rārangi.)
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| He Tauira Mahi
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| Te torotoro tauira, pānga
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| Anei ētahi tauira mahi e taea ai ngā whāinga paetae o tēnei taumata te whakatutuki:
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| 1. Me mōhio te ākonga ki te whakamahi raupapa, tapeke hei whakatauira rapanga tūturu , ka whakamāori ai i ngā otinga;
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| 2. Me mōhio te ākonga ki te whakaahua, ki te whakamahi
raupapa tāpiri, whakarea, tapeke raupapa tāpiri, whakarea rānei
, i roto i ngā pūāhua o ia rangi;
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- he hōpara tauira tāpiri, whakarea rānei me te whakamahi
anō i:
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- he hōpara i ngā tauira tuapapa o roto mai i ngā pūāhua
o ia rangi.
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| 3. Me mōhio te ākonga ki te whakatauira puahua huhua ki te kauwhata;
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- he whakamahi kauwhata hei whakaahua, hei hōpara raupapa, tapeke raupapa
rānei ;
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- he whakatauira pūāhua tūturu , whakatau rānei
;
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- he torotoro i te whakamahia o ngā tikanga taurangi hei whakaahua i ētahi
tauira o roto i ngā raupapa, tapeke raupapa rānei , tae atu
hoki ki ngā nekenga tāpiri, whakarea.
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| 4. Me mōhio te ākonga ki te tuhi kauwhata, ki te
hōpara kauwhata pānga . Me whakamahi tātaitai, me tuhi rānei
ngā puwāhi i ngā wāhi e hiahiatia ana;
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| 5. Me mōhio te ākonga ki te whakamahi tikanga kauwhata
hei hōpara tauira i roto ngā raraunga, ki te kimi i tona āhua
taurangi i ngā wāhi e tika ana;
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- he whakamahi tātaitai, mokihi tuhi kauwhata rorohiko rānei
hei āta tuhi i te kauwhata o tētahi pānga whānui
mai i tētahi tauira kua whakaritea hei whiriwhiri.
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| 6. Me mōhio te ākonga ki te kimi&;ā&;kanohi,
ki te whakamāori tihi, whāruarua, wāhi tupa, rārangi
patata, aputa hoki i roto i ngā kauwhata kua whakaritea hei tirotiro;
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- he hōpara raraunga-ā-mata, raraunga ke rānei kua oti
ke te kohi e wai rā, hei kimi pānga .
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| 7. Me mōhio te ākonga ki te whakaahua hononga panoni
i waenganui i ngā whānau anau;
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- he torotoro pānga (tae atu hoki ki ngā panoni) i waenganui
i ngā momo kauwhata me ngā whārite o aua kauwhata, arā:
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ngā rārangi, pūrua, putoru taurangi-rau
&; ngā porohita, ngā pūwerewere tapawhā hāngai
&; ngā pānga taupu e pēnei ana te āhua : e = a u &; ngā pānga taupu kōaro e pēnei ana te āhua :
e = log a u
&; ngā pānga pākoki e pēnei ana te āhua : e =
a sin (bx + c), y= tan x;
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- he hōpara whānau anau me te whai whakaaro atu anō ki
ngā āhuatanga pēnei i te: hangarite, tihi, wharuarua,
aputa, rārangi patata, (aha ke rānei ).
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| Te torotoro whārite, kīanga
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| Anei ētahi tauira mahi e taea ai ngā whāinga
paetae o tēnei taumata te whakatutuki:
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| 8. Me mōhio te ākonga ki te tuhi wharite, torite
rānei hei whakaahua pūāhua whaitake;
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| 9. Me mōhio te ākonga ki te kowhiri rautaki (kauwhata,
tau, taurangi, pākoki) e kitea mai ai ngā otinga whārite,
torite rānei , ka whakamāori ai i ngā otinga;
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| 10. Me mōhio te ākonga ki te whawhe, ki te whakaruna kianga taurangi;
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- he hōpara pūāhua tūturu , whakatau rānei
me te whakamahi anō i ngā tikanga kauwhata, taurangi, āhuahanga,
hangarau. Hei whakatauira, ko te:
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&; whawhe, whakaruna kianga taurangi, tae atu hoki ki ngā kianga hautanga;
&; whakaoti whārite rārangi, pūrua, tukutahi (ko
tētahi ehara i i te whārite rārangi);
&; whakaoti whārite taurangi-rau me te tirotiro anō
i te āhua o ngā pūtake ;
&; whārite pakoki e pēnei ana te āhua : aho (x+a) = b, whenu
(ax) = b;
&; whawhe taupū, tae atu hoki ki ngā taupu hautanga, toraro rānei
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&; whawhe taupū kōaro.
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| He Tauira Aro Matawai
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| He tauira roa ēnei hei āwhina i te kaiwhakaako:
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- He kimi kīanga, tapeke rānei , i roto i ngā raupapa
me ngā tapeke raupapa, mai i ngā horopaki whaitake. Hei whakatauira,
e toru haora te koiora memeha o te parakawhe i roto i te tinana o te
tangata. Me whakatauira te nui o te parakawhe ki te raupapa, ka āta
whiriwhiri ai i te otinga mehemea ka rite tonu te inu kawhe a te tangata
nōna te tinana e āta tirohia ana.
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mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana
te matatau o ngā ākonga ki te:
| Taurangi 7/1 |
WR-2 |
WR-3 |
WA-4 |
WA-8 |
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- He tito, he whakahangai pānga taurangi e pā ana ki ētahi
raraunga i puta i tētahi whakamātauranga. Hei whakatauira,
mai i tētahi papatau e whakaatu ana i te tawhiti me te tere o te
heke o tētahi paoro i te papa rōnaki (koinei te whakamātauranga),
me tuhi he whārite e whakaahua ana i te pānga i waenganui
i enei mea e rua (arā, te tawhiti me te tere), ka whakahāngai
atu ai i tēnei whārite ki ētahi atu pūāhua
e rite ana ki tēnei .
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mā tēnei tauira ka mōhio te kaiwhakaako e pehea ana te matatau o ngā ākonga ki te:
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- He tuhi, he whakaoti whārite tukutahi mai i ngā pūāhua
whaitake, engari ko tētahi o aua whārite ehara i te whārite
rārangi. Hei whakatauira: tekau mano tāra te pūtea a
tētahi whakahaere hei whakapau ki ngā utu kaimahi ia wiki.
He ōrite te utu a tēnā, a tēnā kaimahi. E rua
ngā wāhanga o te utu, e toru rau tāra te nui o te wāhanga
tuatahi, engari ko te wāhanga tuarua, kei te āhua tonu o te
tokomaha o ngā kaimahi, arā, ka tāpihiria ki te wāhanga
tuatahi tētahi pūtea e whā ke te rahinga ake i te tokomaha
o ngā kaimahihei whakatauira noa ake, mehemea e rua tekau ngā
kaimahi, e $80 te nui o te wahanga tuarua hei tapiri atu ki te wāhanga
pūmau o te utu a ia kaimahi. Ko tā te ākonga , he tuhi
i ētahi whārite e rua e whakaatu ana i te utu-ā-wiki
a ēnei kaimahi, ka kimi ai i te tokomaha o ngā kaimahi ka
taea e te pūtea.
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mā tēnei tauira ka mōhio te kaiwhakaako e pēhea
ana te matatau o ngā ākonga ki te:
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- He whawhe, he whakaruna kianga e pēnei ana te āhua :
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mā tēnei tauira ka mōhio te kaiwhakaako e pēhea
ana te matatau o ngā ākonga ki te:
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&; he whakamahi pūmanawa hanga papatau, tuhi kauwhata rānei hei āta kimi mai i ngā pūtake o waenganui i ētahi tau tōpū e rua;
&; he whakahāngai, whakahoki tikanga whakaawhiwhi;
&; he whakamahi tono tiripou i roto i te pūmanawa rorohiko.
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mā tēnei tauira ka mōhio te kaiwhakaako e pēhea
ana te matatau o ngā ākonga ki te:
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- He kimi tauira pāngarau hei whakaatu i ngā mahi o ia rangi.
Hei whakatauira, tērā tētahi Wira Wherihi, e waru mita
te putoro, tekau mā rua hakona te roa o te wā ka pau ki te
huringa kotahi. Me kimi mai tētahi tauira e whakaaturia ai te pānga
i waenganui i te teitei o te kaieke me te wā - arā, pēhea
nei te tawhiti atu i te papa ki te wā e rewa ana te kaieke a te
wā ka pau te: toru hakona/ono hakona/waru hakona?
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mā tēnei tauira ka mōhio te kaiwhakaako e pehea ana te matatau o ngā ākonga ki te:
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- He whakamahi pūmanawa rorohiko tuhi kauwhata hei tautuhi i ngā āhuatanga tapua o tētahi kauwhata.
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mā tēnei tauira ka mōhio te kaiwhakaako e pehea ana te matatau o ngā ākonga ki te:
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