10 Tauira o ngā Pātai Pokapū o te Taumaha
1. Ngā taunga Te pokapū o te kaha ko te mea e pā ana ki te pūwāhi 0 ko…
Kōrero
E mōhiotia ana :
Te horahanga o te mea (A) = (8)(4) = 32
Te pūwāhi i te tuaka-x (x) = ½ (8) = 4
Te pūwāhi i te tuaka-y (y)= ½ (4) = 2
I pātaihia : Ngā taunga o te pokapū taumaha o te mea e pā ana ki te pūwāhi 0
Whakautu :
2. Tauwāhi te pokapū o te taumaha o tētahi mea ki te tohu 0 ko…
Kōrero
Tuatahi, tatauhia te teitei o te mea. Wehea te mea kia rua ngā tapatoru hāngai, ko te turanga o ia tapatoru hāngai he 4 cm, ā, ko te taha whakararo he 5 cm.
E mōhiotia ana :
Te horahanga o te mea (A) = ½ (turanga)(teitei) = ½ (8)(3) = (4)(3) = 12
Te pūwāhi i te tuaka-x (x) = ½ (8) = 4
Te pūwāhi i te tuaka-y (y)= 1/3 (3) = 1
I pātaihia : Ngā taunga o te pokapū taumaha o te mea e pā ana ki te pūwāhi 0
Whakautu :
Ko ngā taunga o te pokapū taumaha o te mea ko (4, 1) cm.
3. Tirohia te ahua i raro nei! Whakatauhia (a) te taunga o te pokapū taumaha o te mea e pā ana ki te pūwāhi P (b) te taunga o te pokapū taumaha o te mea e pā ana ki te taha PQ.
Kōrero
E mōhiotia ana :
Wehea te mea kia rua ngā wāhanga, te wāhanga 1 = tapawhā rite, te wāhanga 2 = tapawhā rite.
A1 = (6)(2) = 12
A2 = (2)(2) = 4
x1 = ½ (6) = 3
x2 = ½ (2) + 2 = 1 + 2 = 3
y1 = ½ (2) = 1
y2 = ½ (2) + 2 = 1 + 2 = 3
I pātaihia : Ngā taunga o te pokapū o te taumaha e pā ana ki te taha PQ
Whakautu :
(a) Ko te taunga o te pokapū taumaha o te mea e pā ana ki te pūwāhi P ko (3 ; 1,5) cm.
(b) Ko te tūranga o te pokapū taumaha o te mea e pā ana ki te taha PQ he 1,5 cm
4. Pātai Whakamātautau ā-Motu SMA/MA 2015/2016 Nama 10
Tirohia te pikitia e whai ake nei!
Ko ngā taunga o te pokapū o te kaha taumaha o te papa āhua-H ko...
A. (3 ; 4)
B. (3,5 ; 2,5)
C. (3,5 ; 4)
D. (4 ; 3)
E. (4 ; 4)
Kōrero
Wehea te mea kia toru ngā wāhanga.
Te horahanga o te wāhanga 1 (A 1 ) = (2)(6) = 12 cm 2
Ko te pūwāhi o te wāhanga 1 i runga i te tuaka-x (x 1 ) = 1/2 (2) = 1 cm
Ko te pūwāhi o te wāhanga 1 i runga i te tuaka-y (y 1 ) = 1/2 (6) = 3 cm
Te horahanga o te wāhanga 2 (A 2 ) = (4)(2) = 8 cm 2
Ko te pūwāhi o te wāhanga 2 i runga i te tuaka-x (x 2 ) = 2 + (1/2)(4) = 2 + 2 = 4 cm
Ko te pūwāhi o te wāhanga 2 i runga i te tuaka-y (y 2 ) = 2 + (1/2)(2) = 2 + 1 = 3 cm
Te horahanga o te wāhanga 3 (A 3 ) = (2)(6) = 12
Ko te pūwāhi o te wāhanga 3 i runga i te tuaka-x (x 3 ) = 2 + 4 + (1/2)(2) = 2 + 4 + 1 = 7 cm
Ko te pūwāhi o te wāhanga 3 i runga i te tuaka-y (y 3 ) = 1/2 (6) = 3 cm
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-x:
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-y:
Ko ngā taunga o te pokapū o te taumaha o te papa āhua-H ko (x, y) = (4, 3)
Ko te whakautu tika ko D.
5. Pātai Whakamātautau ā-Motu SMA/MA 2014/2015 Nama 6
Mātakihia te horahanga ōrite me ngā inenga e whakaaturia ana i te pikitia!
Ko te tūranga o te pokapū o te kaha taumaha o te āhua i runga ake nei e pā ana ki te tuaka-x ko….
A. 2,0 henemita
B. 2,5 henemita
C. 3,0 henimita
D. 3,5 henimita
E. 4,0 henimita
Kōrero
Wehea te mea kia 4 ngā wāhanga, arā, A, B, C me D.
Tātaihia te horahanga o ia wāhanga.
A A = ½ (turanga)(teitei) = ½ (1,5)(3) = (1,5)(1,5) = 2,25
A B = (roa)(whānui) = (4,5-1,5)(1) = (3)(1) = 3
A C = ½ (turanga)(teitei) = ½ (6-4,5)(3) = (1,5)(1,5) = 2,25
A D = ½ (turanga)(teitei) = ½ (4,5-1,5)(6-3) = ½ (3)(3) = (1,5)(3) = 4,5
y A = 1/3 (3) = 1
yB = 1/2 (1) = 0,5
yC = 1/3 (3) = 1
y D = 3 + (1/3)(6-3) = 3 + (1/3)(3) = 3 + 1 = 4
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-y:
Ko te tūnga o te pokapū o te kaha taumaha o te āhua e pā ana ki te tuaka-x he 2 cm.
Ko te whakautu tika ko A.
6. Ngā Pātai Whakamātautau ā-Motu mō te Ahupūngao SMA/MA 2014/2015 Nama 6
Tirohia te pikitia!
Ko ngā taunga o te pokapū o te taumaha o te ahua e whai ake nei ko….
Kōrero
Wehea te mea kia 4 ngā wāhanga, arā, A, B, C me D.
Tātaihia te horahanga o ia wāhanga.
AA = (roa)(whānui) = (4)(3) = 12
A B = ½ (turanga)(teitei) = ½ (6-4)(3) = ½ (2)(3) = (1)(3) = 3
A C = ½ (turanga)(teitei) = ½ (8-6)(3) = ½ (2)(3) = (1)(3) = 3
A D = (roa)(whānui) = (8)(6-3) = (8)(3) = 24
y A = 1/2 (3) = 1,5
y B = 3 – (1/3)(3) = 3 – 1 = 2
y C = 3 – (1/3)(3) = 3 – 1 = 2
y D = 3 + (1/2)(6-3) = 3 + (1/2)(3) = 3 + 1,5 = 4,5
x A = 1/2 (4) = 2
x B = 4 + (1/2)(6-4) = 4 + (1/2)(2) = 4 + 1 = 5
x C = 6 + (1/2)(8-6) = 6 + (1/2)(2) = 6 + 1 = 7
x D = 1/2 (8) = 4
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-x:
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-y:
Ko te whakautu tika ko B.
7. Ko ngā taunga o te pokapū o te taumaha o te mea ōrite i te ahua i raro nei ko...
A. (14, 15)
B. (17, 11)
C. (15, 11)
D. (15, 7)
E. (11, 7)
Kōrero:
Wehea te mea kia toru ngā wāhanga, kia toru ngā horahanga o ia wāhanga (10-0)x(10-0), (20-10)x(30-0), (30-20)x(10-0)
Ngā taunga o te pokapū o te taumaha o te mea e pā ana ki te tuaka-x:
x1 = te tawhiti o te pokapū o te horahanga 1 mai i te pūwāhi 0, x2 = te tawhiti o te pokapū o te horahanga 2 mai i te pūwāhi 0, x3 = te tawhiti o te pokapū o te horahanga 3 mai i te pūwāhi 0.
Ngā taunga o te pokapū o te taumaha o te mea e pā ana ki te tuaka-y:
y1 = te tawhiti o te pokapū o te horahanga 1 mai i te pūwāhi 0, y2 = te tawhiti o te pokapū o te horahanga 2 mai i te pūwāhi 0, y3 = te tawhiti o te pokapū o te horahanga 3 mai i te pūwāhi 0.
Ko ngā taunga o te pokapū taumaha o te mea ko (15, 11)
Ko te whakautu tika ko C.
8. Ko ngā taunga o te pokapū o te taumaha o te mea i te ahua i raro nei ko...
A. (3 ; 2,7) m
B. (3 ; 3,6) m
C. (3 ; 4,0) m
D. (3 ; 4,5) m
E. (3 ; 5,0) m
Kōrero:
Wehea te mea kia rua ngā wāhanga, ko te horahanga o ia wāhanga ko (5-1)x(3-0), ko te ½ (6-0)x(9-3)
Ngā taunga o te pokapū o te taumaha o te mea e pā ana ki te tuaka-x:
Ngā taunga o te pokapū o te taumaha o te mea e pā ana ki te tuaka-y:
Ko ngā taunga o te pokapū taumaha o te mea ko (3; 3,6)
Ko te whakautu tika ko B.
9. Ko ngā taunga o te pokapū o te taumaha o tētahi mea ōrite e pā ana ki te pūwāhi O i te ahua e whai ake nei ko...
A. (4 3/5, 3 3/5)
B. (4 1/3, 3 1/3)
C. (4 1/3, 3)
D. (3 1/3, 4 1/3)
E. (3, 3 2/3)
Kōrero
Wehea te mea kia toru ngā wāhanga, wāhanga 1 = tapawhā rite, wāhanga 2 = tapawhā rite, wāhanga 3 = tapawhā rite.
Te rohe o te wāhanga 1 (A1) = (2-0)(8-0) = (2)(8) = 16
Ko te pūwāhi o te wāhanga 1 i te tuaka-x (x1) = 1
Ko te pūwāhi o te wāhanga 1 i runga i te tuaka-y (y1) = 4
Te rohe o te wāhanga 2 (A2) = (4-2)(2-0) = (2)(2) = 4
Ko te pūwāhi o te wāhanga 2 i te tuaka-x (x2) = 3
Ko te pūwāhi o te wāhanga 2 i runga i te tuaka-y (y2) = 1
Te rohe o te wāhanga 3 (A3) = (6-4)(8-0) = (2)(8) = 16
Ko te pūwāhi o te wāhanga 3 i te tuaka-x (x3) = 5
Ko te pūwāhi o te wāhanga 3 i runga i te tuaka-y (y3) = 4
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-x:
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-y:
Ko ngā taunga o te pokapū taumaha o te mea e pā ana ki te pūwāhi O ko (x, y) = (3, 3 2/3)
Ko te whakautu tika ko E.
10. Ko ngā taunga o te pokapū o te kaha taumaha o te ahua o te papa rererangi i raro nei ko….
A. (1 1/2, 1 1/2) henimita
B. (2.1/2) henimita
C. (2, 1 1/2) henimita
D. (2 1/2, 1 1/2) henimita
E. (2 1/2, 2 1/2) henimita
Kōrero
Wehea te mea kia toru ngā wāhanga, wāhanga 1 = tapawhā rite, wāhanga 2 = tapawhā rite, wāhanga 3 = tapawhā rite.
Te rohe o te wāhanga 1 (A1) = (1-0)(3-0) = (1)(3) = 3
Ko te pūwāhi o te wāhanga 1 i te tuaka-x (x1) = 0,5
Ko te pūwāhi o te wāhanga 1 i runga i te tuaka-y (y1) = 1,5
Te rohe o te wāhanga 2 (A2) = (3-1)(2-1) = (2)(1) = 2
Ko te pūwāhi o te wāhanga 2 i te tuaka-x (x2) = 2
Ko te pūwāhi o te wāhanga 2 i runga i te tuaka-y (y2) = 1,5
Te rohe o te wāhanga 3 (A3) = (4-3)(3-0) = (1)(3) = 3
Ko te pūwāhi o te wāhanga 3 i te tuaka-x (x3) = 3,5
Ko te pūwāhi o te wāhanga 3 i runga i te tuaka-y (y3) = 1,5
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-x:
Ngā taunga o te pokapū o te taumaha o te mea i runga i te tuaka-y:
Ko ngā taunga o te pokapū taumaha o te mea ko (x, y) = (2, 1 1/2)
Ko te whakautu tika ko C.
Pūtake pātai:
Ngā Pātai Ahupūngao Whakamātautau ā-Motu mō te Kura Tuarua/Kura Tuarua Mahi-ā-ringa
