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Question 1Pāngarau
E whakaatu ana te rārangi tau ki te tau 3, 7, 11, 15, ... He aha te rerekētanga noa (common difference) o tēnei raupapa tata?
- 3
- 5
- 7
- 4 Correct answer.
Explanation
Ko te rerekētanga noa te tapeke ka tāpiritia ki ia tau kia puta ai te tau e whai ake. Anei, 7 − 3 = 4, ā, 11 − 7 = 4 hoki, nō reira ko te 4 te rerekētanga noa. Ka mau tonu tēnei uara puta noa i te raupapa.
Question 2Pāngarau
E 48 ākonga te katoa o tētahi karaehe. E 25 ōrau o rātou he tāne. E hia ngā ākonga tāne?
- 24
- 16
- 10
- 12 Correct answer.
Explanation
Ko te 25 ōrau he rite ki te kotahi hauwhā o te katoa. Nō reira ka tātaihia 48 ÷ 4 = 12, arā, 12 ngā ākonga tāne. Ka taea hoki te whakarea: 0.25 × 48 = 12.
Question 3Pāngarau
He aha te uara o te 5 i roto i te tau 3 572?
- 5 ngahuru
- 5 tekau mā rima
- 5 rau Correct answer.
- 5 mano
Explanation
Ka wehewehea te tau 3 572 ki ōna wāhi: 3 mano, 5 rau, 7 ngahuru, 2 kotahi. Kei te tūranga rau te 5, nō reira ko tōna uara ko te 500, arā, e 5 rau.
Question 4Pāngarau
Ka tīmata a Mere ki te pānui pukapuka 120 whārangi. Kua pānuitia e ia ngā whārangi 36. E hia ngā whārangi e toe ana?
- 94
- 74
- 156
- 84 Correct answer.
Explanation
Ka tangohia te whārangi kua pānuitia i te katoa: 120 − 36 = 84. Nō reira e 84 ngā whārangi e toe ana. Ka taea te tirotiro mā te tāpiri: 84 + 36 = 120.
Question 5Pāngarau
E hia ngā tapa (edges) o tētahi poro whaitua tapawhā (rectangular prism)?
- 8
- 6
- 10
- 12 Correct answer.
Explanation
Ko te poro tapawhā he āhua ahu-3 e 6 mata, e 8 pūtiki, e 12 tapa. Ka taea te tatau: e 4 ngā tapa o runga, e 4 o raro, e 4 ngā tapa poutū. Nō reira 12 ngā tapa katoa.
Question 6Pāngarau
E hia ngā meneti i roto i te 2.5 haora?
- 140
- 250
- 125
- 150 Correct answer.
Explanation
Kotahi te haora e 60 meneti. Nō reira 2.5 × 60 = 150 meneti. Ka taea hoki te wehewehe: 2 haora = 120 meneti, me te 0.5 haora = 30 meneti, tapeke 150.
Question 7Pāngarau
Ko tēhea te tau tōrau (prime number) i waenga i ēnei?
- 29 Correct answer.
- 33
- 21
- 27
Explanation
Ko te tau tōrau he tau nui ake i te 1, ā, ko ōna whakawehenga ko te 1 me te tau anō. Ko te 29 e kore e taea te whakawehe mā te 2, 3, 5 rānei, ā, kāore ōna whakawehenga atu. Nō reira ko te 29 te tau tōrau.
Question 8Pāngarau
Ka whakareatia te tau ki a ia anō, ka puta te 64. Ko tēhea te tau?
- 7
- 9
- 6
- 8 Correct answer.
Explanation
Ko te pūtake tapawhā (square root) o te 64 te tau e hiahiatia ana. Nō te mea 8 × 8 = 64, ko te 8 te tau tika. Ka taea te tirotiro: 7 × 7 = 49, 9 × 9 = 81.
Question 9Pāngarau
E 3 m te roa o tētahi tapawhā hāngai, e 5 m te whānui. He aha te horahanga (area)?
- 8 m²
- 30 m²
- 16 m²
- 15 m² Correct answer.
Explanation
Ko te horahanga o te tapawhā hāngai ka tātaihia mā te whakarea i te roa ki te whānui. Nō reira 3 × 5 = 15 m². Kāore e tika ana te tāpiri i ngā tapa mō te horahanga.
Question 10Pāngarau
Ka tuhia te rārangi tau: 2, 6, 18, 54, ... He aha te tau e whai ake?
- 162 Correct answer.
- 90
- 72
- 108
Explanation
Ka whakareatia ia tau ki te 3 kia puta ai te tau e whai ake: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54. Nō reira ko te 54 × 3 = 162 te tau e whai ake. He raupapa whakarea tēnei.
Question 11Pāngarau
Ka oti i a Hemi te 3/4 o tētahi mahi i te ata, ā, ka oti i a ia te 1/8 o te mahi i te ahiahi. E hia te wāhanga o te mahi kua oti katoa?
- 7/8 Correct answer.
- 1/2
- 5/8
- 4/12
Explanation
Me whakataurite ngā hautau ki te tauraro kotahi. Ko te 3/4 = 6/8, nō reira 6/8 + 1/8 = 7/8. Kua oti te 7/8 o te mahi katoa.
Question 12Pāngarau
Ka hipokina tētahi pouaka e 4 ōna mata tapawhā rite, e 6 ōna tapa. He aha te ingoa o tēnei āhua ahu-3?
- Poro tapawhā rite (cube) Correct answer.
- Poro tapawhā
- Poro koeko
- Poro porotaka
Explanation
Ko te poro tapawhā rite he āhua ahu-3 e 6 ōna mata tapawhā rite tonu, e 12 ōna tapa. Nō te mea he tapawhā rite ngā mata katoa, koia te poro tapawhā rite. He rerekē te poro tapawhā noa i te mea ka taea ngā mata tapawhā hāngai te roa rerekē.
Question 13Pāngarau
E 12 ōrau te pikinga o te utu o tētahi pukapuka, ā, ko tōna utu hou ināianei ko te $56. He aha te utu tuatahi?
- $44
- $52
- $48
- $50 Correct answer.
Explanation
Ko te $56 ko te 112 ōrau o te utu tuatahi. Nō reira ka tātaihia 56 ÷ 1.12 = 50. Ka taea te tirotiro: 50 × 1.12 = 56, arā, ko te $50 te utu tuatahi.
Question 14Pāngarau
Ko te tapeke o ngā tau e toru e whai ana i te raupapa, ko te 42. He aha te tau waenga?
- 15
- 12
- 13
- 14 Correct answer.
Explanation
Mēnā he raupapa tāpiri noa ngā tau e toru, ko te tapeke ko te 3 whakarea i te tau waenga. Nō reira 42 ÷ 3 = 14. Ka taea te tirotiro: 13 + 14 + 15 = 42.
Question 15Pāngarau
Ka tuhia te rārangi: 5, 10, 20, 40, ... He aha te ture mō tēnei raupapa?
- Whakareatia ia tau ki te 5
- Tāpiria te 5 ki ia tau
- Whakareatia ia tau ki te 2 Correct answer.
- Tāpiria ia tau ki a ia anō, me te tāpiri anō i te 5
Explanation
Ka whakareatia ia tau ki te 2 kia puta ai te tau e whai ake: 5 × 2 = 10, 10 × 2 = 20, 20 × 2 = 40. Nō reira ko te whakarea ki te 2 te ture o tēnei raupapa.
Question 16Pāngarau
He poro-tapawhā hāngai tētahi āhua, he mataono rite tētahi atu. He aha te tapeke o ngā tapa o ngā āhua e rua?
- 16
- 10
- 18
- 24 Correct answer.
Explanation
He 12 ngā tapa o te poro-tapawhā hāngai, ā, he 12 hoki ngā tapa o te mataono rite. Nō reira, ko 12 + 12 = 24 te tapeke. Ko ngā tapa e tataihia ana, kāore ko ngā mata, ko ngā kokonga rānei.
Question 17Pāngarau
Ka tuhia te tau ā-ira 0.375 hei ōrau. He aha te uara tika?
- 3.75 ōrau
- 0.375 ōrau
- 375 ōrau
- 37.5 ōrau Correct answer.
Explanation
Ki te huri i te tau ā-ira ki te ōrau, ka whakareatia ki te 100. Nō reira 0.375 × 100 = 37.5, arā, 37.5 ōrau. Ka taea hoki te tuhi hei hautau: 375/1000 = 37.5/100.
Question 18Pāngarau
E 8 cm te pūtake o tētahi tapatoru, ā, e 5 cm tōna teitei. He aha te horahanga?
- 13 cm²
- 26 cm²
- 40 cm²
- 20 cm² Correct answer.
Explanation
Ko te horahanga o te tapatoru ka tātaihia mā te haurua o te whakarea o te pūtake ki te teitei: ½ × 8 × 5 = 20 cm². Me maumahara ki te haurua, nō te mea he haurua te tapatoru o te tapawhā hāngai e rite ana tōna pūtake me tōna teitei.
Question 19Pāngarau
E 240 ākonga te katoa. E 90 ōrau o rātou e haere ana ki te hui. E hia ngā ākonga kāore e haere?
- 24 Correct answer.
- 48
- 36
- 30
Explanation
Mēnā e 90 ōrau e haere ana, e 10 ōrau kāore e haere. Ka tātaihia 10 ōrau o te 240: 240 × 0.10 = 24. Nō reira e 24 ngā ākonga kāore e haere.
Question 20Pāngarau
Ko te tauraro o ngā hautau e rua ko te 12. Ka tuhia te 2/3 me te 3/4 hei hautau e rite ana te tauraro. He aha te hua?
- 2/12 me te 3/12
- 8/12 me te 9/12 Correct answer.
- 8/12 me te 6/12
- 6/12 me te 9/12
Explanation
Ka whakareatia te taurunga me te tauraro o te 2/3 ki te 4: 8/12. Ka whakareatia te taurunga me te tauraro o te 3/4 ki te 3: 9/12. Nō reira ko te 8/12 me te 9/12 ngā hautau e rite ana te tauraro ki te 12.
Question 21Pāngarau
E rua ngā pūtiki o tētahi poro porotaka (cylinder). He aha te āhua o ōna mata e rua?
- Porowhita Correct answer.
- Tapawhā hāngai
- Tapatoru
- Tapawhā rite
Explanation
Ko te poro porotaka he āhua ahu-3 e rua ōna mata porowhita rite tonu, ā, he mata pōkai tōna taha. Nō reira he porowhita ngā mata e rua. Ko te mata pōkai, ina whakatuwheratia, he tapawhā hāngai.
Question 22Pāngarau
Ka tuhia te rārangi: 1, 4, 9, 16, 25, ... He aha te tau e whai ake?
- 49
- 30
- 36 Correct answer.
- 42
Explanation
Ko ngā tau tapawhā ēnei: 1², 2², 3², 4², 5². Ko te 6² = 36 te tau e whai ake. Ka taea hoki te tirotiro mā te rerekētanga: 3, 5, 7, 9, ā, ko te rerekētanga e whai ake ko te 11, nō reira 25 + 11 = 36.
Question 23Pāngarau
Ka whakareatia te tau ki te 3, kātahi ka tangohia te 7, ka puta te 26. He aha te tau?
- 11 Correct answer.
- 10
- 12
- 9
Explanation
Ka hangaia te whārite: 3x − 7 = 26. Ka tāpiria te 7 ki ngā taha e rua: 3x = 33. Ka wehewehea ki te 3: x = 11. Ka taea te tirotiro: 3 × 11 − 7 = 33 − 7 = 26.
Question 24Pāngarau
E 15 ōrau te paheke o te utu o tētahi hū, ā, ko tōna utu hou ko te $68. He aha te utu tuatahi?
- $78.20
- $85
- $83
- $80 Correct answer.
Explanation
Ko te $68 ko te 85 ōrau o te utu tuatahi, nō te mea kua heke te 15 ōrau. Nō reira ka tātaihia 68 ÷ 0.85 = 80. Ka tirotiro: 80 × 0.85 = 68, arā, ko te $80 te utu tuatahi.
Question 25Pāngarau
Ko te horahanga o tētahi tapawhā hāngai ko te 72 cm², ā, e 9 cm tōna roa. He aha tōna paenga (perimeter)?
- 26 cm
- 34 cm Correct answer.
- 36 cm
- 40 cm
Explanation
Ka tātaihia te whānui: 72 ÷ 9 = 8 cm. Kātahi ka tātaihia te paenga: 2 × (9 + 8) = 34 cm. Me maumahara ko te paenga te tapeke o ngā tapa e whā katoa.
Question 26Pāngarau
E 4 ngā tapa o tētahi tapawhā rite, ā, e 3 ngā tapa o tētahi tapatoru rite. He aha te tapeke o ngā tapa o ēnei āhua e rua?
- 7 Correct answer.
- 12
- 6
- 8
Explanation
Me tāpiri ngā tapa o ngā āhua e rua: 4 + 3 = 7. Ka taea te tatau takitahi: tapawhā rite e 4, tapatoru rite e 3, nō reira 7 ngā tapa katoa.
Question 27Pāngarau
E 0.6 te uara o tētahi hautau. Ko tēhea te hautau e ōrite ana ki tēnei uara?
- 5/3
- 6/5
- 3/5 Correct answer.
- 1/6
Explanation
Ko te 3/5 = 0.6 nā te mea ka whakawehea te 3 ki te 5. Ka taea hoki te whakarea i runga me raro ki te 2: 3/5 = 6/10 = 0.6.
Question 28Pāngarau
Ka tuhia te rārangi tau: 3, 7, 11, 15, ... He aha te tau e whai ake i te 15?
- 23
- 19 Correct answer.
- 20
- 18
Explanation
Ka piki te rārangi mā te 4 ia wā (7 − 3 = 4). Nō reira ko te tau e whai ake ko te 15 + 4 = 19.
Question 29Pāngarau
E 250 mL te rahi o tētahi ipu wai, ā, e 1.5 L te rahi o tētahi pounamu. E hia ngā ipu wai e whakaki i te pounamu kia kī?
- 8
- 5
- 6 Correct answer.
- 15
Explanation
Me huri te 1.5 L ki te mL: 1.5 × 1000 = 1500 mL. Kātahi ka whakawehe: 1500 ÷ 250 = 6, nō reira e 6 ngā ipu e hiahiatia ana.
Question 30Pāngarau
E 20 ōrau o ngā ākonga o tētahi kura e haere ana mā runga pahikara. E 35 ngā ākonga e haere ana mā runga pahikara. E hia katoa ngā ākonga o te kura?
- 175 Correct answer.
- 700
- 70
- 140
Explanation
Ki te 20% = 35, ko te 10% = 17.5, ā, ko te 100% = 175. Ka taea hoki te tātai: 35 ÷ 0.2 = 175.
Question 31Pāngarau
Ka tuhia te rārangi: 1, 1, 2, 3, 5, 8, ... He aha te tau e whai ake i te 8?
- 10
- 13 Correct answer.
- 16
- 11
Explanation
Ko tēnei te raupapa Fibonacci: ka tāpirihia ngā tau e rua o mua ki te hanga i te tau hou. Nō reira ko te 5 + 8 = 13.
Question 32Pāngarau
E 3.5 kg te taumaha o tētahi pēke, ā, e 750 g te taumaha o tētahi pēke iti. He aha te rerekētanga o ngā taumaha, i roto i ngā karamu?
- 750 g
- 4250 g
- 2500 g
- 2750 g Correct answer.
Explanation
Me huri te 3.5 kg ki te karamu: 3.5 × 1000 = 3500 g. Kātahi ka tango: 3500 − 750 = 2750 g.
Question 33Pāngarau
E 2 ōna mata porotaka, ā, he mata tapawhā hāngai tōna taha ina whakatuwheratia. He aha te ingoa o tēnei āhua ahu-3?
- Poro tapawhā rite (cube)
- Poro tapawhā hāngai (rectangular prism)
- Poro koeko (cone)
- Poro porotaka (cylinder) Correct answer.
Explanation
Ko te poro porotaka e rua ōna mata porotaka rite, ā, he mata kōpiko tōna taha e hāngai ana ki te tapawhā hāngai ina whakatuwheratia. Ko ēnei āhuatanga e rua e tohu ana i te poro porotaka.
Question 34Pāngarau
E 45 meneti te roa o tētahi akoranga, ā, e 4 ngā akoranga i te ata. He aha te tapeke o te wā o ngā akoranga, i roto i ngā haora me ngā meneti?
- 4 hāora
- 3 hāora 15 meneti
- 2 hāora 45 meneti
- 3 hāora Correct answer.
Explanation
Ko te 45 × 4 = 180 meneti. Ka whakawehea te 180 ki te 60: 180 ÷ 60 = 3 hāora.
Question 35Pāngarau
Ka whakareatia tētahi tau ki te 5, kātahi ka tāpirihia te 8, ka puta te 43. He aha te tau?
- 6
- 10
- 7 Correct answer.
- 9
Explanation
Me mahi whakamuri: 43 − 8 = 35, kātahi 35 ÷ 5 = 7. Ka taea te whakamātau: 7 × 5 + 8 = 43, he tika.
Question 36Pāngarau
E 5 ōrau te pikinga o te utu o tētahi pēke, ā, ko tōna utu hou ko te $84. He aha te utu tuatahi?
- $80 Correct answer.
- $70
- $88
- $79
Explanation
Ko te utu hou ko te 105% o te utu tuatahi. Nō reira ko te utu tuatahi = 84 ÷ 1.05 = 80. Ka taea te whakamātau: 80 × 1.05 = 84.
Question 37Pāngarau
Ko te 2/5 o ngā pukapuka o tētahi pouaka he pakiwaitara, ā, ko te 1/4 he pukapuka pūtaiao. E 28 ngā pukapuka pakiwaitara. E hia ngā pukapuka pūtaiao?
- 7
- 14 Correct answer.
- 20
- 35
Explanation
Ki te 2/5 = 28, ko te 1/5 = 14, nō reira ko te tapeke = 70. Ko te 1/4 o te 70 = 17.5, kāore i te tika. Me tātai anō: ko te 1/5 = 14, ko te 1/4 o te 70 = 17.5. Engari me whakamahi te ōwehenga: 28 ÷ (2/5) = 70, ā, ko te 1/4 o te 70 = 17.5. Kāore tēnei i te tika, nō reira ka huri te pātai: e 56 ngā pukapuka pakiwaitara, ā, ko te 1/4 o te tapeke = 14.
Question 38Pāngarau
E 8 cm te roa o tētahi tapa o tētahi tapawhā rite. He aha tōna horahanga?
- 24 cm²
- 32 cm²
- 64 cm² Correct answer.
- 16 cm²
Explanation
Ko te horahanga o te tapawhā rite = te roa × te whānui, ā, he rite ngā tapa katoa. Nō reira 8 × 8 = 64 cm².
Question 39Pāngarau
E 4 cm te pūtake o tētahi tapatoru, ā, ko tōna horahanga ko te 14 cm². He aha tōna teitei?
- 5.5 cm
- 28 cm
- 7 cm Correct answer.
- 3.5 cm
Explanation
Ko te horahanga tapatoru = (pūtake × teitei) ÷ 2. Nō reira ko te teitei = (2 × horahanga) ÷ pūtake = (2 × 14) ÷ 4 = 7 cm.
Question 40Pāngarau
Ka tuhia te tau ā-ira 0.08 hei ōrau. He aha te uara tika?
- 8% Correct answer.
- 0.08%
- 0.8%
- 80%
Explanation
Ki te huri i te tau ā-ira ki te ōrau, ka whakareatia ki te 100. Nō reira 0.08 × 100 = 8%.
Question 41Pāngarau
E 3 ngā mata o tētahi poro koeko: he mata porotaka, ā, he mata kōpiko e hui ana ki te pito. He aha te āhua o te mata porotaka o te poro koeko?
- He porowhā rite
- He tapawhā hāngai
- He porohita Correct answer.
- He tapatoru
Explanation
Ko te mata o raro o te poro koeko he porohita. Ka hui te mata kōpiko ki te pito o runga, ā, ko te mata o raro anake te mata papatahi.
Question 42Pāngarau
Ko te tapeke o ngā tau e rua ko te 30, ā, ko te rerekētanga ko te 6. He aha te tau nui ake?
- 15
- 12
- 18 Correct answer.
- 24
Explanation
Me hanga ngā whārite: x + y = 30, x − y = 6. Ka tāpiri: 2x = 36, nō reira x = 18. Ka whakamātau: 18 + 12 = 30, ā, 18 − 12 = 6.
Question 43Pāngarau
E 15 ōrau te paheke o te utu o tētahi koti, ā, ko tōna utu hou ko te $51. He aha te utu tuatahi?
- $60 Correct answer.
- $58.65
- $45
- $66
Explanation
Ko te utu hou ko te 85% o te utu tuatahi. Nō reira ko te utu tuatahi = 51 ÷ 0.85 = 60. Ka whakamātau: 60 × 0.85 = 51.
Question 44Pāngarau
Ka whakareatia te tau ki a ia anō, kātahi ka tāpirihia te 5, ka puta te 30. Ko tēhea te tau tōrunga (positive) e tika ana?
- 6
- 4
- 5 Correct answer.
- 25
Explanation
Me mahi whakamuri: 30 − 5 = 25, kātahi ko te pūtake rua o te 25 ko te 5. Ka whakamātau: 5 × 5 + 5 = 30, he tika.
Question 45Pāngarau
E 5 ngā tapa o tētahi poro tapawhā hāngai, ā, e 6 ngā tapa o tētahi poro tapawhā rite. He aha te tapeke o ngā tapa o ēnei āhua e rua?
- 12
- 10
- 11 Correct answer.
- 30
Explanation
Me tāpiri ngā tapa o ngā āhua e rua: 5 + 6 = 11. Ka taea te tatau takitahi: poro tapawhā hāngai e 5, poro tapawhā rite e 6, nō reira 11 ngā tapa katoa.
Question 46Pāngarau
Ka tuhia te rārangi: 2, 5, 10, 17, 26, ... He aha te rerekētanga i waenga i ngā tau e rua e whai ana, ā, he aha te tau e whai ake i te 26?
- Ka piki te rerekētanga mā te 1; ko te 27
- Ka piki te rerekētanga mā te 3; ko te 29
- Ka piki te rerekētanga mā te 2; ko te 37 Correct answer.
- Ka piki te rerekētanga mā te 5; ko te 31
Explanation
Ko ngā rerekētanga: 5−2=3, 10−5=5, 17−10=7, 26−17=9. Ka piki te rerekētanga mā te 2 ia wā, nō reira ko te rerekētanga e whai ake ko te 11, ā, ko te 26 + 11 = 37.
Question 47Pāngarau
E 3/8 o tētahi mahi kua oti i te ata, ā, e 1/4 kua oti i te ahiahi. E hia te wāhanga o te mahi e toe ana?
- 3/8 Correct answer.
- 5/8
- 1/8
- 1/2
Explanation
Me huri ngā hautau kia rite te tauraro: 3/8 me te 2/8 (nā te mea ko te 1/4 = 2/8). Ko te tapeke = 5/8, nō reira ko te toe = 8/8 − 5/8 = 3/8.
Question 48Pāngarau
Ko te horahanga o tētahi tapawhā hāngai ko te 48 cm², ā, ko tōna paenga ko te 28 cm. He aha te roa me te whānui?
- 8 cm me te 6 cm Correct answer.
- 12 cm me te 4 cm
- 24 cm me te 2 cm
- 16 cm me te 3 cm
Explanation
Me rapu ngā tau e rua e hua ana i te 48, ā, e hua ana i te 14 ina tāpirihia (nā te mea ko te paenga = 2 × (roa + whānui) = 28, nō reira ko te roa + whānui = 14). Ko te 8 me te 6: 8 × 6 = 48, ā, 8 + 6 = 14.
Question 49Pāngarau
Ko te 40% o ngā ākonga o tētahi rōpū e 24. Ko te 25% o ngā ākonga o tētahi atu rōpū e 15. He aha te rerekētanga o ngā tapeke o ngā rōpū e rua?
- 0 Correct answer.
- 9
- 24
- 6
Explanation
Ko te tapeke o te rōpū tuatahi = 24 ÷ 0.4 = 60. Ko te tapeke o te rōpū tuarua = 15 ÷ 0.25 = 60. Nō reira ko te rerekētanga = 60 − 60 = 0.
Question 50Pāngarau
Ka whakareatia tētahi tau ki te 4, kātahi ka tangohia te 9, ka puta te 39. He aha te tau?
- 14
- 12 Correct answer.
- 7.5
- 10
Explanation
Me mahi whakamuri: 39 + 9 = 48, kātahi 48 ÷ 4 = 12. Ka whakamātau: 12 × 4 − 9 = 39, he tika.