91037M 910375 SUPERVISOR’S1 USE ONLY Te Pāngarau me te Tauanga, Kaupae 1, 2017 91037M Te whakaatu māramatanga ki te tūponotanga, raraunga hoki 9.30 i te ata Rāhina 20 Whiringa-ā-rangi 2017 Whiwhinga: Whā Paetae Kaiaka Kairangi Te whakaatu māramatanga ki te Te whakaatu māramatanga ki te Te whakaatu māramatanga ki te tūponotanga, raraunga hoki. tūponotanga, raraunga hoki me te tūponotanga, raraunga hoki me te parahau i ngā kīanga me ngā kitenga. whakaatu i te matatau ki te tauanga. Tirohia mēnā e rite ana te Tau Ākonga ā-Motu (NSN) kei runga i tō puka whakauru ki te tau kei runga i tēnei whārangi. Me whakamātau koe i ngā tūmahi KATOA kei roto i tēnei pukapuka. Whakaaturia ngā mahinga KATOA. Mēnā ka hiahia whārangi atu anō mō ō tuhinga, whakamahia ngā whārangi wātea kei muri o tēnei pukapuka, ka āta tohu ai i ngā tau tūmahi. Tirohia mēnā e tika ana te raupapatanga o ngā whārangi 2 – 27 kei roto i tēnei pukapuka, ka mutu, kāore tētahi o aua whārangi i te takoto kau. HOATU TE PUKAPUKA NEI KI TE KAIWHAKAHAERE HEI TE MUTUNGA O TE WHAKAMĀTAUTAU. TAPEKE MĀ TE KAIMĀKA ANAKE © Mana Tohu Mātauranga o Aotearoa, 2017. Pūmau te mana. Kia kaua rawa he wāhi o tēnei tuhinga e whakahuatia ki te kore te whakaaetanga tuatahi a te Mana Tohu Mātauranga o Aotearoa. 2 MĀ TE IKIIKI KAIMĀKA ANAKE http://www.trademe.co.nz/motors/news-reviews/20161005-local-corolla-offers-extra-value/ TŪMAHI TUATAHI (a) Kei te hiahia a Ngaire ki te hoko waka . I tangohia e ia he tīpakonga o nga waka ka tātuhia he kauwhata o te tawhito o ngā waka (ā-tau) me te tawhiti i haerehia (ā-kiromita). Te tawhitiDistance o te haerenga travelled ki vs te car tawhito age o te 100 000 90 000 80 000 (km) 70 000 60 000 haerenga 50 000 te o 40 000 30 000 ( tawhiti 20 000 Te 10 000 0 0 2 4 6 8 10 12 ( Te tawhito (tau) Tuhia te hononga i waenga i te tawhito o ngā waka me te tawhiti i haerehia ME TE kimi i te huringa toharite o te tawhiti i haerehia e ngā waka i ia tau ka piki te tawhito o te waka. Parahautia tō tuhinga. Te Pāngarau me te Tauanga 91037M, 2017 3 ASSESSOR’S TRANSPORTATION USE ONLY http://www.trademe.co.nz/motors/news-reviews/20161005-local-corolla-offers-extra-value/ QUESTION ONE (a) Ngaire wants to buy a car. She took a sample of cars and drew a graph of the age of the cars (in years) and the distance they had travelled (in kilometres). Distance travelled vs car age 100 000 90 000 80 000 70 000 60 000 50 000 40 000 30 000 ( 20 000 10 000 0 0 2 4 6 8 10 12 ( State the relationship that exists between the age of cars and the distance they have travelled AND find the average change in distance travelled by a car each year as the age increases. Justify your answer. Mathematics and Statistics 91037, 2017 4 (b) Ka puta i a Ngaire he kauwhata anō e whakataurite ana i te utu taketake ($) ki te hekenga ōrau MĀ TE KAIMĀKA ki te wāriu i ia tau (hekenga wāriu). ANAKE Heerentage hekenga ōrauereae o te inwāriu ae ki te originautu taketake rie 60 tau) 50 te (i 40 wāriu te o 30 ōrau 20 hekenga 10 He ( 0 5 000 10 000 15 000 20 000 25 000 30 000 He utu taketake (($) (i) Whakaaturia ngā āhuatanga ka kitea i te kauwhata o te utu taketake me te hekenga ōrau ki te wāriu i ia tau. Te Pāngarau me te Tauanga 91037M, 2017 5 (b) Ngaire produced another graph which compared a car’s original price ($) with its percentage ASSESSOR’S USE ONLY decrease in value per year (depreciation). erentage ereae in ae origina rie 60 50 40 30 20 10 ( 0 5 000 10 000 15 000 20 000 25 000 30 000 ( (i) Describe any features visible in the graph of the original price and percentage decrease in value per year. Mathematics and Statistics 91037, 2017 6 (ii) E ai ki te hekenga ōrau o te wāriu, he pai ake te hoko mai i tētahi waka iti ake te utu, nui MĀ TE KAIMĀKA ake te utu rānei? ANAKE Parahautia tō tuhinga. Te Pāngarau me te Tauanga 91037M, 2017 7 (ii) In terms of percentage decrease in value, is it better to buy a cheaper or more expensive ASSESSOR’S USE ONLY car? Justify your answer. Mathematics and Statistics 91037, 2017 8 (c) I te tau 2016, i whakaputaina e Te Manatū Waka he pūrongo. MĀ TE KAIMĀKA ANAKE I tirohia tētahi tīpakonga o ngā kaitaraiwa 298 i whakapā hētia e Ngā Pihirimana mō te taraiwa toatoa e ai ki te whakaaturanga i raro. NgāVehie kaitaraiwa rier waka harge i whakapā with hētiareke mō riingte taraiwa toatoa toatoa 40 WāhineFemale 35 35 taraiwa 32 TāneMale te 30 mō 25 hētia 20 19 17 whakapā 15 15 i 15 14 13 13 13 12 12 10 8 8 7 7 7 6 6 6 6 5 5 5 kaitaraiwa 5 4 4 2 2 ngā o 0 80+ – – – – – – – – – – – – – maha Te He rōpū taipakeke kaitaraiwa ( (tau) (i) He aha te tūponotanga o tētahi kaitaraiwa i tīpakohia matapōkeretia mai i tētahi tīpakonga kaitaraiwa i whakapā hētia mō te taraiwa toatoa i te 2016, he tāne 20–24 ngā tau? (ii) He aha te tūponotanga o tētahi kaitaraiwa i tīpakohia matapōkeretia mai i tētahi tīpakonga kaitaraiwa wāhine i whakapā hētia mō te taraiwa toatoa i te 2016, nō te rōpū tau 15–24? (iii) E ai ki te tīpakonga 2016, e hia whakareanga ake te tūpono, mēnā i tīpakohia matapōkeretia, ko te kaitaraiwa waka i whakapā hētia mō te tarawai toatoa, he tāne kē ehara i te wahine? Te Pāngarau me te Tauanga 91037M, 2017 9 (c) In 2016, the Ministry of Transport released a report. ASSESSOR’S USE ONLY It looked at a sample of 298 drivers charged by police with reckless driving, and displayed it as shown below: Vehie rier harge with reke riing 40 Female 35 35 32 Male 30 25 20 19 17 15 15 15 14 13 13 13 12 12 10 8 8 7 7 7 6 6 6 6 5 5 5 5 4 4 2 2 0 80+ – – – – – – – – – – – – – ( (i) What was the probability that a randomly selected driver from the sample of drivers charged with reckless driving in 2016, was a male aged 20–24? (ii) What was the probability that a randomly selected driver from the sample of female drivers charged with reckless driving in 2016, was in the 15–24 age group? (iii) Based on the 2016 sample, how many times more likely was it that, chosen at random, a vehicle driver who was charged with reckless driving, would be a male than a female? Mathematics and Statistics 91037, 2017 10 MĀ TE TŪMAHI TUARUA KAIMĀKA ANAKE (a) E whakaaturia ana i raro ko te manako ki ngā tae mō ngā waka rerekē. He ōrau ngā tau e whakaaturia ana. e oo waka Pango He waka Hākinakina Whānau Kikorangi 13 10 4 6 11 16 26 1 13 (SUV) / Taraka / Wākena Kākāriki Mangaeka He hākinakina / Iti 15 13 2 6 2 15 18 10 4 15 Ētahi atu Whero Hiriwa He tino hāneanea 22 7 3 2 7 16 25 6 12 Mā / peara mā Kōwhai / kōura He nui / Waenga / Kōwhai / karaka 10 13 4 10 10 25 12 4 12 Waka Whānau Kiwikiwi 0% 20% 40% 60% 80% 100% (i) He aha te tae i tino manakohia i ngā waka tino hāneanea? Parahautia tō tuhinga. (ii) He aha atu anō ngā tikanga ka taea ēnei raraunga te whakaatu? Tuhia ngā hua kino, hua pai rānei o ia tikanga. Te Pāngarau me te Tauanga 91037M, 2017 11 MĀ TE KAIMĀKA ANAKE Te Pāngarau me te Tauanga 91037M, 2017 12 ASSESSOR’S QUESTION TWO USE ONLY (a) The popularity of colours for different types of vehicles is shown below. The numbers shown are a percentage. Te o ehie Black Blue SUV / Truck / Van 13 10 4 6 11 16 26 1 13 Green Sport / Compact 15 13 2 6 2 15 18 10 4 15 Others Red Silver Luxury 22 7 3 2 7 16 25 6 12 White / Yellow / Gold Yellow / Orange Full / Intermediate / Sedan 10 13 4 10 10 25 12 4 12 Grey 0% 20% 40% 60% 80% 100% (i) What is the most popular colour in luxury vehicles? Justify your answer. (ii) What other ways could you display this data? State the advantages and disadvantages of each method. Mathematics and Statistics 91037, 2017 13 ASSESSOR’S USE ONLY Mathematics and Statistics 91037, 2017 14 (b) E whakataurite ana te whakaaturanga i raro i ngā tukunga hauhā (g / km) o tētahi tīpakonga o MĀ TE KAIMĀKA ngā waka 100 i hangaia i te tau 1984 ki ngā tukunga hauhā o tētahi tīpakonga waka i hangaia i ANAKE te tau 2016. Ngā tukunga hauhā me te tau i hangaia 1984 2016 0 100 200 300 400 500 600 700 CO / km 2 (i) He aha te rerekētanga i waenga i ngā rahinga tauwaenga o ngā tukunga hauhā g / km o ngā waka i hangaia i te tau 1984 me ērā i hangaia i te tau 2016? (ii) I tēhea tau hanganga te nui ake o te rerekētanga o ngā tukunga hauhā? Parahautia tō tuhinga. Te Pāngarau me te Tauanga 91037M, 2017 15 (iii) Me kōrero mō te tohatoha o ngā tukunga hauhā mō ngā waka i hangaia i te tau 1984 mē MĀ TE KAIMĀKA ērā i hangaia i te tau 2016.