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
(km)
haerenga
te
o
( tawhiti Te
( 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
(
(
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 ($) ki te hekenga ōrau MĀ TE KAIMĀKA ki te wāriu i ia tau (hekenga wāriu). ANAKE
He er entage hekenga ōrau e rea e o te inwāriu a e ki te origina utu taketake ri e
He hekenga ōrau o te wāriu (i tau) ( He utu taketake ( ($)
(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).
er entage e rea e in a e origina ri e
( (
(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.
Ngā ehi e kaitaraiwa ri er waka harge i whakapā with hētiare k e mō ri ingte taraiwa toatoa Wāhine Tāne
– – – – – – – – – – – – –
maha o ngā kaitaraiwa i whakapā hētia mō te taraiwa toatoa 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:
ehi e ri er harge with re k e ri ing
– – – – – – – – – – – – – (
(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 o o waka He waka Hākinakina Whānau (SUV) / Taraka / Wākena Kākāriki He hākinakina / Iti Ētahi atu Whero He tino hāneanea Mā / peara mā Kōwhai / kōura He nui / Waenga / Kōwhai / karaka Waka Whānau
(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.
T e o ehi e / / / / / / / /
(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
/
(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. ANAKE Me kōrero mō ngā ōritenga me ngā rerekētanga, tae atu ki ngā āhuatanga tino rerekē.
(iv) Ko te whakapae a ngā kaiwhakanao waka ‘ko te tikanga he iti ake ngā tukunga hauhā o ngā waka i hangaia i te 2016 ki ērā i hangaia i te 1984.’
Whakamahia te whakaaro whaitake o te tauanga, e ai ki tēnei tīpakonga waka, hei kōrero mō te whakapae a ngā kaiwhakanao waka. Parahau māramatia tō tuhinga.
Te Pāngarau me te Tauanga 91037M, 2017 16
(b) The display below compares the carbon dioxide emissions (in g / km) of a sample of 100 cars ASSESSOR’S USE ONLY made in 1984 compared to the carbon dioxide emissions of a sample of cars made in 2016.
ar on io i e e i ion an ear i t
/
(i) What is the difference between the median amounts of carbon dioxide emissions in g / km of cars built in 1984 and those built in 2016?
(ii) Which year of build has the greatest variation in carbon dioxide emissions? Justify your answer.
Mathematics and Statistics 91037, 2017 17
(iii) Comment on the distribution of carbon dioxide emissions for both 1984-built and ASSESSOR’S USE ONLY 2016-built cars. Note any similarities and differences as well as any unusual features.
(iv) Car manufacturers claim that ‘cars produced in 2016 tend to produce less carbon dioxide than cars made in 1984.’
Use statistical reasoning, based on this sample of cars, to comment on the car manufacturers’ claim. Justify your answer clearly.
Mathematics and Statistics 91037, 2017 18
MĀ TE TŪMAHI TUATORU KAIMĀKA ANAKE (a) Ka tuhia e Ngā Pirihimana o Aotearoa ngā taipitopito o ngā waka katoa ka whānakohia. Ko ngā tino tauira waka 15 ka whānakohia i roto i tētahi wā 6 marama i te tau 2015 ka whakaaturia ki raro.
Ngā tinoTo waka to en 15 i whānakohia ehi e o e i tētahi in a onth wā 6 marama erio i inte tau 2015
/ hanga me te tauira waka Te Te maha o ngā waka i whānakohia
(i) E hia ngā Nissan Primera i whānakohia i roto i tēnei 6 marama?
(ii) “Ko te Nissan te hanga waka i tino whānakohia i tētahi wā 6 marama i te tau 2015.”
Tuhia mai mēnā ki ōu whakaaro kei te tika tēnei rerenga kōrero, me te tuku take tauanga e hāngai ana ki tō tuhinga.
Te Pāngarau me te Tauanga 91037M, 2017 19
ASSESSOR’S QUESTION THREE USE ONLY (a) The New Zealand police record the details of all vehicles stolen. The top 15 vehicle models stolen in a 6-month period in 2015 are shown below.
To to en ehi e o e in a onth erio in
/
(i) How many Nissan Primeras were stolen in this 6-month period?
(ii) “Nissan was the most stolen make of vehicle in the 6-month period in 2015.”
State whether you think this sentence is true, giving statistical reasons for your answer.
Mathematics and Statistics 91037, 2017 20
(iii) I whakaputaina e AA Insurance ana tauira waka 10 e tino whānakohia ana mai i te MĀ TE KAIMĀKA 1 Haratua 2013 ki te 30 Paengawhāwhā 2014: ANAKE 1. Honda Torneo 2. Subaru Impreza 3. Mazda Premacy 4. Mazda Familia 5. Subaru Forester 6. Mazda Atenza 7. Subaru Legacy 8. Mazda MPV 9. Nissan Sunny 10. Nissan Cefiro
He tino rerekē tēnei rārangi ki ngā raraunga a Ngā Pirihimana.
Homai ngā take tauanga mō ēnei rerekētanga.
Te Pāngarau me te Tauanga 91037M, 2017 21
(iii) AA Insurance released its top 10 stolen vehicle models from 1 May 2013 to 30 April ASSESSOR’S USE ONLY 2014: 1. Honda Torneo 2. Subaru Impreza 3. Mazda Premacy 4. Mazda Familia 5. Subaru Forester 6. Mazda Atenza 7. Subaru Legacy 8. Mazda MPV 9. Nissan Sunny 10. Nissan Cefiro
This list is quite different from the police data.
Give statistical reasons for these differences.
Mathematics and Statistics 91037, 2017 22
(b) Ka tatau a Waka Kotahi (NZTA) i te maha o ngā waka e huri haere ana i ngā huarahi matua. MĀ TE KAIMĀKA Kātahi ka taurite ai i ngā raraunga o tēnei tau, ki te tau kua mahue ake. Kei raro nei e ANAKE whakaatu ana ngā mōhiohio i te tipu haerenga o Ngā Waka Katoa me te tipu haerenga o Ngā Waka Nunui anake.
Tipuranga haerenga o ngā waka i ngā huarahi o Aotearoa
–
Ko te tipuranga haerenga –
–
– Kohitātea Kohitātea Kohitātea Kohitātea Kohitātea Kohitātea Kohitātea Kohitātea Kohitātea Ko te marama me ngā tau Ngā waka katoa Ngā waka nunui
(i) He aha te tau i heke rawa iho ai te tipu haerenga ki te wāhi pāpaku rawa mō ngā Waka Nunui? Parahautia tō tuhinga.
Te Pāngarau me te Tauanga 91037M, 2017 23
(ii) E ai ki ngā hua kua whakaaturia, ka aha pea te tipu haerenga o ngā waka i te tau 2017 MĀ TE KAIMĀKA me te tau 2018 mō Ngā Waka Katoa? ANAKE
Homai kia 2 neke atu rānei ngā tipuranga ka taea, me te hōmai pūtake tauanga mō tō tuhinga.
(iii) Ina tātarihia ngā hua, ka tangohia e Waka Kotahi te tauwaenga o ngā raraunga o ngā marama e 3 kua hipa me te tuhi ki te kauwhata (hei tauira, ko te hua o Kohitātea 2016 kua tuhia kauwhatatia ka ahu mai i te hua tauwaenga o ngā hua o Whiringa-ā-rangi 2015, Hakihea 2015, me Kohitātea 2016).
Homai ngā take tauanga ki ōu whakaaro he aha a Waka Kotahi i pēnei ai.
Te Pāngarau me te Tauanga 91037M, 2017 24
(b) The New Zealand Transport Agency (NZTA) counts the number of vehicles using major ASSESSOR’S USE ONLY roads. It then compares the results from the same period in the previous year. The information below shows the travel growth of All Vehicles and the travel growth of Heavy Vehicles only.
Tra e growth o ehi e on ew ea an roa
–
–
–
–
(i) In what year did travel growth reach its lowest point for Heavy Vehicles? Justify your answer.
Mathematics and Statistics 91037, 2017 25
(ii) Based on the results shown, what could possibly happen to the travel growth in 2017 ASSESSOR’S USE ONLY and 2018 for All Vehicles?
State at least two possibilities, giving statistical reasons for your answers.
(iii) When analysing the results, the NZTA takes the mean of the previous 3 months’ data and plots that result on the graph (e.g. the January 2016 result that is plotted comes from the mean of the November 2015, December 2015, and January 2016 results).
Give statistical reasons why you think the NZTA does this.
Mathematics and Statistics 91037, 2017 26
He whārangi anō ki te hiahiatia. MĀ TE KAIMĀKA ANAKE TAU TŪMAHI Tuhia te (ngā) tau tūmahi mēnā e tika ana.
Te Pāngarau me te Tauanga 91037M, 2017 27
Extra paper if required. ASSESSOR’S USE ONLY QUESTION Write the question number(s) if applicable. NUMBER
Mathematics and Statistics 91037, 2017 91037M YOU MUSTHANDTHISBOOKLETTO THESUPERVISOR AT THEENDOFEXAMINATION. Check thatthisbooklethaspages2 – 27inthecorrect orderandthatnoneofthesepagesisblank. number thequestion. If youneedmorespaceforanyanswer, usethepage( Show You shouldattempt top ofthispage. Check thattheNationalStudentNumber( and data. Demonstrate understandingofchance 91037 English translationofthewordingonfrontcover ALL Level 1MathematicsandStatistics,2017 working. Achievement Demonstrateunderstandingofchanceanddata ALL thequestionsinthisbooklet. 9.30 findings. and data,justifyingstatements Demonstrate understandingofchance
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