for supervisor’s use only - nzqa.govt.nz · (c) he tuhinga roa e 5 000 kupu hoki tā kim hei...

Pāngarau, �au�a�� , ��au�a�� , ��9��9� T�� whakaoti ra�anga māmā whai

rau�a�atanga tauhanga, āhuahanga hoki

9 � � 9 � M

© Mana Tohu Mātauranga o Aotearoa, 2006Pūmau te mana. Kia kaua rawa he wāhi o tēnei tuhinga e tāruatia ki te kore te whakaaetanga a te Mana Tohu Mātauranga o Aotearoa.

For Supervisor’s use only �

Mā te kaimāka anahe Pa��aru Pa��ta��

Pa��ta�� aiaka �airangi

Te whakaoti rapanga māmā whai raupapatanga tauhanga, āhuahanga hoki.

Te whakaoti rapanga whai raupapatanga.

Te tūhura i ngā tūāhua me te whakamāori i ngā putanga o ngā whakaoti rapanga whai raupapa.

Whakakaotanga o t�� tairanga mahinga

Whiwhinga: Rua2.00 i te ahiahi Rāapa 29 Whiringa-ā-rangi 2006

Tirohia mehemea e ōrite ana te Tau Ākonga ā-Motu kei tō pepa whakauru ki te tau kei runga ake nei.

Kia tino mōhio kei a koe tētahi Puka Tikanga Tātai L2–MATHMF.

Me whakautu e koe ngā pātai KATOA kei roto i te pukapuka nei.

Tuhia ō mahi KATOA.

Ki te hiahia koe ki ētahi atu wāhi hei tuhituhi whakautu, whakamahia ngā whārangi kei muri i te pukapuka nei, ka āta tohu ai i ngā tau pātai.

Tirohia mehemea kei roto nei ngā whārangi 2–13 e raupapa tika ana, ā, kāore hoki he whārangi wātea.

HOATU TE PU�APU�A NEI �I TE �AIWHA�AHAERE I TE MUTUNGA O TE WHA�AMĀTAUTAU.

See back cover for an English translation of this cover

Pāngarau 90290, 2006

Kia 30 meneti hei whakautu i ngā pātai o tēnei pukapuka.

“TE MAHI ROROHI�O”

http://gearlog.com

PĀTAI TUATAHI

E āhuareka ana te kaitukumahi o Lesley i te tairanga ake o tāna mahi whakauru raraunga ki te rorohiko. I te rā tuatahi e 750 āna hē i ngā whakaurunga raraunga. He 85% o āna hē o te rā tuatahi ngā hē o te rā tuarua. He 85% o āna hē o te rā tuarua ngā hē o te rā tuatoru, ka pērā haere.

Ki te haere ake noa tēnei tauira, ka hia rā te tapeke o āna whakaurunga raraunga kua hē?

PĀTAI TUARUA

He tuhinga roa e 5 000 kupu tā Grant hei tuhituhi. Tīmata ai a Grant i tāna tuhinga roa i te 3 Poutū-te-rangi me te tuhituhi i ētahi kupu 175. Ia rā ka 290 ake āna kupu tuhituhi i ā te rā o mua.

(a) Ka hia āna kupu e tuhituhi i te 6 Poutū-te-rangi?

2

Mā te Kaimāka anahe

Mathematics 90290, 2006

You are advised to spend 30 minutes answering the questions in this booklet.

“COMPUTING”

http://gearlog.com

QUEsTION ONE

Lesley’s employer is pleased with her improved performance in entering data on the computer. On the first day she made 750 errors in the data entries. On day two she made 85% of the number of errors that she made on the first day. On day three she made 85% of the number of errors that she made on the second day and so on.

If this pattern continued indefinitely, what would be the total number of errors in data entry that she would have made?

QUEsTION TWO

Grant has a 5 000-word assignment to write. Grant begins his assignment on 3 March and writes 175 words. Each day he writes 290 more than he did the previous day.

(a) How many words will he write on 6 March?

3

Assessor’suse only


(b) Ka hia āna kupu tapeke kua tuhituhi tae noa te mutunga o ngā rā e 5?

http://blogs.warwick.ac.uk

(c) He tuhinga roa e 5 000 kupu hoki tā Kim hei tuhituhi. I te rā tuatahi ka 100 āna kupu i āhei te tuhituhi. Ia rā he reatorutanga āna kupu i āna i tuhituhi i te rā o mua.

Ka hia ngā kupu tapeke i tuhituhia e Kim tae noa te mutunga o te rā tuawhā?

�



(b) How many words will he have written in total at the end of 5 days?

http://blogs.warwick.ac.uk

(c) Kim also has to write a 5 000-word assignment. On the first day she manages to write 100 words. Each day she writes three times as many words as she wrote the previous day.

How many words will Kim have written in total at the end of the fourth day?

�



(d) Patohia ai e Emma tāna tuhinga roa ki te rorohiko. E 700 āna kupu pato i te rā ka tīmata ia i tāna tuhinga roa. Ia rā ka 10% iti ake āna kupu pato i ā te rā o mua. Ka pēhea te roa o te wā e oti i a ia te pato i te tuhinga roa e 5 000 kupu?

PĀTAI TUATORU

Kei te mahi ia rā a Lesley i tētahi kaupapa mahi ā-rorohiko. Ko tāna ki a Meg e 60 āna whārangi mahi i tana rā tuaiwa o te mahi. Maumahara ai a Meg, e 25 ngā whārangi i oti i a Lesley i tana rā tuawhā. I mea a Lesley i ia ra i whakapikihia e ia te tataunga whārangi ma te tau rite o te rā o mua.

Kia hia ngā whārangi e manakohia ai e Meg ka oti i a Lesley i te rua tekau o ngā rā?

6



(d) Emma types her assignment on a computer. She types 700 words on the day she begins the assignment. Each day she types 10% fewer words than the day before. How long will she take to type the 5 000-word assignment?

QUEsTION THREE

Lesley is working every day on a computer project. She told Meg she did 60 pages of work on her ninth day on the project. Meg remembers that on Lesley’s fourth day, Lesley had done 25 pages. Lesley said that each day she has increased the number of pages she did by the same number from the day before.

How many pages could Meg expect Lesley to complete on the twentieth day?

�



PĀTAI TUAWHĀ

Whakaaro ai a Karl ki te hoko rorohiko hōu. He tekau tau ki muri, ka whakatakoto e tōna tipuna whaea e $800 ki tētahi pūtea pēke mā Karl. He huamoni 7% tāna i whiwhi ia tau he mea pūhuitia ia marama i roto i ngā tau 10.

Ka hia ngā moni a Karl i te pūtea mō tana rorohiko hōu?WHAKAATURIA NGĀ MAHINGA KATOA.

�



QUEsTION FOUR

Karl decides to buy a new computer. Ten years ago, his grandmother deposited $800 in a bank account for Karl. He received 7% interest per annum compounded monthly over the 10 years.

How much money would Karl have in the account for his new computer?SHOW YOUR WORKING.

9



PĀTAI TUARIMA

http://chiaroscuro.baltiblogs.com

E mōhio ana tētahi kamupene tāpukapuka ko $1 850 te utu whakaputa i ētahi tānga 60 o tētahi pukapuka. Hei whakaputa i ngā tānga 140, ko $2 975 te utu. E whakapono ana ngā kaitāpukapuka nei ko $25.75 he utu hoko tika mō te pukapuka.

He utu pūmau, he utu taurangi anō tā te whakaputanga pukapuka. Ahakoa e hia ngā pukapuka ka whakaputaina, rite tonu te utu pūmau. Hei runga tonu i te nui o ngā pukapuka ka whakaputaina te utu taurangi.

Mā te whakamahi i ēnei hanga utu, he aha te tau mōkito o ngā pukapuka me hokona e riro ai he huanga moni?

10



QUEsTION FIvE

http://chiaroscuro.baltiblogs.com

A publishing company knows that producing 60 copies of a book will cost $1 850. To produce 140 copies, it would cost $2 975. The publishers believe that $25.75 will be a realistic selling price for the book.

There are both fixed costs and variable costs when producing the books. The fixed cost is the same no matter how many books are produced. The variable cost depends directly on the number of books produced.

Using these costings, what is the minimum number of books that must be sold in order to make a profit?

11



Tau Pātai

H�� uka tā�iri h��i whakaoti i ō whakautu mē �� hiahiatia ana. Āta tauria t�� ātai.

12



Question number

Extra �a��r for continuation of answ��rs if r��quir��d.Cl��arly numb��r th�� qu��stion.

13


L��v��l � Math��matics, ��9��9� solv�� straightforward �robl��ms involving

arithm��tic and g��om��tric s��qu��nc��s

© New Zealand Qualifications Authority, 2006All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.

For Assessor’s use only Achi��v��m��nt Crit��ria

Achi��v��m��nt Achi��v��m��nt with M��rit

Achi��v��m��nt with Exc��ll��nc��

Solve straightforward problems involving both arithmetic and geometric sequences.

Solve problems involving sequences.

Explore situations and interpret the results of problems involvingsequences.

Ov��rall L��v��l of P��rformanc��

Credits: Two2.00 pm Wednesday 29 November 2006

Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.

Make sure you have a copy of Formulae Sheet L2-MATHF.

You should answer ALL the questions in this booklet.

Show ALL working.

If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.

Check that this booklet has pages 2–13 in the correct order and that none of these pages is blank.

YOU MUsT HAND THIs BOO�LET TO THE sUPERvIsOR AT THE END OF THE EXAMINATION.

English translation of the wording on the front cover

for supervisor’s use only - nzqa.govt.nz · (c) he tuhinga roa e 5 000 kupu hoki tā kim hei...

Documents