Pāngarau, Kaupae 1, 2006

Transcription

1 For Supervisor s use only M See back cover for an English translation of this cover Pāngarau, Kaupae 1, Te whakaoti rapanga e whai wāhi ai ana te tapatoru hāngai Whiwhinga: Rua 9.30 i te ata Rāere 24 Whiringa-ā-rangi 2006 Tirohia eheea e ōrite ana te Tau Ākonga ā-motu kei tō pepa whakauru ki te tau kei runga ake nei. Me whakautu e koe ngā pātai KATOA kei roto i te pukaiti nei. Whakaaturia ō ahinga KATOA. Ki te hiahia koe ki ētahi atu wāhi hei tuhituhi whakautu, whakaahia te (ngā) whārangi kei uri i tēnei pukaiti, ka āta tohu ai i ngā tau pātai. Tirohia eheea kei roto nei ngā whārangi 2 15 e raupapa tika ana, ā, kāore hoki he whārangi wātea. HOATU TE PUKAITI NEI KI TE KAIWHAKAHAERE I TE MUTUNGA O TE WHAKAMĀTAUTAU. Mā te Kaiāka anahe Paearu Paetae Paetae Kaiaka Kairangi Te whakaoti rapanga e whai wāhi ai ana te tapatoru hāngai. Te whakaoti rapanga e whai wāhi ai ana te tapatoru hāngai, i roto i ngā horopaki whaitake. Te whakaoti rapanga kupu, rapanga ahu-3 rānei. Whakakaotanga o te tairanga ahinga Mana Tohu Mātauranga o Aotearoa, 2006 Pūau te ana. Kia kaua rawa he wāhi o tēnei tuhinga e tāruatia ki te kore te whakaaetanga a te Mana Tohu Mātauranga o Aotearoa.

2 2 Kia 30 eneti hei whakautu i ngā pātai o tēnei pukapuka. HE MEA PUHIPUHI I TE HAU Mā te Kaiāka anahe Whakaaturia ō ahinga KATOA. PĀTAI TUATAHI Kua hanga ngā ākonga o te akoanga hangarau o Rewa i ētahi waka tākaro. Ka whakaterengia e ngā ākonga whakawhiti te kauranga o te kura. E 15 ita te whānui o te kauranga. (a) Ka whakaātau a Rewa te whakatere i tōna waka kia whiti tika tonu i te kauranga, atu i te pūwāhi A. Puhipuhia parori kē tōna waka e te hau, ētahi ita e 8 iho atu o te kauranga. E whakaaturia ana ki te hoahoa te ara, AB, i haere rawa ai tōna waka. Tātaitia te aao, AB, i tere ai te waka o Rewa. A EHARA i te hoahoa āwhata 15 C 8 B AB = (b) Ka whakaātau hoki a Lee te whakatere i tōna waka tākaro kia whiti tika i te kauranga, atu i te pūwāhi F. Haere ai tōna waka te aao e 20 ita. Tātaitia te aao iho atu o te kauranga, ED, i puhipuhia paroritia ai te poti o Lee. F EHARA i te hoahoa āwhata ED = E D Pāngarau 90152, 2006

3 3 You are advised to spend 30 inutes answering the questions in this booklet. Assessor s use only BLOWING IN THE WIND You should show ALL working. QUESTION ONE The pupils in Rewa s technology class have ade odel boats. The pupils sail the across the school pool. The pool is 15 etres wide. (a) Rewa tries to sail her boat straight across the pool, fro point A. The wind blows her boat off-course, 8 etres down the pool. The diagra shows the path, AB, her boat actually sailed. Calculate the distance, AB, sailed by Rewa s boat. A Diagra NOT to scale 15 AB = C 8 B (b) Lee also tries to sail his boat straight across the pool, fro point F. His boat travels a distance of 20 etres. Calculate the distance, ED, that Lee s boat is blown off-course down the pool. F Diagra NOT to scale ED = E D Matheatics 90152, 2006

4 (c) Tere ai te waka o Taa atu i te pūwāhi G ki te pūwāhi H hei te koki o te 31º, pēnā e whakaaturia ana ki te hoahoa. 4 Mā te Kaiāka anahe Tātaitia te aao, IH. G 31 EHARA i te hoahoa āwhata 15 IH = I H (d) Tere ana te waka o Peta i te pūwāhi K, ētahi ita e 20 ki tētahi koki whakawhiti te kauranga. Tātaitia te rahi o te koki, JKL. K EHARA i te hoahoa āwhata JKL = J L Pāngarau 90152, 2006

5 (c) Taa s boat sails fro point G to point H at an angle of 31º, as shown in the diagra. Calculate the distance, IH. 5 Assessor s use only G Diagra NOT to scale IH = I H (d) Peta s boat sails fro point K, 20 etres at an angle across the pool. Calculate the size of the angle, JKL. K Diagra NOT to scale JKL = J L Matheatics 90152, 2006

6 6 PĀTAI TUARUA Kei te herea tētahi porohau wera, B, ki te whenua ā ngā taura 25 ita e rua, BR e BS. Ko te koki ki te papa o tēnā o tēnā taura ko 50. B EHARA i te hoahoa āwhata Mā te Kaiāka anahe Tātaitia te aao i waenganui i R e S R S Te aao i waenganui i R e S = EHARA i te hoahoa āwhata PĀTAI TUATORU Kua herea tētahi atu porohau, A, ki te whenua ā te taura kotahi, TA. Kaha ana te hau, nā wai e ea ana te taura TA anō he rārangi tika. Kei te 40 i runga ake i te papa te porohau. Ko te koki o te taura TA ki te papa ko 26. Tātaitia te roa o te taura. T 26 A 40 G Te roa o te taura TA = Pāngarau 90152, 2006

7 QUESTION TWO A hot-air balloon, B, is tied down to the ground by two 25 etre ropes, BR and BS. Each rope akes an angle of 50 with the ground. B Diagra NOT to scale Assessor s use only Calculate the distance between R and S R S Distance between R and S = Diagra NOT to scale QUESTION THREE Another balloon, A, is tied to the ground by one rope, TA. The wind is strong and the rope TA akes a straight line. The balloon is 40 above the ground. The rope TA akes an angle of 26 with the ground. A 40 Calculate the length of the rope. T 26 G Length of rope TA = Matheatics 90152, 2006

8 PĀTAI TUAWHĀ E tū ana a Mare i te pūwāhi, M, i tētahi onepū e whakatere ana i tana anu aute, K. He 50 te roa o te aho anu aute, KM, otirā kua kukuea kia ārō. Ka au te anu aute ki runga rawa ki tētahi rākau, KT. Kei runga hoki te rākau o tētahi pari, CT. Titiro whakarunga ai a Mare ki te anu aute i te koki o 49. Kei R a Raku e tū ana, i runga i tētahi paparaho tirohanga. E 6 ia o te pūtake o te rākau, pēnei i te hoahoa. Rite ana tōna teitei hei runga i te onepū ki tō te pūtake o te rākau. Titiro whakarunga ai a Raku ki te anu aute i te koki o 58. Tātaitia te teitei o te pari, CT. R 58 EHARA i te hoahoa āwhata 6 T K Mā te Kaiāka anahe 50 M 49 C Teitei o te pari CT = Pāngarau 90152, 2006

9 QUESTION FOUR Mare is standing at a point, M, on a beach flying his kite, K. The kite string, KM, is 50 long and is pulled tight. The kite gets stuck at the top of a tree, KT. The tree is at the top of a cliff, CT. Mare looks up at the kite at an angle of 49. Raku is standing at R, on a viewing deck. He is 6 fro the botto of the tree, as shown in the diagra. He is at the sae height above the beach as the botto of the tree. Raku looks up at the kite at an angle of 58. R Calculate the height of the cliff, CT. 58 Diagra NOT to scale 6 T K Assessor s use only 50 M 49 C Height of cliff CT = Matheatics 90152, 2006

10 PĀTAI TUARIMA Ka hoea e Joe whakawhiti i tētahi awa e rere ana ai i te Uru ki te Rāwhiti. He 37 te whānui o te awa. Tīata ai a Joe te hoe ai i A. I te wāhanga tuatahi o te whakawhitinga, e 32 tāna hoe ki te ahunga 044. I te wāhanga tuarua o te whakawhitinga, ahu kē ana a Joe ki te ahunga 330. Ka hoe haere i runga i tēnei ahunga tae noa ia ki tērā taha o te awa. He aha te aao i hoe ai a Joe, i te wāhanga tuarua o te whakawhitinga? 10 EHARA i te hoahoa āwhata Mā te Kaiāka anahe TAHATAHA AWA KI TE RAKI IA RERE O TE AWA JOE A TAHATAHA AWA KI TE TONGA Pāngarau 90152, 2006

11 QUESTION FIVE Joe rows across a river that flows fro West to East. The river is 37 wide. Joe starts rowing fro A. For the first part of the crossing, he rows for 32 on a bearing of 044. For the second part of the crossing, Joe alters course to a bearing of 330. He rows in this direction until he reaches the other side of the river. What distance did Joe row, in the second part of the crossing? 11 Diagra NOT to scale Assessor s use only NORTH RIVER BANK RIVER FLOW JOE A SOUTH RIVER BANK Matheatics 90152, 2006

12 12 He pepa tāpiri hei whakaoti i ō whakautu ē e hiahiatia ana. Āta tohua te tau o te pātai. Mā te Kaiāka anahe Tau pātai Pāngarau 90152, 2006

13 13 He pepa tāpiri hei whakaoti i ō whakautu ē e hiahiatia ana. Āta tohua te tau o te pātai. Mā te Kaiāka anahe Tau pātai Pāngarau 90152, 2006

14 14 Extra paper for continuation of answers if required. Clearly nuber the question. Assessor s use only Question nuber Matheatics 90152, 2006

15 15 Extra paper for continuation of answers if required. Clearly nuber the question. Assessor s use only Question nuber Matheatics 90152, 2006

16 English translation of the wording on the front cover Level 1 Matheatics, Solve right-angled triangle probles Credits: Two 9.30 a Friday 24 Noveber 2006 Check that the National Student Nuber (NSN) on your adission slip is the sae as the nuber at the top of this page. You should answer ALL the questions in this booklet. You should show ALL working. If you need ore space for any answer, use the page(s) provided at the back of this booklet and clearly nuber the question. Check that this booklet has pages 2 15 in the correct order and that none of these pages is blank. YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION. For Assessor s use only Achieveent Solve right-angled triangle probles. Achieveent Criteria Achieveent with Merit Solve probles in practical situations involving right-angled triangles. Achieveent with Excellence Solve probles in word or 3D situations. Overall Level of Perforance New Zealand Qualifications Authority, 2006 All rights reserved. No part of this publication ay be reproduced by any eans without the prior perission of the New Zealand Qualifications Authority.