915790 3 SUPERVISOR’S USE ONLY 91579 © New Zealand Qualiﬁcations Authority, 2017. All rights reserved. No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualiﬁcations Authority. ASSESSOR’S USE ONLY TOTAL Level 3 Calculus, 2017 91579 Apply integration methods in solving problems 9.30 a.m. Thursday 23 November 2017 Credits: Six Achievement Achievement with Merit Achievement with Excellence Apply integration methods in solving problems. Apply integration methods, using relational thinking, in solving problems. Apply integration methods, using extended abstract thinking, in solving problems. Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page. You should attempt ALL the questions in this booklet. Show ALL working. Make sure that you have the Formulae and Tables Booklet L3–CALCF. 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 – 16 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. Excellence 24

91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

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Page 1: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

915790

3SUPERVISOR’S USE ONLY

9 1 5 7 9

ASSESSOR’S USE ONLY

TOTAL

Level 3 Calculus, 201791579 Apply integration methods in solving problems

9.30 a.m. Thursday 23 November 2017 Credits: Six

Achievement Achievement with Merit Achievement with ExcellenceApply integration methods in solving problems.

Apply integration methods, using relational thinking, in solving problems.

Apply integration methods, using extended abstract thinking, in solving problems.

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

You should attempt ALL the questions in this booklet.

Show ALL working.

Make sure that you have the Formulae and Tables Booklet L3–CALCF.

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 – 16 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.

Excellence

Page 2: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 3: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 4: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 5: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 6: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 7: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 8: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 9: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 10: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 11: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Page 12: 91579 Apply integration methods in solving problems · Subject:’ Integration’ Standard:’ AS91579’ Totalscore:’ 24’ Q’ Grade’ score’ Annotation’ 1! E8

Subject: Integration Standard: AS91579 Total score: 24

Q Grade score Annotation

1 E8

This question provides evidence for E8 because the candidate has gained 1t in part (e) by: - Correctly using a trigonometric identity to change sin²x into a form that can be integrated

- Correctly integrating this expression - Substituting in the limits π and 0 into the expression - Simplifying the Mean Value expression to get ½.

2 E8

This question provides evidence for E8 because the candidate has gained 1t in part (e) by: - Correctly integrating the acceleration expression to get a velocity expression

- Using the variables given to correctly find constant “c” - Substituting t = 10 to correctly find the velocity of 45.8 m/s

3 E8

This question provides evidence for E8 because the candidate has gained 1t in part (e) by: - Correctly integrating the differential equation - Using the initial variables given to find an expression for c in terms of k.

- Using the other variables provided and this expression to correctly calculate k.

- Uses the expression to correctly calculate c - Substituting t = 5 to correctly find y = 10.48.