National 5 Mathematics Assessment Practice Topic 8: Surds and indices

Transcription

1 SCHOLAR Study Guide National 5 Mathematics Assessment Practice Topic 8: Surds and indices Authored by: Margaret Ferguson Heriot-Watt University Edinburgh EH14 4AS, United Kingdom.

2 First published 2014 by Heriot-Watt University. This edition published in 2016 by Heriot-Watt University SCHOLAR. Copyright 2016 SCHOLAR Forum. Members of the SCHOLAR Forum may reproduce this publication in whole or in part for educational purposes within their establishment providing that no profit accrues at any stage, Any other use of the materials is governed by the general copyright statement that follows. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, without written permission from the publisher. Heriot-Watt University accepts no responsibility or liability whatsoever with regard to the information contained in this study guide. Distributed by the SCHOLAR Forum. SCHOLAR Study Guide Assessment Practice Topic 8: National 5 Mathematics 1. National 5 Mathematics Course Code: C747 75

3 Acknowledgements Thanks are due to the members of Heriot-Watt University's SCHOLAR team who planned and created these materials, and to the many colleagues who reviewed the content. We would like to acknowledge the assistance of the education authorities, colleges, teachers and students who contributed to the SCHOLAR programme and who evaluated these materials. Grateful acknowledgement is made for permission to use the following material in the SCHOLAR programme: The Scottish Qualifications Authority for permission to use Past Papers assessments. The Scottish Government for financial support. The content of this Study Guide is aligned to the Scottish Qualifications Authority (SQA) curriculum. All brand names, product names, logos and related devices are used for identification purposes only and are trademarks, registered trademarks or service marks of their respective holders.

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5 1 Topic 1 Surds and indices Contents 8.1 Learning points Assessment practice

6 2 TOPIC 1. SURDS AND INDICES By the end of this topic, you should have identified your strengths and areas for further revision. Read through the learning points before you attempt the questions and go back to the Unit 1 course materials if you need more help. You should be able to: You should be able to: simplify surds; rationalise denominators; multiply and divide using positive, negative and fractional indices; raise a power to a power and know what a power of zero means. HERIOT-WATT UNIVERSITY

7 TOPIC 1. SURDS AND INDICES Learning points Surds and indices To simplify surds. 63 = 9 7 = = = = 8 2 To rationalise a denominator = = = 14 7 Six laws of indices. 1. a m a n = a m+n 2. a m a n = a m n 3. (a m ) n = a m n 4. a 0 = 1 5. a m = 1 a m 6. a m n = n a m HERIOT-WATT UNIVERSITY

8 4 TOPIC 1. SURDS AND INDICES 1.2 Assessment practice Make sure that you have read through the learning points or completed some revision before attempting these questions. Tailor your practice by choosing the most appropriate questions. Surds Questions 1 to 11 Indices Questions 12 to 17 Key point Note: None of these questions assess your reasoning skills. Assessment practice: Surds and indices Go online Surds Q1: Simplify 45 Q2: Simplify Q3: Simplify Q4: Simplify 2( ) Q5: Rationalise the denominator and simply 2 10 Q6: Simplify 3 12 Q7: Simplify Q8: Simplify 8 48 Q9: Simplify ( 3 + 2)( 3 1) Q10: Rationalise the denominator and simplify Q11: Rationalise the denominator and simplify HERIOT-WATT UNIVERSITY

9 Q13: Simplify (3b 3 ) 2 TOPIC 1. SURDS AND INDICES 5 Indices Q12: Simplify a4 a 5 a 7 Q14: Simplify, giving your answer with a positive index 2e5 (e 3 ) 2 1 Q15: Simplify 6b 2 1 3b 2 Q16: Simplify ( ) Q17: Multiply out the brackets and simplify y 1 4 y y 7 4 HERIOT-WATT UNIVERSITY

10 6 ANSWERS: TOPIC 8 Answers to questions and activities 8 Surds and indices Assessment practice: Surds and indices (page 4) Q1: 3 5 Q2: Q3: 4 5 Q4: Q5: 10 5 Q6: 6 3 Q7: 4 2 Q8: 1 6 Q9: Q10: Q11: Hint: 10 2 Multiply the numerator and denominator by Answer: or 5( 5 + 2) Q12: a 2 Q13: 9b 6 Q14: 2 e Q15: 2 Q16: 64 Q17: 1 + y 2 HERIOT-WATT UNIVERSITY