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.
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
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1 Topic 1 Surds and indices Contents 8.1 Learning points................................... 3 8.2 Assessment practice................................ 4
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
TOPIC 1. SURDS AND INDICES 3 1.1 Learning points Surds and indices To simplify surds. 63 = 9 7 = 3 7 32 27 = 16 2 9 3 = 4 2 3 3 6 2+5 2 3 2 = 8 2 To rationalise a denominator. 2 14 = 2 14 14 14 = 2 14 14 = 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
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 50 36 Q3: Simplify 5 5 3 5 + 2 5 Q4: Simplify 2(3 + 2 2) Q5: Rationalise the denominator and simply 2 10 Q6: Simplify 3 12 Q7: Simplify 72 2 2 Q8: Simplify 8 48 Q9: Simplify ( 3 + 2)( 3 1) Q10: Rationalise the denominator and simplify 5 2 2 5 Q11: Rationalise the denominator and simplify 5 5+2 HERIOT-WATT UNIVERSITY
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 16 3 2 ( ) Q17: Multiply out the brackets and simplify y 1 4 y 1 4 + y 7 4 HERIOT-WATT UNIVERSITY
6 ANSWERS: TOPIC 8 Answers to questions and activities 8 Surds and indices Assessment practice: Surds and indices (page 4) Q1: 3 5 Q2: 5 2 6 Q3: 4 5 Q4: 3 2 + 4 Q5: 10 5 Q6: 6 3 Q7: 4 2 Q8: 1 6 Q9: 1 + 3 Q10: Q11: Hint: 10 2 Multiply the numerator and denominator by 5 + 2 Answer: 5 5 + 10 or 5( 5 + 2) Q12: a 2 Q13: 9b 6 Q14: 2 e Q15: 2 Q16: 64 Q17: 1 + y 2 HERIOT-WATT UNIVERSITY