GCSE Laws of Indices with Dr. J. Frost - Study Materials and Exercises

Delve into the world of Indices with Dr. J. Frost's GCSE study materials featuring a collection of useful resources including a starter activity, Laws of Indices reminder, examples, and challenging questions to enhance your understanding of this mathematical concept. Get ready to sharpen your skills and test your knowledge with engaging exercises designed for GCSE level students.

• GCSE
• Laws of Indices
• Mathematics
• Dr. J. Frost
• Study Materials

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1. GCSE: Indices Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 23rd August 2013

2. Starter In pairs or otherwise, try and match the blue and orange cards. ?? ?? ? ? ?? ?? ? ? ? ??? ?? ?? ?? ? ? ? ? ?? ?? ? ? ?? ??? ? ?

3. A reminder of the Laws of Indices ?0= 1 ?? ??= ??+? ? ? ?? ??= ?? ? ?1= ? ? ? ???= ??? ? 1 ?? ? ?= ?

4. Examples ? 2? ?= 2?? 98 9= 97 ? 44 4 42 3=45 46= 4 1=1 ? 4 2? 1=2 ? ? 1 2? 1= ? 2?

5. Mastermind Occupation: Student Favourite Teacher: Dr Frost Specialist Subject: Laws of Indices

6. Instructions: Everyone starts by standing up. Youll get a question with a time limit to answer. If you run out of time or get the question wrong, you sit down. The winner is the last man standing. Warmup: 23 24 = 27? Start Question > (23)4 = 212 ? Start Question > 26 23= 23? Start Question >

7. a b c 911 92= 99? 47 43 = 410? Start Question > (35)2 = 310 ? Start Question > Start Question > e d f 57 53= 54? 74 76 = 710? Start Question > (46)3 = 418? Start Question > Start Question > h g _1_ 2 Start Question > Start Question > (22)2 = 24? 2-1 = ?

8. a b c 105 102= 103 ? 77 7-2 = 75? Start Question > (53)-2 = 5-6 ? Start Question > Start Question > e d f 87 8-2= 89? _1_ 8 8-2 84 = 82? Start Question > 2-3 = Start Question > Start Question > ? h g _1_ 16 Start Question > Start Question > 50 = 1? 4-2 = ?

9. a b c 9-2 9-2= 90 = 1 Start Question > Start Question > Start Question > 4-2 4-2 = 4-4 ? ? (3-2)-2 = 34? e d f 101 10-3= 104 14 16 = 110 = 1 Start Question > Start Question > ? Start Question > ? h g _1_ 56 _1_ 27 Start Question > (5-3)2 =5-6 = ? Start Question > 3-3 = ?

10. a b c 50 5-2= 52? 50 = 1? Start Question > Start Question > (30)2 = 1? Start Question > e d f 51 x 52 x 53 = 56? (24 26)2 = 220 Start Question > Start Question > ? ((41)2)3 = 46? Start Question > h g _1_ 81 Start Question > Start Question > (23 23)3 = 218 ? 3-4 = ?

11. a b c 47 43 42 (35)4 33 (73)3 (72)3= 73 ? = 48? = 317 ? Start Question > Start Question > Start Question > d e f 58 58 51 5-1 ((32)2)2 32 (71)3 (72)1 74 = 75 ? = 516 ? = 36 ? Start Question > Start Question > Start Question >

12. Exercises 5? ? 5 = 5?2+1 Simplify the following. 13 2? 2= 2? 1 ?2 4 ?2 ? ? ?3 ?5= ?8 ? 1 8 2 3 ?8 ?4 14 = ?24 ? ?3 5= ?15 ? 2 9 = ?6 ? 1 2 ?2 5= ? 10 or 53? 54? ? 1 3 15 ?10 ? = 52? ?9 ? 2 2 ?3 4 ?9 ?3= ?6 = ?2 10 ? ? 4 32? 32= 32? 2 2 ?7 2? 7= 16 4?+ 4?+ 4?+ 4? = 4 4?= 4?+1 11 ? 5 ? ? ?8 ? 2= ?10 6 ? 2 ?10 ? 17 2 53? 5? ? = ?18 12 = 54? ? 7? 73= 7?+3 ? 7

13. Fractional Indices 1 2= ? ? And how could we prove this?

14. Fractional Indices 1 3= 3? ? ? 1 ?= ?? ? ?

15. Examples 1 2= 8 1 3= 4 1 2= ? 3 2 64 ?3= ?3 ? ? 160.25= 2 64 ? ? 1 2= 9 2 1 3 2 3 2= 7 81 37 ? ? = 7 1 4= 3 1 3= 10 81 1000 ? ?

16. Harder Examples 3 2= 27 4=1 16 3 9 ? ? 8 2 5= 4 32 ? 2=1 9 1 ? 3

17. Exercises 1000.5= 10 3= 1 64 1 ? 1 7 ? 4 1 3= 5 ? 125 1 16 ? 64 2 2 8 3= 16 0.5=1 ? 3 2 5= 4 4 32 ? 9 3=1 27 2 4 ? 5=1 32 3 9 10 ? 8 4 3= 16 5 8 ? Write the following expression without using indices: 1 ? 11 3=1 8 1 ? 0.5= ? 6 ? 2

18. Applying indices to products and fractions ???= ???? ? =?? ?? ? ? ? ? =?? ?? ? ? ? ?

19. Applying indices to products and fractions 2?2= 4?2 ? 5 1 2 = 32 ? 1 2= 3?3 9?6 ? 1 3 27 8 =3 3?2?3= 9?6?3 ? ? 2 5 2 1 2 1 32 3 27 8 =4 = ? ? 9

20. Flip Root Power method 2 2 3 2 3 27 8 8 27 2 3 4 9 ? ? ? ???? ???? ?????

21. Exercises Evaluate: 1 2 3 Simplify: 2 3 8 27? 9 4 =3 8 7 ? = ??2 3= ?3?6 ? 1 2 1 2= 3? 9?2 ? 2 3 2 3 =27 9 ? 1 2= 4?2? 1 3= 3?3? 3 2 4 3 ? 8 16?4?3 3 1 ? 27?9?4 5 6 =6 4 10 ? 5 2 3= 4?4?8 5 8?6?12 ? 1 11 3 64 27 =3 ? 3 2= 64?9?18 ? 6 16?6?12 4 3 2 9 16 =64 27 12 ?

22. Skill 3: Changing bases What do you notice about all of the numbers: 2,8,4 They re all powers of 2! We could replace the numbers with 21, 23 and 22 so that we have a consistent base. ?

23. Skill 3: Changing bases Solve 4?= 210 83 Solve 2?= 2 22 ?= 210 22?= 210 ? = 10 ? ? ? =17 ? ? 2

24. Difficult GCSE question ? = 2?, ? = 2? a) Express in terms of ? and/or ?. i) 2?+?= 2?2?= ?? ii) 22?= 2? 2= ?2 iii) 2? 1=2? ? ? ? 21=? 2 b) Given that: ?? = 32 2??2= 32 find the value of ? and ?. ? = 6, ? = 1 ? ?

25. Exercises Solve for ?: ? ? = 3 8?= 29 1 ? =3 2?= 2 2 ? 2 2 4?=86 3 ? ? = 7 24 2?+ 2?= 219 ? ? = 18 4 ? ? = 10 27?= 930 5 42?+1= 82? 1 ? =5 ? 6 2