1. Mathematics Ronald Hui Tak Sun Secondary School

2. Ronald HUI Reminder Corrections of Dictation 1 and Standard Homework (I) Corrections of Dictation 1 and Standard Homework (I) Deadline: 14 Sep (Fri) Deadline: 14 Sep (Fri) Standard Homework (II) Standard Homework (II) Deadline: 17 Sep (Mon) Deadline: 17 Sep (Mon) Standard Homework (III) Standard Homework (III) Deadline: 18 Sep (Tue) Deadline: 18 Sep (Tue)

3. Ronald HUI Reminder Corrections of Standard Homework (II) and (III) Corrections of Standard Homework (II) and (III) Deadline: 19 Sep (Wed) Deadline: 19 Sep (Wed) Open Book Quiz (Chapter 0) Open Book Quiz (Chapter 0) Deadline: 19 Sep (Wed) Deadline: 19 Sep (Wed) Closed Book Quiz (Chapter 0), Dictation 2 and Folder Checking Closed Book Quiz (Chapter 0), Dictation 2 and Folder Checking Last week of September Last week of September

4. Ronald HUI Revision for Quiz Textbook 1A Textbook 1A Pages 2 – 31 Pages 2 – 31 Workbook 1A Workbook 1A Pages 1 – 16 Pages 1 – 16 Summer Revision Summer Revision Pages 1 – 19 Pages 1 – 19 My PowerPoint files My PowerPoint files Your own notes Your own notes

5. Ronald HUI Mathematics How to get better results? How to get better results? Understand first! Understand first! Do correction! Do correction! Dictation: 10 times Dictation: 10 times Test/Homework: Other colour pens Test/Homework: Other colour pens Revise! Revise! Try more (workbook) Try more (workbook)

6. Ronald HUI Revision Prime numbers ( 質數 ) Prime numbers ( 質數 ) 2, 3, 5, 7, 11, 13, 17, 19, 23, … 2, 3, 5, 7, 11, 13, 17, 19, 23, … Multiples ( 倍數 ) Multiples ( 倍數 ) Multiples of 2:2, 4, 6, 8, … Multiples of 2:2, 4, 6, 8, … Multiples of 3:3, 6, 9, 12, … Multiples of 3:3, 6, 9, 12, … Factors ( 因子 ) Factors ( 因子 ) 2 is a factor of 2, 4, 6, 8, … 2 is a factor of 2, 4, 6, 8, … 3 is a factor of 3, 6, 9, 12, … 3 is a factor of 3, 6, 9, 12, …

7. Ronald HUI Revision Find all factors of 18. Find all factors of 18. 18 = 1 x 18 18 = 1 x 18 18 = 2 x 9 18 = 2 x 9 18 = 3 x 6 18 = 3 x 6 18 = 6 x 3 18 = 6 x 3 18 = 9 x 2 18 = 9 x 2 18 = 18 x 1 18 = 18 x 1 Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 18: 1, 2, 3, 6, 9, 18

8. Ronald HUI Prime Factors (p.9) Prime factors ( 質因子 ) Prime factors ( 質因子 ) A factor which is prime A factor which is prime Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3 Prime factors of 18: 2, 3 All numbers can be expressed as a product of prime factors only – How? All numbers can be expressed as a product of prime factors only – How?

9. Ronald HUI Index Notation (p.9) Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3 Prime factors of 18: 2, 3 18 = 2 x 9 18 = 2 x 9 = 2 x 3 x 3 = 2 x 3 x 3 18 = 2 x 3 2  Index Notation 18 = 2 x 3 2  Index Notation 3 2 = 3 x 3( 指數記數法 ) 3 2 = 3 x 3( 指數記數法 ) 3 is base 底 3 is base 底 2 is index 指數 2 is index 指數

10. Ronald HUI Index Notation (p.9) 3 2 = 3 x 3 3 2 = 3 x 3 3 to the power 2, 3 squared ( 平方 ) 3 to the power 2, 3 squared ( 平方 ) 3 3 = 3 x 3 x 3 3 3 = 3 x 3 x 3 3 to the power 3, 3 cubed ( 立方 ) 3 to the power 3, 3 cubed ( 立方 ) 3 4 = 3 x 3 x 3 x 3 3 4 = 3 x 3 x 3 x 3 3 5 = 3 x 3 x 3 x 3 x 3 3 5 = 3 x 3 x 3 x 3 x 3 What is 3 1 ? What is 3 1 ? 3 1 = 3 3 1 = 3

11. Ronald HUI Index Notation (p.9) Index notation is very helpful in long expression of prime factors Index notation is very helpful in long expression of prime factors 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 2 4 x 3 3 = 2 4 x 3 3 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 = 2 7 x 3 3 x 5 2 = 2 7 x 3 3 x 5 2

12. Ronald HUI Time for Practice Pages 10 – 11 of Textbook 1A Pages 10 – 11 of Textbook 1A Class Practice Class Practice Questions 6 – 9 Questions 6 – 9 Pages 6 – 7 of Workbook 1A Pages 6 – 7 of Workbook 1A Questions 5 – 9 Questions 5 – 9

13. Ronald HUI Mathematics nearby What is Google? What is Google? http://zh.wikipedia.org/zh- hk/Google#.E5.BB.BA.E7.AB.8B http://zh.wikipedia.org/zh- hk/Google#.E5.BB.BA.E7.AB.8B http://zh.wikipedia.org/zh- hk/Google#.E5.BB.BA.E7.AB.8B http://zh.wikipedia.org/zh- hk/Google#.E5.BB.BA.E7.AB.8B Google was mis-spelt from googol! Google was mis-spelt from googol! Googol = 10 100 Googol = 10 100 = 1000000…00000 (100 zeros!) (100 zeros!)

14. Ronald HUI H.C.F. Highest Common Factor ( 最大公因數 ) Highest Common Factor ( 最大公因數 ) Factors of 18: Factors of 18: 1, 2, 3, 6, 9, 18 1, 2, 3, 6, 9, 18 Factors of 24: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 18 and 24: Common factors of 18 and 24: 2, 3, 6 2, 3, 6 H.C.F. of 18 and 24 is 6 H.C.F. of 18 and 24 is 6

15. Ronald HUI H.C.F. We can find H.C.F. from Index Notation! ( 用指數記數法找 HCF) We can find H.C.F. from Index Notation! ( 用指數記數法找 HCF) 18 = 2 x 3 x 3= 2 x 3 2 18 = 2 x 3 x 3= 2 x 3 2 24 = 2 x 2 x 2 x 3= 2 3 x 3 24 = 2 x 2 x 2 x 3= 2 3 x 3 We know H.C.F. of 18 and 24 is 6 We know H.C.F. of 18 and 24 is 6 6 = 2 x 3 6 = 2 x 3 Can you find the rule? Can you find the rule?

16. Ronald HUI H.C.F. Another example Another example 24 = 2 x 2 x 2 x 3= 2 3 x 3 24 = 2 x 2 x 2 x 3= 2 3 x 3 36 = 2 x 2 x 3 x 3= 2 2 x 3 2 36 = 2 x 2 x 3 x 3= 2 2 x 3 2 Can you guess the HCF? Can you guess the HCF? Their HCF is Their HCF is 2 x 2 x 3= 2 2 x 3 2 x 2 x 3= 2 2 x 3 = 12

17. Ronald HUI H.C.F. Another try: HCF of 700 and 720 Another try: HCF of 700 and 720 700 = 2 2 x 5 2 x 7 700 = 2 2 x 5 2 x 7 720 = 2 4 x 3 2 x 5 720 = 2 4 x 3 2 x 5 Can you guess the HCF? Can you guess the HCF? Their HCF is Their HCF is = 2 2 x 5= 20 = 2 2 x 5= 20

18. Ronald HUI H.C.F. If the numbers did not have common prime factors, their HCF is 1 If the numbers did not have common prime factors, their HCF is 1 49 = 7 2 49 = 7 2 36 = 2 2 x 3 2 36 = 2 2 x 3 2 Their HCF is 1 Their HCF is 1

19. Ronald HUI H.C.F. How about 3 or more numbers? How about 3 or more numbers? 18 = 2 x 3 2 18 = 2 x 3 2 24 = 2 3 x 3 24 = 2 3 x 3 30 = 2 x 3 x 5 30 = 2 x 3 x 5 Their HCF is Their HCF is = 2 x 3= 6 = 2 x 3= 6

20. Ronald HUI L.C.M. Least Common Multiple ( 最小公倍數 ) Least Common Multiple ( 最小公倍數 ) Multiples of 4: Multiples of 4: 4, 8, 12, 16, 20, 24, 28, … 4, 8, 12, 16, 20, 24, 28, … Multiples of 6: Multiples of 6: 6, 12, 18, 24, 30, … 6, 12, 18, 24, 30, … Common multiple of 4 and 6: Common multiple of 4 and 6: 12, 24, … 12, 24, … L.C.M. of 4 and 6 is 12 L.C.M. of 4 and 6 is 12

21. Ronald HUI L.C.M. We can find L.C.M. from Index Notation! ( 用指數記數法找 LCM) We can find L.C.M. from Index Notation! ( 用指數記數法找 LCM) 4 = 2 x 2= 2 2 4 = 2 x 2= 2 2 6 = 2 x 3= 2 x 3 6 = 2 x 3= 2 x 3 We know L.C.M. of 4 and 6 is 12 We know L.C.M. of 4 and 6 is 12 12 = 2 x 2 x 3= 2 2 x 3 12 = 2 x 2 x 3= 2 2 x 3 Can you find the rule? Can you find the rule?

22. Ronald HUI L.C.M. Another example Another example 24 = 2 x 2 x 2 x 3= 2 3 x 3 24 = 2 x 2 x 2 x 3= 2 3 x 3 36 = 2 x 2 x 3 x 3= 2 2 x 3 2 36 = 2 x 2 x 3 x 3= 2 2 x 3 2 Can you guess the LCM? Can you guess the LCM? Their LCM is Their LCM is 2 x 2 x 2 x 3 x 3= 2 3 x 3 2 2 x 2 x 2 x 3 x 3= 2 3 x 3 2 = 72

23. Ronald HUI L.C.M. Another try: LCM of 28 and 30 Another try: LCM of 28 and 30 28 = 2 2 x 7 28 = 2 2 x 7 30 = 2 x 3 x 5 30 = 2 x 3 x 5 Can you guess the HCF? Can you guess the HCF? Their LCM is Their LCM is = 2 2 x 3 x 5 x 7 = 420 = 2 2 x 3 x 5 x 7 = 420

24. Ronald HUI L.C.M. If the numbers did not have common prime factors, their LCM is the product of them If the numbers did not have common prime factors, their LCM is the product of them 20 = 2 2 x 5 20 = 2 2 x 5 63 = 3 2 x 7 63 = 3 2 x 7 Their HCF is 1 Their HCF is 1 Their LCM is 20 x 63 = 1260 Their LCM is 20 x 63 = 1260

25. Ronald HUI L.C.M. How about 3 or more numbers? How about 3 or more numbers? 18 = 2 x 3 2 18 = 2 x 3 2 24 = 2 3 x 3 24 = 2 3 x 3 30 = 2 x 3 x 5 30 = 2 x 3 x 5 Their LCM is Their LCM is = 2 3 x 3 2 x 5= 360 = 2 3 x 3 2 x 5= 360

26. Ronald HUI Time for Practice Find H.C.F. and L.C.M. of the following pairs Find H.C.F. and L.C.M. of the following pairs 10, 15 10, 15 26, 39 26, 39 36, 54 36, 54 56, 98 56, 98 91, 117 91, 117 24, 36, 60 24, 36, 60

27. Ronald HUI Reminder BCA Online Exercise BCA Online Exercise Deadline: 10 Sep (Mon) Deadline: 10 Sep (Mon) Standard Homework (II) Standard Homework (II) Deadline: 17 Sep (Mon) Deadline: 17 Sep (Mon) PowerPoint files PowerPoint files http://personal.tsss.edu.hk/roh http://personal.tsss.edu.hk/roh http://personal.tsss.edu.hk/roh

28. Ronald HUI Good Luck! Enjoy the world of Mathematics!