mathematics ronald hui tak sun secondary school. ronald hui reminder corrections of dictation 1 and...

MathematicsMathematics

Ronald HuiRonald Hui

Tak Sun Secondary SchoolTak Sun Secondary School

Ronald HUIRonald HUI

ReminderReminder

Corrections of Dictation 1 and Corrections of Dictation 1 and Standard Homework (I)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)

Ronald HUIRonald HUI

ReminderReminder

Corrections of Standard Corrections of Standard Homework (II) and (III)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), Closed Book Quiz (Chapter 0), Dictation 2 and Folder CheckingDictation 2 and Folder Checking Last week of SeptemberLast week of September

Ronald HUIRonald HUI

Revision for QuizRevision for Quiz

Textbook 1ATextbook 1A Pages 2 – 31Pages 2 – 31

Workbook 1AWorkbook 1A Pages 1 – 16Pages 1 – 16

Summer RevisionSummer Revision Pages 1 – 19Pages 1 – 19

My PowerPoint filesMy PowerPoint files Your own notesYour own notes

Ronald HUIRonald HUI

MathematicsMathematics

How to get better results?How to get better results? Understand first!Understand first! Do correction!Do correction!

Dictation: 10 timesDictation: 10 times Test/Homework: Other colour pensTest/Homework: Other colour pens

Revise!Revise! Try more (workbook)Try more (workbook)

Ronald HUIRonald HUI

RevisionRevision

Prime numbers (Prime numbers ( 質數質數 )) 2,2, 3,3, 5,5, 7,7, 11,11, 13,13, 17,17, 19,19, 23,23, ……

Multiples (Multiples ( 倍數倍數 )) Multiples of 2:Multiples of 2: 2, 4, 6, 8, …2, 4, 6, 8, … Multiples of 3:Multiples of 3: 3, 6, 9, 12, …3, 6, 9, 12, …

Factors (Factors ( 因子因子 )) 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, …

Ronald HUIRonald HUI

RevisionRevision

Find all factors of 18.Find all factors of 18. 18 = 1 x 1818 = 1 x 18 18 = 2 x 918 = 2 x 9 18 = 3 x 618 = 3 x 6 18 = 6 x 318 = 6 x 3 18 = 9 x 218 = 9 x 2 18 = 18 x 118 = 18 x 1

Factors of 18: Factors of 18: 1, 2, 3, 6, 9, 181, 2, 3, 6, 9, 18

Ronald HUIRonald HUI

Prime Factors (p.9)Prime Factors (p.9)

Prime factors (Prime factors ( 質因子質因子 )) AA factor which is primefactor which is prime

Factors of 18: 1, 2, 3, 6, 9, 18Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3Prime factors of 18: 2, 3

All numbers can be expressed All numbers can be expressed as a product of prime factors as a product of prime factors only – How?only – How?

Ronald HUIRonald HUI

Index Notation (p.9)Index Notation (p.9)

Factors of 18: 1, 2, 3, 6, 9, 18Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3Prime factors of 18: 2, 3

18 = 2 x 918 = 2 x 9

= 2 x 3 x 3= 2 x 3 x 3 18 = 2 x 318 = 2 x 322 Index Notation Index Notation

3322 = 3 x 3 = 3 x 3 ((指數記數法指數記數法 )) 3 is base3 is base 底底 2 is index2 is index 指數指數

Ronald HUIRonald HUI

Index Notation (p.9)Index Notation (p.9)

3322 = 3 x 3 = 3 x 3 3 to the power 2, 3 squared (3 to the power 2, 3 squared ( 平方平方 ))

3333 = 3 x 3 x 3 = 3 x 3 x 3 3 to the power 3, 3 cubed3 to the power 3, 3 cubed ((立方立方 ))

3344 = 3 x 3 x 3 x 3 = 3 x 3 x 3 x 3 3355 = 3 x 3 x 3 x 3 x 3 = 3 x 3 x 3 x 3 x 3 What is 3What is 311 ? ?

3311 = 3 = 3

Ronald HUIRonald HUI

Index Notation (p.9)Index Notation (p.9)

Index notation is very helpful in Index notation is very helpful in long expression of prime factorslong expression of prime factors

432 = 2 x 2 x 2 x 2 x 3 x 3 x 3432 = 2 x 2 x 2 x 2 x 3 x 3 x 3

= 2= 244 x 3 x 333 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 286400 = 2 x 2 x 2 x 2 x 2 x 2 x 2

x 3 x 3 x 3 x 5 x 5 x 3 x 3 x 3 x 5 x 5

= 2= 277 x 3 x 333 x 5 x 522

Ronald HUIRonald HUI

Time for PracticeTime for Practice

Pages 10 – 11 of Textbook 1APages 10 – 11 of Textbook 1A Class PracticeClass Practice Questions 6 – 9Questions 6 – 9

Pages 6 – 7 of Workbook 1APages 6 – 7 of Workbook 1A Questions 5 – 9 Questions 5 – 9

Ronald HUIRonald HUI

Mathematics nearbyMathematics nearby

What is Google?What is Google? http://zh.wikipedia.org/zh-hk/Go

ogle#.E5.BB.BA.E7.AB.8B Google was mis-spelt from Google was mis-spelt from

googol!googol! Googol Googol = 10= 10100100

= 1000000…00000= 1000000…00000 (100 zeros!)(100 zeros!)

Ronald HUIRonald HUI

H.C.F.H.C.F.

Highest Common FactorHighest Common Factor(( 最大公因數最大公因數 )) Factors of 18:Factors of 18:

1, 2, 3, 6, 9, 181, 2, 3, 6, 9, 18 Factors of 24:Factors of 24:

1, 2, 3, 4, 6, 8, 12, 241, 2, 3, 4, 6, 8, 12, 24 Common factors of 18 and 24:Common factors of 18 and 24:

2, 3, 62, 3, 6 H.C.F. of 18 and 24 is H.C.F. of 18 and 24 is 66

Ronald HUIRonald HUI

H.C.F.H.C.F.

We can find H.C.F. from Index We can find H.C.F. from Index Notation! (Notation! ( 用指數記數法找用指數記數法找HCF)HCF) 1818 == 22 x 3 x 3x 3 x 3 = 2 x 3= 2 x 322

24 = 2 x 2 x 2 x 324 = 2 x 2 x 2 x 3= 2= 233 x 3 x 3 We know H.C.F. of 18 and 24 is We know H.C.F. of 18 and 24 is 66 6 = 2 x 36 = 2 x 3

Can you find the rule?Can you find the rule?

Ronald HUIRonald HUI

H.C.F.H.C.F.

Another exampleAnother example 24 = 2 x 2 x 2 x 324 = 2 x 2 x 2 x 3= 2= 233 x 3 x 3 3636 == 22 x 2 x 3 x 3x 2 x 3 x 3= 2= 222 x 3 x 322

Can you guess the HCF?Can you guess the HCF? Their HCF isTheir HCF is

2 x 2 x 32 x 2 x 3 = 2= 222 x 3 x 3

= 12= 12

Ronald HUIRonald HUI

H.C.F.H.C.F.

Another try: HCF of 700 and 720Another try: HCF of 700 and 720 700 = 2700 = 222 x 5 x 522 x 7 x 7 720720 == 2244 x 3 x 322 x 5 x 5 Can you guess the HCF?Can you guess the HCF? Their HCF isTheir HCF is

= 2= 222 x 5 x 5 = 20= 20

Ronald HUIRonald HUI

H.C.F.H.C.F.

If the numbers did not have If the numbers did not have common prime factors, their common prime factors, their HCF is 1HCF is 1

49 = 749 = 722

3636 == 2222 x 3 x 322

Their HCF is 1Their HCF is 1

Ronald HUIRonald HUI

H.C.F.H.C.F.

How about 3 or more numbers?How about 3 or more numbers? 18 = 2 x 318 = 2 x 322

2424 == 2233 x 3 x 3 30 = 2 x 3 x 530 = 2 x 3 x 5 Their HCF isTheir HCF is

= 2 x 3= 2 x 3 = 6= 6

Ronald HUIRonald HUI

L.C.M.L.C.M.

Least Common MultipleLeast Common Multiple(( 最小公倍數最小公倍數 )) 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 L.C.M. of 4 and 6 is 1212

Ronald HUIRonald HUI

L.C.M.L.C.M.

We can find L.C.M. from Index We can find L.C.M. from Index Notation! (Notation! ( 用指數記數法找用指數記數法找LCM)LCM) 44 == 22 x 2x 2 = 2= 222

6 = 2 x 36 = 2 x 3 = 2 x 3= 2 x 3 We know L.C.M. of 4 and 6 is We know L.C.M. of 4 and 6 is 1212 12 = 2 x 2 x 312 = 2 x 2 x 3 = 2= 222 x 3 x 3

Can you find the rule?Can you find the rule?

Ronald HUIRonald HUI

L.C.M.L.C.M.

Another exampleAnother example 24 = 2 x 2 x 2 x 324 = 2 x 2 x 2 x 3= 2= 233 x 3 x 3 3636 == 22 x 2 x 3 x 3x 2 x 3 x 3= 2= 222 x 3 x 322

Can you guess the LCM?Can you guess the LCM? Their LCM isTheir LCM is

2 x 2 x 2 x 3 x 32 x 2 x 2 x 3 x 3 = 2= 233 x 3 x 322

= 72= 72

Ronald HUIRonald HUI

L.C.M.L.C.M.

Another try: LCM of 28 and 30Another try: LCM of 28 and 30 28 = 228 = 222 x 7 x 7 3030 == 2 x 3 x 52 x 3 x 5 Can you guess the HCF?Can you guess the HCF? Their LCM isTheir LCM is

= 2= 222 x 3 x 5 x 7 = 420 x 3 x 5 x 7 = 420

Ronald HUIRonald HUI

L.C.M.L.C.M.

If the numbers did not have If the numbers did not have common prime factors, their common prime factors, their LCM is the product of themLCM is the product of them

20 = 220 = 222 x 5 x 5 6363 == 3322 x 7 x 7 Their HCF is 1Their HCF is 1 Their LCM is 20 x 63 = 1260Their LCM is 20 x 63 = 1260

Ronald HUIRonald HUI

L.C.M.L.C.M.

How about 3 or more numbers?How about 3 or more numbers? 18 = 2 x 318 = 2 x 322

2424 == 2233 x 3 x 3 30 = 2 x 3 x 530 = 2 x 3 x 5 Their LCM isTheir LCM is

= 2= 233 x 3 x 322 x 5 x 5 = 360= 360

Ronald HUIRonald HUI

Time for PracticeTime for Practice

Find H.C.F. and L.C.M. of the Find H.C.F. and L.C.M. of the following pairsfollowing pairs 10, 1510, 15 26, 3926, 39 36, 5436, 54 56, 9856, 98 91, 11791, 117 24, 36, 6024, 36, 60

Ronald HUIRonald HUI

ReminderReminder

BCA Online ExerciseBCA 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 filesPowerPoint fileshttp://personal.tsss.edu.hk/roh

Ronald HUIRonald HUI

Good Luck!Good Luck!

Enjoy the world of Enjoy the world of Mathematics!Mathematics!