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Jarrett

A common mistake made by 2 friends

A mistake made by Zhiming

Using R formular

Trigonmetry Formular O LeveL A Maths That are given

This are the formulars given in Further Trigonmetry

sin²x+cos²x=1

sin(A+B) = sinAcosB+ cosAsinB

sin(A-B) = sinAcosB - cosAsinB

cos(A+B) = cosAcosB-sinAsinB

cos(A-B) = cosAcosB+sinAsinB

tan(A+B) = [tanA+tanB)]/(1-tanAtanB)

tan(A-B) = [tanA-tanB)]/(1+tanAtanB)

sin2A=2sinAcosA

cos2A=cos²A-sin²A

cos2A=2cos²A-1

cos2A=1-2sin²A

tan2A=Tan2A/(1+tan²A)

sinA+sinB=2sin[(A+B)/2]cos[(A-B)/2]

sinA-sinB= 2cos [(A+B)/2] sin [(A-B)/2]

cosA+cosB=2 cos [(A+B)/2]cos[(A-B)/2]

cosA-cosB=-2sin[(A+B)/2] sin [(A-B)/2]

Formulars That are Not given

a cos θ ± b sin θ = R cos (θ ∓ α)

a sin θ ± b cos θ = R sin (θ ± α)

where

and a > 0, b > 0, α is acute

Tough Trigonometry Questions

Summary for O Level trigonometry

Right angle triangles Use
trigonometric ratio
Tan @ = opposite/adjacent
Cos @ = adjacent/hypo
Sin @ = opposite/hypo
Non right angle use Sin and cosine rule

Sin A/a = SinB/b= SinC/c

Partial fractions

Partial fractions Formulars of changing

A) 1/(x-2)(x-3) = A/(x-2) +B/(x-3)

B) 1/(x-3)²= A/(x-3) + B/(x-3)²

C) 1/(2x²-3)(x-3) = A/(x-3) + Bx+C/2x²-3

D) To solve partial fraction Q(x)/F(x) when the degree of Q(x) is higher than F(x) , use long division
(x³ +2x²-3/ 2x²-3)

Caculating time line

How to calculate 2004 oct 10 – 2011 may 16

2004 oct 10

2005 oct

2006 oct

2007 oct

2008 oct

2009 oct

2010 oct  10

nov 10

dec 10

jan

feb

march

april

may 10

11

12

13

14

15

16

its 6 years 7 months 6 days

A P6 Challenging question !

John had 993 tables n chairs at first. After he sold 2/5 of the tables n 5/8 of the chairs, he had 459 tables n chairs left. How many tables did he sell?

New Tax

Calculate A person earning 25550 :) Aldwin Income 25550 How much Aldwin Pays

Secondary 3 A Maths Logarim

Secondary 3 A Maths

Chapter 2.  Logarim

1)Changing indices to log

a^x= b

x  = log_ab

Example

10³=1000

3=log₁₀1000

3^x=2

x=log₃ 2

Do IT

Q1)3^x=4

Q2)2^y=2

2)Changing log to indices

log_ab = y

b       =  a^y

example

log₃ x = 2

x        = 3²

x        = 9

Q1) log₄y = 3

Q2) log₂x =2

3) Changing Of Base

	Log b
Logab =	-------
	Log a

	Log 5
Log45 =	-------
	Log 4

Q1) find log₆7

Q2) find log₈9

 <Logarithm/> tags

4) Power law of log

alog b = log b^a

2log 3 = log 3²

Take note

(Log b)²  = (log b)(logb)

                not equal to log b² 

5) Addition law of log

Log (ab) = Log a + logb

Log (12) = Log 3 + log4

Log (3x) = log 3 + logx

6) Subtraction law of log

log (a/b) = log a – log b

log (x/8)  = log x-  log 8

Qn1) Log(4x)

Qn2) log (7/x)

Secondary 3 A Maths Logarim

Secondary 3 A Maths

Chapter 2.  Logarim

1)Changing indices to log

a^x= b

x  = log_ab

Example

10³=1000

3=log₁₀1000

3^x=2

x=log₃ 2

Qns)

Q1)3^x=4

Q2)2^y=2

2)Changing log to indices

log_ab = y

b       =  a^y

example

log₃ x = 2

x        = 3²

x        = 9

Q1) log₄y = 3

Q2) log₂x =2

3) Changing Of Base

	Log b
Logab =	-------
	Log a

	Log 5
Log45 =	-------
	Log 4

Q1) find log₆7

Q2) find log₈9

 <Logarithm/> tags

4) Power law of log

alog b = log b^a

2log 3 = log 3²

Take note

(Log b)²  = (log b)(logb)

                not equal to log b² 

5) Addition law of log

Log (ab) = Log a + logb

Log (12) = Log 3 + log4

Log (3x) = log 3 + logx

6) Subtraction law of log

log (a/b) = log a – log b

log (x/8)  = log x-  log 8

Qn1) Log(4x)

Qn2) log (7/x)

A Maths points to take note on Surds

Facebook message with a high performance student

 

This is how a great student interact on face book with  a tutor :)

Difference between sulfur,sulphide,sulphite and sulfate

 

 

8:39pm

Hey

8:41pm

ya?

???

8:42pm

Started matrix ?

U took geo or history ?

8:43pm

no leh my teacher super slow sia just finish all the laws of indices today

8:43pm

Haha

8:43pm

combined humans=SS + History

let me test u a chem qn :D

8:44pm

whats the name of ion SO3

8:45pm

Sulphide ions

8:45pm

no la the name

dont check the internet arh

8:58pm

Dunno

No meh ?

8:59pm

ion of SO3 is sulfite

If SO3 is a compound its sulfur trioxide

8:59pm

I dunno how to spell ..... S2- then sulphide

Shit

Haha

9:00pm

I knew u would get wrong

:D

9:00pm

My spelling not so good

Lousy in English

Think must wack jarrette English soon

Haha

9:01pm

So weird sia must have sulfur,sulphide,sulphite and sulfate

agreed :)

9:02pm

Ya I also mixed up some times

 

<chemistry topics>

Quadratic expansion

(a + b) 2 = a 2 + b2 + 2ab 
(a - b) 2 = a 2 + b2 -2ab
(a+b)(a-b) = a2 - b2

Example 
(3a-4)(3a+4) 
=32a2 -42
=9a2 - 16

Chapter 1.2 Solving Non linear Equations

Chapter 1.2

Solving Non linear Equations

Example1

2y-3x=1  ------ (1)

y+9x²=8 ------ (2)

from (1)       y=(4x+1)/2 ----(3)

                  

sub(1) into (3): (4x+1)/2 + 9x²   - 8 =0

x 2                 3x+1+18x² -16=0

                     18x²-15+3x=0

                      (18x-15)(x+1)=0

                      18x-15=0 or      x+1=0

                      18x=15               x=-1

                       x=15/18

find y

Example 2

                   3x/y-2y/x=1 --------- (1)

                   5x-3y=12     --------- (2)

(2):              x=(12+3y)/5 ----------(3)

multiply (1) by xy

                   3x²  -2y²=xy ------------(4)

sub (3) into (4)

                   3(12+3y) ²/5 ²  -2y²=y(12+3y)/5

multiply by 25

                                3(12+3y) ² -50 y²=5y(12+3y)

                   3(144+72y+9y²)-50 y²=60y+15y²

432+216y+27y² -50y² -60y-15y² =0

                   -38y²-60y+432=0

                   19y² +30y-216=0

                   (19y+36)(y-6)=0

                   y=-36/19 or y=6

find x

                  

<Equations> tags