GCE O Level A-Math Topical Revision Programme

Follow Up Email Math Question on "Use of barycentric coordinates and law of levers"

Dear student,

It is really cool to see you exploring an area beyond your scope of book.
This is in fact what true learning is all about.
However, many a times, students are buried with tons and tons of homework assignments and project deadlines that the entire meaning of learning is lost.

Nevertheless,"Use of barycentric coordinates and law of levers" is an area which is definitely of a higher level.
Since yahoo-ing gets you hardly useful info, have you google?

I did, and this is what I found.
Check out the few websites and they should be helpful in some aspects.

Cheers,
alwaysLovely

Email Math Question on "Use of barycentric coordinates and law of levers"

Hello AlwaysLovely!
I am a seconday 4 student this year
if u can remember, you tagged at my blog somewhere last year and mistook me for a secondary 4 student then, this thus led me to your blog.
anyway, i got a maths question to ask. i know that you wrote on your blog to ask you about O level maths but i was reading a book on geometry proofs and saw a question that was proven by the use of barycentric coordinates and law of levers. i am rather interested in this way of proving so i tried to yahoo-ing for tutorials on barycentric coordinates and was lost by some of the very few tutorials posted on the net.
So, i was wondering if you can enlighten me on some basics of barycentric coordinates or perhaps email me some links to tuturials on barycentric coordinates that might be easier for a secondary school student to understand.
i look forward to your reply and thanks!

X'mas Presents?

Hello everyone,

for those who partcipated in the voting of the template of the site.Tks for your response.
for those who didn't vote yet, you still have a few more days to vote.

X'mas coming so I guess most of you are busy preparing x'mas presents or are you busy with clearing up more space to receive more gifts?

Whatever the case, Sean, the co-author of askalwayslovely & the SimpleChemConcepts guru seems to be busy preparing something free for everyone to start the new academic year on the right year.

I will push him to release the gift he's preparing soon okie!

Meanwhile, you may want to check out this site on THE SONG!
http://www.simplechemconcepts.com

btw, have you downloaded your copy of "Be a Squaring Expert within 30 seconds"?
Click here to gain instant access http://www.singaporeolevelmaths.com

Less than 15 days to the start of the new school term!

Yeah!

A qn from June 2007 Qn Coordinate Geometry

Point B is intersection of Line AE & BE
1.find eqn of these 2 lines
2.Solve simultaneously
B= (5,8)


Area of EBC is given
Never use distance to solve this part!

1/2 xBxH = 24
What's the base? What's the height?
Base = EC = (x-3)
Height = Vertical Distance from B to line EC = 4

By simply using the CORRECT base & height strategy allows me more time for the rest of the questions!

C=(15,4)

To find D,
Use Eqn of AD

D=(15,-2)

;)

More elaborate step by step solutions & power tips are
available here.
Click here
We have parents
already purchased a copy for their children. Even students buying for themselves
through Bank Transfer.
I was "scolded" by one of the students who bought the
papers "Why didn't you let me know earlier?"
Well, late better than never,
isn't it? ;)

Well, there's only 1 O level and it's really starting. You
decide how you want to spend your time.
For those who are serious in doing
your best and getting the marks you deserve for your Monday paper, you
should get the step by step solutions today cos price is going up tm(Fri)

What another student did for this qn:
(Click on the image to see clearly)

June 2007 A-Math Paper Step by Step Solutions

Dear students,

Those who have completed your June 2007 Papers! Well Done!

I can't provide the solutions for free as there are already some students who have bought the step by step solutions & Power Tips for June 2007. I need to be fair to them.

Btw, I have received email from a student that I should not be giving out the June papers free as some of you paid $1 for it.

But the ironic is. though I'm giving it for free, only a handful of serious students are downloading and taking actions to do and find out the areas they can improve on.

For those who wants to check the answers, you can perhaps discuss with your friends or you can get your copy of the step by step solutions here
>> Strategies to solve the latest O Level Questions Trends Quickly & Easily
>> http://www.singaporeolevelmaths.com/squaringexpert.html for Maths Strategies

I have provided a tip and answer for June 07 P2 Q12 Co-ordinate geometry qn here
>> http://askalwayslovely.blogspot.com/2007/10/qn-from-june-2007-qn-coordinate.html

All the way!

June 2007 A-Math Paper gives you An unfair advantage over your friends

For all taking A-Math :

This is the only paper you MUST complete before 22nd Oct.

All A-Math students must complete and learn from any mistake that you have made from June 2007 Papers. Y
ou must have at least 30 minutes to check otherwise you are either not managing your time to the optimum or you are using a longer strategy.

By doing so, it gears you up for the big thing and brings you closer to what you want to achieve.

Those whose do not have the Papers, download the papers for free, just a click away! Do it quietly and fastly!

>>http://www.singaporeolevelmaths.com

Almost 30 students have downloaded it! Get yours too!

The BIG THING is starting!!!

You can do it!

For those who have completed the papers, do you want to find out how to complete the papers leaving you time to check, double check, triple check?

A-Math Circular Measure

5 marks, showing qn.

:)

A-Math Integration of tan^2 x

lijun(: said...
i came across this qu that day, and i really want to clarify if the method i used is correct or not.

int(tan^2x - x^3)

i changed it to int(sec^2x - 1 - x^3) instead, cos i don't think we can integrate tan.

is that feasible?

Absolutely. Since tan^2 x can't be integrated, you must think of alternative by making use of the relationship of tan^2 x + 1 = sec^2 x

A-Math P & C Clarification

lijun(: said...
hey. i just want to clarify something that i'm not very sure of.

is nCr x r! = nPr ??


By definition,

nCr = nPr/r!

Well, I never remember this 'rule'
For example, find the number of ways to form a 3 letter word from a,b,c,d,e

Student #1:
5C1*4C1*3C1

Student #2:
5P3

Both answers are correct though different approaches are taken, so no need to remember the 'rule'

:)

A-Math More Trigo Graphs

On the same diagram, sketch the graphs of

y=sin 3x & y=cos2x,
for x between 0 degree and 180 degree
Hence state the number of soutions to the equation
sin 3x=cos 2x
in the interval 0 degree less than or equals to x which is less then or equals to 180 degree


Click on image to have a larger view

A-Math Trigo Qn

If p =( 1 + cosx )/sinx, 1/p= ( 1 - cosx )/( sinx ), find sinx and cosx in terms of p.

A-Math More P & C Qn! On forming numbers

How many even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated?

Conditions
#1: Even
#2: 5-digit number
#3: no digit is to be repeated

Case 1:When the first digit is odd (must be more than or equal to 5)

2C1 * 5P3 * 3C1

Logic & Reasoning:

first digit: either 5 or 7 so 2C1
last digit: either 2,4 or 6 so 3C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Case 2:When the first digit is even

5P3 * 2C1

Logic & Reasoning:

first digit: 6 so no need to choose just put!
last digit: either 2 or 4 so 2C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Total even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated = Case 1 + Case 2 = 480

:)

Application of Differentiation - Maximum/Minimum & Rate of Change

Qn2
A closed box with a square base of length x and height h, is to have a volume, F, of 150m^3. The material for the top and bottom of the box costs $2 per square metre, and the material for the sides of the box costs $1.50 per square metre. Fnd the value of x and h, correct to 3 decimal places, if the total cost of the materials, C is to be a minimum.
Qn3
A viscous liquid is poured onto a flat surface. It forms a circular patch which grows at a steady rate of 6cm^2/s. Find,
a) the radius r, in pie, of the patch 24 seconds after pouring has commenced.
b) the rate of increase of the radius at this instant, correct to 2 decimal places.

Done reading the qns? Do and see if your answers are correct!

:)


Click on image for enlarged view.

Trouble with Integration of Ln & Expo

I seem to have trouble now with integrating ln and e.

Haha, you are having trouble because you are learning sth you don't have to know at O'Level. You don't have to know how to Integrate Ln directly.

Having said this, you note that you must know how to Differentiate Ln, e and Integrate e

For more info on how to differentiate Ln and e, refer to this post >>
http://askalwayslovely.blogspot.com/2007/09/math-differentiation-with-ln.html



Okie how to Int e
Example
Int e^(2x+3) = e^(2x+3)/2 + c (since there are no limits given)

In short to Int e^(wadever) = e^(wadever) OVER (Differentiate wadever)

A-Math P & C Qn!

The no. of applicants for a job is 15. (i)Calculate the no. of ways in which 6 applicants can be selceted for the interview.

The six selected applicants on a particular day. (ii)Caluculate the no. of ways in which the order of the six interviews can be arranged.

Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.


Who's up for this challenge?



******************************

Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.

BBB EE R

So there are 3 groups of people and there are 3! ways of arranging these 3 groups
Within BBB group, there are 3! ways of arrange these 3 B people, similar within EE group, there are 2! ways of arrange these 2E people
so Total = Arrange Big Groups * Arrange within each group = 3! * 3! * 2!

A-Math Qn Involving Ln / Log

Hi, i have a question which i can't solve it.
Qn: Peter deposited $540000 in a bank at the beginning of 1980, which gave a compound interest of 1.8% per annum, which pays directly into his bank account. After a period of t years, the amount of money that peter has in the bank was given by 540000( 1.018)^t. Find
a) the amount of money peter has at the beginning of 1993.
b) the year, in which he would have one million dollars.
If peter wants to have one million dollars in 20 years, he needs to find a bank that gives a compound interest of r% per annum. Find the value of r.


a) 1993-->1980 = 13
when t = 13, amount of $ he has = 540000( 1.018)^(13)

b)1,000 000 = 540000( 1.018)^t
1.85 = ( 1.018)^t
Either take Ln or Log on both sides of the equation ,

Ln1.85 = t Ln1.018
t=34.5 years = 35 years to have the 1 million dollars
1980 + 35 = 2015

***************************************
let r be the compound interest rate
1,000 000=540000(1+(r/100))^20
1.85= (1+(r/100))^20

Taking Ln on both sides,
Ln1.85= 20 Ln(1+(r/100))
Ln(1+(r/100))=0.0308
1+(r/100)=1.0313
r/100=0.0313
r=3.13%

When your unknown is located in the POWER, in order to bring it down, you can either Log or Ln both sides of the equations.

Drawing of Trigo Graphs

Can you give an example of a drawing of tangent graphs? For eg, 3tan2x + 1, what does each stand for and how do i go about drawing?

From the drawing, you see only 1 diagram instead of a few diagrams as what most people will have.

The secret is............ I drew my x and y axis LAST which is the reason why my diagram is so neat and it takes me less than 2 min to complete : )

Click on diagram to have an larger view

Differentiation of e

How to differentiate e^tanx?

first of all to differentiate e^anything = (Diff anything)*e^anything

so to differentiate e^tanx = (Diff tanx)*e^tanx = sec^2x*e^tanx

:)

btw, i couldn't remember what is Diff tanx = to, but i know how to sinx & cosx
so tanx=sinx/cosx Diff using quotient rule, get the ans within 30s :)

A-Math Differentiation with Ln

Qn frm email

Differentiate ln square root (2x+4)

Hint#1: Bring out Laws of Ln which is somewhat the same as Laws Of Log :)
Hint#2: When you are asked to Diff Ln (whatever) = Diff (whatever) OVER (whatever) :)


*************************************************

Amaths Differentiation and Integration techniques.
How to actually remember all the different ways for differentiating and Integrating, I always get mixed up

Hi xxx,

Differentiation = Decrease Power
Integration = Increase Power
(It's often sth OVER another)

Example

Diff e^2x = 2e^2x
Integrate e^2x = (e^2x / 2)

Diff (3x+4)^5 = 5(3x+4)^4 (3)
Integrate (3x+4)^5 = (3x+4)^6/(3*6)

It's suggested that you have a "cheat" sheet with Diff on Left Hand Side and Integration on Right Hand Side.
To familiarise more, work on at least 5 qns just on differentiation and integration :)
You can always scan me any qns or type out any should you face any challenges.

Cheers,
alwaysLovely