Another question from O Level Additional Mathematics (A-Math).
If 
, 
find sinx and cosx in terms of p.
Archives for 2007
How to gain most?
first of all, we would love to thanks all those who have posted your comments, shared your thoughts, asked your questions :)
Keep them coming! we welcome all! Since O Level is coming by in 25 days time, we would love to continue to see this blog active. btw, did i mention that there are on average 100 of you viewing this blog daily? not a huge number but both me and sean are happy that there are people who visit this blog. and we will continue to provide you with tips to do well.
well, to ensure that you gain the most of out this, you yourself must participate! yeah participate is the key! ask all sorts of qns, answer qns the way u think is correct, just do it anyway! it is through participation that we can truly experience and learn at the maximum potential.
so when there are qns, have a pen and paper and work things out! see if your concepts and understanding are firm and clear.
keep the fire burning!
Cheers!
A-Math More P & C Qn! On forming numbers
Another question from O Level Additional Mathematics (A-Math).
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 = 5P3Case 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 = 5P3Total 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.
Do you know some curves are famous?
Have you heard about butterfly curve?
Wanna see its formation live?
Check them out here>>
Click on the curves on the left hand side and see them live on the right white box.
:)
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)