Extenion 1 tricks (1 Viewer)

[BIRUNI]

I started a thread to share the tricks that we know. I know a limited number of tricks.

Tricks in maxima and minima problems:

if h(x)=c/f(x) then mininimizing h(x) is the same as maximizing f(x) and vice versa

if y=V^2(x) then maximizing or minimizing v is the same as maximizing or minimizing V^2

 

[fishy89sg]

oh thanks i knew the 1st one, but didnt know the 2nd one

 

[speedie]

using the calculator to work out sin60 etc without the need for a triangle

---> plug sin60 into ur calc..=0.866025.....
then square it = 0.75= 3/4
that means sin60= root3/2

etc...

 

[Riviet]

Circle geometry: cover up different parts of the diagram if it's complex with alot of lines. If trying to prove angles are equal, use angle chasing with no more than 2 variables.

 

[hyparzero]

using the calculator to work out sin60 etc without the need for a triangle

---> plug sin60 into ur calc..=0.866025.....
then square it = 0.75= 3/4
that means sin60= root3/2

etc...

or you can just remember sin60 has root 3 on 2

 

[Slidey]

I started a thread to share the tricks that we know. I know a limited number of tricks.

Tricks in maxima and minima problems:

if h(x)=c/f(x) then mininimizing h(x) is the same as maximizing f(x) and vice versa

if y=V^2(x) then maximizing or minimizing v is the same as maximizing or minimizing V^2

Suppose you have y=x^2 let's find the minimum: at x=0, of course. Now, the maximum of 1/y=1/x^2 doesn't exist, however.

Be careful of zero denominator and asymptotics.

 

[drynxz]

was planning to start a thread like this but u beat me to it -_-

i know a third derivatave method

If f''(x0)=0 and f'''(x0) exists and �*0 then (x0, f(x0)) is an inflection point.
...............
http://community.boredofstudies.org/14/mathematics-extension-2/107895/
third-derivative-method.html?highlight=third+derivative+method
................
Example

Show (0,0) is an inflection point for f(x)=x5.

Solution

f''(0)=f'''(0)=f''''(0)=0 but f'''''(0)=5!=120�*0. Hence (0,0) is an inflection point.

usually people have to test both sides to test it is an inflexion point.


there is inplicit
differentiation..but i think its 4 unit..
and theres also something called synthetic division...which i forgot ><

 

[shinji]

using the binomial probability : the number of of times u want an outcome should be the power of the probablility of the outcome.

eg: 1/4 chances of picking blue.
out of 7 tries, whats probability of pcking 5 blue.
⁷C₅ (1/4)⁵ (3/4)²

 

[Riviet]

there is explicit differentiation..but i think its 4 unit..

I think you meant implicit differentiation, where you apply the chain rule.
e.g d/dx (y²) = d/dy (y²) . dy/dx
=2y.dy/dx

 

[followme]

lol.. isn't it too late to learn new stuff this stage (for 06's)? just stick to the way ur most comfortable with and don't make any mistakes.

 

[Slidey]

Wasn't that method disproven or something like that a long time ago?

No. The nth derivative test works except in cyclic cases (which are generally rare).

 

[housemouse]

lol.. isn't it too late to learn new stuff this stage (for 06's)? just stick to the way ur most comfortable with and don't make any mistakes.

You do have at least 2 weeks left

 

[JBakaka]

true we have some time, but i agree with housemouse - just stick to what your're comfortable with because thats probably the easiest to use in the exam

and anyway, i didnt really understand much of the derivative tests that were mentioned above

 

[housemouse]

Actually I think anyone can cover a lot of stuff they may not know in the days that we have left. Just depends how you go about it.

 

[SoulSearcher]

i.e. cramming

 

[drynxz]

I think you meant implicit differentiation, where you apply the chain rule.
e.g d/dx (y²) = d/dy (y²) . dy/dx
=2y.dy/dx

yup my bad