Do you have to learn proofs for different formulas? (1 Viewer)

[leesh95]

I know it helps to know where the formula came from but for the HSC do you have to know the proofs for different formulas by heart?

 

[asianese]

Generally, no. Thinks like the chain rule or the proof for differentiation from first principles...things that like won't be asked, especially in 2U.

 

[TimeGoesTooFast]

Generally, no. Thinks like the chain rule or the proof for differentiation from first principles...things that like won't be asked, especially in 2U.

You probably won't be asked for the proof in 2u but most likely in 3&4u; for some formulas (can't think of one atm), it's best that you learn how to derive them.

 

[RishadM]

I did quite a few 2u and ext1 past papers in preparation for my HSC exam - and if your really trying to ace these exams and get like mid/high band 6, I would recommend learning the important proofs for formulas. I have seen them in some of the past papers, and some schools love to internally test these. We had the differentiation formula tested in one of our exams. The long fraction with the (x+h) and that stuff.

 

[Carrotsticks]

Proofs for formulas are very rarely examined nowadays. So if you don't have the mental capacity to memorise every single proof (as I did), I suggest you have a ROUGH idea of where each formula comes from, so in the *rare* case that say the Trapezoidal Rule formula is asked, you at least have a starting point to derive the expressions from scratch (as I did too).

However, some things cannot be proven with the scope of the 2U (sometimes even 3U and 4U) syllabus, like the Fundamental Theorem of Calculus (the whole subbing in limits thing when you integrate) and reason why the derivative of e^x is itself etc.

 

[twinklegal19]

Proofs for formulas are very rarely examined nowadays. So if you don't have the mental capacity to memorise every single proof (as I did), I suggest you have a ROUGH idea of where each formula comes from, so in the *rare* case that say the Trapezoidal Rule formula is asked, you at least have a starting point to derive the expressions from scratch (as I did too).

However, some things cannot be proven with the scope of the 2U (sometimes even 3U and 4U) syllabus, like the Fundamental Theorem of Calculus (the whole subbing in limits thing when you integrate) and reason why the derivative of e^x is itself etc.

I remember reading a straightforward-looking proof in in my tutoring notes why d/dx(e^x)=e^x, using

does that count?

 

[Carrotsticks]

I remember reading a straightforward-looking proof in in my tutoring notes why d/dx(e^x)=e^x, using

does that count?

Then you have to ask yourself, from where did the limit definition of e come? It can easily be observed by considering the curve y=1/x and an upper and lower bound rectangle, but a stretch for a 2U student. In fact it was in the extension 2 paper question 8 2009 hsc.

 

[RealiseNothing]

Then you have to ask yourself, from where did the limit definition of e come? It can easily be observed by considering the curve y=1/x and an upper and lower bound rectangle, but a stretch for a 2U student. In fact it was in the extension 2 paper question 8 2009 hsc.

The probabilty question that followed was really nice.

 

[leekeenyan]

FYI The question from the 2009 Extension 2 Paper was:



This is from 2002 HSC Extension 1 Paper (no diagram):