I think for now you can ignore all those gobbledygooks. The highest order of polynomial I have ever encountered is only 4, so I can't comment on the higher powers. But for STPM, you do not need any thing else that it outside STPM syllabus.

About the bolded part in your above statement, does it holds true for Maclaurin series too?? My teacher gave us a few practices on that chapter, and 1 question required us to obtain the Maclaurin expansion up to and including x⁵! The steps were extremely tedious and taxing for me, and I usually made careless mistakes in when it comes to expanding.

For Maclaurin series, the highest derivative I've ever encountered is 6, and it involved differentiating tan. Haha so you can imagine how tedious it is!

Maclaurin Series is actually very simple, you just have to be very careful so that you don't make mistakes as then it is very difficult for you to trace back where you did wrong.

Since Cardano's formula is not covered in STPM, you can simply use CASIO fx570 to get the roots of the cubic equation. Unless you are instructed to apply Newton-Raphson's method to find the root, I believe you can just use the built-in feature in the CASIO calculator. STPM Pure Math is still relatively straightforward.

Stick to STPM Math as what Just Visiting By advised. Cardano's formula is intended for those who are into the real "Pure Maths", by which a cubic equation is solved analytically.

In fact, I'm more worried about the way you interpret the math problems like the third (iii) problem. The techniques you apply to solve a problem reflect your understanding of what the question requires you to do.

While (iii) was designed to test your algebraic manipulation skill and your critical thinking skill to relate the cubic equation to the rational function, did you realize that (iii) also could be solved by obtaining the roots of x³ – 6x – 1 = 0?

This post has been edited by Critical_Fallacy: Feb 20 2015, 06:37 PM

I haven't got the clue on which equation to pick, and most importantly, I never truly fathom on why x³ – 6x – 1 = 0 is picked in this case, instead of .

No, I did not realize that.

It doesn't matter which equation you pick.



Because it is derived from the fundamental cubic equation f(x) = 0, they all have the same set of solutions.



Check the intersections of the graphs.



This post has been edited by Critical_Fallacy: Feb 20 2015, 09:45 PM

Oh, now I get it, I even manipulated the equation in my previous Third problem(iii).

When the (blue)graph of function h(x)=x³ – 6x – 1 =0, the graph cuts the x-axis at 3 different x-coordinates, which are x₁=-2.362, x₂=-0.1675, x₃=2.5289.

You did a pretty good job on answering my challenge, but here are the correct answer:

https://www.dropbox.com/s/k8k4n5t9c8i70kz/Book1.xlsx?dl=0

No, I don't think I answered your question correctly, and if anything, I totally misinterpreted your previous question.

Thank you for the solution.

THe solution provided by chocobo7779 is similar to the Bisection method—simple but slow to converge.

From the practical side, because the cubic function is continuously differentiable, Newton–Raphson method (covered in STPM) is highly recommended.



To answer chocobo7779's challenge without using calculus, I have modified an optimization method (to find the extremum) to locate the root that is known to exist within a certain interval.



The results converge to 2.5289 (4 d.p).

Oh, thank you for your solution. But, it looks much complex than the Bisection method and Newton–Raphson method.

This is the full version algorithm of chocobo7779's method. It requires at least 50 iterations and a series of tests to arrive at the accuracy of 5 decimal places. Compared to the Modified Golden Section Search, the rate of convergence is much slower. Of course, both cannot beat Newton–Raphson method.

Just Visiting By, can you recommend me some good sites on where I can find the literature review for my Physics assignment? My assignment revolves around the Interference of Sound Waves. I'm in a muddle here, because my teacher informed me a few days ago that without an adequate literature review, I will be coerced to switch my title of experiment. Now, I'm halfway done on Abstract, Theory, Problem Statement, Objectives and Methodology.

My friends and I went to USM last December to find some stuffs pertaining to our Physics/Chemistry assignments and we already took some photos for our bibliography, so that just leaves us with literature review and and a few more components(Observations, Discussions...). And yes, my friend and I did searched the Internet for days, and we found a handful of literature reviews, but they weren't related with our assignments. We could hardly find any suitable samples from ResearchGate and Scribd. It will be really appalling to restart our Physics assignment all over again back to square one.

Thanks in advance.

Thanks for the reminder. It's already way below the 100 days mark and yet I don't feel ready at all.

This post has been edited by regan96: Feb 23 2015, 10:31 AM

Does anybody know how to do the metodologi. My teacher ask us to try first but i dont even know what to write and all my classmates are bust with chinese new year. I am the only indian in that class

There are tons of free scientific literature, university lecture notes, and archived books available online. Search carefully. Type 'sound interference pdf' and you'll find a lot of good ones. Tip: Type something, then 'pdf', chances are you'll find quite a few good university lecture notes.

Sorry for the late reply.

I don't know any websites that provide literature review.

And I've sadly lost my chemistry project document so I am afraid I can't help. Sorry.

By the way, why did you guys go to USM? Your school doesn't allow you all to bring camera to school for the project?

Thanks for the tip. I'll try look them up.

It's alright, we still have some time left.

Simply because we could find lots of information and materials pertaining to our experiments and assignments in Physics, Chemistry and Biology. Our school library didn't help. I must say that I'm really amazed by some of the huge collections of books in USM's library. My teacher deemed it redundant to bring cameras to school just for the sake of our projects, she added that her smartphone will do the job for us.