# Welcome!

Congratulations on joining Brilliant!

In this blog, you’ll find a discussion of Key Techniques and how we can use them to approach various challenges that you might come across during the competition. We will start with mathematics concepts that you have learned in school, explain their applications and work through some examples. We will also look at the solutions to the bonus challenge from the previous week, and other interesting solutions that other students have sent in. Feel free to explore through the categories listed above.

Comments currently are open and not moderated. Please do not post solutions to Test Yourself questions, so that other students can benefit from the experience of working things out themselves. Questions marked with a (*) often require additional knowledge, which may be covered in another post. You may send solutions / your working to math@brilliant.org (or physics@brilliant.org), and I will review it and provide appropriate feedback. Please not that I do not discuss numerical answers, nor state the solutions to problems.

All the best for the Brilliant Challenge!

P.S. In order to type LaTex on the blog, you will need to type it as $_latex code$ , with the _ between $and latex removed. Give it a try, e.g. $a^2 + b^2 = c^2$. 134 Comments 1. Yash Dhanuka permalink can I answer problems anywhere else other than challenges? • On the main site, you can answer the weekly challenges. On the blog, you can work on the problems listed in Test Yourself. 2. Priyatam Roy permalink Sir,could u kindly conduct the live challenge after 31st march. As a class 10th student boards are very crucial to me and all . Like me many more brilliant users are also likely to face trble. • hkapur97 permalink it is optional to give boards, not compulsory. and whats more, they finish before 15th, if you take them 3. zoey permalink Dear Calvin, I just happened to come across your blog. May I know this mathematical blog caters to which grade of singapore school syllabus? What are the minimum basic mathematical foundation a student has, in order to understand your postings? • Hi Zoey, The bare minimum for a student would be being comfortable with algebraic expressions and functions. The basic knowledge required in understanding Level 1-3 posts will be taught by secondary 1-2. This includes topics like functions, polynomials, trigonometry identities, exponentials, permutations, etc. Comfortability with mathematical proofs would be ideal, as most of the ideas extend beyond mere rote computation, and require students to apply their thinking / problem-solving abilities. Most of these posts extend beyond textbook knowledge, so students should have some familiarity with those concepts. For example, in Completing the square, I do not derive the entire formula all over again (which is done repeatedly in school), but instead choose to present different ways that a student could use this idea. The posts also cater to a wide variety of student abilities, and some of the Level 4-5 posts do assume a lot of mathematical knowledge. In particular, questions marked with a (*) often require knowledge beyond what has been presented within the post. Note that the indicated Level corresponds to what a student on Brilliant.org would find challenging, and need to understand in order to improve beyond their level. A good way to start will be to determine the level on Brilliant, and then look up the corresponding posts according to the Level. 4. Zoey permalink Dear Calvin, Thank you very much for details explanation. Your effort in teaching beyond classroom text is very much applauded . I hope one day children from all over will learn from you through online interactive classroom teaching. May I suggest a bridging level from upper primary level so it can spark these children interest n curiosity mind as earlier as possible to real world phenomenon problem solving rather than just dull numbers. • Hi Zoey, Certainly, we do intend to extend across a wide range of students over time. Our current focus is on students who are familiar with material introduced in Sec 3 – JC 2 (equivalent of high school Year 9-12), and as such have created the bridging gap down towards Sec 1-2 (Years 7-8). Singapore also tends to have a more advanced education syllabus, as it introduces material early and reinforces it through yearly review and addition of supplementary material. Talented primary school students would certainly find out problems engaging and interesting. 5. Revankumar permalink how to give solutions to the solved problems? • If you are referring to the weekly problems on the main site brilliant.org, then students who provided the correct numerical answers will have a random chance to submit their solutions to the problems. If you are referring to the problems in the blog post, you can comment on the individual blog post. Note that I might retroactively edit out your solution, especially for posts which explicitly state not to submit your solution, so that other students will have a chance to work on the problems themselves. 6. Jaibe permalink Test1 :$ \int_{0}^{+\infty}e^{-x^2}\rm{d} x=\frac{\sqrt{\pi}}{2} $• You are missing the word latex right after the first$

Hi Calvin could you please tell me as to how I could find the Test Yourself section of the blog !!!!!
Compliments on a well setup blog …. UNESCO might someday give you the Kalinga prize !!!!!

• For the Key Techniques post, there is a write up of the approach, several Worked Examples with solutions, and then a section of Test Yourself questions.

Wer in d world r u dude,boards r frm 16-31.nd though extrnal is nt cmpulsary but intrnal nd externl hv no diff.other than cnduction.But this is only gonna shape ur future,if i’m ri8

25$for shipping d lanyards to me , is dat supposed 2 b a joke ? 11. Anonymous permalink ⁯Sir,i don’t find brilliant very cmfortable these days because: 1.i can’t find any discussion space these days(it was a very nyc system,so y did u remove it?) 2.in points exchange,master sessions are no more under existence(we used to learn much 4rm u and other cmpetitors) 4.points exchange lanyards are now limited to only lev. 4 and 5(y rn’t u promoting equality ? 5.ebooks are being provided these days(sir, i am already using specs and sitting infrnt of the comp. for very long strains my eyes(y dnt u prvide a hardcopy of the books ?) lastly,problem of the week column used to be fun,but now , it’s no more under existence ;-(⁮ • 1. The discussion space is the same, there were no changes (apart from splitting out feature requests to a separate section, since those are not really discussions). 2. There wasn’t enough interest from students for the master sessions, which is why we decided to discontinue with it. 4. We want students to associate the lanyards with excellence on Brilliant.org. Students should strive to improve their capabilities. 5. It’s a lot easier for us to distribute ebooks than hardcopy versions, due to various logistics. You can always print out the book. Note that you are offered and opportunity, and not forced to redeem any books. 6. Once again, we were not getting enough interest from students in physics for the Problem of the week, which is why we discontinued with it. • Anonymous permalink Sadly, the Kindle App is not available in my country, Indonesia, so I can’t read the e-books from Points Exchange. 12. Anonymous permalink Sir, i hav claimed the lev. 2 and 3 lanyards in jan 2013, will i recieve those? 13. I truly wanted to make a rrmeak in order to appreciate you for all the nice techniques you are showing at this website. My particularly long internet investigation has now been honored with awesome concept to go over with my best friends. I would mention that most of us site visitors are very lucky to dwell in a wonderful place with so many awesome professionals with great concepts. I feel quite lucky to have seen your web pages and look forward to tons of more awesome moments reading here. Thank you once more for everything. 14. Anonymous permalink Sir,in the mob. version of the site,latex coded words are invisible and can’t be read. Also some more errors like incomplete display,problem in claiming a dispute are often noticed.Also ,the service of sending prob. to mob. still does not work.please review these prob. 15. Advitiya permalink Latex check$_latex \int x^2 \cdot \sin^{-1}x \text{dx}$• Remove the _ between$ and latex.
$\int x^2 \cdot \sin^{-1}x \text{dx}$