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Archives for 2010

The Exclamation Mark ! in Binomial Theorem

factorial-sign-binomialBinomial Theorem came out as a 9 marks question in 2009 GCE 'O' Level Additional Mathematics Paper (Subject Code: 4038) so you know as well as I do the importance of Binomial.

Read about other useful posts on Binomial Theorems:

I'm looking at the question now. It is testing on the usage of the Binomial formula, including the 'n choose r' formula. Many students call this sign: '!' 'exclamation mark' which is known correctly as factorial.

I will be using the following question to illustrate how to simplify the 'n choose r' formula without memorizing. (I understand some schools want students to memorize)

Let's begin by understanding what's 'n choose r' all about:

n-choose-r-binomial
Click on image for larger view

Do you know how to simplify 'n choose 3'?

Here's the question which requires us to apply what we have discussed. I would suggest you attempt it on your own before clicking here for the solution.

binomial-question
binomial-question

Official: Release of 2009 GCE O-Level Examination Results on 11 January 2010

School candidates may collect their results from their schools at 2.00 pm on 11 January 2010. Private candidates will be informed of their results by post. They may also access their results through the Singapore Examinations and Assessment Board website from 2.00 pm on 11 January 2010.

More details here: http://www.moe.gov.sg/media/press/2010/01/o-level-results-jae-jpsae-2010.php

All the best!

E-Math: Interesting Probability Math Teaser (Plus usage of Tree Diagram)

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die."

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

Do you know how? ;) Leave your answer in the comment section. I will reveal the answer if anyone is interested to know.

In E-Math, we discussed about probability on possibility diagram, tree diagram, mutually exclusive events, independent events. Fortunately we do not go into permutation and combination where things get slightly more exciting.

Do you use more of tree  or possibility diagram  to help you in your probability question?

I'm going to show you an example of modified tree diagram to solve the following question

Bag A contains 15 bronze rings, 6 silver rings and 4 gold rings. Three rings are drawn at random, one after the other without replacement from bag A.

Calculate the probability of not drawing any gold ring.

modified-tree-diagram

Additional question: Calculate the probability of drawing all three rings that are different.

GCE 'O' level Results 2009 Tentative Release Dates

According to SEAB website, 2009 GCE O level results will be scheduled for to be released between 11 - 13th January 2010.

Wishing all candidates the best of everything, may you get what you want!

Here's a list of polys & JCs open house 2010 between 7 - 13 Jan :

  1. Singapore Poly
  2. Temasek Poly (TP has a live chat room for students to find out more)
  3. Ngee Ann Poly
  4. Republic Poly
  5. Nanyang Poly
  6. NJC
  7. Hwa Chong
  8. ACJC
  9. SAJC
  10. TJC
  11. Yishun, Anderson, Innova, Serangoon JC
  12. NYJC (Facebook page)
  13. Meridian JC

Most Polys are holding their open house from 7 - 9 Jan while most JCs are having theirs on 13 Jan. [Read more...] about GCE 'O' level Results 2009 Tentative Release Dates