Ai Ling Ong

A-Math: Standard Equation of Circle - Derived from Distance Formula

I notice many students had a hard time making sense of the standard equation of circle which is nothing new! The standard equation of circle is simply the Distance formula learnt in Coordinate Geometry in E-Math and A-Math.

Standard equation of circle:

Example:

Test Yourself:

To ensure you have understood the standard equation of circle, attempt the question below by selecting the correct option and leave your answer in the comments section.

In my future post, I'm going to discuss the other type of equation of circle: General equation of circle.

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Should I Drop A-Math (Additional Mathematics)?

Some of the common questions I get around this period (before registration of GCE 'O' level exams) is that 'Should I Drop A-Math?', 'Can I still study H2 Math in JC if I didn't take A-Math at O level?'

This post is also suitable for Secondary two students who will be choosing their subject combination at the end of the year.

'Should I Drop A-Math?'

This question usually pops out after a long period of unsuccessful attempts to pass A-Math or when it was recommended by teachers to drop the subject.

I have a poem to share: To Drop Or To Perserve On, Read the “Don’t Quit” Poem (Click to read)

'Can I still study H2 Math in JC if I didn't take A-Math at O level?'

I have also answered this question previously in this post: What happens if I do not take A-Maths?

Just a note : I have recently communicated with Temasek Junior College (TJC) Math teacher. For students intending to study H1 Math (Art Stream), 'O' level A-Math is not a requirement.

E-Math: Introduction to Vectors

In Secondary 4, students are going to learn this chapter 'Vectors'. Some love it, most hate it.

In today post, I'm going to share some basic concepts on Vectors.

What is a vector?

A vector is a quantity that has direction and magnitude. Common examples of vector include velocity, acceleration, displacement and force.

The opposite of vector is scalar, a quantity that has only magnitude. Examples include time, speed, distance and mass.

As you see, vector is closely associated with physics!

How do we represent a vector?

Since vector involves magnitude and direction, there will always be an arrow indicting the direction. We call this vector

Vectors can be expressed in a column format called column vector. For this example, which means, starting from point A, 3 units to right and 1 unit up. It is similar to our coordinate system 3 units along x axis and 1 unit along y axis. In general, moving right and up have positive sign while moving left and down have negative sign.

In general:

How to find magnitude of a vector?

Using the same example,to find magnitude of , we use Pythagoras's Theorem. (Refer to diagram above)

Magnitude of can be written as .

I hope you have understood the basic concepts of vectors. In future post, I'm going to write more about the application of vectors.

The Exclamation Mark ! in Binomial Theorem

factorial-sign-binomial Binomial 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:

Binomial Expansion Teaches how to choose the RIGHT partner (:

A-Math Binomial Expansion: Finding Term Independent of x By A Shortcut Method

Exam Question : Usage of Binomial Formula

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.

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.

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