singaporeolevelmathscoordinate geometry | singaporeolevelmaths

Coordinate Geometry Mindmap

Ai Ling — Tue, 14 Sep 2010 11:01:58 +0000

For today, I decided to have some fun with the online mindmap software – MindMeister to create the summary for coordinate geometry topic for Secondary 3 and 4 students.

It’s a simple mindmap which includes almost all if not everything on Coordinate Geometry.

Do let me know if there’s anything I’ve left out.

Feel free to save the image on your desktop too.

Click on image for larger view.

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

Ai Ling — Thu, 14 Jan 2010 06:00:09 +0000

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.

Diagram for Standard Eqn of Circle

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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E-Math: Introduction to Vectors

Ai Ling — Tue, 12 Jan 2010 03:36:12 +0000

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?

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.