Archives for 2010

A-Math: Type of Stationary Point through First Derivative

One of the applications of Differentiation is to determine the type of stationary point. This application is common in maximum and minimum problems.

There are two ways to go about finding the type of stationary point. The more frequently used method is through Second Derivative (Watch the video here). (d^2y/dx^2)

However, I'm not going to discuss on that method. Instead I want to share with you on the less popular method which is First Derivative. The reason: I have observed that last 2 years, questions appearing in the GCE 'O' level Additional Mathematics were less commonly seen, least expected and definitely more nerve breaking for candidates who aren't prepared.

Let's take a look at how First Derivative is applied. [Read more...] about A-Math: Type of Stationary Point through First Derivative

E-Math: Basic Concepts On Distance, Speed, Acceleration - Time Graphs

Photo Credit:Viernest

In E-Math, one of the commonly asked questions in Paper 1 usually involved Kinematics (which is closely associated with motion) and in E-Math, we discuss about Distance, Speed and Acceleration.

One of the important definitions all students must know is acceleration. It's defined simply as the change of velocity with time.

I'm going to use the following example to highlight the types of information we can obtain from a speed-time graph. It contains my handwriting, hope it works well for you ;)

Try out the question before peeping at my solutions. (Highlighted parts = important formula)

A-Math: Solving Indices Equation (Involving Common Base)

This topic is taught in Secondary 3 after introduction of Indices Law.

In solving indices equation involving the same base, one of the common techniques is by Substitution. But before you can do substitution, you need to apply indices law to 'break down' the equation. This process of breaking down is sometimes challenging for students. Knowing how to solve quadratic equation is also essential.

Sometimes, solving Indices Equation will also involve the concept of taking lg on both sides as well.

In the following example, you will Substitution and 'Breaking down' in action: [Read more...] about A-Math: Solving Indices Equation (Involving Common Base)

E-Math: How To Multiply Matrices (Video)

This is my first attempt this year to produce a video. Should the response be good, I will use video to share more tips and strategies with my audience, so please leave me a comment.

Please pardon me the 'echo' effect in my introduction and also the low resolution. I was using my new logitech webcam :D

I'm working towards producing better quality videos. Share tips on this if you have any. Would appreciate it.

For more posts on matrix, please refer to the related posts below.

I look forward in hearing your comments and the answer to the question in the video.

A-Math: Differentiation Shortcut Lies In Pausing & Simplifying

Differentiation is a big thing in fact major chapter for all Secondary 4 'O' level students.

Read all about the basics Differentiation techniques here. (Examples included) I would like to share one question from my A-Math Ultimate Leap Programme (weekly coaching class) which has 2 different approaches to solve it.

Example:

Very often, I notice students will jump into Quotient rule whenever a fraction is given. Just like this student here:

May I suggest that you pause for 3 seconds to think about the approach. Ask yourself 'Is there anything I can simplify?'

Here's another student who pauses:

Notice this student spends his time simplifying before applying chain rule in differentiation.

I hope you enjoy this example. Both students are correct in their answers, which one do you prefer more? A or B?

Foods for Better Memory

One of the interesting questions I discuss with my students every year before major examinations is

'What foods would you recommend for brain?'

Photo Credit: Bob.Fornal

Generally, I have heard about 'berries' and fish help in memory.

It wasn't until recently that I came across an interesting article on Pickthebrain.com

Here's a summary of the foods recommended in the article:

Herb: Rosemary
Tea (Yes! The beverage)
Fruits & Vegetables; colors for boosting memory are dark red, blue and green.
Fish & Nuts
Dessert: Honey

More details here: '5 Foods To Remember For Better Memory'.

So are there any specific foods you take to better your memory? I would love to hear from you! Leave me a comment.