A-Maths Tuition

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

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)

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?

A-Math: General Equation of Circle - Linked to Completing Square

In the previous post, I have discussed the standard equation of circle which is derived from distance formula.

The other equation of circle is known as General.

Example

To answer this question easily, you need your completing square technique (Read about the steps here) which many students dislike!

You notice in the step by step solution, the general equation is converted into a standard equation through the following steps:

Arrange all x terms and y terms together
Start completing square
Simplify all constants
Set equation into standard equation of circle

General Equation to Standard Equation of Circle

Radius = 5 and Centre of circe = (4, 1)

I hope you have a better understanding on equation of circle.

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.