Photo Credit: mysza831

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. (more…)

differentiation, maximum minimum Hide

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?

chain rule, differentiation, quotient rule, shortcut Hide

A-Math Workshop, differentiation, integration Hide

Update: Click here for early bird registration.

Dear Students,

Do you know that Differentiation & Integration are 2 very important sections for O Level A-Math? Based on 2008 GCE O Level Additional Mathematics Papers, the weightage of Differentiation & Integration is almost 30%!

We received feedback from students and parents that due to time constraint, many schools rush through these 2 very important topics, leaving many students totally lost in their understanding. This coupled with the fact that Differentiation & Integration are totally new concepts for all A-Math students, made matter worst.
So with less than 7 weeks to GCE O Levels are you equipped with the tools and strategies to score in Differentiation & Integration or are you facing problems in understanding the concepts?

4 Days Differentiation & Integration Mastery Workshop

5, 12, 19, 26 Sep 2009, 2 – 6pm, YMCA Orchard (Tentative venue)

(Click on image for clearer view)

In this workshop, you will learn:

• Comprehensive 100% coverage of Differentiation & Integration
• Understand abstract concepts in an easy to relate manner
• Learn and Apply strategies (’approved’ short-cuts) on real examination questions
• Time management enforced during every workshop
• Pre & Post review assessment for checking level of understanding

Scope of the workshop:
Skills In Differentiation:

• Basic Techniques of Differentiation
• Differentiation involving trigonometrical functions
• Differentiation involving exponential & ln functions

Applications In Differentiation:

• Equations of Tangent & Normal
• Connected Rate of Changes
• Increasing & Decreasing Functions
• Maxima & Minima Problems

Skills In Integration:

• Basic Techniques of Integration
• Integration involving trigonometrical functions
• Integration involving exponential & ln functions

Applications In Integration:

• Hence question (reversed differentiation)
• Equation of curve
• Area under the curve
• Kinematics

Registration will open on 21st Aug 2009.(Update: Click here for early bird registration.)
This is the last workshop for O level students.

(Click on image for clearer view)

A-Math Revision, differentiation, integration, intensive revision programme Hide

I was looking through 2008 GCE O Level Additional Mathematics Exam Papers (Subject Code: 4038) and as expected, there was a Kinematics question (worth 6 marks) in Paper 1.

Kinematics is a application topic for Differentiation and Integration. To master this topic, you do not necessarily need to bring in your physics knowledge though it could be useful at times.

Instead, how I get my students to be a master in this topic is to be familiarize with a KINEMATICS VOCABULARY LIST.

Here’s some of the vocabulary words that are useful and common:

• Momentarily at rest, instantaneously at rest, changes direction of motion, stationary
• Initial displacement, initial velocity, initial acceleration
• Greatest displacement, greatest velocity, greatest acceleration
• Distance travelled in the 4th second VS Distance travelled in the first 4 seconds
• Maximum distance from Point O
• Particle returns to Point O
• Constant Velocity

I would say for Kinematics, it is one of the few topics in A-Math which uses extensive vocabulary. This is also the reason for you to decipher the meaning behind these words.

So do you know the meaning behind these words? I would love to hear about it in the comments section.

I have also taken a few questions from my A-Math TREQ book(Topical Real Exam Questions) to illustrate some common exam questions on Kinematics, further highlighting the importance of knowing your Kinematics well. (Click on the image for bigger view)

Click on image for a larger view

I would be sharing the step by step solutions for Question 8 in the next post. Subscribe to my blog to be updated again!

differentiation, Exam Questions, integration, kinematics, Topical Real Exam Questions, vocabulary list Hide