integration

Integration: The Reverse of Differentiation

After I've completed my O-Level Maths Revision Differentiation workshop for a small group of Secondary 4 O-Level A-Maths students, I understood from them why a handful of them finds Integration challenging.

They get confused when differentiation is mixed within a question with integration! Are you just like them? Is your child facing the same problem too?

The three major topics for O-Level Additional Maths are:

Trigonometry
Differentiation
Integration

Having a great understanding in these topics is crucial to pass O-Level A-Maths with distinction! When you have a clear understanding of the differences between differentiation and integration, you then can solve fundamental differentiation or integration techniques questions. And this is important as there are so many applications questions on:

Property of integral
Equation of curve
Integration is the reverse of difference (I term it 'The HENCE concept' question)
Partial fraction in integration
Area under the curve
Kinematics

Let's take a look at comparisons between differentiation and integration questions:

(click on the image to view a larger size)

When you have a good understanding on how basic differentiation and integration rules are used in each question, you will be absolutely clear on the correct approach to take. All confusion will be transformed to confidence!

Many students need to be shown the comparison, taught the strategies, understand the reasons then they will be enjoying the topic happily.

If you have found this post useful, click on share on Facebook so that more students can benefit from this.

For students who are committed to be extraordinary, I would like to invite you to join me on my 4 days of O-Level Maths Revision: Integration Workshop on 3, 10, 17, 24 July 2014 (Thursday) from 6pm to 9pm. I will be sharing with you the strategies on Integration my students have used to pass their O-Level A-Maths with distinction.

This is exclusively for committed students who will do whatever it takes to turn their results around as they know deep inside them, they deserve better results as long as they are willing to work hard.

For registration, please go to www.PassWithDistinction.com.

PS: I've only 7 seats left.

I would like to share with you what Paxton has sent us after he received his O-Level results last year. He stays in Jurong and he was one of the committed students who showed up for several of our A-Maths Workshops last year, despite the distance from ACS(Br) to Winners Education back to Jurong, despite the long hours in schools, despite the fatigue, despite everything... He does not allow any factors to hold him back, his parents supported his decision... His commitment pays off handsomely for him. We are proud of his achievement and his determination in truly unleashing his potential.

PassWithDistinction.com: only for the committed.

A-Math: How to Integrate Trigonometry with Square Power [video]

Some students get really confused between differentiation and integration of Trigonometry. In fact, I personally feel that integration of Trigonometry is easier as there are only 3 general formulas (as shown). In this video, I've shown the thinking process, step by step approach on how to integrate Trigonometry with square power, an advanced concept. Hope you find the approach and explanation useful.

I would love to hear your comments.

Click on this link to view the video: http://www.youtube.com/watch?v=E3ykmKa4MLU

A-Math: Kinematics Vocabulary List on Displacement, Velocity & Acceleration (Includes a printable note)

Many students don't like the topic in A-Math known as 'Kinematics'. My guess is that it is linked closely to Physics which is a subject not favourited by many too.

To be able to understand Kinematics, I always get my students to be familiar with what I call a 'Kinematics Vocabulary List'. [Click here to download a printable note]

I hope you find this list useful. I would like to hear from you how you find Kinematics in Differentiation & Integration. Do you like it or dislike it? Leave me a comment.

$A-Math-KinematicsVocabList$

Protected: Differentiation & Integration Solutions (For workshop participants only)

Differentiation & Integration Mastery Workshop (Includes Kinematics too!)

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: Differentiation & Integration Application : Examples of Typical Kinematics Questions

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)

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