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:

  1. Trigonometry
  2. Differentiation
  3. 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)

Comparison between differentiation and integration page 1

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.

Pass With Distinction! Workshops

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

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. only for the committed.

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Change in O-Level Elementary Maths 4016 Paper 1 Date

SEAB has made the following changes to the 2014 Singapore-Cambridge GCE O-Level Examination Timetable due to the change of date for Deepavali :

New date for O-Level Elementary Maths Paper 1 4016: 17 October 2014, 230pm - 430pm

O-Level E-Maths Change of Date

Change of date for O-Level Elementary Maths 4016 Paper 1 2014


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Differences between O-Level Additional Maths new and old syllabus

For Secondary 4 or 5 school candidates (in Singapore) taking the O-Level Additional Maths this year, many are likely to have registered for the new syllabus 4047. 

In this post, I would like to highlight the main differences between the new (4047) and old (4038) syllabus:

  • Matrices, Factor formula are excluded from the new syllabus
  • Intercept, Intersecting chord and Tangent-secant theorem are excluded from the new syllabus
  • Sum and differences of cubes in Polynomials are included in the new syllabus

Sum and Differences of Cubes New Syllabus for Additional Maths 4047

In conclusion, since there are more exclusions than inclusions. We should be expecting more application questions which can be linked to everyday life applications in the fields of Biology, Chemistry, Physics, Engineering etc.

The keys to achieve distinction in O-Level Additional Maths are still:

  1. a solid foundation in basic concepts,
  2. well-equipped with application strategies,
  3. wide exposure to carefully selected application questions,
  4. good management of time for doing and checking
  5. exam-smart strategies

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