A-Maths

A-Maths: Differentiation Application - Stationary Value [Video]

Differentiation - Find Minimum Gradient of Curve Question

I received this question on finding minimum gradient of a curve and it is confusing for many students as they probably lack the flexibility in seeing gradient beyond dy/dx.

I have presented this question in a slightly different manner by reducing the usage of first derivative (dy/dx) and second derivative (d^2y/dx^2).

Check the 3 minutes video by clicking on the video to find out the step-by-step solutions and the explanations.

Video URL: https://youtu.be/K5-LaQUXo94

httpv://www.youtube.com/watch?v=K5-LaQUXo94

2015 GCE O-Level Additional Maths 4047 Paper 1 Post Mortem Not Solutions

After doing the revised syllabus 4047 GCE O-Level Additional Maths Paper 1, it reconfirms that Cambridge is testing basic concepts but presented in a different manner.

There are a few questions which are truly testing your application like the one on quadratic curve is always negative, range of m for which the graphs have two intersection points ...

I highly recommend all candidates to read your question carefully, keep asking yourself if you have answered the question.

An additional point to highlight is look at the allocation of marks to gauge the amount of working to present, the choice of approaches to use.

Based on what have been tested in Paper 1, we are looking forward to the following concepts in Paper 2:

Indices
Sum & Product of roots
Factor Remainder Theorem (solving cubic equations)
Equation of circle (*Draw if you don't understand the question)
Trigonometry R formula
The Hence concept (Differentiation & Integration combined)
Partial Fraction & Integration
Properties of Integral
Differentiation & Integration of exponential function and ln function
Differentiation: Eqn of Tangent & Normal
Coordinate Geometry
Equation of circle
Binomial Expansion
Linear Law

I would be expecting cross-chapters questions on Monday. Just like you, I'm a candidate so the above list is just my suggestion.

All the best for the final Maths paper. See you at the finishing line.

PS: Don't worry about bell curve! It's beyond our control!

A-Maths: Find Equation of Circle Given Tangent & Circle + More

Many students after reading the question take a long time to begin as they don't know how to start. The trick is to draw! Drawing helps us to see and understand the question better.

Drawing is one of the keys to answer this question. To answer part (a), we need to notice the property of radius is perpendicular to tangent. Also, in part (b) of the question, we need to apply discriminant from the topic of Quadratic.

I have shared my thinking process and step-by-step solutions in the following videos.

How did you find the videos? Did they help you to understand better? Leave me your feedback in the comment section.

Part (a) URL: Click here to watch part (a) 7 minutes

Part (b) & (c) URL: Click here to watch part (b) & (c) 5 minutes.

A-Maths: Application Question on Modulus Graph

Based on my observations on recent mid-year exams papers, prelims papers, it seems like many schools are setting highly application questions for many topics. In this post, I would like to share with you an example of how modulus graph can be tested by applying our basic concepts on equations of lines.

I have been reminding my students to keep their mind open to 'new - trend' questions which might require their fast thinking on the spot so we keep our mind flexible when we do our O-Level examinations.

I hope you learn useful concepts and thinking skills on this question. Do leave me a comment if you have any other questions.

A-Maths: Full Derivation of R-formula

Last week, I taught my class on the topic of R-formula in A-Maths Trigonometry.

I highlighted that schools taught the usage of the two formulas as shown:

In my years of teaching, I have also come across schools which have insisted students to understand and use the full derivation of R-formula to solve the questions. Last night, my student who was sure that her school did not teach full derivation contacted me to help her as she was told at the very last minute that full derivation of R-formula will be tested in her test.

I have included the step-by-step working here. It includes the usage of addition formula and identity formula.

For those who prefer to hear from my explanation, I have included the video (duration: 6 minutes).

I would love to hear from you if you understand how R-formula is derived. Leave me your comment below.

O-Level Maths December 2014 Revision Workshops

How will our Year End Revision Workshops benefit your child ?

The Year End Revision Workshops will get your child to gain the momentum and confidence to:

Revise comprehensively on key essential concepts on a topic – by – topic basis.
Gain a better understanding of the topics.
Apply concepts on application examination questions

We know it isn’t easy for students to accomplish all the mentioned by themselves, with distractions from Internet, handphones, TV, friends, going out, no interest in subject, almost totally giving up on the subject…

Basic Essential Concepts Workshop 2013

Here’s what we have to help your child:

Annual Year End Revision Workshops for GCE O-Level Additional + Elementary Mathematics:

Designed into workshops with a focused topic(s) coverage, including key essential concepts, application strategies, relationship linkage, easy-to-remember analogies for understanding abstracts.

Our lessons are delivered in an interactive manner: participants are encouraged to take part in questioning and answering in every workshop. This ensures your child learns effectively within the shortest period of time.

Mole Calculations Revision

How can we be sure that our Year End Revision Workshops will help your child?

She is also the invited book author for the latest GCE O-Level Ten Years Series (2004-2013) for Additional and Elementary Maths, Mentor Series for Secondary 3 and 4 Elementary Maths.
She is also a full-time professional trainer who has over 15+ years of teaching experience.
Ai Ling has also worked with thousands and thousands of students (& parents) from more than 160 schools.
Ai Ling is writer for popular academic website widely read by almost ten thousands of local and international readers every month. She also produces Math videos which are viewed almost 220,000 times.
Proven track record: In 2013, the average O-Level grade for Elementary Maths and Additional Maths is A2!
Ai Ling & his colleague Sean had been invited by CDAC , SINDA and Mendaki to conduct revision programmes and public talks for O-Levels.

O-Level Elementary Maths Ten Years Series Book Topical Ai Ling Ong 300 O-Level Additional Maths Ten Years Series Book Topical Ai Ling Ong 300 Elementary Maths Mentor 3 Cover Elementary Maths Mentor 4 Cover

"I especially enjoyed the functions and graphs workshop as I learnt many different ways to remember the shapes of curves. The workshop allowed me to gain confidence in handling the graph questions in the future. Besides, recaps in basics Trigonometry in E Math also allowed me to be more aware of concepts taught in school that I have get to grasp. I’d recommend anyone who’s unable to cope with studies to join Winners Education. Thank you Ai Ling!" Doreen Gan | Commonwealth Secondary

" The workshop explained challenging concepts in simple ways. Along with examples and a variety of questions that tested our understanding of the topic, this workshop helped me better understand the more complex chapters of math! " Nicholas Lam | St. Gabriel’s Secondary

Schedule for O-Level Revision Workshops

Maths Schedule