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:

R-formula Trigonometry


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.

R-formula Trigonometry Full Working

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O-Level Maths December 2014 Revision Workshops

 EM Functions & Graphs

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 O-Level Elementary Maths Ten Years Series Book Yearly Ai Ling Ong 300 O-Level Additional Maths Ten Years Series Book Yearly 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

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2014 GCE O-Level Additional Maths 4047 Paper 1 Post Mortem

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 many small details that candidate should look out for. I was underlining these small details eg acute angles, exact value, in radians, the acute angle, x coordinate.

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
  • Logarithms
  • Sum & Product of roots
  • Factor Remainder Theorem (solving cubic equations)
  • Equation of circle (*Draw if you don't understand the question)
  • Trigonometry Graphs
  • Trigonometry Double Angle
  • Geometry Proof (Please know your congruent and similar triangles tests) 
  • Parabola & General shapes of graphs in the form y = ax^n (where n is a fraction)
  • Area under curve
  • The Hence concept (Differentiation & Integration combined)
  • Kinematics 

I would be expecting cross-chapters questions tomorrow. 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!

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