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!

2015 GCE O-Level Elementary Maths 4016 Paper 1 (Post Mortem not Solutions)

I have just completed the 2015 GCE O-Level Elementary Maths 4016 Paper 1 and found it to be more applications based.

Some questions are indirect and required more analysis. Some of the questions I enjoyed doing were:

  • Mode, median and mean
  • Mean and standard deviation
  • HCF and LCM
  • Coordinate geometry linked to vectors
  • Matrix

Once again, just like last year, there are about 2-3 questions which are 5 marks. (If I remembered correctly)

Based on what were tested, we are logically make some guesses of what we are expecting in Paper 2. The following topics are what I'm suggesting and they are for reference only:

  • Indices
  • Proportion
  • Quadratic equations & graphs (Skill: completing the square)
  • General shapes of graphs
  • Everyday Maths (Compound interest, simple interest, hire purchase, exchange rate, taxation, utilities, profit and loss)
  • Proving of congruency and similarity
  • Angle & symmetry properties of circles
  • Trigonometry (sin rule, trigo ratio of obtuse angle, angle of elevation or depression, shortest distance, area of triangle formula)
  • Vectors
  • Cumulative frequency (includes frequency table), box & whisker, stem & leaf, dot diagram (Concept on lower quartile, upper quartile)
  • Kinematics
  • Mensuration

Regardless of how you think you have fared for Paper 1, continue to work hard for Paper 2 which is 2 days away. Practice daily!

All the best!

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

Equation of Circle Qn






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.

modulus graph

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