singaporeolevelmaths
Simple Tips for Better Maths Results!
Do you know that roots of a quadratic equation can also mean the solutions, the x intercepts or simply put it the answers to the equation?
It is something we have learnt since lower secondary.
In 2019, GCE O Level Additional Maths Paper 2 Q10 tested candidates on their basic understanding of roots.
11 marks! Wow!
If you have been simply surface learning, you won't get past part (i) of the question.
See the video to see how I approach this question: https://www.youtube.com/watch?v=CPtbpO4At9w
I am selecting unique questions from 2017 GCE O-Level Additional Mathematics to discuss in my upcoming videos.
This first one is on linear law.
Basic concepts that you must know are:
In this video, I share with you a strategy I teach my student to make linear law easier to understand and reduce careless mistakes to a minimum. I called it "Capital Letter". I use capital letters to represent the complicated horizontal and vertical axes. Even my equation of line is in capital letters too.
Look at my video to understand my thinking process and apply it to yours when it's your turn to solve a linear law question.
This question is interesting as we do not have to draw the graph which is commonly asked in the past.
This question will cause your downfall if you are not absolutely clear on the concepts of linear law.
httpv://www.youtube.com/watch?v=wmYj8pu6-dc
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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
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.
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.
For many Secondary 3 A-Maths students, this topic called Factor - Remainder theorem or Polynomials is usually introduced in the first 3 months of the year.
In this topic, they are introduced to the method to find the factors of a cubic equation so that it can be solved. They also learnt when and how to use Remainder theorem to find the remainder when a dividend is divided by a divisor.
They also know to rewrite an expression into function f(x).
In the following two videos, I use less than 6 minutes to bring across the concepts of Factor theorem and Remainder theorem.
I hope through these videos, you will have a better understanding of these two concepts.
Also, I have included a page which contains all the O-Level Maths videos I have produced since 2007.