Category Archives: Weekly Question

E-Math: What is Direct Proportion and Inverse Proportion?

Proportion is a topic taught in Secondary 1 and 2. In fact, we have learnt about direct proportion much younger.


A real simple example of Direct Proportion would be the more money I have, the more things I can buy. When amount of money increases, the number things I can buy increase too. (Notice the increase in both things)

Another example, the less I eat, the thinner I become, so as the amount of food eaten decreases, my weight decreases too.


An example of inverse proportion most of you can relate to would be: the more time I spent on Facebook (PSP, WII, Internet), the less time I have on my books!

Allow me to add in another example of Inverse Proportion, the more I spent, the less I have in my bank.

These are some examples (simple) to understand the true meaning of Direct or Inverse proportion.

In the next post, I will be sharing with you how we can translate a statement into an equation involving proportion. I'm also going to highlight the 'tricky' proportion question in 2008 GCE O Level Elementary Mathematics Paper 1.

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A-Math: Differentiation & Integration Application : Examples of Typical Kinematics Questions

I was looking through 2008 GCE O Level Additional Mathematics Exam Papers (Subject Code: 4038) and as expected, there was a Kinematics question (worth 6 marks) in Paper 1.

Kinematics is a application topic for Differentiation and Integration. To master this topic, you do not necessarily need to bring in your physics knowledge though it could be useful at times.

Instead, how I get my students to be a master in this topic is to be familiarize with a KINEMATICS VOCABULARY LIST.

Here's some of the vocabulary words that are useful and common:

  • Momentarily at rest, instantaneously at rest, changes direction of motion, stationary
  • Initial displacement, initial velocity, initial acceleration
  • Greatest displacement, greatest velocity, greatest acceleration
  • Distance travelled in the 4th second VS Distance travelled in the first 4 seconds
  • Maximum distance from Point O
  • Particle returns to Point O
  • Constant Velocity

I would say for Kinematics, it is one of the few topics in A-Math which uses extensive vocabulary. This is also the reason for you to decipher the meaning behind these words.

So do you know the meaning behind these words? I would love to hear about it in the comments section.

I have also taken a few questions from my A-Math TREQ book(Topical Real Exam Questions) to illustrate some common exam questions on Kinematics, further highlighting the importance of knowing your Kinematics well. (Click on the image for bigger view)

Click on image for a larger view

I would be sharing the step by step solutions for Question 8 in the next post. Subscribe to my blog to be updated again!

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A-Math: How Do You Sketch A Modulus Graph?

Last Sunday while coaching my A-Math students on a question on Modulus Functions, we did solving of Modulus equation which is of no big problem as long as you get the basic concept correct.

|x| = x when x >= (more than and equal to) 0 or |x| = -x when x < 0

When we came to the next part of the question which involves Sketching of Modulus Graph, that's where the interesting happens.

Read about the Differences between Drawing and Sketching in this post.

When question involves sketching of graph, we usually do not need
- a table of values
- axis which are evenly marked out.

Sketching of Graph should however includes
- critical points (i.e x - intercept(s), y-intercept, turning point (if you are sketching a quadratic graph))

Let's take a look at the working of 2 different students:

Student A:

  • Sketch the modulus graph using table of values
  • Join up the points in a straight line manner

Student B:

  • Sketch the modulus graph using a series of 2 other graphs

Note the difference in the shape of the 2 graphs.

I certainly hope that my student A is convinced that using a table of values is not recommended for drawing modulus graphs. Moreover, many questions involving modulus could be that of Trigonometry graphs! So be like student B, draw modulus graph using a transformation of a series of graphs

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