modulus graph

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-Math: How to Sketch Modulus Graph [video]

Modulus Graph Sketching_Page_01

This morning, I received an email from a student on asking how to draw a modulus graph with and without boundary condition.

What is boundary condition?
It is usually the range of values of x (otherwise known as domain) for the graph.

Though I have written a similar post in 2009 here, I feel that a video will show you clearly the step by step and important points to consider. Note that my drawing isn't perfect, afterall it's a freehand draw on my tablet, so you got to bear with my 'not so straight' lines :)

The video is about 7 minutes long. Around 6min 30s, I've included a bonus question to challenge yourself. Go ahead and answer it on the comment section.

Click here to view the video: http://www.youtube.com/watch?v=eTdo_zK9XLk

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