singaporeolevelmaths

Simple Tips for Better Maths Results!

straight line graphs

E-Maths: General Equation and Graphs of Line

Line is part of us, in almost everything you see.

You must understand

  • what equation of line is,
  • how to find gradient,
  • how to find the x and y intercepts,
  • what's the relationship between a pair of parallel lines, (perpendicular lines are out of syllabus for E-Maths 4016)
  • how to write the equation of line given the diagram and lastly,
  • how to draw a line.

Do you love this topic on straight lines? Leave me your thoughts and reasons for your love/hate relationship toward lines.

Maths Tuition Centre Singapore

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

Linear Law,Just 1 Strategy Makes A Grade Difference

What is Linear Law?

It is a tool which will allow you to transform non-straight line equation to straight line equation so that you can plot a straight line. Most of the time, the axis will consist of x and/or y

One of the techniques involving taking lg (log base 10) on both sides of the given equation.

linearlawquestion1.PNG

Common Mistake! STOP
y=Ax^b=>lgy=blgAx=>blgA+blgx

This is one of the common mistakes I have highlighted in Top 7 Commonly Made Mistakes in Logarithm

How To Counter This Mistake

Very simple. Just add in a bracket on the right hand side of the equation.
y=(Ax^b)<br> =>lgy=lg(Ax^b)<br> => lgy=lgA+lgx^b<br> => lgy=lgA+blgx<br>

Now, your y-axis will be lg y and x-axis will be lg x. Gradient = b and y-intercept = lg A

What Is The Difference Between Sketch And Draw?

It is important to know the difference between Sketch A Graph & Draw A Graph.

Sketch ==>

  • On foolscap paper
  • Best Representation of the graph
  • Less time as it reflects only the general shape of the graph.

Draw ==>

  • On graph paper
  • Accurate representation of the graph
  • More time needed as it usually involves more points on the graph
  • Curve rule/french curve is usually required.

Example:

Sketch y=-3x+1

What I will do :

  1. Find x-intercept (i.e. set y = 0)
    x=\frac{1}{3}
  2. Find y-intercept (i.e. set x = 0) y = 1
  3. Put the 2 points on the axes I have drawn on foolscap, join the 2 points, label the line.

Draw y=-3x+1

  1. Set up a table of 3 values of x choosen randomly i.e x = -1 , 0, 1
  2. Find out values of y for each value of x by substituting into the equation of the line.
  3. Plot the points on a graph paper accurately.
  4. Join the 3 points, label the line.

Good in straight line? You might want to check out how you can draw Exponential Graph here even with NO Math knowledge.