Summary of what we have learnt - T3 W03 (12 July - 16 July)

• When we are factorising expressions by grouping we need to take care of the signs ... for instance ... 1 + 2t - k - 2kt = (1+2t) - k(1 + 2t) ... the LEFT hand term (1 + 2t) is the same as 1(1 + 2t) ... hence, when we factorise the expression, there is a COMMON factor of (1+2t) ... leaving us with ... (1+2t)(1 - k) ... some of you have forgotten the (1) in the term (1 - k) !!!
• When we work with algebraic fractions, make sure that you FACTORISE both the NUMERATOR and DENOMINATOR !!!

Term 3 Week 2 - 5th to 9th July 2010

Most of the class can understand what was being taught today, but some still have doubts about the equation "undefined" .

QUESTION -

Why 2/0 is undefined when 2÷0=0?

Well, firstly, note that 2/0 is the SAME as 2÷0 & hence, it would still be UNDEFINED!

Anyway, if 2 ÷ 0 is possible, we will be able to see that

letting 2 ÷ 0 = x

0 ( 2 ÷ 0) = 0( x ) .................................................................... convince yourself that 3( x ÷ 3) = x

2 = 0

This is a CONTRADICTION and hence we can see that 2 / 0 is not POSSIBLE ...

Which means that if we have 1÷x, this would be UNDEFINED if x = 0.

QUESTION -

If we have 1÷(x+1), for what value of x would render this undefinable?

For 1÷(x+1), it will be UNDEFINABLE when (x + 1) = 0 ... that means that solving it would make x = -1 ... hence, when x = -1, the function will be undefinable ... Consider the GRAPH of the function y = 1÷(x+1) (using grapher), what do you notice at x = -1?

What about 1÷(2x-3)? Hence, what would be general concept be that would make the expression 1÷(ax+b), undefinable? Does this change if the numerator was something else?

Hence, for functions of the form y = 1÷(ax+b), the DENOMINATOR can never be equal to ZERO ... and this will happen when x = -b ÷ a ... CHECK TO SEE THAT YOU KNOW WHY???

QUESTION -

In order to solve 2x - 5 = 3, we need to find the value of x, that SATISFIES (we discussed this in class today) the equation. Hence, we will have to leave x alone on the left-hand side. That means, we need to remove the constant (-5) and the coefficient (2) ...

How can this be done? I believe that Zhi Qi has a slight issue with this.

Well, when 2x - 5 = 3, we need to REMOVE the 5 on the LEFT ... hence,

2x - 5 + 5 = 3 + 5 ... NOTE that we have ADDED 5 on both sides ... leaving us with 2x = 8 ...

removing the coefficient 2 requires a DIVISION

2x ÷ 2 = 8 ÷ 2 ... leaving us with x = 4 ...

Hence, the EQUATION is SATISFIED when x = 4

CHECKING ... 2 (4 ) - 3 = 5 when is the same as the VALUE as provided in the question!

QUESTION -

When you're trying to SOLVE equations involving algebraic FRACTIONS, what is the general principal involved for questions of this form?

The general principal is to ensure that only 1 fraction is present on both sides of the equal sign!

Welcome Back for a New Semester

Dear students,

Welcome back to school after your June Holidays.

Let us start the new semester with this task.

Under the comment section, post up

1) 1 interesting thing you have done / see during the June Holidays.

2) 1 interesting knowledge that you have learn during the June Holidays.

3) The expectation that you are going to set for yourself in the learning of Mathematics.

Chapter 9.2 : Average Rate (Lesson 1)

Rate is a ratio between two quantities with different units of measurement.

Rate allows us to express a quantity as a proportion of another quantity thus enable us to make comparison between different quantity.

Examples of rate being used in our daily life are:
1) Speed of a car, where the distance is measured against time (Kilometer per Hour or Meter per Second)

2) Buying of food and drink, where the price is measured against the weight or volume (Dollars per Kilograms or Dollars per Litres)

3) Frequency of Buses (Number of buses in operation per Hour)

4) Heart Rate (Number of beat per Minute)

The examples of rate in our daily life in countless.....

Thus give 2 examples of the use of Rate in your life and briefly describe how you can make use of these information to help you make better decisions in your life.

Please also refer to your Textbook 1B from Pg 9 to 11 and your Ace - Learning Portal for more materials and examples.

Chapter 5.1 : Like Terms and Unlike Terms

Dear 103s,

We are back into our study of Algebra....

Like English & Chinese, Mathematics is another form of communication between people and Algebra is part of this big family....

Thus, let us now get to find out more about the Algebraic Language...

The Algebraic Language

How to Understand the Vocabulary Of Algebra

Chapter 9.1 : Ratio

The Golden Ratio in Human Body

The Golden Ratio in Architecture

Chapter 16 : Data Handling Lesson 4

Dear 103s,

Welcome back from Common Test.

We are still in our study of Statistics.

Often we hear others compare a group of data using the MEAN, the MEDIAN and the MODE.

But what exactly is MEAN, MEDIAN, MODE?

Do an online search to find out about the meaning of MEAN, MEDIAN and MODE.
Post your findings under the Comment Section.
Please also include in examples on how you determine the MEAN, MEDIAN and MODE of a data set.