## Tuesday, September 21, 2010

## Tuesday, September 14, 2010

### Summary of today's maths lesson (14/9/10)

**For today, we recapped that:**

- (a+b)² = a²+2ab+b²
- (a-b)² = a²-2ab+b²
- (a+b)(a-b)=a²-b²
- x²+y² is NOT equals to (x+y)²
- x²+y² is equal to (x+y)²-2xy

**As for today, we learnt that:**

- 201² -402+1 = (201)² -2(201)(1)+(1)²

- 823² -177² = (800-23)² -(800-3)²
**Do not do this method.**

- All the above sums are called factorisation.
- In factorisation, there are four different methods (but we only learnt two of them today) — By common factors and perfect square.

**HIGHEST common factors,**which means

**ALL t**he factors must have the same common factors

**. NOT**only one or two of the factors.

## Monday, September 13, 2010

### Summary of Linear Equations

- What we had learnt from today's maths lesson (for the first 3, let p & q the x-intercepts)

- The roots of a parabola are the x-intercepts and right them in the proper way like (p,0)
- To find the y-intercept of the parabola, the person must find the result without the x in it such as from equation (x-p)(x-q) and the result from equation without the x in it is pq so the y-intercept would be (0,pq).
- To find the line of symmetry of the parabola, we must find the centre of the x-intercepts and the equations would be p+q/2.
- The way to expand equations, let the integer in a bracket multiply with the equation in the other bracket. eg. (2-k)(4+k)= 2x4, 2xk= -k(8+2k)=-kx4, -kxk= 8+2k-4k-k square= 8-2k-k square
- Equations needed to remember

- (a+b)square=a square + 2ab+ b square
- (a-b)square= a square - 2ab +b square
- (a+b)(a-b)= a square - b square

## Tuesday, September 7, 2010

### REMEDIAL SESSION ...

**Good morning everyone,**

**This is to confirm that we'll be having our remedial this THURSDAY (9th SEPTEMBER) at 0930 ... we'll meet in the LEARNING OASIS ... bring loads of writing paper and your calculator ... you would also need your LEARNING DEVICE in order to download the worksheet ...**

**Come prepared to work ... there is some issue with the notion of GRAPHS, its GRADIENT and the ALGEBRAIC PROBLEM SOLVING ...**

**JASON INGHAM**

## Sunday, August 29, 2010

### Summary of Maths Lesson(27 August 2010)

- convert all equations to y = mx + c
- Visualise the gradient; increasing/decreasing
- X-intercept= -c/m
- Y-intercept is when x=o
- Do working step-by-step to prevent error and careless mistakes
- Substitute the given values of x and y values into y = mx + c if two variables are unknown.
- Gradient

- It is the CHANGE IN Y-AXIS/ CHANGE IN X-AXIS
- Look at the slope; increasing or decreasing slope.
- Expansion of Quadratic Expressions:

- write in alphabetical order
- convince that (a-b)2 = (a-b)(a-b) using expansion
- answers can leave in improper fraction unless state the co-efficient of the term.
- reduce to simpler form
- decimal is also possible
- did (a+b)2, (a+b)3 , (a+b)4 and so on as practice

- a shortcut way of attaining answers for quadratic expansion.
- Co-efficient of the number.

## Wednesday, August 25, 2010

### new summary-tan kein shuen

2.the product of two linear factors will be the y intercept of its parabola.

3.we learnt that the line of symmetry is (a+b)/2.

4.question: why must both the two lines be parallel to each other to form a parabola?

## Tuesday, August 24, 2010

### Summary of Math Lesson (24/08/10)

## Friday, August 20, 2010

### Summary for the lesson (19/08/10)

1) If (a,b) lies at y=mx+c, then b=m(a)+c

2) Gradient is = rise divided by run = change in y coordinate divided by change in the x coordinate.

THE ORDER IS IMPORTANT

3) y - 1x +c (Coordinates 1,5 and -3,1)

To find c, you have to find x. It can go two ways;

Either you substitute the coordinates (1,5) and get

5=1(1)+c

=1+c

c = 4#

OR

1 = 1(-3)+c

= -3+c

.: c = 4

4) To satisfy an equation means to balance both sides of an equation.

## Wednesday, August 18, 2010

### Summary of Linear Equations

1) Discuss if there is an equation, when c is not the y intercept.

2) At y-intercept, x is 0

3) c is not always the intercept. For example, y= 1÷x + c. Therefore, the value of y is undefined when x=0 and c would not be the y- intercept.

4) x= -c÷m

5) m= gradient

= (change in y-coordinate) ÷ (change in x-coordinate)

## Tuesday, August 17, 2010

### SUMMARY OF LINEAR EQUATIONS ...

- Today we reconsidered the linear equation & the general form of a linear equation is y = mx + c
- where by the m refers to the GRADIENT
- where c is the Y-INTERCEPT (or the value of y when x = 0)
- m is POSITIVE when as x increases, y also increases
- m is NEGATIVE when as x increases, y will decrease
- m is ZERO when as x changes, y is constant (HORIZONTAL LINE)
- m is undefined when x is constant and y changes (VERTICAL LINE)
- X-INTERCEPT would be equal to -c / m ... (or the value of x when y = 0)

## Sunday, August 15, 2010

### Question 1 by Iskandar B Dzulkarnain

### Question 4 by Iskandar b Dzulkarnain

### Question 5 by Iskandar B Dzulkarnain

### Question 4 by Niloy Faiyaz

### Question 2 by Niloy Faiyaz

## Saturday, August 14, 2010

### Question 1,4,5

### Questions 1, 4 and 5 by Gavin Lim

4)No. The sides of a square must all be perpendicular to each other while the sides of a parallelogram may not be perpendicular.

1) A square is a rhombus as it has 2 pairs of parallel lines of equal length but a rhombus is not a square as the sides of a square must all be perpendicular to each other while the sides of a rohmbus may not be perpendicular.

## Friday, August 13, 2010

### Problem with posts below

Thanks,

Azeem Arshad Vasanwala

(Class S1 - 03)

School of Science and Technology, Singapore

### Question 1,2,4 by Gregory Chew

### Question 1, 2 and 4 by Azeem Arshad Vasanwala

### Questions 1,4 and 2 by Brandon Yeo

**Question 2:**

**Question 1:**

**'A square is a rhombus but a rhombus is not a square'.***-A square has 4 equal sides and all opposite sides are parallel to each other, just like a rhombus.*

*-However, A rhombus has*

*4 equal sides and all opposite sides are parallel to each other BUT does not have 4 right angles like a square.*

*That is why a*

**square is a rhombus but a rhombus is not a square.**

**D ) All the above**

**Question 4:**

**'All parallelograms are squares?' Do you agree with this statement?**

**No. The parallelogram's two pairs of opposites sides are not equal to each other. When a square is slanted to the side it forms a rhombus instead of a parallelogram.**

### Question 1, 2, and 4 by Goh Jin Hao

The statement is not justified as although all the sides of both the rhombus and the square are equal, the corners of a square must be exactly 90 degrees so a rhombus cannot be a square which makes the statement unjustified.

Question 2

D ) All of the above

Both squares and parallelograms are quadrilaterals as they both have four sides.

Both the squares' and the parallelograms' opposite sides are parallel as the other two sides are of equal length.

A trapezoid has a pair of parallel sides as it is made out of a rectangle and a triangle and a rectangle has a pair of parallel sides.

Question 4

I do not agree with the statement. A parallelogram cannot be a square as all corners of the square must be 90 degrees and all of the sides must be equal.

### Question 1, 2, 4 by Justin Ong

"A square is a rhombus but a rhombus is not a square".

A rhombus is a quadrilateral whose four sides all have the

same length.

However, a square has four equal sides and four equal right

angles at the corners.

If a square is turned into a rhombus, it loses its four

right angle corners. Therefore, it cannot be counted as a

square. However, if the rhombus is turned into a square, it

retains its length and still counts as a rhombus.

Question 2:

Which of the given statements is correct? Justify your

answers with examples.

A ) A square and a parallelogram are quadrilaterals.

Correct, because a square has 4 sides and 4 corners, and so

does a parallelogram.

B ) Opposite sides of a square and a parallelogram are

parallel.

For the square, it is correct as 4 corners are supposed to

be 90°.

For the parallelogram, it is also correct because even

though it does not have 4 equal angles, it still has 2 sets

of parallel lines.

href='http://img269.imageshack.us/i/trapezium.png/'><img

src='http://img269.imageshack.us/img269/5461/trapezium.png'

border='0'/></a>

C ) A trapezoid has one pair of parallel sides.

Correct as well, refer to diagram below.

href='http://img237.imageshack.us/i/squareparallelogram.png/'><img

src='http://img237.imageshack.us/img237/9694/squareparallelogram.png'

border='0'/></a>

D ) All the above

Question 4

"All parallelograms are squares?" Do you agree with this

statement?

I do not agree with this statement. A parallelogram refers

to a figure with 2 sets of parallel lines. However, a square

has 2 sets of parallel lines, 4 sides of the same length AND

must have the corner angles equal to 90° each. A rectangle

has 2 sets of parallel lines. However, it does not have 4

equal sides. Another example is a rhombus. A rhombus has 2

sets of parallel lines. However, it again does not have 4

corner angles, making it not qualify as a square.

### Re: Question 4 by Looi Wei Chern

My answer would be No as Parallelograms are squares only if all four sides are of the same length and all interior angles are 90^{o}.

### Question 4 by Looi Wei Chern

^{o}.

### Question 1 by Looi Wei Chern

` `__Question for discussion__

Based on the above conversation discuss, with examples and justification whether the following statement is justified.

'A square is a rhombus but a rhombus is not a square'.

A rhombus is a quadrilateral whose four sides are all congruent.

A square is a quadrilateral whose four sides are all congruent and whose angles are all right angles.

In other words, a square is a rhombus that is also a rectangle.

The above two quadrilateral are both rhombuses but the four sided, with vertex of 90 degrees is a square, not a rhombus:

### Question 3 by Looi Wei Chern

` `__Question for discussion__

Based on the above conversation discuss, with examples and justification whether the following statement is justified.

'A square is a rhombus but a rhombus is not a square'.

A rhombus is a quadrilateral whose four sides are all congruent.

A square is a quadrilateral whose four sides are all congruent and whose angles are all right angles.

In other words, a square is a rhombus that is also a rectangle.

The above two quadrilateral are both rhombuses but the four sided, with vertex of 90 degrees is a square, not a rhombus:

### Question 3 by Looi Wei Chern

__Question for discussion__

Based on the above conversation discuss, with examples and justification whether the following statement is justified.

'A square is a rhombus but a rhombus is not a square'.

A rhombus is a quadrilateral whose four sides are all congruent A square is a quadrilateral whose four sides are all congruent and whose angles are all right angles In other words, A square is a rhombus that is also a rectangle These are both rhombuses: +--------+ | | +--------+ | | / / | | / / | | / / +--------+ +--------+ But only this is a square: +--------+ | | | | | | | | +--------+

### Question 2 by Looi Wei Chern

**Question 2:**

Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

D is Correct.

Evidence for A) A square and a parallelogram are both quadrilaterals as the definition of a **quadrilateral** is a polygon with four **sides** and four **vertices** or **corners**. Thus, the following are all quadrilaterals, which includes squares and parallelograms:

Evidence for B) Parallel lines are two lines lying in the same plane but never meeting no matter how far extended as it can be clearer seen below in the pictures of the square and the parallelogram.

Evidence for C) Like I said above, the definition of parallel lines is two lines lying in the same plane but never meeting no matter how far extended thus from the diagram below, only DC and AB is parallel to one another but AD and BC are not parallel to one another thus the definition of a trapezoid simply means a four-sided figure with one pair of parallel sides.

## Thursday, August 12, 2010

## Tuesday, July 13, 2010

### 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 !!!

## Friday, July 9, 2010

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

## Tuesday, June 29, 2010

### Welcome Back for a New Semester

## Thursday, May 13, 2010

### Chapter 9.2 : Average Rate (Lesson 1)

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

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

## Monday, May 10, 2010

## Thursday, April 29, 2010

### Chapter 16 : Data Handling Lesson 4

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.

## Tuesday, April 13, 2010

### Chapter 16 : Data Handling Lesson 3

2) Let us now make use of an online sticky pad to search for more examples of Statistics Graphs in our daily life.

## Wednesday, April 7, 2010

### Chapter 16 : Data Handling Lesson 2

Congratulations on your completion of the first round of data collection.

Thus, I will like the class to reflect on your experience this morning.

Please post your reply under the Comments Section for the following questions.

1) What are some of the difficulties you have encountered during the data collection process?

2) What are some of the improvement you can make to the data collection process?

## Monday, April 5, 2010

### Chapter 16 : Data Handling Lesson 1.2

Thus what exactly is Statistics?

Please go through the 2 videos posted below.

Video 1

Video 2

Thus do you have a better understanding of Statistics?

In your own words,

1) Explain what do you think Statistics is all about?

2) How can you apply Statistics in your decision making?

Please post your reply under the Comment section by 9 April 2010 (Friday)

### Chapter 16 : Data Handling Lesson 1.1

Please pay close attention to the assessment requirement for this chapter.

## Thursday, April 1, 2010

## Friday, March 5, 2010

### Introduction to Algebra Part 2

### Introduction to Algebra Part 1

Please look through the introductory information below as we start our discussion on Algebra.

## Thursday, February 25, 2010

### Significant Figures

We have look at the Singapore Budget Report 2010 for a start.

Please post your suggestions under the comments section by Sunday (28 Feb 2010).