Chapter 8 - Triangles and Polygons

End of Year Examination 2010

1.         Format

·            2 Papers

·            Paper 1 – 60 minutes

·            Paper 2 – 1 hour 15 minutes

·            Calculator is allow for both papers

·            Students are required to bring along all necessary stationery inclusive of mathematical instrument sets

·            No borrowing of stationery is allow during the examination

2.         Topics tested

·            Chapter 1 – Factors and Multiples

·            Chapter 2 – Real Numbers

·            Chapter 3 – Approximation and Estimation

·            Chapter 4 – Introduction to Algebra

·            Chapter 5 – Algebraic Manipulation (Include Expansion of Quadratic expression, Use of Algebraic rules in Expansion and Factorisation of Quadratic expression, Factorisation of Quadratic expression using Cross-Multiplication method)

·            Chapter 6 – Simple Equation in One Unknown

·            Chapter 7 – Angles and Parallel Lines

·            Chapter 8 – Triangles and Polygons

·            Chapter 9 – Ratio, Rate and Speed

·            Chapter 10 – Percentage

·            Chapter 11 – Number Pattern

·            Chapter 12 – Coordinates and Linear Graphs (Include calculation of Gradient using 2 coordinates point, Equation of a straight line, y = mx + c)

·            Chapter 16 – Data Handling (Include Mean, Mode and Median)

Viva Voce Assessment 2010

Objective

The objective of the Viva Voce Assessment is to enhance students' problem solving skills and Mathematical communication abilities.

Students will be assessed based on the following 2 criterions

1) Problem Solving Skills and Strategies

2) Concept and Mathematical Communication

Format of assessment

1) Students are to download a list of questions from their Mathematics Google Site on the 8 October 2010.

2) The questions are divided into 3 Categories, namely, Speed and Time, Area and Perimeter, and General questions.

3) Students are required to choose 1 question from each category, work out its solution and video their explanation and solution of the question using Photo Booth.

4) Each video should be label as follows "Class-Index No-Question No" eg. 107-01-Q2

5) All videos are to be email to edmund_ng@sst.edu.sg by 10 pm on 10 October 2010 (Sunday) and the written solution to be submitted on 11 October 2010 (Monday).

6) Late submission will not be assessed.

Chapter 7 - Introduction to Angles Part 3

The diagram below shows a quadrilateral ABCD.

Prove that ABCD is a parallelogram. Input your solution / explanation in the Google form below.

Chapter 7 - Introduction to Angles Part 1

Quadratic Factorisation

Questions 2, 3 and 4 by Goh Chin Fan

Question 2:
Option D is correct.
A square and a parallelogram are quadrilaterals as they are both 4-sided.
Opposite sides of a square and a parallelogram are parallel:

Question 3:
The quadrilateral is a trapezium. A trapezium has one pair of opposite sides equal in length, which is the pair of lines that are not parallel to each other, and the other pair not equal in length, which is the pair of lines that are parallel to each other. It also has a pair of opposite angles that are supplementary.

Question 4:
No, I do not agree with the statement. The lines of a parallelogram are not of equal length, only the opposing lines are of the same length, while for the square, all lines are of equal length. Therefore I do not agree that all parallelograms are of equal length.

Question 1 by Elgin Low (the post below not named is also mine, please see the comment inside to determine question)

A rhombus is just a quadrilateral with equal length. It does not mean that the angles of the 4 sides have to be the same. However, a rhombus is not a square as that means that all rhombuses are squares. Squares are quadrilaterals with 90 degrees on each of its four sides. Rhombuses have different angles that do not for 90 degrees. They however, can have any random angle as long as all the angles equal to 360 degrees. A square can be a rhombus as its angles equal to 360 degrees, and its sides are of equal length.

My answer: all of the above are correct.

1. A quadrilateral is a figure with 4 sides. Both a parallelogram and a square have 4 sides exactly.
2. Opposite sides of a square and parallelogram are equal. This is proved on a square as all the sides are 90 degrees. For a parallelogram, proof that its sides are parallel, is that each pair of sides are all of equal length.
3. A trapezoid does have only 1 pair of parallel lines. It is a figure that has one pair of parallel lines of equal length, and 2 other sides with unequal length.

Question 4 by Elgin Low

Parallelograms are not squares. A square's sides are all equal while a parallelogram is not. Here is proof of it. As you can see, a pair of the sides of a parallelogram is 1.22m, while the other is 2m. This is not a square.

Question 1 - 5 by Marcus

Q 1 : I agree with the statement because a square may be a rhombus because, it has four equal sides, two pairs of parallel lines while a rhombus may not be a square because a square has 4 perpendicular corners which a rhombus does not have.
Q 2 : Options A, B, C and D are all correct. A is correct      (as you can see in the picture)
Q 3 : The figure is a trapezium. The two sides that are equal are the sides that are not parallel to each other, the sides that are parallel to each other is the sides that are not of equal length and in this way, the opposite angles will sum up to 180.

Q4 : Not all parallelograms are squares. Evidence : this definitely does not have four equal sides

Q5 : BFDE is a parallelogram because line BC and AD are equal, so when you draw a new line from B to E and D to F, those two are same in length and is parallel

Q2 (Continued)

Sorry for the double post. I only realised that I missed out a section of Q2 after I sent the email.

*Continued*

Q2

All of the statements are correct. Squares and Parallelograms are quadrilaterals as they both have 4 sides each. Opposite sides of Squares and a Parallelograms are parallel as the two lines never meet even if they go on forever. A Trapezoid only has one pair of parallel sides as the of the other pair  of sides if extended, will eventually meet each other. Meaning that a Trapezoid only has one pair of parallel sides.

eLearning Maths Activity 3 (Sean Phua Aik Han) Q1, Q2, Q4

Q1

A Square is a Rhombus as a Square has all the properties that a Rhombus has, two pairs of equal sides that are parallel to each other and that all sides are of equal length . However, all the angles in a Square are right angles (90 degrees). While in a Rhombus, the angles in it are not right angles (90 degrees). Thus, it can be said that a Square is a Rhombus but a Rhombus is not a Square.

Q2

All of the statements are correct. Squares and Parallelograms are quadrilaterals as they both have 4 sides each. Opposite sides of Squares and a Parallelograms are parallel as the two lines never meet even if they go on forever. 

Q4

No, I do not agree with this statement. Parallelograms do not have 4 equal sides, which is a property of a square. This alone makes it impossible for all Parallelograms to be a square. Unless it is a Parallelogram which has 4 equal sides, in which the shape would be called a Rhombus instead of a Parallelogram. 

Q1, Q2, Q4(Shawn Lim)

Question 1
A square is a rhombus because it fills all the properties of a rhombus. The square has two pairs of opposite sides that are parallel and all its sides are of equal length. A conventional rhombus is not a square because the angles of a rhombus are not right angles.

Question 2
I think that the statement D is correct. A square and a parallelogram both are four sided figures so they are quadrilaterals. The opposite angles of a square and parallelogram are equal so the opposite sides are parallelogram and a trapezoid indeed has a pair of parallel sides.

Question 4
Not all parallelograms are squares because not all sides of a parallelogram are equal and one of the properties of a square is that all the sides have to be equal.

Maths answers(Shawn Lim)

Question 2, 3 and 4 (Elgin Patt)

Q2. (All of the above)Quadriletral means 4 sided. So both a Square and Parallelogram have 4 sides.
Both the square and parallelogram have opposite sides that are equal.
A trapezoid has 4 lines, and only 1 pair is parallel.

Q3. It is a trapezium. If you add up the 2 opposite sides of a Trapezium, it would be equal to 180 degrees. Its top and bottom lines are also parallel to each other.

Q4. I do not agree with the statement. Parallelograms can have different lengths and can still be called a parallelogram. Whereas in the case of squares, they need to have equal lengths for all sides.

chuazongwei q1,2,4

question 1:

i think that the statement is justified, as a square has a equal length for each of its sides, and qualifies the requirements to be a rhombus. but a rhombus might not fulfill the requirements to be a square, like the requirement that all sides of the figure must be parallel in order to be a square.

question 2: 

i think that all of the answers are correct, as a trapezoid is indeed a four sided figure with only one set of parallel lines, while Squares and parallelograms are quadrilaterals as both have 4 sides each, and the opposite sides of a square and parallelogram are parallel, because as far as they go on, they will never meet.

question 4:

No. I do not agree with this statement as not all of the different types of parallelograms have equal length in each side, therefore it does not fufill the requirement to be a square

Question 1 by Liau Zheng En

I agree with the statement.

A square is a rhombus as all of its sides are equal and the sum of supplementary angles is 180°. But the rhombus is not a square as the angle of a rhombus is not always a right angle. The angle of a rhombus may differ.

Question 5 by Liau Zheng En

Question 5

Since the point of intersection is in the midpoint, the figure would already be divided equal, being that the side of the figure would be parallel. If a line is cut through form point E to point F, The parallelogram will form two parallelogram. The sides of the figure can then be concluded that they are parallel. Using the points noted down, it can be concluded to be a parallelogram.

Question 4 by Liau Zheng En

Question 4

I disagree with the statement.

A parallelogram has opposite sides which are parallel, similar to a square. The sum of the angles of both shapes are the same too. 

But the square has 4 equal sides, unlike the parallelogram which opposite sides are the same. The corner of a square is a right angle while the angle of the parallelogram differs.

                Square

                                  Parallelogram 

Question 5 by Dionne Choo

BFDE is a parallelogram as we know that AD is parallel to BC, so DE is definitely parallel to BF. Since BC and AD are of the same length, then BE and DF should be parallel too. Thus, BFDE is a parallelogram as it has 2 sets of parallel sides.

Question 4 by Dionne Choo

No. I do not agree with this statement. All parallelograms do not have equal sides, and so are not considered squares.

Question 3 by Dionne Choo

This figure is a trapezium. A trapezium has a pair of parallel sides, and one set of opposite sides are parallel but not equal. Also, there is a pair of opposite angles that are supplementary.

Question 2 by Dionne Choo

D) All of the above

Squares and parallelograms are quadrilaterals as both have 4 sides each.

The opposite sides of a square and parallelogram are parallel, because as far as they go on, they will never meet.

A trapezoid has only one pair of parallel sides, because the other pair is not parallel.

Question 1 by Dionne Choo

The statement ' a square is a rhombus but a rhombus is not a square' is justified. This is because the definition of a square is that all opposite sides are parallel, all sides are equal and adjacent sides are perpendicular. However, the definition of a rhombus is that all opposite sides are parallel and all sides are equal. Adjacent sides need not be parallel. So, a square is a rhombus, but a rhombus is not a square.

Question 1, 4 & 5 by Lim Hao Yang

Question 1

 

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

I agree with this statement.

The square and the rhombus share similar properties. Both the square and the rhombus has 4 equal side, opposites which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equals.

However, not all rhombi are squares. A rhombus may not always have right angles.

Question 4

All parallelograms are squares.

 

I disagree with this statement.

The parallelogram and the square share similar properties. Both the parallelogram and the square have their opposite sides of the same length, which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equal.

However, not all parallelograms are squares as the lengths of all 4 sides may differ.

Question 5

BFDE must be a parallelogram.

According to the picture, the length of BC and AD is x. So, the length of ED and BF must be 1/2 x. Since ED and BF are of the same length as are parallel, we can conclude that BE and DF are both parallel and of the same length.

Sun Jie Min

The earlier post was by Sun Jie Min

Activity 3 Questions 1,2,4

Q1: The statement is true. A rhombus has four sides with the same length. The opposite sides are parallel. A square has four sides with the same length, parallel opposite sides and four right angles.

Q2: Statement D is correct. Squares and parallelograms are quadrilaterals as they are polygons with four sides. Opposite sides of a square and a parallelogram are parallel as the adjacent angles are supplementary. A trapezoid has one pair of parallel sides as it has two pairs of supplementary angles. 

Q4: I do not agree with the statement. Not all parallelograms are squares. Parallelograms have two pairs of parallel sides. The opposite sides are of equal length and the opposite angles are of equal measure. A square has four sides with the same length, parallel opposite sides and four right angles. Parallelograms do not have four sides with the same length and four right angles. Thus, parallelograms do not necessarily have to be squares.

Question four by Tam Wai Hang

BFED has 4 sides, so it is a quadrilateral.

BF//ED and BE//FD

BF=ED and BE=FD

<BFE=<EFD, making the figure a parallelogram.

question 2 by Yeo Jun Jie

Solution to question 2:


Question 2
D) all of the above.

Squares and parallelograms have four sides, therefor they are quadrilaterals.
Squares and parallelograms have 2 sets of opposite sides.
A trapezoid has only 1 pair of parallel lines.

Question 3 by Yeo Jun Jie

Here is my solution to question 3.

The quadrilateral is a trapezium

Question three by Tam Wai Hang

The figure is a trapezium.

Question 5 by Yeo Jun Jie

Solution to question 5.

Question two by Tam Wai Hang

Answer: D) All of the above

Reason:

1) A quadrilateral has four sides. And both the parallelogram and a square fulfills that criteria.

2) Both the parallelogram and the square have parallel lines.

3) The trapezoid only has one pair of parallel lines while the other two sides are not.

Activity 3 by Yeo Jun Jie

Here are my solutions. I have put them together in a pdf file

Question 5 by Tang Wen Yue

The distances between lines BF and ED are constantly the half the distance between BC and AD,which means they are parallel.

BF and ED are parallel as they are on lines BC and AD,which are parallel.

That makes BFDE a parallelogram.

Question 3 by Tang Wen Yue

The quadrilateral is a trapezium

Question 2 by Tang Wen Yue

D )All of the above

Both a square and a parallelogram are quadrilaterals,both have 4 sides each

Opposite sides of a square and parallelogram are parallel,because a square is a parallelogram and the opposite sides of a parallelogram are equal

A trapezoid has one pair of parallel sides,because the other pair is not parallel and a trapezoid only has 1 pair of parallel lines

E-learning Activity 2 - Examples of Special Quadrilaterals at Home

Are all straight lines the same?

Straight lines are use to illustrate the linear relationship between TWO variables / unknowns.

We have also been creating straight lines using Geo-Gebra.

How do we differentiate one straight line from another?

What are some of the properties that will cause one straight line to be different from another.

A Thinking Question....

When 1 is divided by 1, the answer as we know the answer will be 1. Similarly when 2 is divided by 2, 3 is divided by 3 and 4 is divided by 4, we know that the answer will still be equal to 1.

However, is it true that when x is divided by x, the answer will always be 1? If not, when is x  divided by x not equal to 1?

Post your reply under the Comment Section.

Reflection on Solving of Linear Equations

Dear 107s,

We have started on with the solving of Linear Algebraic Equation last week.

Let us now do a quick recap of the important ideas that we have learn using the Wall Wisher.

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 107s,

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

Like English & Chinese, Mathematics is another form of communication between people and Algebra is an essential part of this language.

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

Golden Ratio and Architecture



The Golden Ratio and the Human Body

Chapter 16 : Data Handling Lesson 4

Dear 107s,

We are still looking at Statistics at the moment.

Often when we compare data, we heard about people comparing the MEAN, the MEDIAN and the MODE.

Thus what does this terms actually means?

Do an online search on the meaning of MEAN, MEDIAN and MODE and input the meaning under the comment section. Please also include in examples on how to determine the MEAN, MEDIAN and MODE in a data set.

Chapter 16 : Data Handling Lesson 3

Dear 107s,

Welcome back after the second round of Data collection along Clementi Ave 6.

Here are some of the tasks we are going to complete by today.

1) Uploading of data collected.

Please access the spreadsheet titled "SST 2010 Traffic Data Combined" through the Mathematics Google Site. Only the team member nominated for Data input during the last session can edit the table. The rest of the team members please helped to consolidate the data for your team mates.

2) Examples of Statistical Diagram (Bar Chart, Pie Chart & Line Graph) found in daily life

The wallwisher is an online Post-IT board.


Find one example of either a Bar Chart or a Pie Chart and another example of a Line Graph. Give a short descriptions on the diagram you have selected.

Chapter 16 : Data Handling Lesson 2

Dear 107s,

The job of data collection is definitely not an easy one. It requires detail planning and thinking.

Based on your experience today, I will like you to think about the following questions and post your responses under the Comment section.
1) What are some of the difficulties you have encountered today?
2) What some of things you could have done better?
3) How do you ensure that the data you collected is as accurate as possible?

Chapter 16 - Data Handling Lesson 1.2

Please refer to Introduction slides as shared with the class this morning.



Please pay close attention to the assessment requirement.

I have also put up the Data Collection Map for the class.


View 107 Data Collection Map in a larger map

Chapter 16 - Data Handling Lesson 1.1

Data Handling is a major part to the broad topic of Statistics.

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)

Introduction to Algebra Part 2

Dear 107s,

Please solve the following problem using both the Model Method and the Algebra Method.



Look at both of your solutions and consider what are some of the similarities and differences in both methods?

Introduction to Algebra Part 1

Dear 107s,

Please look through the presentation slide before we start our discussion on Algebra in coming week (8 Mar to 12 Mar 2010)

The History of Numbers (15 January 2010)

The use of numbers has started since the ancient time till now.

In your groups,

1) List out some of the Ancient Civilizations that have once existed in our world.

2) Decide on one Civilization that your group has listed out and carry out a research on the number system that was associated with this civilization.

3) Using a 5-slides Keynote presentation, develop a presentation that describe the development history of this set of number system, describe the number system and depicts digit from 0 to 9, the number 10, 100 & 1000.

4) Hence, develop a simple worksheet using Pages, which required your friends to convert numbers from your choice of number system to our present Hindu - Arabic number system. You should have 4 questions that involved a 2-digits number, 4 questions that involved a 3-digits number and 2 questions that involved a 4-digits number.

5) Please submit your presentation slide and worksheet by 25 January 2010.

6) Please acknowledge all information that the team has taken from the Internet. The method of acknowledgement is (a) The Title of the website. (b) The URL. (c) The Date and Time where the information was view.

The Need of Numbers (15 January 2010)

As an individual, consider

1) Why is there a need of having numbers?

2) When did the first use of numbers, based on your imagination, occur?

Please post your comment by 16 January 2010.

Review Assignment on 15 January 2010

Dear 107,

Please note that I will be conducting a review assignment in class on 15 January 2010.The topics involve are those you have come across during your PSLE.The review assignment will last for 30 minutes and please note that no calculators will be allowed for this assignment.

Your Expectation (12 January 2010)

Dear Class 107,

Welcome to a brand new year.Before we start our lesson, I will like you to think of the following questions as an individual.

1) What are your success / joys you have experienced in the learning of Mathematics in your primary school?

2) What are your fear / difficulties you experienced in learning Mathematics?

3) What are your expectation of me as a Mathematics Teacher?

12 January 2010 : Welcome to Class 107 Maths Blog

Dear Class 107,

Welcome to the Maths Blog for the class. Please become a follower of this blog as we will be using this blog for our discussion beyond curriculum. I have the following rules that I hope everyone in the class can observed.

1. Everyone must participate in the discussion.

2. No one shall put down another person on the blog.

3. Be respectful and responsible in your choice of words.

4. Use of proper English in your postings.