Saturday, February 6, 2010

WELCOME TO OUR REVISION FORUM

WELCOME RANG AODHÁN!!!!!

Well lads, welcome to your blog! This is the first time I have ever tried writing a blog and I really hope you find it helpful. The blog supplements our last 3 classes during which we revised Theorems 1 - 7.
It is the first time that lessons have been supported with online resources in this way.
Please remember that one of the 7 Theorems revised here will appear in your Pre Junior Certificate exam next week. Below, I have explained exactly what's contained in the blog - please make use of all the resources available. All the best in your preparations for the exams and I hope this blog helps with your studies.



So whats in this blog?

This blog is divided into 6 sections:

1. This introductionary section which explains what the blog contains

2. Lesson 1 which covered Theorems 1,2 and 3.

3. Lesson 2 which covered Theorems 4 and 5.

4. Lesson 3 which covered Theorems 6 and 7.

5. A quiz section which provides 3 distinctly different methods of assessment. There is an interactive quiz for you to complete based on these Theorems, a very good Powerpoint question page assessing these Theorems and a third timed quiz based on the Theorems.

6. A final section which provides examination specific resources including:

  • past examination papers
  • solutions and a detailed marking scheme for the papers
  • The layout of each maths paper


How will this blog help you?

It will do so in many ways! After a review of each theorem, I have provided a link to the following resources.....

  • A Powerpoint Presentation of each Theorem
  • A second (interactive) presentation of each Theorem
  • Background information on Alternate Angles, Corresponding Angles, Congruent Triangles etc
  • Revision questions after each Theorem
  • Detailed, worked solutions of each question
  • A link showing a stunningly handsome teacher teaching each Theorem !!!!

So the very best of luck, hope this blog helps, study well and talk soon lads.

Friday, February 5, 2010


LESSON ONE


Topics revised during the lesson:
~ Theorem 1
~ Theorem 2
~ Theorem 3

Resources used during todays class

  • The Interactive Powerpoint Presentation of the Theorems. Click HERE. Then simply click on Theorem 1, 2 or 3 where appropriate
  • The Geogebra interactive construction of Theorem 1. Click HERE.(*** When finished, click the back arrow to return to the blog. Do not click exit***)
  • The Geogebra interactive construction of Theorem 2. Click HERE.
  • The Geogebra interactive construction of Theorem 3. Click HERE.
  • The quiz which you completed is contained later on in the blog. It is linked in the link entitled 'Quiz 1'

The homework sheets which we reviewed today are contained below. Revise todays lesson by using this blog and complete the homework sheets below in your softback copy. Check the detailed solutions given within this blog

  • Question sheet one. Click HERE
  • Question sheet two. Click HERE
  • Question sheet three. Click HERE



THEOREM 1

Theorem 1 proves that

"Verticially Opposite Angles Are Equal In Measure".


About Theorem 1
Theorem 1 is the shortest and most basic on the Junior Cert Higher Level Course. Although it has never actually been directly asked in the Junior Certificate, it certainly could be so please don't ignore it. It is relatively easy so do revise it properly.


Second powerpoint presentation of Theorem 1
Click HERE to view a powerpoint presentation of Theorem 1. This template must be followed whenever you are proving Theorem 1

Video clip of Theorem 1 being taught

To see a stunningly handsome teacher teach Theorem 1, CLICK BELOW. And no laughing!!!


Further presentation of Theorem 1
Click HERE to see a different view of the Theorem. Simply click the red arrow to progress the presentation.

Solutions to Homework sheet 1 based on Theorem 1

Click HERE to view the solutions to the theorem 1 questions


THEOREM 2

Theorem 2 states that

"The measure of the three angles in a triangle add up to 180"


About Theorem 2

Theorem 2 is relatively straightforward but is not as easy as first glance might indicate. Please view the resources available here and play particular attention to the section explaining 'Alternate Angles'. An understanding of these is necessary within this theorem.

Background information relevant to Theorem 2

Please click HERE to see background information relating to Alternate angles and Corresponding angles. This is important to understand Theorem 2

Revision Presentation of Theorem 2

Please click HERE to view Theorem 2 displayed in Powerpoint format. This template is to be followed whenever you are proving Theorem 2.

A practical exercise based on Theorem 2

Click here for a practical exercise based on Theorem 2. Please only do this if you have time and have utilised the remaining revision aids on the blog

Solutions to homework sheet 2 based on Theorem 2

Click here to view the solutions to the revision questions on Theorem 2. Solutions are explained thoroughly so please read carefully.

Theorem 2 being taught

Click below to view Theorem 2 being explained in a lesson.

http://


THEOREM 3

Theorem 3 states that

"The Exterior Angle of a Triangle is Equal in Measure to the Sum of the Measures of Two Interior Opposite Angles"

About Theorem 3

Theorem 3 is very basic indeed. Very little background knowledge is required but still, it must not be overlooked when studying the Theorems section of the course.

Revision Presentation of Theorem 3

To view a Powerpoint Presentation of Theorem 3, please click here. Please follow the template shown whenever you are asked to prove theorem 3

A second presentation of Theorem 3

To view Theorem 3 presented in a different manner, click here.

Solutions to Homework Sheet 3

To view the solutions of the Homework questions, please click here. Revise these solutions carefully.

Theorem 3 being taught

To view Theorem 3 being taught, just click below

http://

Funny maths clip 1!!!!

Here's the way maths should be done lads. Click here. Afterwards, click to go back to the blog - dont click to exit

Thursday, February 4, 2010

LESSON TWO


Topics covered during today's class-

~Theorem 4~

~Theorem 5~

Review of the teaching material used in class

  • Powerpoint Presentation of the Theorems used in class. Click HERE. Then simply click on the relevant Theorems.
  • The quiz which you completed in class is contained in the final section of the blog. It is saved in the link entitled 'Quiz 2'

Homework for tonight. Complete each sheet in your copy remembering the quality, careful layout emphasised in class.

  • Homework sheet on Lesson 2. Click HERE

Revision Resources on Theorem 4
Theorem 4 states that

"In an Isosceles Triangle, the Equal Sides are, respectively, equal in measure"


About Theorem 4
Theorem 4 is the first Theorem whose proof involves Congruent Triangles. Please view the supplementary material on Congruent triangles before looking at the Theorem proof.

Congruent Triangles
It is vital you fully understand all about Congruent Triangles. They are extremely popular as a full question in The Junior Certificate Examination.

Please click here to view revision material on Congruent triangles. There are also worked questions for revision purposes.

Interactive Presentation on Congruent Triangles

To view the interactive presentation relevant to this Theorem, click here

Powerpoint Demonstration of Theorem 4

To view a second Powerpoint Presentation of Theorem 4, please click here. Please follow the template shown whenever asked to prove Theorem 4.

Lesson covering Theorem 4

To view Theorem 4 being taught, click the link below

http://

THEOREM 5

Theorem 5 states that

"The Opposite Sides and Opposite Angles of a Parallelogram are Equal in Measure"

About Theorem 5

Again, Theorem 5 involves proving that two triangles are congruent. It would certainly be no harm to revise Congruent Triangles. This you can do in the next section below.

Revision of Congruent Triangles

Another revision of Congruent Triangles is contained here.

Interactive presentation of Congruent Triangles

To view the interactive presentation relevant to this Theorem, click here

A second Powerpoint Presentation of Theorem 5

To view another Powerpoint Presentation of Theorem 5, please click here. Please follow this template whenever asked to prove Theorem 5.


A step by step analysis of Theorem 5

This section presents Theorem 5 in a step by step manner (simply click the red arrow inside). Please click here to access.


Associated Constructions

The Constructions alluded to in class are often asked in conjunction with this Theorem. To view them, click here

Wednesday, February 3, 2010

LESSON THREE

During todays lesson, we covered the following topics:
~Theorem 6~
~Theorem 7~
Resources used during todays lesson
  • To view the Powerpoint presentation of Theorem 6 and Theorem 7, click those theorems in the following link. Click HERE
  • The Geogebra Interactive Construction of Theorem 6. Click HERE. (***Please click the back arrow to return to the blog - do not press the exit button***)
  • The Geogebra Interactive Construction of Theorem 7. Click HERE.
  • The quiz reviewed towards the end of the class is linked in the final section of this blog and saved as 'Quiz 3'
  • Tonights homework sheet. Click HERE Solutions are further down the blog.

Theorem 6

Theorem 6 states that

"The diagonal of a Parallelogram bisects its area"

About Theorem 6
Theorem 6 is one of the most basic theorems on the course. It involves a straightforward proof that two triangles are congruent. Therefore, I have included a review of Congruent triangles below for your convenience.
Review of congruent triangles
If you wish to review the theory behind Congruent Triangles, please click here.
Interactive presentation of Congruent Triangles
For an instructional presentation relevant to this Theorem, click here
Powerpoint Presentation of Theorem 6
To view a Powerpoint Presentation of Theorem 6 please click here.
Second presentation of Theorem 6
To view a second Presentation of Theorem 6, please click here. (** when exiting, close current tab only**)

An extra question on Theorem 6 for you to try when revising
To see a very typical examination question on the theorem (and quite a difficult question at that!!) click here.
Worked solution to the extra question
To view a worked solution to the extra question, please click here.
Videoed lesson showing Theorem 6 being taught
To view this video, click on the screen below.




Theorem 7
states that
"if a line touches a circle at point t and is perpendicular to the diagonal of the circle at point t, then it is a tangent to the circle at that point"
About Theorem 7
Theorem 7 is quite a complex theorem and one of the most difficult which we have studied. It is, however, a very popular theorem in the Junior Certificate so please know it backwards!
A Powerpoint Presentation of Theorem 7
To view a second Powerpoint Presentation of Theorem 7 please click here. Please follow the template shown whenever you are asked to prove Theorem 7
The interactive presentation of Theorem 7
To view this presentation, click here
Further important information on Theorem 7
For further information on this Theorem presented in an interactive manner, click here
Worked solution to tonights homework
To view a worked solution to the homework, please click here. (Please note that the solution covers 2 slides)

Tuesday, February 2, 2010

ASSESSMENT BASED ON THEOREMS 1 - 7

ASSESSMENT BASED ON THEOREMS 1 - 7

In this section, we will assess our learning so far. Below I have prepared three seperate quizzes.
1. A quiz which requires you to draw diagrams from information given, mark in information and use your work to answer questions. Detaild solutions are given
2. A quiz which is timed. It is based on the theorems we have covered.
3. A traditional quiz which is quite difficult and examines the material in quite an amount of detail

QUIZ ONE
This quiz is quite short but requires you to draw your own diagram from information given. Worked solutions are given to each question. Try Quiz 1

QUIZ TWO
So lets see how fast you can do this quiz ..............
Try Quiz 2

QUIZ THREE
This quiz is more like the type you are used to. It covers the Theorems but is quite challenging. If you know the material on this quiz, you will be fine in the Junior Certificate
Quiz three


RESOURCES RELEVANT FOR THIS SECTION OF THE COURSE

Now that you have revised the Theorems, lets see the type of questions which have been asked in the past. While we are at it lets look at the Junior Certificate maths paper as a whole. In this section we will:
  • look at the layout of the Junior Certificate maths paper
  • look at past exam papers
  • look at solutions and marking schemes for these papers
  • look at each theorem on the Junior Certificate course presented in interactive, powerpoint form

REVIEW EACH THEOREM IN A QUALITY, INTERACTIVE, POWERPOINT PRESENTATION

To view all theorems in an interactive, powerpoint form click here.

To view a link to online Theorem lessons in addition to a 'dictionary' type explanation of all Theorem related terms, click here


Layout of both Junior Certificate maths papers
For an overall view of both maths papers, please click here.

Past Junior Cert maths papers
To view past exam papers, please click below.



Solutions and marking scheme of the papers
This information is very beneficial as it shows where marks are awarded and lost. To view the marking scheme, please click below

Post a comment on your 'class discussion forum'!!!

Simply click the link below to join in on the discussion forum

http://www.colaistechoilmteachers.org/moodle/mod/forum/view.php?id=35

Wednesday night grinds - work to complete for Christmas

Algebra

2007 Paper 1 Question 3

Quadratic graph

2007 Paper 1 Q5 (b) & (c) ..... look up part (c) in revision book (p 53)

2007 Paper 1 Q6 (c)

Area and Volume

2007 Paper 2 Question 1

Coordinate Geometry

2007 Paper 2 Question 2

Ststistics

2007 Paper 2 Question 6

Please give this work your very best. If you require help with the work, please let me know. Otherwise, have a mighty holiday and I will see you in January.

Take care,

Marc