Transformation of Functions

This is a useful topic as it brings a lot of ideas abut patterns, equations, functions, tables and graphs together.

All the transformations can be studied here. 


Also, make sure that you know how to get the roots of a quadratic equation from the graph. this is often included in the same question.

_

Mocks 2015

You can find the marks per question here.

The general topic of each question is listed below - use this to check the areas that need most work. The exact number of questions and the order of topics can be exected to change from year to year.

Paper 1
1	Number
2	Sets
3	Sets
4	Algebra
5	Compound interest type
6	Quadratic
7	Speed
8	Simultaneous
9	Inequalities
10	Pythagoras
11	Length
12	Subject of Equation
13	Linear Pattern
14	Quadratic Pattern
15	Functions
16	Quadratic Graph
Paper 2
1	Length, Area etc
2	Stats
3	Probability
4	Statistics
5	Trigonometry
6	Geometry triangles
7	Counting  and %
8	Trigonometry
9	Coordinate Geometry
10	Transformations
11	Theorem
12	Construction

_

Co-ordinate Geometry Part 1
Worksheet - remember to find the hypotenuse you will need to use the theorem of Pythagoras. Spend a bit of time on question 1-3 it will help you to understand some of the ideas in co-ordinate geometry. You will find the applet for Q.3 here. Although you have the formulas in the tables it is very important to know where to find them, which ones you need to use and how to use them. Some notes and questions on co-ordinate geometry are available here.

Earlier this year you did an exercise on the equation of a line. The last part of the revison worksheet is on the equation of a line - remember that there are two formulas for the equation of a line in the maths tables - make sure that you use the right one. some answers for Q1-3 are here and the answers to Q4 to 6 are available below as a pencast.

Equation of a line worksheet Q.4 to Q.6
brought to you by Livescribe

_

Circle Theorems

Play around with these so that you become familiar with the different shapes and patterns.

Interactive animations on circle theorems and corollaries.

Four things to know about angles and circles.

1. The angle at the centre is twice the angle on the circle that marks out the same arc - the diagram below shows different examples of this.

2. Angles  standing on the same arc are equal.

3. The angle in a semi-circle is a right angle (the angle on a diameter is a right angle).

4. The sum of the opposite angles in a cyclic quadrilateral is 180.

_

Numberphile

Root 2 - Numberphile Paper size and irrational numbers

Beautiful Card Trick - Numberphile 

Numbery Card Trick - Numberphile

 Pythagoras and Irrational Numbers from Vi Hart (also drawing snakes and stuff)

_

Sample Answer Using Chomp

2013 Paper 2 Sample Paper Click on each image to see the question, read it carefully then close it and watch the solution, don't forget to make the video larger so that you can see the writing.

Q.1 (a)

Video of Solution

(b) 

Video of Solution

(c)

Video of Solution

(d)

Video of Solution

(e)

Video of Solution

3rd Year Junior Cert

Probably the most important advice is to really read the question carefully - there can be a lot of writing and students often misinterpret the question. Make sure that you clearly identify what the question is asking you to do.

Read (and heed!) the advice on pages (iii) to (v) of your exam papers. Also see the instructions for students e.g. on p.2 of your exam papers.

Below is an outline of topics on Paper 1 and 2 and how they relate to the chapters in your book.

The Maths course is divided into 5 Sections or Strands and the content is divided between the two papers as shown in the table. However, a question may require knowledge or skills from more than one strand. See below table for examples.

  

Paper 1	Topic	Chapter in book
	Number	1 Sets 2 Number Systems 9 Indices 10 Applied Arithmetic 11 Speed and Time
	Algebra	4 Patterns 5 Expressions 6 Factorising 13 Algebraic Fractions 14 Changing Formulae 15 Linear Equations 16 Inequalities 17 Quadratic Equations
	Functions	22 Graphing functions See also Chapters 30, 31 and 32 in Book 1
Paper 2	Topic	Chapter in book
	Probability	3 Counting and Probability
	Statistics	8 Statistics
	Applied Measure	12 Area and volume
	Geometry	7 Constructions 18 Geometry 19 Formal Proofs 20 Co-ordinate Geometry
	Trigonometry	21 Trigonometry

Probability on Paper 2 may require you to draw a Venn diagram. Algebra may be used in lots of questions for example Area or Trigonometry on Paper 2. These are just some examples – prepare to be flexible in your approach.

_

Manipulating Formulae

In a formula like that for speed we can say that speed is the subject of the equation because the formula tells us what speed is. We can rearrange or manipulate the formula so that either distance or time is the subject of the equation. See image below.

Instead of asking you to make distance the subject of the equation you may be asked to express distance in terms of speed and time. In the Khan Academy videos they say solve for distance. These all mean the same thing.

These videos and exercises are quite short and are worth working your way through them. 

Remember:

1. Anything you do to one side of an equation you must do to the other.
2. Be able to identify how many terms an equation has.
3. When multiplying or dividing an equation each term must be multiplied or divided.
4. If the letter that you are looking for is in more than one term then you need to bring these terms together and then factorise.
5. In the video Sal says "cancelling" - What he means is "divides into once".

There are some more examples done as a pencast below.

Subject of Equation 1
brought to you by Livescribe

_

Long Division in Algebra

This can be tricky, it is not just the method students find difficult - it is easy to make simple mistakes. Be especially careful when subtracting.

Don't spend too long on this topic, it is only a small section of your course.
Note: A polynomial is an algebraic expression with 2 or more parts with different powers of x (or an x term and a number).

Dividing polynomials 1: Dividing polynomials 1




The second example is about as hard as they get!



How does she write backwards so well!

_

Census at School 2M 2014-15

 2^nd Year Census at School Report

There is a copy of the questions here and your data here, it is probably easier to work with the file if you download the file. When it opens click File and Download to save a copy of the file.

What you need to do
Write a report on your class based on the data you collected for Census at School. Include the following.

• Describe the results for your class (you do not have to do every single question). Use words like Mean, Median, Mode, Minimum, Maximum, Range etc
• Include at least one of each type of chart, you can draw these or use a computer to create them.Line plot, pie chart, bar chart, stem and leaf and histogram.
• Describe a typical girl in your class.
• Deadline Wednesday 5^th November 2014 - Marks 10% Christmas grade 

The world's most accurate pie chart!

Sets - 3 Set Problems

There are a number of questions and partial solutions in this document. It is important that you try these yourself, if stuck look at the solution and then finish it.

_

Pythagorean Theorem

Pythagorean Theorem - notes and examples. These animations show demonstrations of the Pythagorean theorem - they are visual proofs. 

There are more examples and questions to try from Project Maths here. Note how the answer is written out - this is how you should write your work (at least three or four lines).

with this online calculator you can enter values and check your answers.

Click on the picture to see this turn

Angry Surds - this is a great game. You can practice the Pythagorean Theorem, Arithmetic and Surds all at the same time.

The Pythagorean theorem is very important in maths - you will use it regularly all the way up to sixth year and possibly beyond! Make sure that you have a full understanding of it.

_

Sets - Activity Book Solutions

3rd Year Sets Activity Book 2 Solutions

Exercise 1.2

Exercise 1.3

Exercise 1.4

Exercise 1.5

_

Indices for 3rd Years

Make sure that you understand the work covered in second year. 

Summary for third year.

_

Fractions

If you have difficulty with fractions you could try working through the videos and activities at Khan Academy.

You could start with these lessons on ordering fractions. If you sign in you can gain points and track your progress, check your emails for more information - search in your emails for Khan Academy.You could then try adding and subtracting here, then multiplying and finally move onto division. There is an entertaining approach to fractions here! 

_

2nd Year Summer 2015

The following is an outline of the summer exam for last year- there may be a few small changes but it will mainly be like this.

Pick an easy topic and get that revised first. Just take the sections one at a time, if you start now you will have enough time. 

Test 2.5 hours, 8 questions, no choice.

1. Statistics - Chapter 14
2. Income Tax, Compound Interest, Distance and Speed - Chapter 16 and 7
3. Area and Volume - Chapter 18
4. Algebra - two questions from the chapters below.
5. Algebra - Chapters 19 Notes on Simultaneous Equations, 21 Notes on Factors, 22 Notes on Quadratic Equations, 23 and some Indices from Chapter 15 Notes on Indices
6. Geometry, Constructions and Transformations - includes Chapters 24, 25 and 27 (only parts of Chapter 24 that we have done).
7. Coordinate Geometry - Chapter 26 Notes on Coordinate Geometry
8. Trigonometry and Pythagorean Theorem - Chapters 24.3 Notes on the Pythagorean Theorem and 28 Notes on Trigonometry

:¬)=

Pi Day

March 14 is Pi Day - 3.14 ...... 

Fun anti-Pi rant from the Khan Academy - actually there is a lot of serious maths in here!

Happy Pi Day.



Anti-Pi Rant, 3/14/14: Sorry, Pi lovers! Maybe pick a better favorite number next time?

_

1M Probabiliity

Patterns 2 M

The aim in this module is to see the connections between

• Word Descriptions
• Tables of Values
• Graphs
• Equations

These are all different ways of looking at the same relationship. Each has its own advantages.

In this activity you will use the maths program GeoGebra to investigate further, especially graphs and equations.

Click here to find the applets for this activity - use your worksheet to go through them in order, make sure to complete each step.

_

Length and Area

Rectangles, Parallelograms and Triangles
You should know how to calculate the area of each shape.
You can go through five animations here.

Circles
See here.

Remember there is useful information in your tables, see pages 8,9 and 10. Click on each page to see a larger view.

  _