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
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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!

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.

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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

:¬)=

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.

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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.

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Applied Arithmetic

Revision of percentages - notes.

Speed, Distance and Time - PowerPoint.

Compound Interest, Saving and Borrowing - PowerPoint.
For second year just study this example (€5000 at 4% compound interest for three years):-

Income Tax - notes - make sure you know the vocabulary used in this topic and study the example in the notes.

Vocabulary: Standard Rate, Cut Off Point, Tax Credit, Gross Income, Net Income, Gross Tax, Net Tax.

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Indices for 2nd Year

Make sure you understand the three rules for indices or powers. The Poweroint and a Summary can be downloaded below. The summary includes reciprocals and scientific notation. For the summer exam you should be able to do these when the base number is represented by a letter.

Be careful with powers of negative numbers. Learn these two examples - this is the way your calculator works.

Orders of Magnitude

There is a famous video which shows very large and very small objects called "Powers of 10", you can see a short version here or the original here.

To find the order of magnitude between two numbers follow these steps

• Both numbers must be written in scientific notation.
• Round off the first part to either 1 or 10, whichever it is closer to.
• Tidy up to just powers of 10.
• Subtract the smaller power from the bigger power - this is your answer (subtract the powers not the numbers).

If there is a very big difference between two numbers then normal rounding off is not very useful. The order of magnitude gives us a rough comparison. For example if the order of magnitude is 2 then one number is about 10² or 100 times bigger than the other. If the order of magnitude is 6 then one number is about 10⁶ or a million times bigger than the other.

Click the link for the PowerPoint used in class, you can view it on-line without any animations or download it to see the animations (it looks better!). Summary for Second Year.

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I Love Statistics

Vocabulary for Statistics
Do you understand all these words? 
Could you write a sentence using each word.

Move your mouse over the words - click on each one for more information.

Created with Tagul.com

Did you know that 2013 was the International Year of Statistics?

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Histograms

Histograms are used to display continuous numeric data.
Look at the examples below (click the picture to enlarge it). 
The bars must touch and the data must be continuous - do not confuse with bar charts.

What can you say about the heights of 15 year old girls and boys?

Female: Basic Statistical Measures
"Averages"		Variability
Mean	162.38	Range	119.00
Median	163.15	Interquartile Range	11.00
Mode	160.00

Male: Basic Statistical Measures
"Averages"		Variability
Mean	169.46	Range	124.00
Median	171.00	Interquartile Range	18.00
Mode         160.00

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Mean, Mode and Median

Most students don't realise that when they say "average" there are in fact three different ways of measuring the "average".

They are 

• the Mode - the most common number in the data
• the Median - the number in the middle of the data when it is in order
• the Mean - the sum of the data divided  by the number of pieces of data

These three terms are all called "Measures of Central Tendency".

Try the Project Maths quiz on mean and adding a constant to the data.
Try the Project Maths quiz on mean and multiplying by a constant to the data.

Try the Project Maths quiz on mean adding a value to the data.

Try the Project Maths quiz on mean, median and mode.

Bar charts quiz
Pie charts quiz
Stem and leaf quiz


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Bar Charts

Short quiz on Bar Charts from project Maths.

Remember when drawing a bar chart

• Always include a title
• Clearly label the axes
• The bars should be the same width and the gaps between them should all be equal - use a ruler!
• Have a look at the example below from Census at School.

 

Surveys and Questionnaires

How not to do your survey!

With proper use of statistics you could be a prize winner! Irish students win  in the International Statistical Literacy Project competition for 2013.
Information on this years competition.

2nd prize

Ireland

Tracing the Roots of Irish Vegetables

Dominican College, Taylor's Hill, Galway

Aoife Troxel, Sive Neary

3rd prize

Ireland

Think Organic!

Coláiste Mhuire, Askeaton, Co Limerick

Mary Aherne, Zoe Barry, Lucy Ward

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Census at School

Go to  Take the CensusAtSchool 13 online questionnaire  and follow the instructions below.

You must enter this user name dhobson0797 and 

the school roll number 60820E and the school name. 
You will need to know to the nearest one tenth of a cm the following

• Height                        
• Length of right foot
• Open arm span 
• Circumference of your wrist 
• Open hand span of the hand you write with
• Also the weight of your bag, if you don't know just put in 9.0

 Note: Answers must be in cm
           Just type numbers - do not type "cm"
           If you are 1 m 65.4 cm Just Type 165.4

You can see some interesting results from previous years here - notice how the information is presented. Do the charts help to get the information across?

Sample from 2010/11

Census at School

The Joy of Statistics

Some very impressive graphics showing how powerful statistics can be. Double click to view in full screen.

You can see the full program here.

The Joy of Stats from Gapminder Foundation on Vimeo.

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Solving Inequalities

Inequalities - you need to know

• The inequality signs. 

• The number sets (N, Z and R) and 
• how to graph them on the number line. (see this post)
• How to solve double inequalities (3^rd year only).
• How to solve practical problems based on inequalities.

Inequalities are like equations but with one important difference - if you multiple or divide both sides by a negative number the sign changes direction. To see this try the examples here. The solutions and some simple examples can be found here.

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Constructions - Introduction

When you see the word "construction" in a question this means that 

• you should draw an accurate and neat diagram
• use a compass, ruler etc
• use a sharp pencil (a normal pencil e.g. HB)
• show "construction marks" e.g. if you drew arcs with a compass you should not rub these out when you are finished.

You will find step by step instructions for all the first year constructions here.


Second years need to be able to construct the triangles given - SSS, SAS, ASA or RHS
See chapter 25

Doing lots of constructions helps you when you move onto tackling problems in geometry.

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Factors in Algebra

It is important to know the four methods for finding factors that we use in algebra. These notes cover all four methods. they include guide number method for finding the factors of quadratic expressions, this method works for all quadratic expressions that have factors with whole numbers and does not require guessing or trial and error. Initially it may look complicated but that is because it includes explanations, once you get used to working this way it is quick and effective. It is a good idea to practice multiplying your factors together to check your answer and to help your understanding of factorising.

Tip: When factorising by grouping copy the first bracket and then work out what to put in front of it.

When factorising this

2cd – 2ca –3bd+ 3ab

factorise the first two terms

2c(d – a)

then repeat what is inside the bracket

2c(d – a)     (d– a)

then work out what should go in front of the bracket

2c(d – a) –3b(d– a)

finish by grouping the common factors

(2c–3b) (d –2a)

You are less likely to make mistakes with the signs when you do this.

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Inequalities and Number Sets

It is important to know the sets N, Z and R and how to graph these on the number line.

On page 23 of the Maths tables the sets of numbers that you need to know are listed - however it is easier to learn them here. When written in this order each set includes the numbers in the previous set.

Natural Numbers - Symbol N = {1, 2, 3, 4, ... }, whole positive numbers.

Integer Numbers - Symbol Z = { ... – 3, – 2, – 1, 0,  1,  2,  3 ...}, whole positive and negative numbers (and zero)

Rational Numbers - Symbol Q = any number that can be written as a fraction using two integers, but you cannot have zero as the denominator because it is impossible to divide by zero. You will only be asked to show the sets N, Z and R on the number line. The set Q is used when you are asked to write your answer as a fraction.

Real Numbers - Symbol R = all the numbers on the number line.  This includes the rational numbers and the irrational numbers (numbers that cannot be written as fractions e.g. pi, √2 etc. 

An open or empty circle is placed around the 2 because 2 is not included. For less than or equal use a full or coloured in circle.


This video explains what rational and irrational numbers are.

Simultaneous Equations

These consist of two equations and two unknowns. They can be solved in two ways; you can be asked to use either method so learn both.

Method 1

Solve the equations algebraically there are notes here –  and  a pencast here.

(See p.124-126 in your book for examples and questions)
Worksheet 1 
Worksheet 2
Worksheet 1 answers
Worksheet 2 answers

Method 2

Draw a graph of each line on the same page and find the point at which they meet, this point is the solution. There is a pencast on plotting lines below, for simultaneous equations just do both lines on the same page. Note this method finds where the line crosses the x-axis and the y-axis. If it is convenient you can pick any number for x or y and substitute this in to the equation and find the value of the other variable.

Graph of a Line
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