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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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
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LCM & HCF

The following pencast shows you how to use the product of prime factors to find the HCF or LCM of two or more numbers.

This is very useful, especially for large numbers.
LCM - pick the highest power of each prime factor and multiply together.

HCF -  pick the lowest power of the common prime factors and multiply together.

HCF and LCM with Prime Factors
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Product of Prime Factors

If we take any number that is not a prime number we can write it as the product of 2 or more prime numbers. This means it can be made by multiplying prime numbers together. 

Click below to watch some examples using the "factor tree" method. Click the yellow arrow to make it bigger, you can jump backwards and forwards by clicking anywhere on the page.

Starter Notebook p. 13
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You can break these down in lots of different ways but the final answer will always be the same.

Remember: Product means "multiplied together".
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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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Indices and Surds

Indices
The notes below summarise the rules for powers or indices. It is important to know the rules and how to use them. If you understand the rules for multiplication and division then all the other rules follow from this.

Make sure that you know what to do when

• the index is negative
• the index is zero
• the index is a fraction

Notes on Indices The notes open in a new page and if you download them to your computer the maths symbols may be easier to read.

Surds
There are notes below on simple problems with surds and a pencast on some harder examples.

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

This video has lots of examples of working with surds 
(radicals are roots and surds are expressions that have irrational roots)





Pencast on some more complicated examples with surds.

Surds
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Graphing Lines

2x + 3y = 4 and 3x = 4y are typical examples of linear equations. The solutions for these come in pairs - for every possible value of x there is one value of y that will work and vice versa. If the solutions of these equations are plotted is it found that all the points lie on a straight line.

The pencast below shows the method for finding the points where the line crosses the X-axis and the Y-axis. This method is useful when you want to draw a graph of the line.

You can use this method to solve simultaneous equations, just put both lines on the same graph.

Graph of a Line
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Simultaneous Equations

This is a pencast showing how to solve simultaneous equations. Notes on Simultaneous Equations are here and more on Co-ordinate Geometry can be found here.

Click the orange circle to see the solution and then click Full Screen to see it in full size. You can use the controls to zoom in on the solution. You can also use the controls to show all the writing immediately. If you don't want to listen to the solution you can just jump to the end. The the solutions are on three pages, click on the right to jump to the other pages. If this does not work with Chrome try Firefox etc.

Simultaneous Equations
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