Term 4 Week 3

Coordinate Geometry continued...

We have hopefully reached an understanding that any line can be defined by an equation of this form:

y = mx + b

where 'm' is the gradient of the line, and 'b' is the place the line crosses the y axis - ie the y intercept.

By understanding 'm' we can compare lines with each other. We can say that if two lines have the same 'm' value that they must be parallel. Furthermore we find that if we want to check if two lines are perpendicular we can multiply their 'm' values and if the result is -1 then we can conclude that they are.


Coordinate Geometry Assignment 2 is here

Coordinate Geometry Assignment 3 is here

Term 3 Week 9

The new topic is Coordinate Geometry

This is where pictures can be described by numbers.

To do this we use a two dimensional space called the 'number plane'. This is an extension of the number line into two dimensions: left/right (the 'x' axis) and up/down (the 'y' axis)

To specify a 'point' on this number plane we use a pair of numbers like this: (3,5), where the first number '3' is how far left/right it is, and the second number '5' is how far up/down it is. The point (3,5) would be in the top right hand side of the number plane 3 across and 5 up.

By putting multiple points on we can build up lines, and then we can make any shape or picture that we want. So we could draw a black and white Mona Lisa simply be specifying a whole series of points.

This system was worked out by a French dude name Renee Descartes about 400 years ago, and is also known as the 'Cartesian' coordinate system. Most computer games use this system to calculate and display objects on the screen.

The Coordinate Geometry Assignment 1 is here

Term 3 Week 8

Greetings maths beings!

Quite a long break there, what with trips to NZ and a couple of weeks to recover from the flu!

We have just finished a week of Indices, and there are only two or three more days before the exam. This means the exam will be either on Friday or Tuesday.

SO, keep up the practice!

Indices 3 Assignment is here

General Revision Assignment 3 is here

Term 3 Week 3

More Indices

The new shortcuts this week are:

A power divided by a power:

a^m / aⁿ = a<sup>m-n

example</sup>
2⁵ / 2² = 2^5-2= 2³

A power to a Power:

(a^m)ⁿ = a^{m x n
example:}
(5²)⁴ = 5^2x4 = 5⁸

Powers of products and quotients

(ab)ⁿ = aⁿb^n
example:
(2b)³ = 2³b³

(a/b)ⁿ = aⁿ/b^n
example:
(3/7)⁵ = 3⁵/7⁵

Class 9 is on camp for the next two weeks - enjoy, and leave the maths until you get back!

Here is the Indices 2 Assignment

Term 3 Week 2

Our new topic is Indices.

An Indice or Index is a bit of mathematics speak for writing down how many times you want to multiply something together:

10³ = 10 x 10 x 10 = 1000

We say in words 'Ten to the power of three' and this means we multiply three 10s together. The '3' is the Indice or Index or Power which tells us how many 10's we want to multiply. The '10' is the 'Base' which is 'raised' to the Indice.

It means we can work with very large and very small numbers in a simple and easy way.

For instance if we wanted to work out a problem that involved the number 'one million billion' we could write 1000000000000000 down and work with that, or we could simply write 10¹⁵

There are some excellent short cuts that can be taken with Indices. If we had to multiply two numbers like 10² and 10³ we notice this:

10² x 10³ = (10 x 10) x (10 x 10 x 10) = 10 x 10 x 10 x 10 x 10 = 10⁵

And we realise that we can use a more general rule when multiplying anything with the same 'base':

a^m x aⁿ = a^m+n

Which means that we can simply add up the indices to find the answer:

9⁵ x 9³ = 9^{5 + 3} = 9⁸

How easy is that!

More good shortcuts with Indices next week.

The Indices Assignment 1 is here

Term 3 Week 1

Welcome back for term 3!

Apologies for the delay, my home computer has been down this week.

We are still just finishing perimeter area and volume - test on Wednesday.

General Revision Assignment 2 is here

Term 2 Week 9

The final week of Perimeter Area and Volume

This week we consolidate this topic and will have an end of topic test Wednesday of week 10.

Volume. We will get our heads around the idea that we can calculate the volume of any prism by multiplying the area of the base times the vertical height.

So if we had a triangular prism (looking at the end you see a triangle) all we have to do is multiply the area of that triangle (1/2 base x height) by the length of the prism.

This is true for any prism - ie any shape that is 'extruded' like pasta. It does not matter how tricky the end looks if we can calculate the area of it then we can work out the volume of the whole shape.

The Perimeter, Area and Volume Assignment 3 is here

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