# Archive for the '4º ESO'

## Piecewise functions

Posted by ricardogm on 18th March 2019

Piecewise functions video

And the theory:
Piecewise functions

Here you can take a look at the most usual families of functions:

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## Functions II, increasing, decreasing, etc.

Posted by ricardogm on 13th March 2019

1. Increasing and decreasing functions:

b) Geogebra applets:

2. Continuous or discontinuous functions:

a) The theory

b) An applet with piecewise functions to help visualize this concept.

3. Periodic functions:

a) The definition

b) And an applet:

And a video about rate of change:

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## Functions I

Posted by ricardogm on 5th March 2019

Hi

We are starting with functions today:

1. The basic information is in this page. You should find what a function is, what rules it has and what domain means, at least.

2. Open this Geogebra applets with a simple example of a function.

Now, play with them and try to answer these questions:

a) What does f(3) mean? How much is it? How can you calculate that?

b) Are there more than one value of a with the same value of f(a)? Is that possible in a function?

3. Now we are going to create something similar. Pay attention and send me the file.

4. Read pages 40 and 41 of this book . They show you how to calculate the domain of a function.

5. With this information, solve these exercises:

domain.pdf

Solutions.

You can find the same exercises with solutions in this link.

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## Functions

Posted by ricardogm on 26th February 2019

Hi

Starting with functions:

oupgraphs.pdf

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## Line. slope, y-intercept, cockroaches…

Posted by ricardogm on 12th February 2019

Hi

1. In order to better fight cockroaches, we are going to usee a Geogebra file, and I hope that this way you are going to visualize the slope and the y-intercept of a line really fast. It’s going to be something like that:

With this information, we can hopefully kill more cockroaches:
Algebra vs cockroaches.

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## Flatland

Posted by ricardogm on 11th February 2019

Hi

It’s time to discover this classic:

(Extract from Wikipedia):  “Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by “A Square”,[1] the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella’s more enduring contribution is its examination of dimensions.[2]

Book (pdf format)

Another version.

And the movie:

You can get it as a free ebook.

Y una versión en castellano: Planilandia.

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## Lines

Posted by ricardogm on 7th February 2019

Hi

0. First thing, use geogebra to correct some of the exercises from wednesday. Pay attention

17. Now we are going to  create something like this:

Send the file to me, as usual.

145. A game to practice the explicit equation (or slope-intercept) of a line. Read the instructions carefully. The aim is to kill the cockroaches with lines.

(NOTE: it’s an old game in flash, you must allow flash in the page, and maybe it will work easily in Chrome than in Firefox)

Algebra vs cockroaches

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## Moving Homer with vectors

Posted by ricardogm on 31st January 2019

Hi

We are going to use vectors to create animations, similar to this applet:

Pay attention and send me the files, as usual.

The math thing we are going to use is “linear combinations of vectors“, which is simply a·u+b·v, being  u and v vectors and a and b, numbers.

1. First, an easier construction. We are going to generate something similar to this:

2. Now, the Homer thing. It’s more difficult, so you have to pay even more attention than usual .

The images you need are in this folder:

Images

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## Vectors

Posted by ricardogm on 28th January 2019

Basic things:

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## Trigonometric ratios in every quadrant

Posted by ricardogm on 28th January 2019

Hi

We have seen this thing before:

Now we are going to work with it a little more. Go to this page.

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