Mates y TIC - Maths and ICT

Actividades de Matemáticas con TIC - Math Activities with ICT - - - (matesytic@gmail.com) Ricardo García Mesa

The All Mighty Zero Product Property

Posted by ricardogm on November 12th, 2018

That’s it. The Zero Product Property simply states that if ab=0 , then either a=0  or  b=0 (or both). A product of factors is zero if and only if one or more of the factors is zero. Pretty logical, huh?

As simple as it seems, it’s so powerful that we can solve polynomial equations of any degree using this method,  if we can factor the polynomial (using Ruffini, for example).

Here, we have found, for example, that 1 and -2 are solutions of

There’s one solution more that we could find with Ruffini. Can you find it?

It also explains the relationship between factors of a polynomial and x-intercept of a function:

For example, if we plot this polynomial as a function:

capturafunction.PNG

We get this:

capturaroots.PNG

And you can see that the function crosses the x-axis on x=1 and x=-2 (and in x=-1, because we could also get this with ruffini)

All in all, it´s clear that zero is a very interesting number (although very feared by students all over the world Wink).

A very complete (and lenghty) summary of this can be found here.

Some exercises to practice:

Exercises

And some more.

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Equations review

Posted by ricardogm on November 8th, 2018

Hi

1. First of all, 5 minutes to check the equations from yesterday using this page of Symbolab.

2. Now solve as many of these equations as you can in a blank sheet of paper (to give to the teacher at the end of the class, with your name on it) and check the solutions with Symbolab.

a) x4 − 10x2 + 9 = 0

b) Biquadratic Equation Exercise

c) x4 − 61x2 + 900 = 0

d)Radical Equation Exercise

e) Radical Equation Exercise

f) Radical Equation Exercise

g) Two natural numbers differ by two units and the sum of their squares is 580. What are these numbers?

h) A rectangular garden 50 m long and 34 m wide is surrounded by a uniform dirt road. Find the width of the road if the total area of the garden and road is 540 m².

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Ruffini’s rule rules!

Posted by ricardogm on October 25th, 2018

Hi!

We are going to practice a little bit about division of polynomials, including Ruffini’s rule.

1. The teacher is going to show you some tools to correct these type of exercises. Pay attention. (NOTE: The programs use to show the answer in this format: D/d=Q+R/d)

2. Use these tools to correct the exercises from this week, at least the products and divisions.

3. Work out these divisions (in your notebook) using ruffini’s rule:

ruffini.png

5. Use the tools mentioned above to correct them.

6. Send me an email with the answers.

7. Now do the same thing with this exercise from your book: page 49, ex. 7.

8. Last thing to do: Find out who Paolo Ruffini was, and send me a few notes about him.

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Exam review

Posted by ricardogm on October 22nd, 2018

 First exam

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Alternative math (video)

Posted by ricardogm on October 10th, 2018

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Back to the roots

Posted by ricardogm on October 4th, 2018

Hi

0. First thing to do, a little bit of mental calculation: “10 seconds of math”, five minutes, but this time click squares and roots as well.

2. We are going to insist in the rationalizations of fractions. Go to this page and try to understand the two (some say three) different cases. Solve the questions at the end (only 1, 2 and 3).

4. Use Symbolab to correct your homework.

6. And some exercises. Rationalize these expressions in your notebook:

Radical Exercise

Radical Exercise

Radical Exercise

Radical Exercise

8. Now open your books, page 29, and solve in your notebook exercises 15, 17, 18, 19, 20 and 21.

10. This is the video we saw in the classroom. You can take a look at it and try to understand as much as possible.


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Soluciones tema I

Posted by ricardogm on October 3rd, 2018

 

Muy buenas

Enlazo soluciones del tema 1

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Powers and roots (radicals)

Posted by ricardogm on September 27th, 2018

Howdy!

0. First thing to do: a little history project. Search in the internet to find when and by whom the different sets of numbers were “discovered”. Write the information in a word document and send it to me via email. You have 20 minutes for this task.

1. Some reading about roots. Solve the exercises of the end of the page in your notebook.

2. Same thing with fractional exponents.

3. Well, it’s time for a new thing, and a bit difficult. We are going to learn to rationalize a fraction. Go to this page and try to understand the two (some say three) different cases. Copy in your notebook the theory and try to solve the questions.

5. More rationalizing.


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La primera en la frente…

Posted by ricardogm on September 26th, 2018

 

Pues eso, nos vamos a la EBAU del curso pasado, a ver que podríamos hacer con lo que sabemos de matrices (poco):

Examen de junio 2018

El mismo, resuelto.

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Posted by ricardogm on September 20th, 2018

Hi

First day in the computers room:

0. We are going to meet some new tools today (Symbolab, Geogebra, 10 seconds…), to use during the course.

1. First thing, 5 minutes of mental calculations. Use “10 seconds of math” for this purpouse.

2. Try to find out in the internet the name of the man who proved the existence of irrational numbers. Send me an email with this story (my mail is up there ↑ ). Use the email that you are going to use for all the year. You will have to send me lots of work in the following months.

3. Read this page about intervals. Solve the questions at the end of the page.

4. Solve some exercises (2, 3, 10 and 11) about rational numbers. Do it in your notebook and correct them with Symbolab.

5. Some reading about roots. Solve the exercises of the end of the page in your notebook.

6. Same thing with fractional exponents.

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