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Archive for the '4º ESO'


Posted by ricardogm on 30th November 2017



1. First of all, check the equations from last days using this page of Symbolab.

2. Now solve these equations in your notebook 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) Nonlinear System of Equations

h) Nonlinear System of Equations

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Algebraic fractions

Posted by ricardogm on 16th November 2017



1. Now it’s time for practice a bit with algebraic fractions (AKA rational expressions). Solve these in your notebook and check them with Symbolab.

a) Simplify:

Algebraic Fraction Exercise

Algebraic Fraction Exercise

Algebraic Fraction Exercise

Algebraic Fraction Exercise

Algebraic Fraction Exercise
b) Calculate and simplify: (HINT: before multiplying, factor everything, and simplify as much as possible)

Algebraic Fraction Exercise

Algebraic Fraction Exercise

Algebraic Fraction Exercise

Algebraic Fraction Exercise

And the solutions are here.

Next week we are going to learn to add and substract fractions:

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Ruffini’s rule doesn’t rule all

Posted by ricardogm on 9th November 2017


Today we are going to use the quadratic formula to factor second degree polynomials. Sometimes, when you are using ruffini, you factor until you get a second degree polynomial. If this polynomial doesn’t have integer roots, you are not going to find them, but using the famous formula for second degree equations, you can get to them.

1. Use Symbolab to correct the exercises from yesterday. Call me if something doesn’t match.

2. Now try to factor these polynomials. In some of them you are going to need this method. Do it in your notebook, and use Symbolab to check your answers.


Halloween is over, but…

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Polynomials I

Posted by ricardogm on 26th October 2017

We are going to practice a lot. Really. Solve the exercises in your notebook and use Symbolab to correct them.

1. Given the polynomials:

P(x) = x4 − 2x2 − 6x − 1

Q(x) = x3 − 6x2 + 4

R(x) = 2x4 − 2x − 2


  • P(x) + Q(x) − R(x) =
  • P(x) + 2 Q(x) − R(x) =
  • Q(x) + R(x) − P(x)=
  • P(x)·Q(x)=
  • Q(x)·R(x)=

2. Multiply:

  • (x4 − 2x2 + 2) · (x2 − 2x + 3) =
  • (3x2 − 5x) · (2x3 + 4x2 − x + 2) =
  • (2x2 − 5x + 6) · (3x4 − 5x3 − 6x2 + 4x − 3) =

3. Divide:

  • (x4 − 2x3 − 11x2 + 30x − 20) : (x2 + 3x − 2)
  • (x 6 + 5x4 + 3x2 − 2x) : (x2 − x + 3)
  • P(x) = x5 + 2x3 − x − 8 : Q(x) = x2 − 2x + 1

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Logarithms II

Posted by ricardogm on 10th October 2017


Today we are going to work mostly about logarithms:

1. Send me an email telling me the origin of  “logarithms” and some uses of them in real life.

2. Now we are going to use geogebra to create some models about the typical situations related to exponential grown and decay. Pay attention and send me the geogebra files you are going to make: one for compound interest and another for depreciation.

3. Solve these problems in your notebook:


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Percentages, compound interest, Logarithms

Posted by ricardogm on 5th October 2017

1. A thorough explanation of Compound interest.

Try to solve the questions at the end of the page.

2. Two practical cases. Solve them in your notebook:

1. Interest:
Marisa invests $300 at a bank that offers 5% compounded annually.

a.) What is the growth factor for the investment?

b.) Write an equation to model the growth of the investment.

c.) How many years will it take for the initial investment to double? And to be $1000?

2. Depreciation:
Matt bought a new car at a cost of $25,000. The car depreciates approximately 15% of its value each year.

a.) What is the decay factor for the value of this car?

b.) Write an equation to model the decay value of this car.

c.) What will the car be worth in 10 years?

d.) When will the car be worth $100?

Well, some questions need this:

Yes, it’s time for a new operation: logarithms.

Introduction to logarithms.


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Posted by ricardogm on 28th September 2017


1. First of all, I’m gonna show you some interesting tools (Symbolab, for example). Pay attention and use it to correct the exercises from yesterday.

1.1 5 minutes of mental calculations, using “10 seconds of math”.

2. A little theory. Read this page and solve the questions at the end.

3. Some exercises.

4. Exercises 3 and 4 from here. Solve them in your notebook and correct them with Symbolab.

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Sets of numbers

Posted by ricardogm on 17th September 2017


First day in the computers room.

Let’s start with a little history:

1. 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. 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.

1. Open this worksheet, read it (is about converting decimals into fractions) and solve the exercises in your notebook. Check the answers with the calculator.

2. Now you can do some exercises about intervals.

3. And some more.

4. These are the exercises we did in the classroom. Finish them.

5. Here you have a complete unit about real numbers.
A little video about sets of numbers. We are going to listen to a part of it, and take notes.

Now another one about intervals:

For you curiosity, here are the first 1000000 decimals of piAnd time to start with radicals.

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The project

Posted by ricardogm on 31st May 2017


I hope you have something to work on today, because the deadline for the project is tomorrow.  Time goes by… so fast. Anyway, this class is for you to work on the final document. Some advise:

1. Try to create a clean document, easy to read. Forget the tacky things. Seriously.

2. Explain your intentions in the introduction as enthusiastically as posible. As in “I’m going to win the nobel prize” enthusiasm.

3. I suppose you are going to use geogebra for the analisis and calculations, but you can use Excel as well, at least to create nicer tables, with colors and all. I’m going to show you how.

4. If you find that the correlation is strong, write some example of interpolation: How many … will … if ….?

5. If your correlation is very low, that’s a result as well. Simply put, your study show that likely the variables aren’t  correlated.

6. In the conclusions part, make some hypothesis pointing to the cause of the correlation.

7. Check the document for errors, specially spelling mistakes. You can’t send anything with this type of defect, and your mark is going to be much lower.

8. And the most important: take this seriously and follow my instructions, your marks will be much higher.

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Practicing for the project

Posted by ricardogm on 24th May 2017

We are going to practice a little about our statistics project. I’m giving you two examples of situations with two variables, and the goal is to use them the same way you are going to treat your data. For each example you should send me a Word document, or Powerpoint, but with the same structure as the final project. At the very least it should have:

1. Frontpage with your names and the title of the project

2. Introduction (in another page). Explaining the goal of the project, what you want to know, how you got the data, etc.

3. Another page with the data, in table form.

4. Another page with graphics

5. One more with all the calculations

6. And one with the final conclusions.

1. Una compañía de seguros considera que el número de vehículos (y) que circulan por una determinada autopista a más de 120 km/h , puede ponerse en función del número de accidentes (x) que ocurren en ella. Durante 5 días obtuvo los siguientes resultados:

Accidentes xi 5 7 2 1 9
Vehículos yi 15 18 10 8 20

a) Calcula el coeficiente de correlación lineal.

b) Si ayer se produjeron 6 accidentes, ¿cuántos vehículos podemos suponer que circulaban por la autopista a más de 120 km/h?

c) ¿Es buena la predicción?

3. Las notas obtenidas por 10 alumnos en Matemáticas y en Música son:

Problemas estad�stica

a)  Calcula la covarianza y el coeficiente de correlación.

b)  ¿Existe correlación entre las dos variables?

c)  ¿Cuál será la nota esperada en Música para un alumno que hubiese obtenido un 8,3 en Matemáticas?

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