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Archive for the 'General'

Combinatorics 3

Posted by ricardogm on 10th May 2017


Only one thing today: solve as many problems of this worksheet as you can, and send me the file with your answers.

And some problems with solution.

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Posted by ricardogm on 11th October 2016


You have a lot to do today:

1. Go to Mathisfun to learn a bit about logarithms. Write the definition and solve the questions at the end in your notebook.

2. Finish the powerpoint about sets of numbers and send it to me.

3. Solve these exercises in your notebook:

a)Calculate the value of y.

Logarithmic Exercise

Logarithmic Exercise

Logarithmic Exercise

Logarithmic Exercise

Logarithmic Exercise

b) Apply the definition of logarithms and calculate the value of x:

Logarithmic Exercise

Logarithmic Exercise

 Logarithmic Exercise

 Logarithmic Exercise

 Logarithmic Exercise

 Logarithmic Exercise

 Logarithmic Exercise

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Piecewise, Exponential and Logarithmic functions

Posted by ricardogm on 27th April 2016


1. First of all, I’m going to show you how to draw piecewise functions. Pay attention.

2. Now you can repeat the exercises from class with geogebra. Send me one file for the piecewise functions and another one with the hyperbolas.

3.The teacher is going to show you an example of using Excel to calculate exponential growth. Do the same thing with this situation: A candy costs 0.05 € today, and the inflation is 4 % a year. Calculate the cost up to 1000 years.



4. Last thing: When is the candy going to cost exactly 0.50 €? There are two ways to calculate it, the first one trial and error, and the second one is logarithms. Find out what logarithms have to do with this question. Send me the answer.

¿What do you think about the question in this cartoon?

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Feliz navidad…

Posted by ricardogm on 22nd December 2015

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Trigonometry and measuring heights

Posted by ricardogm on 23rd November 2015


Part 1: Geogebra

Today we are going to enter the awesome world of trigonometry. Pay attention to the teacher, you are going to create a very interesting Geogebra applet.

A finished version can be found here:

Part 2: clinometer


The picture above shows you the materials you’ll need to create a very simple clinometer (that is, a device to measure degrees of inclination, or slope). There are other designs, maybe better, but that’s mine, and it’s pretty cheap. In fact, other than the wooden lath, the rest of the materials should be in your school bag, or at home. This particular example is a bit ugly, I hope yours to be much nicer.


1. You’ll need to make a little hole in the right place of the protractor (the center of the circle, it’s usually marked clearly). You can use sophisticated machines, but a hot needle is probably the easier way. Just be careful. Don’t use a nuclear weapon, please.

2. Draw a line in the wooden lath, parallel to the side. The lath, of course, should be perfectly straight. Mine is a bit swill

3. Fix the nut (or another weight) to exactly 90º. You can use a reversible solution to not ruin your protractor (adhesive tape, for instance)

4. Nail down the protractor to the lath, in the middle of it and on the line you just draw.

5. Put your name on the device. I suggest using the wooden part, it’s easier.

6. At this point, it’s time to free your artistic part of the brain. Decorate the thing with something fun, or significant for you. Paint it, for example, write a song, draw a scary tatoo… It’s up to you.

Deadline: friday 4rd. No excuses allowed. Examples of popular excuses: my dog ate it, my brother ate it, I ate my dog, etc.

NOTE: one clinometer per each one of you.

Next thursday or friday we are going to measure the height of different things with this humble device and your amazing trigonometry knowledge: trees, a hill, this school… so:

For today:

1. Search in the web how to measure heights of things using trigonometry and a clinometer. Write it in a blank sheet of paper, at least, these two cases: a tree or something similar, and a mountain. Give it to the teacher at the end of the class (one pupil, one sheet).

2. Solve these problems in your notebook.

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Corrección examen y más

Posted by ricardogm on 29th October 2015


Inesperado, ¿no?

Muy buenas

Hoy vamos a corregir el examen de ayer. Lo tenéis aquí enlazado:


Vamos a utilizar las herramientas tecnológicas que tenemos (Wiris, WolframAlpha, Geogebra). El profesor os hará una demostración. Después corregís el examen, pegando las respuestas como podáis en un documento de word y me las enviáis.

Y ya vamos a empezar tema nuevo, representación de funciones. Como recordatorio, eran todos estos apartados. Después de echarle un vistazo (ahí os quedan para el futuro), probad a resolver estos ejercicios:

Pues eso, ejercicios.

Ayudaos para ello de wiris, geogebra o lo que os parezca, pero hay que tocar todos los puntos.

Menos mal, ya vuelve a ser el de siempre…

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Posted by ricardogm on 15th October 2015


Muy buenas

Comenzamos a lidiar con ese bonito evento, la PAU. Enlazo en el blog los examenes de años anteriores. Están los de todas las materias, obviamente, por si os es útil. También os he enlazado sólo los de mate, resueltos, para un futuro.

En todo caso, hoy toca este tipo de problemas:

1 Dada la parábola f(x) = x2, hallar los puntos en los que la recta tangente es paralela a la bisectriz del primer cuadrante.

2 Dada la curva de ecuación f(x) = x2 − 3x − 1, halla las coordenadas de los puntos de dicha curva en los que la tangente forma con el eje OX un ángulo de 45°.

3 Determinar los valores del parámetro b, para qué las tangentes a la curva de la función f(x) = b2x3 + bx2 + 3x + 9 en los puntos de abscisas x = 1, x = 2 sean paralelas.

4 Calcular los puntos en que la tangente a la curva y = x3 − 3x2 − 9x + 5 es paralela al eje OX.

5 Se ha trazado una recta tangente a la curva y= x3, cuya pendiente es 3 y pasa por el punto (0,−2). Hallar el punto de tangencia.

6 Buscar los puntos de la curva f(x) = x4 + 7x3 + 13x2 + x +1, para los cuales la tangente forma un ángulo de 45º con OX.

Resolvedlos en la libreta y mandadme un geogebrismo que muestre la solución.


Enlazo un video de los muchos que hay en internet explicando cosas de todo tipo, en este caso derivación logarítmica:

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Mathematical cumbia

Posted by ricardogm on 15th May 2014


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Imperial and metric measurements

Posted by ricardogm on 12th March 2012


Here you are some information about imperial measurements.

Frankie is going to tell you some facts about the units they use in Britain. Then you can do the following exercises: Send the questions to me in a word document, you can use copy and paste, this time ;)

2. Then, do this quiz.

3. And, at last, play this game.

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Negative numbers

Posted by ricardogm on 8th December 2011


First of all, do the exercises in parts 2 and 3 of the unit

Open your book, page 81, and do exercises 5, 8 and 10

Two applets with geogebra: adding and subtracting integers.

The same thing, in spanish, with activities (Gauss proyect)

And some more easy exercises:

3 + (-8) = (-9) - (-4) = 7 - 5 =
6 - (-4) = (-4) - (-2) = (-4) - 10 =
6 - 5 = (-2) - 5 = 4 + 1 =
4 + 2 = (-4) - (-10) = 9 - (-7) =
8 - 5 = 9 - (-9) = (-8) + (-2) =
(-9) + 10 = (-5) + (-10) = 8 + (-10) =
8 + 6 = 2 - (-10) = (-4) - 4 =
(-2) + 6 = 1 - (-7) = (-2) - 7 =
7 - 5 = 8 - (-2) = (-1) - 0 =
(-1) - (-2) = (-2) + 5 = (-6) + 2 =
7 - 4 = 8 - (-2) = (-5) - (-6) =

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