# Mates y TIC - Maths and ICT

## The project

Posted by ricardogm on May 31st, 2017

Hi

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 May 24th, 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 Vehículos yi 5 7 2 1 9 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:

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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## Bidimensional statistics

Posted by ricardogm on May 17th, 2017

1. The teacher is going to show you how to use Geogebra to process data. Pay attention.

2. Some problems to solve with geogebra. Send me the files.

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## Combinatorics 3

Posted by ricardogm on May 10th, 2017

Hi

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

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## Combinatorics 2

Posted by ricardogm on May 3rd, 2017

Hi

1. In England, they talk about permutations and combinations. Find out the differences between them and send me a mail.

2. Now I’m going to give you a lot of problems to solve. Copy them in a word document, solve as many as you can and send it to me at the end of the class.

NOTE: you can use this fantastic tool.

1.  Find the total possible amount of eight-digit palindromics. Also, how many nine-digit palindromics are there? (Palindromic: a number whose digits read the same backwards and forwards.)

2.  Four different math, six different physics and two different chemistry textbooks are placed on a shelf. What is the number of possible combinations of arranging the textbooks if:

a. The textbooks from each subject must be grouped together.

b.Only the math textbooks need to be grouped together.

3.  A boy has five coins, each of a different value. How many different sums of money can be totalled with these five coins?

4.  5 red, 2 white and 3 blue balls are arranged in a row. If the balls of like color are not distinguished from each other, how many possible ways can they be ordered?

5.  With the dot and dash system of Morse code, how many different signals can be sent using four clicks or less?

6.  Eight people are seated at a dinner table at a political function. How many ways can they sit if the president and secretary always have to be seated next to one another?

7.  How many diagonals does a pentagon have and how many triangles can be formed with its vertices?

8.  A group composed of five men and seven women form a committee of 2 men and 3 women. How many different combinations can there be if:

a. The group can be formed by 5 people of any sex.

b. A particular woman has to belong to the committee.

c. Two particular men cannot be on the committee.

B) And some problems about combinations:

1 . How many different combinations of management can there be to fill the positions of president, vice-president and treasurer of a football club knowing that there are 12 eligible candidates?

2 . How many different ways can the letters in the word “micro” be arranged if it always has to start with a vowel?

3 . How many combinations can the seven colors of the rainbow be arranged into groups of three colors each?

4 . How many different five-digit numbers can be formed with only odd numbered digits? How many of these numbers are greater than 70,000?

5 . How many games will take place in a league consisting of four teams? (Each team plays each other twice, once at each teams respective “home” location)

6 . 10 people echange greetings at a business meeting. How many greetings are exchanged if everyone greets each other once?

7 . How many five-digit numbers can be formed with the digits 1, 2 and 3? How many of those numbers are even?

8 . How many lottery tickets must be purchased to complete all possible combinations of six numbers, each with a possibility of being from 1 to 49?

9 . How many ways can 11 players be positioned on a soccer team considering that the goalie cannot hold another position other than in goal?

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## Combinatorics

Posted by ricardogm on April 26th, 2017

Hi

0. Before you get to work, you  have to send me a mail regarding the statistics project. Specify name of the team, members of the group, and an initial idea of the topic.

Now it’s time to get into combinatorics:

1. First, the basic counting principle: the rule of product. Read this and solve the questions.

3. More activities to solve in the notebook.

4. And some videos:

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## Tree diagrams problems

Posted by ricardogm on April 19th, 2017

Hi

2. Now some problems. Solve them in a word document. If needed, draw tree diagrams (you can use “autoformas”, see this tutorial . Or use Geogebra and paste the drawing). Send me the file, of course.

- A box has 8 red balls, 5 yellow and 7 green. If a ball is extracted at random, calculate the probability that it will be:

• Red.
• Green.
• Yellow.
• Not red.
• Not yellow.

-A box contains three red balls and seven blue. Two balls are drawn at random. Define the sample space and find the probability of events when:

• The first ball is replaced before the second is drawn.
• The first ball is not replaced before the second is drawn.

-A ball is drawn from a box containing 4 red balls, 5 blue and 6 green. What is the probability that the ball will be red or white? What is the probability that it is blue? If you take out another ball, what are the chances of being red?

3. And now practice with this really large worksheet. Send me the two most interesting problems (the ones you think should be in the exam).

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## Tree diagrams

Posted by ricardogm on April 19th, 2017

Theory:

Tree diagrams with independent events:

And with no independent events.

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## Probability 3

Posted by ricardogm on April 5th, 2017

Hi

We are going to study some cases involving probability:

For example, in this game we can study spinners and dice rolling.

1) Choose the dice. The game is a simulation of the rolling of two dice. Play a little with it and answer these questions?

a) Which results are more and less likely?

b) What are the theoretical probabilities of each result? Make a diagram to solve this question.

2) Now we are going to create a couple of very basic simulations with Geogebra. Pay attention, because the tools you are going to see are quite useful. Send me the files at the end.

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## Probability 2, the Monty Hall problem

Posted by ricardogm on March 31st, 2017

Hi let’s start with a video from the movie “21 Black Jack” about what it’s known as the Monty Hall Problem:

And another more thoroughly explanation:

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