# Archive for the '4º ESO'

## Logarithms II

Posted by ricardogm on 10th October 2017

Hi

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.

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

Hi

First day in the computers room.

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

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 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 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 17th May 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.

3. Go to this page, read everything and solve the questions.

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## Combinatorics 2

Posted by ricardogm on 3rd May 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.

A) Some problems about permutations:

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 26th April 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.

2. Now things get a bit complicated. Read this page about combinations and permutations 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 19th April 2017

Hi

1. Read this page and solve the questions at the end.

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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