HAVE A GOOD SUMMER!
18 / 6 / 12 NEXT STEP IN OUR STATISTICS
After taking all the surveys, it's time to collect the data.
We'll use a spreadsheet so, data will be organised in tables.
Spreadsheets allow us to have nice graphs and calculate some statistical parameters.
If you've not taken the surveys yet:
Groups 2 and 3 questionnaires are available in twinspace (etwinning site).
If you've not taken the surveys yet:
Groups 2 and 3 questionnaires are available in twinspace (etwinning site).
15 / 6 / 12 WORKING WITH STATISTICS
Please, have your questionnaires ready on google docs and share them.
On monday I'd like you to take the surveys.
If you have any problem, don't worry and ask.
8 / 6 / 12 SOME MORE FUNCTIONS
Some important concepts to study functions:
Here, you'll find some useful graphs, so that, you can try to study their functions.
But, remember that for a complete study of the function you'll have to wait one more year.
To graph functions, you can use this link (or another one you like better):
QUESTION OF THE WEEK
CAN YOU GUESS?...
WHAT'S THE DOMAIN AND RANGE OF THESE FUNCTIONS?
a) y = | x |-1/2
b) y = (-x)-1/2
30 / 5 / 12 INTRODUCTION TO FUNCTIONS
To introduce functions it's very useful to remember some concepts:
To graph functions you can use this link:
But, it´s possible to work with a graphic calculator. There are some of them on line:
19 / 5 / 12 EXAM PREPARATION
¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿¿
Check older posts related to inequalities and geometry.
Practise exercises
Take notes
Ask your questions
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
QUESTION OF THE WEEK
Do you know the angle between two vectors if drawing is not allowed?
a = (1,1)
b = (-2,2)
2 / 5 / 12 MEAN PROPORTIONAL IN A RIGHT TRIANGLE
TO LEARN HOW TO USE THE MEAN PROPORTIONAL IN A RIGHT TRIANGLE:
TO PRACTISE USING IT:
24 / 4 / 12 DO YOU LIKE GEOMETRY?
As an introductuion, we'll start reviewing what you already know about Thales' Theorem:
Do you remember similar triangles?
In the next link there are useful information to work with. Go ahead!
17 / 4 / 12 GRAPHING INEQUALITIES IN TWO VARIABLES
THE BEST WAY TO UNDERSTAND INEQUALITIES IN TWO VARIABLES IS USING GRAPHS.
11 / 4 / 12 QUESTION OF THE WEEK
WHAT'S THE SOLUTION FOR THESE INEQUALITIES?
a) x2+2x+1<0
b) x2+2x+1>0
10 / 4 / 12 QUADRATIC INEQUALITIES, RATIONAL AND ABSOLUTE VALUE INEQUALITIES
Some linear inequalities can be solved easily if we know some tips:
To learn how to deal with fractions:
regentsprep.RationalInequalities
To learn how to deal with absolute value inequalities:
regentsprep.absinequal
To learn how to deal with absolute value inequalities:
regentsprep.absinequal
10 / 4 / 12 INEQUALITIES
Here you´ll find some help for solving inequalities and graphing their solutions:
19 / 3 / 12 EQUIVALENT SYSTEMS OF LINEAR EQUATIONS
Two systems of linear equations are equivalent if they have the same solutions set.
In order to get an equivalent system we do elementary operations. That means that we can:
In the Gaussian Elimination Method for solving a system of linear equations we´ll try to get an equivalent system in a triangular form and after that, we´ll obtain the solutions by back substitution.
- Interchange two equations
- Multiply an equation by a non zero constant
- Add a multiple of one equation to another equation
In the Gaussian Elimination Method for solving a system of linear equations we´ll try to get an equivalent system in a triangular form and after that, we´ll obtain the solutions by back substitution.
16 / 3 / 12 EQUATIONS AND STRAIGHT LINES
TO KNOW MORE ABOUT EQUATIONS SYSTEMS AND ITS APLICATIONS , LET´S HAVE A LOOK AT THIS GEOGEBRA EXERCISE AND MOVE THE BUTTONS:
7 / 3 / 12 GRAPHING LINEAR EQUATIONS IN TWO VARIABLES
In order to learn how to draw linear equations in two variables:
21 / 2 / 12 STUDENTS' EXERCISES
m
These are some of your exercises using a spreadsheet program:
Change the values for a, b and c in the quadratic equation ax2+bx+c=0.
You´ll see the real solutions for x, straightaway.
quadratic equation solver (mmp) (by Marcos M.P.)
quadratic equation solver (ngm) (by Nicolás G.M.)
QUADRATICS (by Aida F. B. and Imanol G. A.)
quadratic equation solver (ngm) (by Nicolás G.M.)
QUADRATICS (by Aida F. B. and Imanol G. A.)
CONGRATULATIONS!
m
21 / 2 / 12 EQUATIONS AND LOGARITHMS
ll
logx logx logx logx logx logx logx logx logx logx logx logx logx logx logx logx logx logx logx logxlogx logx logx logx logx logx
Our next step will be to include logarithms and trigonometric functions in our very well known one-variable equations.
Can you solve this equation?
log(x+21)+logx=2
If you need help, you can vist these links:
lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx lnx
llnlllllllll
l11 / 2 / 12 QUESTIONS OF THE WEEK
1) If x=k is a solution of the equation ax2+bx+c=0, can we assure that x=k belongs to D(c)?
2) Is it always possible to find a solution for ax2+bx+c=0?
10 / 2 / 12 EQUATIONS. INTRODUCTION
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Let´s check if you remember what you know about equations.
As a warm up, you can start by checking these links:
As a warm up, you can start by checking these links:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
6 / 2 / 12 QUESTION OF THE WEEK
WHICH IS ONE OF THE THIRD DEGREE POLYNOMIALS, P(x), IF WE KNOW P(-1)=P(2)=P(0)=0?
27 / 1 / 12 ALGEBRAIC FRACTIONS
Let me introduce something new for some of you: ALGEBRAIC FRACTIONS
You can find an interesting introduction, here:
In order to start with operations using algebraic fractions:
As usual, simplification is needed.
22 / 1 / 12 FACTORING POLYNOMIALS
P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x)
HERE, YOU WILL FIND A SET OF RULES FOR FACTORING POLYNOMIALS AS WE HAVE SEEN IN THIS LESSON:
BUT, THERE ARE SOME TIPS FOR FACTORING POLYNOMIALS IN A VERY QUICK WAY:
P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x) P(x)
20 / 1 / 12 INTRODUCTION TO POLYNOMIALS
CHECK YOUR KNOWLEDGE ABOUT POLYNOMIALS AND OPERATIONS USING THEM:
Subscribe to:
Posts (Atom)