Ib Maths Tutors-Types of functions(part-3)

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Types of Functions-

IB Maths Tutors should give twenty-two hours for teaching functions and equations as per IBO recommendations. This is my third article on functions in the series of ib mathematics

IB Maths Tutors should give twenty hours in teaching functions and equations.This is my third article on functions in the series of ib mathematics

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here.

1.Greatest Integer Function–  This is an interesting function. It is defined as the largest     integer less than or equal to x

                                                         y = [x].

For all real numbers, x, this function gives the largest integer less
than or equal to x.

For example:   [1] = 1      [2.5] = 2      [4.7] = 4      [5.3] = 5
Beware!    [-2] = -2      [-2.6] = -3      [-4.1] = -5      [-6.5] = -7

domain=R
range=Z

<img src="ibmathstutors.jpg" alt="ibmathstutors">

greatest integer function

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IB Tutors-useful pdfs

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I am sharing few documents prepared by experienced IB Tutors

 

Below is a past year paper for ib mathematics

 

ib_elite_tutor.com

 

Below is an important worksheet for Differentiability of Functions

 

Worksheets_on_Differentiability_(22-09-15)

 

Below is an important worksheet for logarithms

 

Worksheets_on_Log

 

Below is an important worksheet for maxima and minima value of Functions

 

Worksheets_on_Maxima_&_Minima_(22-09-15)

worksheet of INDUCTION (PMI)

You can request PDF of any IB BOOK, we shall try to provide that to you for free

<img src="demo.png" alt="demo">

IB Mathematics Tutors- types of mathematical function(part-1)

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IB Mathematics Tutors should give a fair number of hours in teaching functions.This is my third article on functions in the series of ib mathematics

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here

For the sake of a comprehensive discussion, some standard functions and their graphs are discussed here
1.Constant Function-
                                                F(x)=k
Domain= ℝ    

                                            Range    = {k}                                       

<img src="constant-function.jpg" alt="constant-function">

constant-function

                                   
Range    = {k}

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IB Mathematics (part-2)-Domain and Range of a function

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In IB Mathematics both HL and SL, functions are one of the most important areas because they lie at the heart of much of mathematical analysis.here I am discussing domain and range of a function

Domain of a Function

Suppose I say that f is a real function.This means that for real input, the output should be real. For example

 F(x)=√x

if F is real, then x can only take non-negative values because only then the output will be real. Set of all real values of R is called domain

“Domain is the set of all possible inputs for which the output is real ”

In some cases, x is defined explicitly. for example,

                                     y=f(x)

                                       =x²;    1<x>2 here domain is defined explicitly as (1,2)

If no domain is mentioned explicitly, the domain will be assumed to be such that “F” produces real output

These are a few examples

  1. y=f(x)=√x
    Domain D= x≥0

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IB Maths (Part-1)- Functions-An Introduction to functions in Mathematics

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An Introduction to functions in Mathematics

In IB Maths both HL and SL, functions are one of the most important areas of mathematics because they lie at the heart of much of mathematical analysis. The concept of function is easy to understand.
Suppose I say that:

      y=x²  

where x∈R. This says that y depends on x this can be said that y is a function of x. or

   y=f(x)

We can also say that x=√y here x depends on y or x is a function in y or

  x=f(y)  

so it can be said that a function is an operator which takes an input and gives an output.The input is called independent variable while output is called dependent variable

<img src="functions.jpg" alt="functions">

ib elite tutor explained functions

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How to Become a Good Learner in Classroom or in Online sessions

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Every moment of our life offers something to learn.We should always be ready to grab the opportunity.In this post, I have tried to identify characteristics of a good learner in classroom as well as with online tutors

Positive Attitude- A positive attitude plays a very important part in improving our learning capacities.Actually, its the backbone of our learning capacities.If we believe that we can do it, we will surely be able to accomplish the work <img src="good learner.png" alt="good learner"> Read more

How to represent irrational numbers on number line

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irrational number

Representation of irrational numbers on the number line

Irrational numbers are the numbers which have a non terminating and non-repeating decimal expansion. They don’t have any fixed value so we can’t represent them directly on the number line. we have to use a few tricks for this

Before understanding representation of irrational numbers on number line first, we need to understand Pythagoras’ theorem
Pythagoras’ Theorem:: Over 2000 years ago there was an amazing discovery about triangles:
When a triangle has a right angle (90°) and squares are made on each of the three sides then the biggest square has the exact same area as the other two squares put together!

irrational numbers

pythagorus theorem

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Classroom conflicts

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"classroom conflict"

 CLASSROOM  CONFLICT-

Classroom conflict is a general problem. Every teacher should be ready to face it.

  • As a teacher, we should be supportive, encouraging, and respectful of student ideas in the classroom. We should provide them proper space to put their views, we should correct their wrong answers, we should point out their academic weaknesses but we should never discourage our students.
  • We should always listen to our students carefully and we should respond to them properly whenever they offer an idea.
  • We should not dismiss a weak or incorrect idea immediately, we should ask our pupil to clarify it using the class material. Often, they can talk their way into a more thoughtful response.
  • We can try some funny things in the classroom to engage our students but we should know that this act require extra care as it can easily be misunderstood

We are also less likely to fall into conflict with our pupils if we resolve any mixed feelings we have about our superiority as a teacher. Students expect us to set clear boundaries and to hold them to their academic responsibilities.

TRICKS FOR MANAGING CHALLENGES-

Arguments in Class

When arguments erupt in class, or when a pupil makes any wrong comment, our role as the teacher is to save the learning atmosphere of our classroom. This task is two-fold: Read more

Teaching Maths-Classroom discussions

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"class room"

Teaching Maths-Classroom discussions

Teaching Mathematics is an art but there are certain factors about it that we can learn and improve our academic delivery.

Creating productive classroom discussions is one of them

Lecture method may work very well for some subjects but not all the time in  Mathematics classes.
Engaging students by constantly asking them some questions is a nice method but only when the explanation and the questions are Mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on Mathematical theories.
Creating a productive classroom discussion is probably the most difficult part of Mathematics teaching. I suggest five methods for moving beyond Lecture methods in teaching Mathematics.
I have always tried to practice these methods in my own teaching whether with students or with teachers and I have found them very useful

1. Predict the Pupils’ Responses of Mathematics
All the teachers should know about each and every student how he/she is going to react to the instructional tasks(s) that they are asked to work on. Read more

Pi day-14th March

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In the whole history of Mathematics, the calculation of the ratio of a circle’s circumference and diameter is one of the biggest challenges.
This value is represented by the Greek letter π (pie). From ancient civilization of Babylonia to present age of supercomputers, Mathematicians have been trying to calculate this mysterious number.

They have searched for exact fractions value, formulas, and, more recently, patterns in the long string of numbers starting with 3.14159…….. which is generally shortened to 3.14.

Its an irrational number in Mathematics. Read more

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