## Permutations and Combinations-algebra tutors

### Permutations and Combinations(part-2)

In my previous post, we discussed the fundamental principle of counting and various methods of permutations. In this post, I shall discuss combinations in details.

Meaning of Combination- If we are given a set of objects and we want to select a few objects out of this set, then we can do it by many different ways. These ways are known as combinations.
Example- If we are given three balls marked as B, W and R and we want to select two balls then we can select like this- BW, BR, WR.

These are known as the combination of this selection.

Combination of n different objects taken r at a time when repetition is not allowed– If repetition is not allowed the number of ways of selecting r objects out of a group of n objects is called

=

In latest notation system   is also known as C(n;r) or

Properties of  – It’s a very useful and interesting Mathematical tool. It has following properties.

(i)

(ii)

(iii)      known as Pascal’s law

(iv) r.

(v)

(vi) If n is even then we should put r=n/2 for maximum value of   and if n is odd then   is greatest when r=

(vii) In the expansions of  if we put x=1 then

## Permutations and Combinations-

‘Permutations and Combinations’ is the next post of my series Topics in IB Mathematics.It is very useful and interesting as a topic. It’s also very useful in solving problems of Probability. To understand Permutations and Combinations, we first need to understand Factorial.

Definition of Factorial-  If we multiply n consecutive natural numbers together, then the product is called factorial of n. Its shown by n! or by

for example :

Some Properties of Factorials-
(i) Factorials can only be calculated for positive integers at this level. We use gamma functions to define non-integer factorial that’s not required at this level
(ii) Factorial of a number can be written as a product of that number with the factorial of its predecessor

(iii)    you can watch this video for the explanation.

## Applications of Integration

In my previous posts, we discussed Definite and Indefinite Integrations. Now we shall learn about Applications of Derivatives. Initially, we shall discuss “Area Under Curves”.

Area Under Curve-: If we want to calculate the area between the curves y=f(x) and y=g(x) then there are actually two cases-

First Case when   Below is the figure showing this case

here area under these  two curves

The second Case When  Below figure shows this case

# Continuity of functions-

The word continuous means without any break or gap. Continuity of functions exists when our function is without any break or gap or jump . If there is any gap in the graph, the function is said to be discontinuous.

Graph of functions like sinx,cosx, secx, 1/x etc are continuous (without any gap) while greatest integer function has a break at every point(discontinuous).

1. A function f(x) is said to be continuous at x = c,  if  .

symbolically f is continuous at x = c if .

It should be noted that continuity of a function at x = a is meaningful only if the function is defined in the immediate neighborhood of x = a, not necessarily at x = a.

## 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

greatest integer function

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

### 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

ib elite tutor explained functions

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

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  Read more

## 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

## How to Get 7 in Ib Maths hl

Many of my students got “7” in their IB Maths HL paper people so I believe my suggestion would be useful regarding this-

I think that students should solve their problems in one go. I don’t believe in following some “10 minute before your sleep” tips. All your hard work will go in vain if you forget chapter 3 while doing chapter 4 and because many times the hard questions a require knowledge across many chapters. What you need is a period of intense and thorough revision, in which your free study time is totally devoted to Math HL.

In the process of revision, Students should study the sections one after another.Textbooks split chapters into different sections with practice questions given at the end of each section.If you do not have such a textbook, please buy a good and I think there should be NO “I don’t know how to buy” issue).

### Students should follow these instructions-

Instruction 1. Read the whole body of the section carefully.Students should understand it in the best possible way

Instruction 2.Try the practice questions in the order of their difficulty level.you should not waste time on questions which you know, are very easy for you.Make a list of the questions you can’t do.Once the number of the listed questions reached 25-30% of the whole practice set, you should stop solving the questions and go back and study the body text because there is surely some concept that you are still missing.Once you are done with your reading, you can try your listed questions again.If the problem persists, you need expert help.you should go to your teacher or seek online help at ib elite tutor. Read more

## Online IB Tuitions

In Live Online IB Tuitions, an online tutor and student are not in the same location they use the Internet to teach and learn remotely. The tutor communicates real-time with the student using Skype or Zoom (Voice over the Internet), a digital pen tablet, enabling tutor and student to interact through a shared whiteboard or paint page (on which both teacher and student can write using different paint tools).Online Tutors and students can interact in a fun and dynamic learning environment, choosing individually customized set of the online tools which best help the student achieve his/her academic target. It is like having a tutor sitting right in front of you and is extremely popular with today’s tech savvy younger generation.

IB Elite Tutor offers LIVE ONLINE TUTION CLASSES for INTERNATIONAL BACCALAUREATE (all Groups HL, SL), IGCSE, Cambridge A.I.C.E Diploma, International A-S, A, O- levels, SAT and SAT 2nd (for all subjects). WE have 7 years’ of ONLINE TUTORING experience. The service is ‘‘very effective’’ and helps the students from anywhere in India and the world to access the leading and finest of the tutors. Our online classes have stretched to countries like UK, UAE, USA, Singapore, Australia, Canada, India, Mexico, Spain, China Ecuador, Argentina, Hong Kong, Germany Switzerland, Sweden, Poland, Turkey, Oman, Bahrain, Netherlands, Egypt, Qatar and Japan. By every passing year, the number of our online students is increasing.

IB Elite Tutor’s team of Online tutors is highly experienced and well trained to give online tutoring. Our Live Online tutors have been selected from the highest performing tutors across the world. They have great track records of tutoring students online and bring the best of the International education system.

## Why join Live Online IB Tuitions?

• Best Quality Teachers. Our  Online  Tutors are highly experienced & well qualified IB well Trained teachers. The quality of IB online tutors is far more than IB Home Tutors and avail all the supporting material viz, past ten-year papers chapter wise notes, Chapter wise assignment sheets, chapterwise PPTs and solved past papers to all the students.
• It’s Effective. Way more effective than face-to-face home tuition.
• It’s Convenient. A student can access their tutor and have lessons anywhere and anytime.
• It’s Flexible. A student can fix the time for an online session according to his/her’s comfort and need and it can be done wherever the student happens to be – home, school, travel, university etc.
• It’s Simple. All you need is a broadband connection and a Skype account.
• It’s Safe. Online tutoring avoids the busy and hectic traffic travelling for both tutor and  pupil
• It’s Fun. Many young people like online IB tuitions (to Face-to-Face) due to their life-long familiarity with computers.

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