Monday 30 July 2012

list of irrational numbers

In the previous post we have discussed about is pi a rational number and In today's session we are going to discuss about list of irrational numbers. Real numbers which are not rational are defined as irrational numbers. We can't write irrational number in an simple fractional form as p/q.It is cannot be written in form of p/q, where p and q are integer and q≠0. The decimal point goes on endlessly without any specific pattern called irrational number.
Example:             1.5 = 3/2 (Rational Number)
                                ∏ = 3.1415926535897….. =  ?/? (No ratio, Irrational Number)
The List Of Irrational Numbers consists of number that cannot express in the form of ratio:
List Of Irrational Numbers

Present Form
∏ (pi)
3.14159625358…
e (Euler Number)
2.71828182459…
Ñ°
1.61803398874…
√2
1.41421356237…
√3
1.73205080756...
√5
2.23606797749…
√7
2.64575131106…
√11
3.31662479035…
√13
3.60555127546…
√17
4.12310562562…
√19
4.35889894354…
√23
4.79583152331..
√29
5.38516480713…
√31
5.56776436283…
√37
6.08276253029…
√41
6.40312423743…
√43
6.55743852430…
√47
6.85565460040…

Listed below are a few facts related to Irrational Numbers:
·         If r is Irrational Numbers then –r also Irrational Numbers.
·         Irrational Numbers + Rational Numbers = Irrational Numbers
·         √2 + 6 = 7.618033988… (Irrational Numbers)
·         Irrational Numbers  x  Rational Numbers= Irrational Numbers
·          3 x √7 =  Irrational Numbers
·         ∏ x ∏ = Irrational Numbers
·         √2 x √2 = Rational Numbers
·         √2 + √2 = Irrational Numbers
·         √2 - √2 = Rational Numbers
·         √2 / √2 = Rational Numbers
 The other example of Irrational Number is Uniform Circular Motion. Uniform Circular Motion defines, an object traveling in a circular path at a constant speed. In Uniform Circular Motion a equation related the magnitude of the acceleration of the speed:
Y= 2∏r/T                    a = 2∏Y/T
Where r is the radius of the path and T is the time taken to make a circle.
So final equation is:
a = Y*Y/r (centripetal equation)
So result from the Uniform Circular Motion is always Irrational.
In Iit Jee Papers some questions also based directly and indirectly on Irrational numbers and Last List Of Irrational Numbers. (know more about list of irrational numbers, here)

Saturday 21 July 2012

is pi a rational number

In the previous post we have discussed about Types of Angles and In today's session we are going to discuss about is pi a rational number. Before studying is pi a rational number, it is necessary to discuss about the rational and irrational. In mathematics, a number can be written in the fraction form or written in x/y (in ratio) are known as rational number. For example: 0.8 the number is rational because it is also written in the fraction form. So we can write it as 4/5. A real numbers which cannot be written in the fraction form or cannot be written in x/y form are known as irrational number. For example:  ’√2’ is not written in the ratios. So √2 is included in the categories of irrational number. In other word we can say that the numbers are not rational are included in irrational numbers categories.

Now we will see is pi a rational number? Using the definition of rational number and irrational number we can easily find that ‘pi’ is irrational number because it cannot be written in the form of x/y or in form of fraction.  We can easily compare any number by the definition of rational number and irrational number.  Suppose we have given some number 2.66, 5, 1.87, √2, 0.111, √3, √99, now find which number is rational number and which one is irrational number.
Using the definition of rational number and irrational number we can easily compare the given number. (know more about Rational number, here)
2.66 can be written as 8/3, so it is rational number. 1.87 can be written as 15/8 so it is also rational number. √2, √3 and √99 cannot be written in the fraction form so these numbers are irrational number. And 0.111 can be written as 1/9 so it is also a rational number. This is how we can find the number should be rational or irrational.
Now we will see the Unbalanced ForceUnbalanced forces are forces which produce a non-zero net force. Before entering in the iit examination hall please focus on iit question paper 2013. It is very beneficial for exam point of view.

Friday 13 July 2012

Types of Angles


In the previous post we have discussed about Point and In today's session we are going to discuss about Types of Angles. By the term angle, we mean the distance in degrees between the two rays, which have the same vertex. There are different Types Of Angles.

Let us take them one by one. The angles are classified based on the measure of the angles.
1.  Acute Angle : We say that the angle is an acute angle if we have  the measure of the angle less than 90 degrees.
2.  Right Angle : If we have the measure of the angle equal to 90 degrees, then we say that the angle measure is a right angle.
3.  Obtuse Angle : If the angle measure of the angle is greater than 90 degrees and the measure ls less than 180 degrees, then we say that the angle is obtuse angle.
4.  Straight Angle : If the measure of the angle is 180 degrees, then we say that the angle is a straight angle. It simply forms a straight line by  the two arms of the angle.
5.  Reflex angle: All the angles with the measure  of greater than 180 degrees and less than 360 degrees, then we say that the angle is a reflex angle.
6.  Complete Angle: Any angle measure of 360 degrees is called the  complete angle. (know more about Angle, here)
We come across the terms complementary angles and the supplementary angles : If the sum of the two angles is equal to 90 degrees, then we say that the two angles are complementary. On the another hand we say that if the measure of the two angles sum up to 180 degrees, then it is the pair of complementary angles.
To learn about the  Average Speed Formula, we can take the help of online tutor for math which can help us to clear the concepts. Icse 2013 Solved Papers are also available online, which the students can download and understand the concepts.


Thursday 12 July 2012

Point

Point indicates the location on the plane. When we talk about a point on the plane, it can be indicated by a small decimal, which can not be further broken.  We us a point to locate the position on the plane, so we say that a point is used to mark the position which is marked with the respect to x and y axis. In case we have many collinear points on the plane, then we say that the line is formed by joining these points.
In order to find the location of a point on the plane, we will relate it with the coordinates of x axis and y- axis. Thus we say that  the coordinates of x , y axis of the point can be written which shows that the point exist at a particular place which has a particular location.  We always represent the point on the plane by the capital letters say Point A, B, C etc.
 If  we say that the point on the plane exist at the position ( 3 , 2), it simply means that the point  is at the distance of 2 units from the origin towards the x axis and it is at the distance of 3 units towards y axis. (know more about Point, here)
An interesting fact about the point is that  if a point is drawn on the plane then infinite number of lines can be drawn from that given point.  Also if we have two given points, then we can only draw one and only one line which can pass through the two given points. In case we have 3 points and one line is drawn passing through the tree given points, it simply indicates that the three lines are collinear, otherwise  3 line segments will be drawn passing through the given  lines and the closed figure so formed will be  called as a triangle. 
To learn about  Instantaneous Speed, we can visit online tutor. cbse paper for class 9 is also available online and In the next session we will discuss about Types of Angles


Tuesday 10 July 2012

parts of a circle

By the term circle, we mean that the circular closed curve which is formed by joining the points which are plotted with the  compass around the fixed point and at the equal distance around it. This fixed distance is called the radius of the circle.  
There are different parts of a circle, some of them are as follows :
The point in between the circle is called the center of the circle. It is normally represented  by the alphabet O.
The boundary of the circle is called the circumference of the circle. It is also termed as the perimeter of the circle.
The distance from the center of the circle to the boundary of the circle is called the radius of the circle. 
If we draw any line segment in the interior of the circle, such that the end point of the line segment touches the boundary of the circle at both the ends, then we say that it is the chord of the circle.
There can be any number of chords which can be drawn inside the circle.  The chord of the circle which  passes from the center of the circle is the longest chord of the circle. We also call it as the diameter of the circle.  When a diameter is drawn inside the circle, we observe that the  diameter of the circle is equal to the two times of the radius of the circle. Thus it can be written as follows :
 Diameter = 2 * Radius
Or Radius of the circle = diameter / 2
 The line which we draw outside the circle and it touches only at one point  on the circle is called the tangent to the circle.  Also we must remember that the tangent to the circle is always perpendicular to the  radius of the circle at that particular point.
To learn about the Sampling Methods, we can take the help of maths online tutorials. We also come across the questions based on the sampling methods in the  icse board papers and In the next session we will discuss about area of circle


area of circle

In today session we are going to discuss how to find the area of circle. The area of circle can be obtain by the following ways.
1: If we know the radius of the circle then the area of circle can be calculated by the using the method
   Area of circle = pi * r2
Where r is the radius of the circle and  (pi) is the constant having fixed value 3.142 or 22/7
2: We can also understand how to make a pie chart by using circle. If we know the diameter d of the circle. If diameter d is given then the area of circle can be calculated by the using the method
Area of the circle = pi * d2/4 .Where d is the diameter of the circle and  (pi) is the constant having fixed value 3.142 or 22/7
3: Now the circumference of the circle, if circumference c is given then the area of circle can be calculated by the using the method
 Area of the circle = c2/4*pi.Where c is the circumference of the circle and  (pi) is the constant having value 3.142 or 22/7.At the end of the above method we determine the area of the circle .There is an another way to find the area of the circle. By using the method of area of sector of the circle = (pi*R2*angle) / 360
Where r is the radius of the circle and (pi) is the constant having fixed value 3.142 or 22/7.For the area of whole circle angle must be equal to 360 degree. Therefore the area of the circle will be = (pi*R2*360) / 360 it implies that Area of the circle = pi*R2  

The questions on how to make pie chart and area of circle can be asked in icse question papers 2013 and In the next session we will discuss about parts of a circle.(want to Learn more about area of circle, click here),

Wednesday 4 July 2012

proportion

Ratio and proportion are the mathematical concept that basically deals with expressing the relationship between similar kinds of values. The concept of ratio can be define as a way to perform the task of comparing the two values to each other and represent their relationship between them. On the other hand, the concept of proportion can be described as tools that perform the task of equalizing the two ratios to each other. (Know more about proportion in broad manner, here,)
In a simple mean we can say that proportion is a way to set two ratios as equal. It means proportion is a special term of an algebra equation to compare two ratios or make them as equivalent fractions. In ratio, we just focus on what is the impact on another number when we make any changes in first number. But in proportion we need to focus to equalize the one ration to another ratio. Generally the concept of ration can be represented by using four variables u, v, w and x as:
 u : v = w : x,
 or
u / v = w / x.
Normally in the case of proportion, mostly we need to calculate the unknown value of the ratio. To perform the task of getting the unknown value of proportion we need to follow some of the task that are given below:
Suppose there is a statement in which we need to calculate the value of n in below given proportion.
6 / 15 = n / 10
Here first we need to perform the task of cross multiplication of proportional values:
   6 * 10 = n * 15,
    60 = n * 15,
    n * 15 = 60,
      n = 60 / 15,
     n = 4.
Now using the value of n we can represent the proportion as;
6 / 15 = 4 / 10
In mathematics,  Discrete Variable can be define as  a variables that can't be take all values through out the limits of the variable. In examination, cbse previous year question paper describe possibility of what type of questions have higher possibility to come in exam.