coordinate plane worksheets

When we want to show any geometrical shape in mathematics then we required to use the concept of co-ordinal plane system. In mathematics, a coordinate plane can be specified as a plane which express any point of geometrical shape identical on a plane which is drawn by using pair of numerical coordinates points. If we specify coordinate plane in a more understandable language we can say that it is a 2 – D plane through which we can plot the points of different geometry shape. The coordinate points have two kinds of scales which is popularly known as y – axis and x- axis.

The coordinate plane is formed by two lines which intersecting to each other a point which is known as origin of coordinate plane. The horizontal line called as x – axis and vertical line called as y – axis. When these lines are intersecting to each other then they form four quadrants. Here we are going to discussing about the coordinate plane worksheets. It is kind of mathematical worksheet that contains several kinds of questions that helps the students to understand the concept of coordinate plane. The concept of coordinate plane basically deals with ordered pair which is exactly a pair of numerical values. On the basis of ordered pair we can easily plot the numerical value in a very easier manner.

At that of plotting coordinate point on a plane we need to remember some points that are given: in the first quadrant which top of right, all the values must be positive of x and y coordinates. As same in second quadrant, it contains negative x value and positive y value. Third quadrant contains the both negative and fourth quadrant has negative y and positive x values.

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Power Set

Generally a set is defined as any collection of different objects which are present around us. It means that no object is repeated and other word we use in place of different that is distinguishable. The term ‘distinguishable ‘ mean whether that object is in out collection or not. The object belonging to a set are called as element or member of that set.

For Example: A=pen, pencil, Eraser, B = Lucknow, Bihar, Bhopal

Here A is set of stationary used by an Student and B is a set of capital of states.

Like that a set or family of all the subsets of a given set A is said to be power set of A and expressed by P(A).

Mathematically we can say P(A)= x : x ⊆A Here the value of power set of A is equal to the x value of subset  A.

So, x ϵ P(A) ( Here x is belongs to power set of A). In this way x ⊆A it means value of x is subset of set A.

Here are some condition for power set;

(i): ɸ ϵP(A) and A ϵ P(A) for all sets A (Here ɸ is null set which is equal to power set of A and another is set A which is also equal to Power set of A ).

(ii): The element of P(A) are subset of set A.

For example if A= 1, then P(A)= ɸ ,1 here the value of power set A is two sets first one is null set and second one is first element of set.

If A1, 2 , then P(A)= ɸ , 1, 2, 1, 2.

Here the value of power set A is two sets first one is null set and second  is first element of set , second element of set, third is combination of first and second set.

Similarly if A =1,2,3, then P(A)= ɸ , 1, 2, 3, 1, 2, 1, 3, 2, 3, 1, 2, 3.

So, the above trend show that if A has n elements, then P(A) has 2n elements. It is not only true for n =1, 2,3 but it is true for all n.

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exponential function

In the previous post we have discussed about How to Find Vertical Asymptotes and In today’s session we are going to discuss about exponential function.  An exponential function with reference to the mathematics is a function that is generally expressed by the notation ‘ex’ where ‘e’ is said to be a number the value of which is closely 2.718281828. This type of the function is the one that possesses the derivative which is same as itself which means that the derivative of any exponential function ‘ex’ also comes out as ‘ex’.

There are many functions which we come across in the mathematics for example the logarithm function, the trigonometric functions like the tangent function, the cosine function and the sine function, the greatest integer function, etc. And the exponential function is just one of them but we can say that it is very commonly used unlike several other functions.

Let us now talk something about the uses of the exponential functions. The exponential functions are very commonly used under the modeling of a type of a relationship in which a constant kind of the variation in the variable that is independent gives a variation in the variable that is dependent, which is equally proportional. By the above line we mean that it gives an increase or a decrease which is equally proportional when we consider it percent wise.

The exponential functions are commonly expressed as exp ( x ) and mainly in the situations where it practically not possible to write the independent variable as a superscript. It should be known that the inverse of the exponential functions are known as the logarithm functions. (know more about exponential function, here)

The graph of the exponential functions is of sloping kind which slopes in the upward direction and it rises sharply as the value of the x increases.

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How to Find Vertical Asymptotes

In the previous post we have discussed about trigonometry worksheets and In today’s session we are going to discuss about How to Find Vertical Asymptotes.
In analytical geometry, we will study different types of asymptote such as horizontal, slant and so on. Here we will discuss about vertical asymptote. Vertical asymptote can be defined as a straight line towards a function that approaches closely but never touches the line. The equation of vertical line is given by x = a;

The equation mention above is a vertical asymptotes of the graph that has a function y = f (a); this given function is applicable if one of the given condition is true. The conditions are as follows:

1. lim u → s- f (u) = + ∞;

2. lim u → s+ f (u) = + ∞;

At the given point‘s’ the given function f (a) may or may not be defined and at point x = a the value does not affect the value of asymptote.

Let’s see How to Find Vertical Asymptotes. Here we have to define the function for which we are trying to calculate a vertical asymptote. These vertical asymptote values are just like rational functions. If the denominator value of a rational function tends to zero, it has a vertical asymptote. (know more about Asymptote, here)

After then we need to calculate the value of x that makes the denominator value equal to zero. If you have fraction value of function is y = 1 / (x + 4), then we have to solve the denominator equation that is x + 4 = 0, which is x = -4.

Let’s have small introduction about Horizontal Asymptotes. It can be defined as the horizontal line in such a way that we obtained the graph of a given function tends to a → + ∞.

The horizontal line is given by:

⇒a = c; the given equation is a Horizontal Asymptotes of a function a = f (p). Stoichiometry Help us in solving the reactions in chemistry. It is a branch of chemistry. To get more information about stoichiometry please prefer icse syllabus for class 8.

 

trigonometry worksheets

In the previous post we have discussed about Parametric Equations and In today’s session we are going to discuss about trigonometry worksheets. A branch of mathematic which treated with the angles and sides of triangle is called as trigonometry. Now we will see the trigonometry worksheets. It means how to solve trigonometry equations. In mathematic, there are different methods to solve the trigonometric equations. Now we will see the quadratic equation of trigonometry.

Suppose we have trigonometric quadratic equations 2 sin2 p + sin p – 1 = 0, p Ñ” [0, 2Π], Now see how to solve the given trigonometric quadratic equation.

= 2 sin2 p + sin p – 1 = 0, we can write it as:

= (2 sin p – 1) (sin p + 1) = 0, its because of its factor. Now separate both the values. Now it can be written as:

= 2 sin p – 1 = 0 or 2 sin p + 1 = 0, so we get two values of sin p that is:

sin p = ½ and sin p = -1.

The value of p = Π / 6 or 5Π / 6, and in other case p = 3Π / 2. So we get the value of p is 300, 1500, and 2700. This is how we can solve the trigonometric equations. Now we will discuss about the Trigonometric Identities. There are so many identities in the trigonometric which are mention below: (know more about trigonometry worksheets, here)

First we will talk about the sum – difference formula:

Sin (S + T) = sin S cos T + cos S sin T;

Cos (S + T) = cos S cos T + sin S sin T;

Tan (S + T) = (Tan S + Tan T) / (1 + tan S tan T)

 

These are the sum – difference formulas.

Now discuss even – odd identities of trigonometric function:

Sin (-t) = – sin t;

Cos (-t) = cos t;

Tan (-t) = – tan t;

Cosec (-t) = – cosec t;

Sec (-t) = sec t;

Cot (-t) = – cot t;

These are even – odd identities. Let’s talk about the Types of Chemical Reactions. There are different types of chemical. To get more information about the chemical reaction then follow on line tutorial of iit jee syllabus.

 

 

 

 

Parametric Equations

In the previous post we have discussed about Hyperbolic Functions and In today’s session we are going to discuss about Parametric Equations. In plane, parametric equation is a pair of functions that is given by:

⇒ s = f (d) and t = g (d); which is used to define the ‘s’ and ‘t’ coordinate graph of the given curve in the plane (‘s’ is plot along to the horizontal direction and ‘t’ is plotted along the vertical axis). In mathematics, a set of equations that is used to denote a set of quantities as unambiguous functions of a number of independent variables, said to be parameters. For example, Circle equation in the Cartesian coordinate is defined as: (know more about Parametric equation, here)

r2 = s2 + t2, and circle equation for the parametric equations is given as:

⇒ s = r coos d and t = r sin d;

Commonly the parametric equation is denoted as non unique equation, so the same quantities are defined by number of different parameterizations. Now we will see the different types of two dimensional and three dimensional parametric equations. In the two dimensional parametric equations parabola and circle are included. Parabola: The equation of parabola is defined as: ⇒t = s2;

If we use another parameter then the equation of parabola is defined as:

⇒ s = p and,

⇒t = p2.

In case of circle, the ordinary equation of circle is defined as: ⇒s2 + t2 = 1; Here we obtained the equation which is in the parameterized form. Let’s discuss about the three dimensional parametric equations. In geometry, ‘Helix’ involve in three dimensional parametric equations. Commonly parametric equation is used to define the curve in higher- dimensional space. For example: s = a cos (d), ⇒ t = a sin (d) and ⇒ u = bd; given equation defines a three dimensional curve, the radius of Helix ‘a’ and riser to 2⊼b unit per turn. The syllabus of andhra pradesh state board of secondary education is very interesting. It is very helpful to solve math problems for me.

Hyperbolic Functions

The hyperbolic functions of the mathematics are just the analogs of the simple functions of the trigonometry or the functions which are circular.

The common functions which are hyperbolic are the hyperbolic cosine which is represented by cosh and the hyperbolic sine which is represented by sinh. From these 2 functions the other hyperbolic functions are being derived according to the different functions of the trigonometry for example the hyperbolic tangent which is represented by tanh, etc. (know more about Hyperbolic function, here)

We also come across the inverse hyperbolic functions in the trigonometry. For example the area hyperbolic sine which is represented by arsinh or asinh and may also be sometimes denoted by arc sinh.  

We already know that the points which are represented by ( cos x, sin x ) make a circle which has radius equal to the unity. Similarly if we have the points which are represented by ( cosh x, sinh x ) then they will make the right half of the equilateral type of the hyperbola.

Also the functions which are hyperbolic are found in the solutions of many crucial differential equations which are linear like in the equation which defines a centenary.

The functions which are hyperbolic take the values which are real for any argument which is real and is known as the hyperbolic angle. According to the complex type analysis, these functions are just the rational type functions of the exponentials.

It should be known that these functions were discovered in the 1760’s by the V Riccati and the J H Lambert.

In order to get more help in understanding the topics: Hyperbolic Functions, How To Solve Proportions and Board Of Secondary Education Tamilnadu, you can visit our next article and In the next session we will discuss about Parametric Equations. 

 

Cylinders

In this blog we are going to focus on an important topic that is ‘cylinder’. In Cylinders, base of a cylinder is always perpendicular to its sides. If a line joining the center of circle of a given cylinder is perpendicular to the base then the cylinder is a circular cylinder. Let’s discuss some formulas and properties of cylinder. If length and radius and length or height is defined for cylinder then volume of a right circular cylinder is given by:

V = ⊼r2h, where ‘r’ represents the radius of a cylinder and ‘h’ is the height of Cylinders.

The lateral surface area of Cylinders is given by: A = 2⊼rh (this area is defined for lateral area or without top or bottom), The total surface area of cylinder with top and bottom is defined as:

A = 2⊼r2+ 2⊼rh, We can also write it as:

A = 2⊼r (r + h).

Let’s see some properties of a cylinder are given as:

The axis of a right circular cylinder is a line joining the center of cylinder which has a base. Let’s see how these formulas are used? Suppose the radius of cylinder be r = 7 inch and h= 5 inch, then we have to find the volume and surface area of cylinder. (want to Learn more about Cylinders, click here),

As we know that the volume of cylinder = ⊼r2h,

And surface area of cylinder = 2⊼r (r + h),

We know that the value of ⊼ = 3.14, Given, radius = 7 inch, Height = 5 inch,

On putting the value we get,

Volume of right circular cylinder = ⊼r2h,

V = 3.14 * (7)2 * 5,

V = 3.14 * 49 * 5,

V = 3.14 * 245,

V = 769.3 inch3,

Surface area of right circular cylinder = 2⊼r (r + h),

SA = 2⊼r (r + h),

= 2 * 3.14 * 7 (7 + 5),

= 2 * 3.14 * 7 (12),

= 2 * 3.14 * 84,

= 527.52 inch2.

This is all about Cylinders.

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How to Solve Mathematical Induction Problems

In the previous post we have discussed about Composition of Functions and In today’s session we are going to discuss about How to Solve Mathematical Induction Problems. In Mathematics, sometimes there is a need to prove statements that is in the form of theorem or formula. Mathematical induction is the process in which on the basis of hypothesis ,conclusion is generated and there are mainly threes steps for define mathematical induction. In the blog we are defining all the steps of proving mathematical induction that is as follows:

In the first step we prove the hypothesis or statement that is given for the variable having the value equal to 1, means when the statement is true for n = 1 then go to the next step. (know more about Mathematical induction, here)

In the second step prove that given statement for value of variable equals to k means n = k prove statement for an arbitrary value. And when statement is true for the second step then in the last or final step prove the statement or formula for n = K + 1 that is a value increased by one.

At last when for all the three steps given statement is true that means for all the values statement will be true.

If there is a statement such as 1 + 2 + 3… + s = s (s + 1) / 2

For the statement p (s) have some integer s then according to the mathematical induction p (1) is true for the given expression as 1 ( 1+ 1) / 2 = 1 * 2 / 2 = 2 / 2 = 1 .

In next step find this statement true for any integer value as p (4) = 4 ( 4 + 1) / 2 = 4 * 5 / 2 = 10 that is also true as 1 +2 + 3+ 4 = 10.

at last find that statement is true for p (K +1) that is true ,so p (s) is true for all the values n >= 1.

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Composition of Functions

In the previous post we have discussed about How to solve Matrix Calculator
and In this blog we are going to learn about the composition functions in mathematics. Composition function is define as the pipelining of the functions in which result of one function applying on other function. It is simply define by an expression if there is a function f (n) and another function is g (n) and these functions are composed that means result of function f (n) applied to the function g (n) that is written as g (f (n)) that is also written as (g â—¦ f ) (n). Basically the symbol of the composed function is define by a small circle as (â—¦) as if there are two functions f (n) and g (n) then composite function is expressed as (g â—¦ f) (n).

If there is function f (n) = 2 n + 3 and another function g (n) = n2 and in the given functions n is define as the input value then composed function g (f (n)) is defined as (2 n + 3) 2 . It is in the order In which first apply the function f (n) and then function g (n) and when we reverse the operation as first we apply the function g (n) and then apply function f (n) then the composition function is describe as f(g(n)). So it should be keep in the mind at the time of solving that composition function based on the order of functions and if the order of functions are changed then result of the composition function will also be changed.

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