Ninth Grade Math

 In the previous post we have discussed about Circle Area and In today's session we are going to discuss about Ninth Grade Math.


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In Ninth Grade Math, we study polynomials, in which we will learn about the types of polynomials, their degrees and thus we can calculate the zeros of polynomials. This chapter also includes the study of Remainder theorem and Factor theorem.

When we write the polynomial of 1 degree, we write it as ax + b. In case of a quadratic polynomial, we get two values of zeros and similarly a cubic polynomial has three zeros Further we say that to find the zeros of the given polynomial, we will equate the given polynomial to zero and thus we get the value of the variable.

Let us look at the following example : If p(x) = 3x - 6, then to find the value of zero of the polynomial, we proceed as follows:

3x – 6 = 0,

Or 3x = 6,

Or x = 6 / 3 = 2,

Thus we say that on putting the value of x = 2, we will get the value of the polynomial as zero. Let us check the above statement:

3 * (2) – 6 = 0,

6 – 6 = 0,

Now we will take the quadratic polynomial. Standard form of quadratic polynomial is ax² + bx + c, where we have a, b, c as rational numbers and 'a' is not equals to zero.

Now we say that if 25x² – 9 is the quadratic polynomial, then to find its zero, we say:

25x² – 9 = 0,

(5x)²  - 3² = 0,

Now applying the formula a² – b² = (a + b) * (a – b), we get:

 (5x + 3) * (5x – 3) = 0,

So either 5x + 3 = 0 or 5x – 3 = 0,

So, either x = -3/5 or x = 3/5,

Question based on Lateral Area of a Cone, is often found in the icse 2013 board papers.

Circle Area

In the previous post we have discussed about Tenth Grade Math and In today's session we are going to discuss about Circle Area. Circle is studied under conic section it is a branch of mathematics and there are other conic sections like ellipse, hyperbola, etc. Circle is a kind of conic section or a kind of ellipse whose eccentricity is zero and its two foci are coincident.

We can also define circle as a simple shape in geometry having different points in the plane which are equidistant from a particular point which is called as center of circle and you should also know that distance between any of these points in the plane and center is known as radius.

For calculating area of circle we must know some of the terms related to circle:

Circumference of the circle is the distance around the circle. Diameter of the circle is the distance traveled across the circle through the center.

In calculation of area of circle we use a Greek letter called pi (π) and approx value of pi is 3.14.

Actually, if we understand the real meaning of area of circle then it is just the number of square units inside a circle. You just have to know the total number of squares in the circle and area of each square and only then by multiplying the area of Single Square and total number of squares, we can get area of circle.

But there is one easier formula for this:

A = π. R²,

Where 'A' is the area of circle and 'r' is the radius of circle. In calculations we use π = 3.14.

There is one fact which says that area of a circle is equals to area to the area of a triangle if the base of triangle is of the length of circle’s circumference and height is equal to the circle’s radius.

Mastering Chemistry Answers can be done by understanding the concepts of chemistry.

Icse sample papers 2013 helps in understanding the pattern of question papers.

Tenth Grade Math

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Tenth Grade Math comprises of various important theories like algebra, geometry & trigonometry, understanding number system, probability or data organization and measurements. In case of algebra we discuss concepts like rationalization, factorization, solving linear and quadratic equations, sketching graphs and understand the characteristics of different equations etc. Questions based on algebra can be solved by using general mathematical formulas.

In probability and data management we would study about problems regarding arrangement of statistical data, arithmetic and geometric means, discrete & continuous frequency distribution techniques etc. Measurements include theorems like Pythagoras theorem, construction of angle bisectors, perpendiculars bisectors, medians and measures of various angles using compass. In trigonometric math we study about the trigonometric functions like sine, cosine, tangent etc. and their uses in solving the problems related to heights and distances. Let us take some examples of 10th grade math.

Example 1: Factorize the quadratic equation 4 x² + 9 x + 5 = 0?

Solution: Method that we can use here for factorizing the quadratic polynomial is mid – term splitting. We do it as follows:

4 x² + 9 x + 5 = 0

4 x² + 4 x + 5 x + 5 = 0

4 x (x + 1) + 5 (x + 1) = 0

Or x = -1, -5 /4

Example 2: If the triangle ABC is a right angled triangle with side of the longest side equal to 5 units and that of base equal to 4 units then find base?

Solution: Here we make use of Pythagoras theorem:

5² = 4² + x²

Or x = 3 units.

Next we discuss about the concept of Latent heat of vaporization which can be defined as the amount of warmth that is freed or absorbed by any system or a substance when it alters its state without altering the temperature. For instance, melting of ice.

In icse 2013 solved papers these concepts have been detailed. In the next session we will discuss about Circle Area.

9th Grade Math

In 9th Grade Math, we have a chapter of a polynomial, in which we will learn about the concepts related to the polynomial. Firstly we will start with what all is a polynomial. We define a polynomial as the combination of the terms which are classified as the linear polynomial, quadratic polynomial or the cubic polynomial.
In case the polynomial is a linear polynomial, its standard form is ax + b, where a <> 0. On the other hand , we write quadratic polynomial in the form of ax>2 + bx + c , where a <> 0. Similarly cubic polynomial is written as ax>3 + bx>2 + cx , where a <> 0.
To find the zero of the given polynomial, we mean that the roots of the polynomial are to be calculated. So we will equate the given polynomial to 0 and get the value of x. Suppose we have a linear polynomial say P(x) =3x + 6. So we say that to find the zero of the polynomial we write P(x) = 0
So 3x + 6 = 0,
Or 3x = -6 ,
Or x = -6 /3 = -2 Ans.
Similarly we can find the zero of the other polynomials. We must remember that the number of zeros of the given polynomial is equal to the degree of the polynomials. So a quadratic polynomial has two zeros, a cubic polynomial has 3 zeros and so on….
To learn more about the different Organic Chemistry Practice Problems, we can take the help of online tutors and understand the concept more clearly. We can download the iit jee sample papers, from the internet which will surely help the students to understand the pattern of the question papers. If some of the series of such question papers are solved, it develops the confidence level of the child.  

Rational Exponents

Rational exponents in the field of mathematics can be defined as a fractional number play a role of exponents for nay number. To understand this concept we need to first understand the definition of rational number and definition of exponents. In mathematics, exponents can be define as a power of any number which shows no. of times a number can multiplied by itself. The mathematical representation of an exponent can be defined by following given notation that is a^b .

The above mathematical notation can be define as exponential representation where ‘a’ and ‘b’ are integer value and the value of a can be consider as base value and value of b can be consider as value of exponent. On the side Rational can be specified as a number which is able to represent two integer values in the form of quotient. Suppose x and y are two different integer value then they can be represented as x / y form.

Now we come to the point that is rational exponent, it can be define as a number where base value has a power of any fractional number. These are also able to for representing an integer and nth root value. Some of the popular rational exponents are square root exponents, cube root exponent and 4th root exponent. Suppose there is a number 5, now it can be represented as 5^1/2 = √5, 5^1/3 = ³√5,

5^1/4 = ⁴√5 and so on. In mathematics, generally these are defined as:

X^y/z = ^z√xy.

In the field of chemistry the Properties of Acids can be define as feature of acids with different chemical in different situations. In India, those school who affiliated from ICSE board then they have to follow icse syllabus 2013 for better result.  In the next session we will discuss about Geometric Progression. 

Geometric Progression

Geometric Progressions in mathematics are the successions which have a particular relation between the numbers in the series like other progressions. Every number is achieved by multiplying the previous number by a constant value. A definite proportion is maintained between the successive terms of the sequence. Suppose we have a geometric sequence given as follows: s, s * p, s * p², s * p³, s * p⁴ and so on. Where, s denotes the first term of the GP and p represents the definite ratio maintained between the terms.

For example, the sequence 8, 16, 32, 64 is a geometric progression with the first term as 8 and the fixed ratio as 16 /8 = 2.

We solve the geometric progression questions as follows: 1^st we have to write down the specified facts or figures given regarding the progression. It can be any combination of data that is available to us, it can either be the 1st term and the relation between the numbers or the 1st term and the succeeding term of the progression.

For instance, if the 1st term is 4 and the successive term is 20. The GP can be written as:

4, 4 * 5, 4 * 5², 4 * 5³, 4 * 5⁴ and so on.

Next we discuss another concept of maths that is related to the product differentiation of a function. The derivative of a function that contains the product can be solved as follows:

Suppose we have a function: y = f (x) * g (x),

D (y) / D (x) = g (x) D (f (x)) / D (x) + f (x) D (g (x)) / D (x).

We solve such problems by differentiating the two functions simultaneously. These concepts are important in maths and we can free download cbse books to refer these topics. In the next session we will discuss about Rational Exponents. 

properties of exponents

Exponents can be defined as the power to the base of any expression. Any mathematical expression is expressed in the form of base and exponents. If there is no exponent then it is said to have 1 as an exponent. There are different properties of exponents that are defined in this section. The first property of exponents is product of power property according to this property if two expressions are multiplied having same base and different exponents then in their resultant the powers are added having base as same. Second property is of Zero exponent according to this property, when two expressions of same base but one of them having 0 as exponent then on adding 0 to any other power will produce the same exponent in the resultant also. Third property is Negative Exponent property in which base are same of both the expressions but one power is negative and since it is negative therefore the exponent in resultant is obtained by subtracting the exponents.

Fourth property is quotient of powers property according to which when two expressions of same base having different exponents are divided then in the resultant their powers are subtracted.
Fifth property that is power of product property says that if two different base having same exponents are multiplied then their resultant can also be determined by first multiplying and then taking power of it. According to power of quotient property, if two expressions are divided having different base but same exponent then their power can be taken after dividing the terms.
Protein purification is termed as the process used for the extraction of single type of protein from a mixture or we can say complex mixture. It is used for the characterization of structure or function and also for the interactions of the proteins. CBSE is termed as Central Board Of Secondary Education which runs all over India in every state. Cbse syllabus for class 11 consists of serial pattern of topics for each and every subject and can be easily checked on internet also.