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Problems on divisibility rules will help us to learn how to use the rules to test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. 1. Is 7248 is divisible (i) by 4, (ii) by 2 and (iii) by 8?

Continue reading "Problems on Divisibility Rules | Rules to Test of Divisibility | Divisible by 4"

Worksheet on divisibility rules will help us to practice different types of questions on test of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11. We need to use the divisibility rules to

Continue reading "Worksheet on Divisibility Rules | Questions on Test of Divisibility | "

We will discuss about the introduction of quadratic equation. A polynomial of second degree is generally called a quadratic polynomial. If f(x) is a quadratic polynomial, then f(x) = 0 is called

Continue reading "Introduction of Quadratic Equation | Quadratic Polynomial | General Form"

Division of whole numbers is discussed here step by step. 1. Division is repeated subtraction. (a) 25 ÷ 5 = 5 (Repeated Subtraction) (i) 25 - 5 = 20 (ii) 20 - 5 = 15 (iii) 15 - 5 =10 (iv) 10 - 5 = 5

Continue reading "Division of Whole Numbers |Relation between Dividend, Divisor, Quotient, Remaind"

Here we will learn how to solve different types of problems on Geometric Progression. 1. Find the common ratio of the Geometric Progression whose, sum of the third and fifth terms is 90 and its

Continue reading "Problems on Geometric Progression | Common Ratio of the Geometric Progression "

We will discuss here about what are the properties of divisibility. The following properties are: (i) When a number is divisible by another number, it is also divisible by the factors of the number.

Continue reading "Properties of Divisibility |Factors of the Number|Co-prime Numbers|Divisibility"

Worksheet on multiples and factors contains various types of questions. We know, 1 is a factor of every number. And, a multiple of a number is always greater than or equal to the number.

Continue reading "Worksheet on Multiples and Factors | Prime Number or Composite Number"

We will discuss here about some of the important relation between Arithmetic Means and Geometric Means. The following properties are: Property I: The Arithmetic Means of two positive numbers

Continue reading "Relation between Arithmetic Means and Geometric Means | Solved Examples"

What are the prime and composite numbers? Prime numbers are those numbers which have only two factors 1 and the number itself. For example, these numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,

Continue reading "Prime and Composite Numbers | Prime Numbers | Composite Numbers"

Subtraction of whole numbers is discussed in the following two steps to subtract one large number from another large number: Step I: We arrange the given numbers in columns, ones under ones

Continue reading "Subtraction of Whole Numbers | Whole Numbers | Subtract One Large Number"

Prime factor is the factor of the given number which is a prime number also. How to find the prime factors of a number? Let us take an example to find prime factors of 210.

Continue reading "Prime Factors | Prime Factors of a Number | First Prime Number | Prime Numbers"

We will discuss about some of the properties of Geometric Progressions and geometric series which we will frequently use in solving different types of problems on Geometric Progressions.

Continue reading "Properties of Geometric Progression | Geometric Series | Problems on G. P."

We will discuss about different types of Geometric Progression formulae. 1. The general form of a Geometric Progression is {a, ar, ar^2, ar^3, ar^4, ......}, where ‘a’ and ‘r’ are called the

Continue reading "Geometric Progression Formulae | General Form of a Geometric Progression "

The sum of an infinite Geometric Progression with first term a and common ratio r (-1 < r < 1 i.e., |r| < 1) is S = a/(1 - r)

Continue reading "Sum of an infinite Geometric Progression | Geometric Progression | Examples"

We will discuss here about multiples and factors and how they are related to each other. Factors of a number are those numbers which can divide the number exactly. For example, 1, 2, 3 and 6 are

Continue reading "Multiples and Factors | Infinite Factors | Multiply Counting Numbers"

Addition of whole numbers is discussed in the following steps how to add large numbers: Step I: We arrange the given numbers in columns, ones under ones, tens under tens, hundred under

Continue reading "Addition of Whole Numbers | Add Large Numbers | Whole Numbers | Numbers"

Sometimes we need to assume certain number of terms in Geometric Progression. The following ways are generally used for the selection of terms in Geometric Progression.

Continue reading "Selection of Terms in Geometric Progression | Geometric Progression"

We will learn how to find the position of a term in a Geometric Progression. On finding the position of a given term in a given Geometric Progression We need to use the formula of nth

Continue reading "Position of a Term in a Geometric Progression | Geometric Sequences"

We will learn how to solve step-by-step the word problems on multiplication and division of whole numbers. We know, we need to do multiplication and division in our daily life. Let us solve some

Continue reading "Word Problems on Multiplication and Division of Whole Numbers | Large Numbers"

In worksheet on multiplication and division of large numbers we will get different questions for multiplying and dividing 7-digit, 8-digit and 9-digit numbers. Find the following products:

Continue reading "Worksheet on Multiplication and Division of Large Numbers | Word Problems"

We will learn how to find the sum of n terms of the Geometric Progression {a, ar, ar^2, ar^3, ar^4, ...........} To prove that the sum of first n terms of the Geometric Progression whose

Continue reading "Sum of n terms of a Geometric Progression | Find the Sum of the Geometric Series"

Definition of Geometric Mean: If three quantities are in Geometric Progression then the middle one is called the geometric mean of the other two.

Continue reading "Definition of Geometric Mean | Geometric Progression | Solved Examples"

We will learn how to find the position of a point with respect to a parabola. The position of a point (x1, y1) with respect to a parabola y^2 = 4ax (i.e. the point lies outside, on or within the

Continue reading "Position of a Point with respect to a Parabola | Equation of the Parabola"

We will discuss how to find the equation of the parabola whose vertex at a given point and axis is parallel to y-axis. Let A (h, k) be the vertex of the parabola, AM is the axis of the parabola which

Continue reading "Parabola whose Vertex at a given Point and Axis is Parallel to y-axis | Examples"

We will learn how to solve step-by-step the word problems on addition and subtraction of whole numbers. We know, we need to do addition and subtraction in our daily life. Let us solve some word

Continue reading "Word Problems on Addition and Subtraction of Whole Numbers | Large Numbers"

In worksheet on addition and subtraction of large numbers we will get different questions for adding and subtracting 7-digit, 8-digit and 9-digit numbers. Note: To make it easy to add or subtract we

Continue reading "Worksheet on Addition and Subtraction of Large Numbers | Arrange in Columns"

We will discuss here about the general form and general term of a Geometric Progression. The general form of a Geometric Progression is {a, ar, ar^2, ar^3, .......}, where ‘a’ and ‘r’ are called the

Continue reading "General Form and General Term of a Geometric Progression | nth Term of a P. G."

We will discuss how to find the equation of the parabola whose vertex at a given point and axis is parallel to x-axis. Let A (h, k) be the vertex of the parabola, AM is the axis of the parabola which

Continue reading "Parabola whose Vertex at a given Point and Axis is Parallel to x-axis | Examples"

We will discuss about the standard form of parabola x^2 = -4ay Equation y2 = -4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0)

Continue reading "Standard form of Parabola x^2 = -4ay | length of latus rectum | Solved Examples"

We will discuss about the standard form of parabola x^2 = 4ay Equation y2 = 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates

Continue reading "Standard form of Parabola x^2 = 4ay | Co-ordinate of the Vertex |Solved Examples"

We will discuss here about the Geometric Progression along with examples. A sequence of numbers is said to be Geometric Progression if the ratio of any term and its preceding term is always a

Continue reading "Geometric Progression | Geometric Series | Common Ratio | Solved Examples"

We will discuss about the standard form of parabola y^2 = - 4ax. The equation y^2 = - 4ax (a > 0) represents the equation of a parabola whose co-ordinate of the vertex is at (0, 0), the co-ordinates

Continue reading "Standard form of Parabola y^2 = - 4ax | Equation of a parabola | Solved Examples"

We will discuss about the standard equation of a parabola. Let S be the focus and the straight line ZZ’, the directrix of the required parabola.

Continue reading "Standard Equation of a Parabola | Parametric form of the Parabola "

We will discuss the definition of ellipse and how to find the equation of the ellipse whose focus, directrix and eccentricity are given. An ellipse is the locus of a point P moves on this plane

Continue reading "Definition of Ellipse |Focus & Directrix of Ellipse| Eccentricity of the Ellipse"

We will learn how to solve different types of problems on hyperbola. 1. Find the position of the point (6, - 5) relative to the hyperbola x^2/9 - y^2/25 = 1. Solution:

Continue reading "Problems on Hyperbola | Equation of Hyperbola | Transverse Axes of Hyperbola"

Hyperbola formulae will help us to solve different types of problems on hyperbola in co-ordinate geometry. x^2/a^2 - y^2/a^2 =1

Continue reading "Hyperbola Formulae | Problems on Hyperbola | Standard Equations of Hyperbola"

We will learn in the simplest way how to find the parametric equations of the hyperbola. The circle described on the transverse axis of a hyperbola as diameter is called its Auxiliary Circle.

Continue reading "Parametric Equation of the Hyperbola | Auxiliary Circle | Transverse Axis"

What is rectangular hyperbola? When the transverse axis of a hyperbola is equal to its conjugate axis then the hyperbola is called a rectangular or equilateral hyperbola.

Continue reading "What is Rectangular Hyperbola? | Equilateral Hyperbola | Solved Examples"

What is conjugate hyperbola? If the transverse axis and conjugate axis of any hyperbola be respectively the conjugate axis and transverse axis of another hyperbola then the hyperbolas are called the

Continue reading "Conjugate Hyperbola | Transverse Axis and Conjugate Axis "

We will learn how to find the position of a point with respect to the ellipse. The point P (x1, y1) lies outside, on or inside the hyperbola x^2/a^2 - y^2/b^2 = 1 according

Continue reading "Position of a Point with Respect to the Hyperbola | Solved Examples | Hyperbola"

We will discuss about the latus rectum of the hyperbola along with the examples. Definition of the latus rectum of an hyperbola: The chord of the hyperbola through its one focus

Continue reading "Latus Rectum of the Hyperbola | Definition of the Latus Rectum of an Hyperbola"

We will learn how to find the two foci and two directrices of the hyperbola. Let P (x, y) be a point on the ellipse. x^2/a^2 - y^2/b^2 = 1 or, b^2x^2 - a^2y^2 = a^2b^2 Now form the above diagram

Continue reading "Two Foci and Two Directrices of the Hyperbola | A Point on the Hyperbola"

We will discuss about the transverse and conjugate axis of the hyperbola along with the examples. Definition of the transverse axis of the hyperbola: The transverse axis is the axis of a hyperbola

Continue reading "Transverse and Conjugate Axis of the Hyperbola | Length of Transverse Axis"

We will discuss about the centre of the hyperbola along with the examples. The centre of a conic section is a point which bisects every chord passing through it. Definition of the centre

Continue reading "Centre of the Hyperbola |Definition of the Centre of a Hyperbola|Solved Examples"

We will discuss about the vertex of the hyperbola along with the examples. Definition of the vertex of the hyperbola: The vertex is the point of intersection of the line perpendicular

Continue reading "Vertex of the Hyperbola | Definition of the Vertex of a Hyperbola | Hyperbola"

We will learn how to find the standard equation of a hyperbola. Let S be the focus, e (> 1) be the eccentricity and line KZ its directrix of the hyperbola whose equation is required.

Continue reading "Standard Equation of an Hyperbola | Standard Formula of a Hyperbola"

Here we will learn how to solve different types of problems on sum of n terms of Arithmetic Progression. 1. Find the sum of the first 35 terms of an Arithmetic Progression whose third term is 7

Continue reading "Problems on Sum of 'n' Terms of Arithmetic Progression | Arithmetic Progression"

Here we will learn how to solve different types of problems on arithmetic progression. 1. Show that the sequence 7, 11, 15, 19, 23, ......... is an Arithmetic Progression. Find its 27th term and the

Continue reading "Problems on Arithmetic Progression | General term of an Arithmetic Progression"

We will discuss about different types of Arithmetic Progression formulae. Let ‘a’ be the first term and ‘d’ the common difference of an Arithmetic Progression. Then its General term = a + (n - 1)d

Continue reading "Arithmetic Progression Formulae | General Term of an Arithmetic Progression"

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