Math Blog

Straight line in Two-point Form | Equation of a line passing through two Points

We will learn how to find the equation of a straight line in two-point form or the equation of the straight line through two given points.

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Point-slope Form | Equation of a Straight Line | Symmetrical Form of a Line

The equation of a line in point-slope form we will learn how to find the equation of the straight line which is inclined at a given angle to the positive direction of x-axis in anticlockwise

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Slope-intercept Form |Equation of a Straight Line|Slope-intercept Form of a Line

We will learn how to find the slope-intercept form of a line. The equation of a straight line with slope m and making an intercept b on y-axis is y = mx + b Let a line AB intersects the y-axis

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Equation of a Line Parallel to y-axis |Find the Equation of y-axis|Straight Line

We will learn how to find the equation of y-axis and equation of a line parallel to y-axis. Let AB be a straight line parallel to y-axis at a distance a units from it.

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Equation of a Line Parallel to x-axis |Find the Equation of x-axis|Straight Line

Let AB be a straight line parallel to x-axis at a distance b units from it. Then, clearly, all points on the line AB have the same ordinate b. Thus, AB can be considered as the locus of a point

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Collinearity of Three Points | Condition of Collinearity | Concept of Slope

We will find the condition of collinearity of three given points by using the concept of slope. Let P (x1, y1), Q (x2, y2) and R (x3, y3) are three given points. If the points P, Q and R

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Slope of a Line through Two Given Points | Slop of Two Parallel Lines are Equal

How to find the slope of a line through two given points? Let (x$$_{1}$$, y$$_{1}$$) and (x$$_{2}$$, y$$_{2}$$) be two given cartesian co-ordinates of the point A and B respectively referred

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Slope of a Straight Line | Angle of Inclination of a Line | Solved Examples

What is slope of a straight line? The tangent value of any trigonometric angle that a straight line makes with the positive direction of the x-axis in anticlockwise direction is called the

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Straight Line | Represents a Straight Line | Equation of the Straight Line

A straight line is a curve such that every point on the line segment joining any two points on it lies on it. If a point moves on a plane in a given direction then its locus is called

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Problems on Surds | Simplest form of Surd | Express the Surd | Rationalization

We will solve different types of problems on surds. 1. State whether the following are surds or not with reasons (i) √5 × √10 (ii) √8 × √6

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Worksheet on Days of the Week | Fun with Days of the Week!

Practice the questions given in the worksheet on days of the week. We know, 7 days makes one week. Starting from the first day of the week, the names of different days of the week are:

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Rules of Surds | Every Rational Number is not a Surd | Rationalization of Surds

Some of the important rules of surds are listed below. 1. Every rational number is not a surd. 2. Every irrational number is a surd.

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Express of a Simple Quadratic Surd | Unlike Quadratic Surds | Rational Quantity

We will learn how to express of a simple quadratic surd. We cannot express a simple quadratic surd by the following ways:

Product of two unlike Quadratic Surds | Product of Surds|Multiplication of Surds

The product of two unlike quadratic surds cannot be rational. Suppose, let √p and √q be two unlike quadratic surds. We have to show that √p ∙ √q cannot be rational.

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Properties of Surds | Simple Quadratic Surd | Represent Rational Numbers

We will discuss about the different properties of surds. If a and b are both rationals and √x and √y are both surds and a + √x = b + √y then a = b and x = y If a not equal to b, let us assume

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Conjugate Surds | Complementary Surds | Binomial Quadratic Surds

The sum and difference of two simple quadratic surds are said to be conjugate surds to each other. Conjugate surds are also known as complementary surds.

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Rationalization of Surds | Rationalizing the Denominator of the Surd

We will discuss about the rationalization of surds. When the denominator of an expression is a surd which can be reduced to an expression with rational denominator, this process

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Division of Surds | Divide a given Surd by another Surd | Rationalizing Factor

In division of surds we need to divide a given surd by another surd the quotient is first expressed as a fraction. Then by rationalizing the denominator the required quotient

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Multiplication of Surds | Product of Two or more Surds | Product of Surd-factors

In multiplication of surds we will learn how to find the product of two or more surds. Follow the following steps to find the multiplication of two or more surds. Step I: Express each surd

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Addition and Subtraction of Surds | Sum or Difference of Surds | Examples

In addition and subtraction of surds we will learn how to find the sum or difference of two or more surds only when they are in the simplest form of like surds. Follow the following steps

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Aug 11, 2014

In comparison of surds we will discuss about the comparison of equiradical surds and comparison of non-equiradical surds. I. Comparison of equiradical surds.

Pure and Mixed Surds | Definition of Pure Surd | Definition of Mixed Surd

We will discuss about the pure and mixed surds. Definition of Pure Surd: A surd having no rational factor except unity is called a pure surd or complete surd.

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Similar and Dissimilar Surds | Definition of Dissimilar Surds and Similar Surds

We will discuss about similar and dissimilar surds and their definitions. Definition of Similar Surds: Two or more surds are said to be similar or like surds if they have the same surd-factor.

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Simple and Compound Surds | Definition of Simple Surd and Compound Surd

We will discuss about the simple and compound surds. Definition of Simple Surd: A surd having a single term only is called a monomial or simple surd.

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Measuring Capacity | Addition and subtraction of Measurement of Capacity

We will discuss about measuring capacity. The milkman measures milk in liters. Petrol is given in liters. Mobil oil is sold in liters. Two milk bottles contain 1 liter of milk. One milk bottle

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Addition and Subtraction of Measuring Capacity | Measurement of Capacity

We will discuss about addition and subtraction of measuring capacity. The standard unit of measuring capacity is liter and the smaller unit is milliliter.

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Measuring Mass | Addition and Subtraction of Mass | Measure of Mass

We will discuss about measuring mass. We know the vegetable seller is weighing potatoes in kilogram. The goldsmith is weighing a ring in grams. The wheat bags are weighing in quintals.

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Addition and Subtraction of Measuring Mass | Measuring Mass | Measure of Mass

We will discuss about addition and subtraction of measuring mass. When there are two objects; we guess which is heavier and which is lighter.

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Addition and Subtraction of Measuring Length | Unit of Length |Measuring Length

We will discuss about addition and subtraction of measuring length. We know the measure of length is required to know how tall a boy or a girl is or, how long the cloth is.

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Measuring Length | Relationship between Meter and Centimeter | Unit of Length

Measuring length will help us to know the measure of how tall a boy or a girl is or, how long the cloth is. Meter is the standard unit of length. If we divide the length of a meter in 100 equal parts

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Aug 07, 2014

If two or more surds are of the same order they are said to be equiradical. Surds are not equiradical when their surd indices are different. Thus, √5, √7, 2√5, √x and 10^1/2 are equiradical surds.

Order of a Surd | Quadratic Surd | Cubic Surd | Fourth Order Surd|nth Order Surd

The order of a surd indicates the index of root to be extracted. (i) A surd with index of root 2 is called a second order surd or quadratic surd. Example: √2, √5, √10, √a, √m, √x, √(x + 1) are second

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Number Puzzles | Circle Pattern | Missing Number | Recognize the Pattern

Fun with number puzzles! For sharp students these puzzles are created to widen the mental horizon of the sharp students. 1. Look at the circle pattern below. The first row contains one circle

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Definitions of Surds |Rational Number|Irrational Number|Incommensurable Quantity

We will discuss here about surds and its definition. First let us recall about rational number and irrational number. Rational number: A number of the form p/q, where p (may be a positive or negative

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Theorem on Properties of Triangle | p/sin P = q/sin Q = r/sin R = 2K

Proof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circum-centre and R the circum-radius of any triangle PQR. Let O be the circum-centre and R

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Worksheet on Numbers 1 to 100 | Numbers using 2, 6 and 7 | number using 6

Practice the worksheet on numbers 1 to 100. We will find out some specific number using the specific digit from the numbers 1 to 100. 1. When writing the numbers 1 to 100, how many times do we write

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The Law of Sines | The Sine Rule | The Sine Rule Formula | Law of sines Proof

We will discuss here about the law of sines or the sine rule which is required for solving the problems on triangle. In any triangle the sides of a triangle are proportional to the sines

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Law of Tangents |The Tangent Rule|Proof of the Law of Tangents|Alternative Proof

We will discuss here about the law of tangents or the tangent rule which is required for solving the problems on triangle. In any triangle ABC,

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Worksheet on Ordinals | Use the Codes | Color the Turtles|Color as per the Codes

We need to follow the instruction to complete the worksheet on ordinals. The turtles are rounding up the bushy path, we term the step number 1 as the first step, 2 as the second step

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Problems on Properties of Triangle | Angle Properties of Triangles

We will solve different types of problems on properties of triangle. 1. If in any triangle the angles be to one another as 1 : 2 : 3, prove that the corresponding sides are 1 : √3 : 2.

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Properties of Triangle Formulae | Triangle Formulae | Properties of Triangle

We will discuss the list of properties of triangle formulae which will help us to solve different types of problems on triangle.

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The Law of Cosines | The Cosine Rule | Cosine Rule Formula | Cosine Law Proof

We will discuss here about the law of cosines or the cosine rule which is required for solving the problems on triangle. In any triangle ABC, Prove that, (i) b$$^{2}$$

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Area of a Triangle | ∆ = ½ bc sin A | ∆ = ½ ca sin B | ∆ = ½ ab sin C

If ∆ be the area of a triangle ABC, Proved that, ∆ = ½ bc sin A = ½ ca sin B = ½ ab sin C That is, (i) ∆ = ½ bc sin A (ii) ∆ = ½ ca sin B (iii) ∆ = ½ ab sin C

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Proof of Projection Formulae | Projection Formulae | Geometrical Interpretation

The geometrical interpretation of the proof of projection formulae is the length of any side of a triangle is equal to the algebraic sum of the projections of other sides upon it. In Any Triangle

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Projection Formulae | a = b cos C + c cos B | b = c cos A + a cos C

Projection formulae is the length of any side of a triangle is equal to the sum of the projections of other two sides on it. In Any Triangle ABC, (i) a = b cos C + c cos B

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Jul 14, 2014

In trigonometry we will discuss about the different properties of triangles. We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.

Problems on Inverse Trigonometric Function | Inverse Circular Function Problems

We will solve different types of problems on inverse trigonometric function. 1. Find the values of sin (cos$$^{-1}$$ 3/5)

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General Values of Inverse Trigonometric Functions | Inverse Circular Functions

We will learn how to find the general values of inverse trigonometric functions in different types of problems. 1. Find the general values of sin$$^{-1}$$ (- √3/2)

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Principal Values of Inverse Trigonometric Functions |Different types of Problems

We will learn how to find the principal values of inverse trigonometric functions in different types of problems. The principal value of sin$$^{-1}$$ x for x > 0, is the length of the arc of a unit

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