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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.

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

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

Continue reading "Point-slope Form | Equation of a Straight Line | Symmetrical 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

Continue reading "Slope-intercept Form |Equation of a Straight Line|Slope-intercept Form of a 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.

Continue reading "Equation of a Line Parallel to y-axis |Find the Equation of y-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

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

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

Continue reading "Collinearity of Three Points | Condition of Collinearity | Concept of Slope"

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

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

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

Continue reading "Slope of a Straight Line | Angle of Inclination of a Line | Solved Examples "

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

Continue reading "Straight Line | Represents a Straight Line | Equation of the Straight Line"

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

Continue reading "Problems on Surds | Simplest form of Surd | Express the Surd | Rationalization"

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:

Continue reading "Worksheet on Days of the Week | Fun with Days of the Week!"

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.

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

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

Continue reading "Express of a Simple Quadratic Surd | Unlike Quadratic Surds | Rational Quantity "

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.

Continue reading "Product of two unlike Quadratic Surds | Product of Surds|Multiplication of Surds"

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

Continue reading "Properties of Surds | Simple Quadratic Surd | Represent Rational Numbers"

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.

Continue reading "Conjugate Surds | Complementary Surds | Binomial Quadratic Surds "

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

Continue reading "Rationalization of Surds | Rationalizing the Denominator of the Surd"

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

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

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

Continue reading "Multiplication of Surds | Product of Two or more Surds | Product of Surd-factors"

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

Continue reading "Addition and Subtraction of Surds | Sum or Difference of Surds | Examples"

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

Continue reading "Comparison of Surds | Comparison of Equiradical Surds and Non-equiradical Surds"

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.

Continue reading "Pure and Mixed Surds | Definition of Pure Surd | Definition of Mixed Surd"

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.

Continue reading "Similar and Dissimilar Surds | Definition of Dissimilar Surds and Similar Surds"

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.

Continue reading "Simple and Compound Surds | Definition of Simple Surd and Compound Surd"

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

Continue reading "Measuring Capacity | Addition and subtraction of 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.

Continue reading "Addition and Subtraction of Measuring Capacity | Measurement of Capacity"

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.

Continue reading "Measuring Mass | Addition and Subtraction of 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.

Continue reading "Addition and Subtraction of Measuring Mass | Measuring Mass | Measure of Mass"

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.

Continue reading "Addition and Subtraction of Measuring Length | Unit of Length |Measuring 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

Continue reading "Measuring Length | Relationship between Meter and Centimeter | Unit of Length"

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.

Continue reading "Equiradical Surds | Different Types of Surds | Non-equiradical Surds "

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

Continue reading "Order of a Surd | Quadratic Surd | Cubic Surd | Fourth Order Surd|nth Order Surd"

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

Continue reading "Number Puzzles | Circle Pattern | Missing Number | Recognize the Pattern "

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

Continue reading "Definitions of Surds |Rational Number|Irrational Number|Incommensurable Quantity"

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

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

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

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

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

Continue reading "The Law of Sines | The Sine Rule | The Sine Rule Formula | Law of sines 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,

Continue reading "Law of Tangents |The Tangent Rule|Proof of the Law of Tangents|Alternative Proof"

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

Continue reading "Worksheet on Ordinals | Use the Codes | Color the Turtles|Color as per the Codes"

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.

Continue reading "Problems on Properties of Triangle | Angle Properties of Triangles"

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

Continue reading "Properties of Triangle Formulae | Triangle Formulae | Properties of Triangle"

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\(^{2}\)

Continue reading "The Law of Cosines | The Cosine Rule | Cosine Rule Formula | Cosine Law Proof"

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

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

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

Continue reading "Proof of Projection Formulae | Projection Formulae | Geometrical Interpretation "

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

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

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.

Continue reading "Properties of Triangles | Semi-perimeter| Circum-circle|Circum-radius|In-radius "

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

Continue reading "Problems on Inverse Trigonometric Function | Inverse Circular Function Problems"

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)

Continue reading "General Values of Inverse Trigonometric Functions | Inverse Circular Functions "

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

Continue reading "Principal Values of Inverse Trigonometric Functions |Different types of Problems"

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