When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ <math...

AREAS RELATED TO CIRCLES

TRIANGLES | SPEED NOTES | MATHEMATICS | CBSE | CLASS 9 TRIANGLES | CHAPTER NOTES Similar Geometric Figures: Two geometric figures which...

Pre-Requisites BASICS OF TRIANGLES Similar Geometric Figures: Two geometric figures which are same in shape, such that one is simply a...

Pre-Requisites Circle: Circle is a round shaped figure has no corners or edges. A circle is the locus of all points in a plane which are...

Probability: Probability is a measure of uncertainity (an event may happen or may not happen). Probability is classified into the...

Probability Probability is the study of the uncertainty. The uncertainty of any doubtful situation is measured by means of Probability....

IMPORTANT DEFINITIONS AND FORMULAE An angle is positive if its rotation is in the anticlockwise and negative if its rotation is in the...

SOME APPLICATIONS OF TRIGONOMETRY | CHAPTER NOTES Introduction : One of the main applications of trigonometry is to find the distance...

Chapter –13 Exponents and Powers Exponents: Exponents are used to express large numbers in shorter form to make them easy to read,...

Chapter –12 Algebraic Expressions Algebraic expressions are formed from variables and constants. We use the operations of addition, ...

Chapter –15 Visualising SolidShapes The circle, thesquare, the rectangle, the quadrilateral and the triangle are examples of plane...

Chapter –11 Perimeter and Area Perimeter is the distance around a closed figure whereasarea is the part of plane occupied by the...

Chapter –10 Practical Geometry In thisChapter, we looked into the methods of some rulerand compasses constructions. Given a line l and a...

Chapter – 9 Rational Numbers Rational Number: A number that can be expressed in the form 14. Every positive rational number is greater...

Chapter –6 The Triangle and its Properties Triangles: A closed plane figure bounded by three linesegments. The six elements of a triangle...

Class 7 Important Formulas Chapter 5– Lines and Angles We recall that (i) A line-segment has two end points. (ii) A ray has only one...

CHAPTER – 4 SIMPLE EQUATIONS An equation isa condition ona variable suchthat two expressions in the variable should have equalvalue....

The collection, recording and presentation of data help us organiseour experiences and draw inferences from them. Before collecting data...

4. A fraction whose numerator is less than the denominator is called a proper fraction. 5. A fraction whose numerator is more than or...

CHAPTER – 1 Integers Integers are a bigger collection of numbers which is formed by whole numbers and their negatives. You have...

CHAPTER – 14 Practical Geometry Using the ruler and compasses, thefollowing constructions canbe made: A graduated ruler, The compasses,...

CHAPTER – 13 SYMMETRY Application in everyday life: Symmetry has plenty of applications in everyday life as in art,architecture, textile...

CHAPTER 12 Ratio and Proportion Comparison by taking difference: For comparing quantities of thesame type, wecommonly use themethod of...