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NCERT Solutions for class 10 Maths Chapter 4 Quadratic Equations

The study material contains an exhaustive explanation to all the questions. These answers are written clearly and step by step to maximise retention. While going through these solutions, students will find themselves understanding the concept better.

Practising regularly is a prerequisite if students want to score well in mathematics. You can consult the guide to brush up your memory or help you if you get stuck.

There are 4 Exercises present in this chapter. Students will learn about real numbers and irrational numbers in the 1st chapter of Class 10 Maths. Exercise 1. Ch 4 maths class 10 pdf 400 are a total of 4 Exercises including an optional Exercise in the 2nd chapter of class 10 Maths.

The first Exercise is about to find zeros of polynomials p x. In the second Exercise, the students need to find a quadratic polynomial. The third Exercise has questions on division of polynomials. The last Exercise covers questions from all the concepts of Class 10 Maths Chapter 2.

Exercise 2. The third chapter of class 10 maths is about the linear equations in two variables. It describes what a linear equation in two variables is ch 4 maths class 10 pdf 400 how to solve the problems on linear equations in two variables. In the first Exercise Ex 3. The second Exercise, i. The next four Exercises, Ex 3. The methods explained here are algebraic method, cross-multiplication method, elimination method and substitution method.

Exercise 3. It contains questions from all the Exercises. This chapter explains what a quadratic equation is and the methods of solving quadratic equations. It also explains the factorization method of solving quadratic equations and the square method.

The chapter gives the details of relationships between discriminant and nature of roots. Also, the problems of real life have been solved as examples in this chapter. Exercise 4. This chapter introduces a new topic to the students - Arithmetic Progression, commonly called as AP.

Students will learn what is AP, derivation of nth term, finding the sum of first n terms of the AP and solving the real life problems using AP in this chapter. The first Exercise of the chapter teaches how to represent ch 4 maths class 10 pdf 400 problem or situation in the form of AP, how to find the first term and difference of the AP, and to find whether the ch 4 maths class 10 pdf 400 series is Ap or not.

The next Exercise, Ex 5. The third Exercise describes how to find the sum of first n terms of AP and contains Class 9 Maths Ch 10 Ex 10.3 For Pdf questions related to the topic.

The last and fourth Exercise have questions related to the topics taught in the chapter. Exercise 5. The chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes.

It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles. Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of pythagoras theorem is explained. Exercise 6. Class 10 Maths Chapter 7 explains coordinate geometry, the maths of locating a given point with the help of an ordered pair of numbers. The coordinate or cartesian geometry helps to find the distance between two points whose coordinates are given.

The concept of finding the area of ch 4 maths class 10 pdf 400 triangle formed by three given points. Also, the ways of finding the coordinates of the point which divides a line segment joining two given points in a given ratio is explained in the chapter.

Exercise 7. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles. Students will also learn to ch 4 maths class 10 pdf 400 trigonometric ratios for the given angles and also a few trigonometric identities. Exercise 8. Chapter 9 is the continuation of chapter 8 where the students will learn about the application of trigonometry which they learnt in the previous ch 4 maths class 10 pdf 400. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects.

They will also learn how trigonometry is applied and used in navigation, construction and determining the position of any piece of land based on their latitude and longitudes. Exercise 9. In this chapter, students will be introduced to ch 4 maths class 10 pdf 400 concept of tangents and number of tangents from a point on a circle. Exercise Chapter 11 is one of the interesting chapters.

This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle. The methods of construction are well explained in the chapter to clear the concepts. As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a ch 4 maths class 10 pdf 400 is clarified.

This chapter further explains how to find the area of the figures that contains a circle or part of a circle. In the five Exercises of this chapter, finding the surface area of any object which is made up of two or ch 4 maths class 10 pdf 400 different solid shapes.

The solid shapes include cuboid, cone, sphere, hemisphere and cylinder. Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions which ask about the conversion from one shape to. This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone.

This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data. In the next Exercise, they will learn about the cumulative frequency distribution and drawing cumulative frequency curves.

It elaborates and explains the difference between experimental probability and theoretical probability. The chapter is full of examples to clear the concept of probability to the learners.

Students can download the PDF easily and start going through the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score. The exam is of marks where 80 marks is for theory whereas 20 marks is given for internal assessment. To understand the marking ch 4 maths class 10 pdf 400 in a better way, you should understand the exam pattern clearly.

To score good in the exam, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers and marking schemes so that all the doubts of the students are cleared. The number of questions are increased and the marks per question are reduced.

This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has reduced. CBSE focuses on all-round development of Class 10 students to prepare them for their further education. To perform well in Class 10 then becomes fairly important. CBSE marking scheme is stepwise so you have scored accordingly. Therefore students should write each step clearly and give a proper conclusion at the end of the answer.

The unit wise marks weightage of the mathematics paper is as follows:. The paper has four sections. There are a total of 30 questions for 80 marks. Number System. Coordinate geometry. Statistics and probability. The question paper design will be:.

Sl No. Type of Questions. Total Marks. Memory: Terms, answers, basic concepts and recalling of facts. Understanding: Compare, organize, interpret, translate, describe and stating main ideas. Apply: Solving problems by applying the knowledge, facts, theorems ch 4 maths class 10 pdf 400 rules in different ways.

Analyse: Analyse the information provided and making inferences. Evaluate: Opine about the validity of quality of work and validity of ideas. Create: Creating alternative solutions of the given problem and grouping the elements.

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A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a root or solution of the quadratic equation. There are three algebraic methods for finding the solution of a quadratic equation.

Brahmagupta an ancient Indian Mathematician A. Later Sridharacharya A. An Arab mathematician Al-khwarizni about A. It is believed that Babylonians were the first to solve quadratic equations.

Greek mathematician Euclid developed a geometrical approach for finding lengths, which are nothing but solutions of quadratic equations. Hence, the given equation is a quadratic equation. No doubt that Maths is a subject which is not easy to learn. The formulas are not easy to learn, and students don't catch tricks easily where they should apply. Chapter 4 Maths Class 10 contains quadratic equations to find the value of x.

Apart from this, there are approximately three methods given in Class 10 Maths Chapter 4 for this. But, not all three methods are easy to understand to an individual. All concepts of quadratic equations and formulas have been explained well. From where the formula comes, how it is discovered, by whom it is discovered, and many other things are mentioned first for the basic knowledge. For the ease of the students, it is also mentioned which question came in which year.

Referring to these detailed NCERT Class 10 solutions will enable students to complete their assignments on time and help them at their initial stage of exam preparation. Download � Algebra Formulas for Class You can go through the solved exercises for Class 10 Maths Chapter 4 below.

Chapter Description: This chapter deals with equations involving quadratic polynomials, i. The shape of the graph of a quadratic equation is a parabola. Thus, we need the formula to solve for x.

Suppose a charity trust decides to build a prayer hall having a carpet area of square meters with its length one meter more than twice its breadth. What should be the length and breadth of the hall?

Quadratic Equations have unique properties that fascinate mathematicians, and they can be used as a model to understand more complex polynomials.

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