NCERT Solutions For Class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.1) Exercise 3.1
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Mathematics is one of the most crucial and essential subjects taught to students in Class 8. The mathematical ideas covered in Class 8 may also prove valuable in the following years. Engineers, Architects, Economists, Computer Programmers, Weather Forecasters, Market Analysts, Physicists, and other employment opportunities are available to students who specialise in Mathematics. Since mathematical concepts are essential in both everyday life and education, it is critical for students to understand them. Mathematics may help students become better problem solvers. A strong understanding of mathematical principles can prepare students to use them in a variety of occupations and professional responsibilities. A degree in Mathematics may open up a world of interesting and intellectually stimulating professional prospects for students. Students should get registered with Extramarks by visiting its website or mobile application.
Students must learn mathematical principles thoroughly in order to use them constructively in life. A solid understanding of Mathematics may help students develop a plethora of skills that will be valuable to them in the future. Students may use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to help them comprehend the mathematical ideas discussed in Class 8 Maths Chapter 3 Exercise 3.1. The mathematical ideas covered in the NCERT Class 8 Mathematics textbook are critical to the development of students’ mathematical abilities. Students can use Extramarks’ study materials and learning tools to improve their comprehension of the fundamentals of Mathematics. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, are available on the Extramarks website or mobile application. Students should pay close attention to the mathematical concepts taught in Class 8 Maths Chapter 3.1.
NCERT Solutions For Class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.1) Exercise 3.1
Extramarks is an educational website that students use to obtain study material for various examinations. It is one of the most reputed educational websites, with students and parents relying on it to provide extensive and comprehensible preparatory materials. The Extramarks website offers online live sessions conducted by individuals who are experts in their domain. Students must make a conscious effort to learn and comprehend the mathematical concepts covered in the Class 8 Mathematics curriculum. Students must improve their comprehension of mathematical concepts. This has a significant impact on the performance of Class 8 students in the Senior Secondary Examination of Mathematics. The Extramarks website provides students with the required study materials in PDF format. Extramarks has made this service accessible to assist students in obtaining the essential study material in a timely and optimised manner. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, may also be obtained via the Extramarks website or learning application. Students in Class 8 may use the Extramarks website to get the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, in PDF format to help them prepare for the Senior Secondary Mathematics Exam.
If students have any questions regarding the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, they may attend doubtsolving sessions on Extramarks or inquire about them on the Extramarks website or mobile application. Extramarks offers NCERT solutions for all classes, from Class 1 to Class 12. Extramarks offers students the option of accessing study material in PDF format. In light of the fact that students may not always be able to access the internet, Extramarks has provided students with the option of downloading the essential study material in PDF format. Students may use the downloadable NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to help them prepare for the Senior Secondary Mathematics Examination.
Class 8 Maths Chapter 3 Exercise 3.1
Students must improve their knowledge of mathematical concepts. This has a significant impact on the success of Class 8 students in the Senior Secondary Examination in Mathematics. It is advised that students practice the NCERT Class 8 Maths Chapter 3 Exercise 3.1 problems and solutions in order to obtain a thorough understanding of the senior secondary examination syllabus. It is recommended that students use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to solve the problems in Class 8 Mathematics Chapter 3 Understanding Quadrilaterals. Furthermore, it is critical to put in extra effort when studying the chapters that have the highest weightage in the senior secondary examination. Students are urged to use the Class 8 Maths Chapter 3 Exercise 3.1 Solutions on a regular basis to practise the exercise problems and solutions.
When solving problems in the Mathematics examination, students must manage their time effectively. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, assist students in understanding how to successfully manage their time throughout the Mathematics examination. Students choose their academic specialisation for Classes 11 and 12 based on their performance in the Senior Secondary Examinations. Students are advised to practice the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 in order to get higher scores and choose a field of study of their interest in Class 11 and Class 12. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, can be obtained by students from the Extramarks website and mobile application.
Exercise 3.1
Exercise 3.1 of Chapter 3 Understanding Quadrilaterals is one of the essential exercises in the Class 8 Mathematics curriculum. Students must rigorously practice the Class 8 Mathematics Exercise 3.1 Solutions to have a thorough comprehension of the ideas taught in Exercise 3.2. Extramarks’ NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 that can be availed from the Extramarks website. It is recommended that students practice NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, on a daily basis. Exercise 3.1 includes a number of fundamental ideas that students must understand in order to do well on the Senior Secondary Examination of Mathematics. Students may acquire the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 from the Extramarks website or mobile application.
Students must attempt all the questions on the Senior Secondary Mathematics Examination question paper in order to enhance their chances of receiving higher marks. It is also recommended that students practice sample papers and past years’ papers in order to better prepare for the Senior Secondary examination. Practising example papers and previous years’ exams can provide students with a sense of the final exam, which can help them overcome any anxiety or apprehension they may have regarding the examination. Students may refer to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, provided by Extramarks.
What Is A Plane Curve?
A curve that lies in a single plane is a Plane Curve. Chapter 3 Understanding Quadrilaterals of the NCERT Mathematics textbook for Class 8 provides an overview of the topic of the Plane Curve. In the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, topics such as What is a Polygon?, Classifications of Polygons, Irregular and Regular Polygons, and Angle Sum Property are covered. Students are advised to thoroughly study the topic “Plane Curve” because it is one of the most practical and applicationbased topics covered in the Mathematics curriculum of Class 8. It is essential that students understand the importance of thoroughly understanding the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1. Students must make it a point to practice the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 regularly and repeatedly. It may be timeconsuming to attempt Plane Curve questions during the Senior Secondary examination; thus, it is recommended that students practice such questions ahead of time in order to be prepared for the final examination. Students can use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, if they have any questions about the topic. While preparing for the Senior Secondary examination, students should establish and adhere to a timetable. Having a timetable may assist students in achieving higher scores in the Senior Secondary Examination of Mathematics in Class 8.
What Is A Polygon?
It is crucial that students understand What a Polygon is to have an overall understanding of Class 8 NCERT Mathematics Chapter 3 Understanding Quadrilaterals. Students can use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 provided by Extramarks to gain a better understanding of the concepts introduced in Chapter 3 of the NCERT Mathematics textbook for Class 8. Students can acquire the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 from the Extramarks website or mobile application for their preparation.
The Senior Secondary Examination in Mathematics for Class 8 is based on the NCERT curriculum. It is advisable to study with the help of the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, as they have been prepared as per the requirements of the NCERT curriculum. Students may access any required study material or learning resources for their preparation from Extramarks. In case of any doubts, students have the provision of attending doubtsolving classes in relation to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 on the Extramarks website.
Classifications Of Polygons
Classifications of Polygons is one of the most important topics that are a part of the syllabus of NCERT Mathematics Chapter 3 Understanding Quadrilateral. Understanding the concerned topic and its concepts is crucial to students’ preparation for the Senior Secondary Mathematics Examination of Class 8. Students may refer to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, to understand the concepts of the Classifications of Polygons. Referring to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, can benefit students’ preparation in terms of scoring higher marks in the senior secondary examination. Students can obtain the required learning resources to prepare for the Senior Secondary Examination of Mathematics from Extramarks by registering themselves on the Extramarks website. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 can be availed by students of Class 8 from the Extramarks website or learning application.
Irregular & Regular Polygons
The topic of Irregular and Regular Polygons has been covered in the syllabus for Class 8 Mathematics Chapter 3 Understanding Quadrilaterals. The topic of Irregular and Regular Polygons and their differences is one of the most important areas of Mathematics that has been covered in the concerned syllabus. Students are suggested to thoroughly comprehend the mathematical principles of Irregular and Regular Polygons. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, expand on the concerned topic in an elaborate manner for students to be able to efficiently learn about the concerned topic. Students of Class 8 that are appearing for the Senior Secondary Examination of Mathematics are encouraged to work on the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 regularly for better preparation. Class 8 students may acquire the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 for their preparation from the Extramarks website or mobile application.
Angle Sum Property
Students of Class 8 must understand the mathematical concepts of Angle Sum property to master NCERT Mathematics Chapter 3 Understanding Quadrilateral. Angle Sum Property is a complex topic. It requires a substantial amount of time and effort from students to understand the mathematical concepts related to this topic. Students may refer to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to better understand the concepts introduced in Chapter 3 Understanding Quadrilaterals of Mathematics.
It is essential that students understand all the topics that have been covered in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to perform well in the Senior Secondary Mathematics Examination. Students can increase their chances of securing high marks in the Mathematics examination by being regular with their practice of the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 are available on the Extramarks website and mobile application for students of Class 8 to access for their preparation.
NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1
Students are advised to begin preparing for the Senior Secondary Examination of Mathematics at the start of the academic year, as Mathematics can be a complex subject. Mastering this subject takes time, practice, and effort. It takes a considerable amount of time to develop the skills required to master Mathematics. Students must thoroughly comprehend the mathematical principles in order to build the necessary skills to master Mathematics. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, which are available on the Extramarks website, can assist students in preparing for the Senior Secondary Examination of Mathematics.
The NCERT Chapter 3 Understanding Quadrilaterals is one of the most important chapters taught in the Class 8 NCERT Mathematics syllabus. It is critical for students to understand that chapter 3 Understanding Quadrilaterals has a significant weightage in the Senior Secondary Examination of Mathematics. Students must devote more time and practice to the chapters that carry the most weightage in the examination. Focusing on chapters with a greater mark distribution can help students study for their exams more constructively. Students may practice for the Senior Secondary Mathematics Examination with the help of the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1.
The question paper for the senior secondary examination is based on the NCERT textbooks. Students must work hard to thoroughly cover and understand the NCERT textbook syllabus. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, include all of the concepts required for students to excel in the examination of Mathematics. To secure exceptional marks in the senior secondary examination, students must practice the NCERT exercise questions and answers with the assistance of the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1.
NCERT Solutions for Class 8
Students are recommended to study the NCERT exercise problems and solutions in order to prepare for the senior secondary examinations, as the question paper pattern for the pertinent examinations is based on the NCERT curriculum. The NCERT curriculum serves as the primary source of reference for the framework of the senior secondary examination. The concepts covered in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, are essential for the Senior Secondary Mathematics Examination. When preparing for these exams, using the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, can be advantageous. Students should make an effort to understand the concepts presented in the concerned exercise in order to be adequately prepared for the final exam. In order to adequately prepare for the senior secondary examination, students must adhere to a schedule that commits significant time to each topic covered in the curriculum. Students can use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, for their preparation.
Extramarks offers thorough performance reports to help students track the progress of their preparation. Students may engage in online live sessions while studying NCERT Class 8 Mathematics Chapter 3 – Understanding Quadrilaterals for a better understanding of the key topics. It is recommended that students regularly practice the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 in order to do well in the senior secondary examination. Students must attentively study the chapters, and answering the practice questions will help them understand the concepts more accurately. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1, may help students better comprehend the numerous concepts of Mathematics introduced in Chapter 3.
Q.1 Given here are some figures.
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c)Polygon
(d) Convex polygon
(e) Concave polygon
Ans
(a) Simple curve: 1, 2, 5, 6, 7
(b) Simple closed curve: 1, 2, 5, 6, 7
(c) Polygon: 1, 2
(d) Convex polygon: 2
(e) Concave polygon: 1
Q.2 How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle
Ans
(a)
A convex quadrilateral has 2 diagonals.
(b)
A regular hexagon has 9 diagonals.
(c)
A triangle does not have any diagonal.
Q.3 What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a nonconvex quadrilateral and try!)
Ans
Let ABCD be a convex quadrilateral. Draw a diagonal BD. Now, this quadrilateral is divided into two triangles ABD and BC
\begin{array}{l}\text{We know that, the sum of interior angles of a triangle is 18}{0}^{\circ}.\\ \therefore \text{The sum of interior angles of a quadrilateral}=\text{18}{0}^{\circ}\text{+18}{0}^{\circ}\\ \text{}={360}^{\circ}\\ \text{Hence,the sum of the measures of the angles of a convex}\\ \text{quadrilateral is}\text{\hspace{0.17em}}{360}^{\circ}.\end{array}
If the quadrilateral is not convex, then also this property holds.
This quadrilateral can also be divided into two triangles ABD and ACD.
\begin{array}{l}\text{We know that, the sum of interior angles of a triangle is 18}{0}^{\circ}.\\ \therefore \text{The sum of interior angles of a quadrilateral}=\text{18}{0}^{\circ}\text{+18}{0}^{\circ}\\ \text{}={360}^{\circ}\\ \text{Hence,the sum of the measures of the angles of a concave}\\ \text{quadrilateral is}\text{\hspace{0.17em}}{360}^{\circ}.\end{array}
Q.4 Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
What can you say about the angle sum of a convex polygon with number of sides?
(a) 7 (b) 8 (c) 10 (d) n
Ans
From the table it can be observed that the angle sum of a convex polygon of n sides is (n – 2)×180°.
Therefore, for given number of sides, the sum of the angles are:
$\begin{array}{l}\left(\mathrm{a}\right)\text{}7:(72)\times {180}^{\circ}={900}^{\circ}\\ \left(\mathrm{b}\right)\text{}8:(82)\times {180}^{\circ}={1080}^{\circ}\\ \left(\mathrm{c}\right)\text{}10:(102)\times {180}^{\circ}={1440}^{\circ}\\ \left(\mathrm{d}\right)\text{}\mathrm{n}:(\mathrm{n}2)\times {180}^{\circ}\end{array}$
Q.5 What is a regular polygon? State the name of a regular polygon of
(i) 3 sides (ii) 4 sides (iii) 6 sides
Ans
A polygon which is “equilateral” and “equiangular” is called a regular polygon.
(i) 3 sides: Equilateral triangle
(ii) 4 sides: Square
(iii) 6 sides: Regular Hexagon
Q.6 Find the angle measure x in the following figures.
Ans
$\begin{array}{l}\text{We know that the sum of interior angles of a}\\ \text{quadrilateral is}{360}^{\circ}.\\ \\ \therefore \text{From the given quadrilateral ,we have}\\ {50}^{\circ}+{130}^{\circ}+{120}^{\circ}+\mathrm{x}={360}^{\circ}\\ \Rightarrow 300\mathrm{\xb0}+\mathrm{x}={360}^{\circ}\\ \Rightarrow \mathrm{x}={360}^{\circ}300\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=60\mathrm{\xb0}\end{array}$
$\begin{array}{l}\mathrm{From}\text{}\mathrm{the}\text{}\mathrm{figure},\\ \text{}90\mathrm{\xb0}+\mathrm{a}=180\mathrm{\xb0}\text{}\left(\mathrm{Linear}\text{}\mathrm{pair}\right)\\ \Rightarrow \mathrm{a}=180\mathrm{\xb0}90\mathrm{\xb0}=90\mathrm{\xb0}\\ \\ \mathrm{Now},\mathrm{the}\text{}\mathrm{sum}\text{}\mathrm{of}\text{}\mathrm{all}\text{}\mathrm{the}\text{}\mathrm{interior}\text{}\mathrm{angles}\text{}\mathrm{of}\\ \mathrm{a}\text{}\mathrm{quadrilateral}\text{}\mathrm{is}\text{}360\mathrm{\xb0}.\text{}\\ \\ \therefore \mathrm{in}\text{}\mathrm{the}\text{}\mathrm{given}\text{}\mathrm{quadrilateral},\\ 60\mathrm{\xb0}+70\mathrm{\xb0}+\mathrm{x}+90\mathrm{\xb0}=360\mathrm{\xb0}\\ \Rightarrow 220\mathrm{\xb0}+\mathrm{x}=360\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=140\mathrm{\xb0}\end{array}$
From the figure, we have
70+a =180° (Linear Pair)
a = 110°
Also, 60°+b = 180° (Linear Pair)
b= 120°
Since the pentagon has 5 sides, so the sum of all the interior
angles of a pentagon is 540°.
Therefore, we have
120°+110°+30°+x+x = 540°
260° + 2x = 540°
2x= 280°
x = 140°
$\begin{array}{l}\text{We know that the sum of all the interior angles of a}\\ \text{pentagon is 54}{0}^{\circ}.\\ \text{Since, all the sides are equal,therefore, all the angles are equal,}\\ \text{Hence, it is a regular pentagon.}\\ \therefore \text{5}\mathrm{x}=\text{54}0\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=\text{1}0\text{8}\mathrm{\xb0}\end{array}$
Q.7
(a) Find x + y + z
(b) Find x + y + z + w
Ans
$\begin{array}{l}\left(\text{a}\right)\\ \mathrm{x}+\text{9}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \Rightarrow \mathrm{x}=\text{9}0\mathrm{\xb0}\\ \\ \mathrm{z}+\text{3}0\mathrm{\xb0}\text{}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \Rightarrow \mathrm{z}=\text{15}0\mathrm{\xb0}\\ \\ \text{We know that, the exterior angle is equal to the}\\ \text{sum of interior opposite angles.}\\ \therefore \mathrm{y}=\text{9}0\mathrm{\xb0}\text{}+\text{3}0\mathrm{\xb0}\text{}\\ \Rightarrow \mathrm{y}=\text{12}0\mathrm{\xb0}\\ \\ \mathrm{Hence},\\ \mathrm{x}\text{}+\text{}\mathrm{y}\text{}+\text{}\mathrm{z}=\text{9}0\mathrm{\xb0}+\text{12}0\mathrm{\xb0}+\text{15}0\mathrm{\xb0}\text{}\\ \text{}=\text{36}0\mathrm{\xb0}\end{array}$ $\begin{array}{l}\text{(b)}\\ \text{We know that, the sum of the measures of all interior}\\ \text{angles of a quadrilateral is 3}{60}^{\circ}.\text{}\\ \\ \text{Therefore,}\\ a+\text{6}0\mathrm{\xb0}+\text{8}0\mathrm{\xb0}+\text{12}0\mathrm{\xb0}=\text{36}0\mathrm{\xb0}\\ \Rightarrow a+\text{26}0\mathrm{\xb0}=\text{36}0\mathrm{\xb0}\\ \Rightarrow a=\text{1}00\mathrm{\xb0}\end{array}$ $\begin{array}{l}\mathrm{Also},\\ \mathrm{x}+\text{12}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \Rightarrow \mathrm{x}=\text{6}0\mathrm{\xb0}\\ \\ \mathrm{y}+\text{8}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \Rightarrow \mathrm{y}=\text{1}00\mathrm{\xb0}\\ \\ \mathrm{z}+\text{6}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \Rightarrow \mathrm{z}=\text{12}0\mathrm{\xb0}\\ \\ \mathrm{w}+\text{1}00\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Linear pair}\right)\\ \mathrm{w}=\text{8}0\mathrm{\xb0}\\ \\ \text{Hence,}\\ \mathrm{x}+\mathrm{y}+\mathrm{z}+\mathrm{w}=\text{6}0\mathrm{\xb0}+\text{1}00\mathrm{\xb0}+\text{12}0\mathrm{\xb0}+\text{8}0\mathrm{\xb0}\\ \text{}=\text{36}0\mathrm{\xb0}\end{array}$
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FAQs (Frequently Asked Questions)
1. Where can Class 8 students obtain study materials to help themselves prepare for the Senior Secondary Examination of Mathematics?
Extramarks is one of the most reliable educational websites. Students are advised to register on the Extramarks website or mobile application in order to get the necessary study material. To prepare for the senior secondary examination, students in Class 8 can use the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 have been meticulously compiled by professionals. Students can use the Extramarks website to access a variety of study materials, including online live sessions, example papers, past years’ papers, mock tests, revision notes, and so on, for their preparation.
2. Why is using the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 to prepare for the senior secondary examination advised for students of Class 8?
The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 on the Extramarks website and mobile application are incredibly trustworthy and genuine resources. Students must continue to review the chapters and do as many exercise questions as possible in order to gain higher scores on the Mathematics examination. Students in Class 9 are urged to utilise the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.1 for their preparation since they have been thoroughly prepared by professionals to assist students to understand the Mathematics topics better.