Studying for class 10 students is becoming more critical each passing year. The competition is tough and all parents expect their children to perform at the top level. At times the expectations take a toll on students and they get confused about what to do. **R D Sharma Solutions for Class 10** brings the students, a great relief as they can comfortably understand the concepts of each chapter of maths and secure impressive marks.

Each student desire to acquire the highest marks that can guide their successful career. However, there could be some gaps in the effort and these gaps can be bridged by studying solutions along with the textbooks. Many times we see parents taking a lot of tension over their child’s study and success in class 10 but finally, it depends on the student’s capability to grasp and express in the exam.

Table of Contents

**Mathematics **

**Chapter-wise Summary**

**Chapter 1 – Real Numbers**

Any number, excluding complex numbers, is a real number. Positive & negative integers, irrational numbers, and fractions are all examples of real numbers. Natural numbers are used to count objects, integers are used to measure temperature, rational numbers are used to represent fractions, irrational numbers are used to calculate the square root of a number, etc. In this chapter, the students will learn Euclid’s Division Lemma, Euclid’s Division Algorithm, the fundamental theorem of Arithmetic, prime factorization, method of finding LCM, method of finding HCF, a product of two numbers, applications of LCM & HCF in real-world problems, revisiting irrational numbers, proof of contradiction, and terminating & nonterminating decimals.

**Chapter 2 – Polynomials**

In this chapter, the students will learn what is polynomials & their types, algebraic expressions, the degree of a polynomial expression, graphical representation of the polynomial equation, factorization, relationship between zeroes & coefficient of a polynomial, etc, geometric representation of a linear polynomial, geometric representation of a quadratic polynomial, the graph of a polynomial, division algorithm, and algebraic identities.

**Chapter 3 – Pair of Linear Equations in Two Variables**

An equation ax+by+c is called a linear equation with two variables where a, b, and c are real numbers and a & b are not zero. In pair of linear equations with two variables, we see two such equations. From this chapter, the students will learn about pairs of linear equations in two variables & their representation, graphical representation, and algebraic methods of solving a pair of linear equations.

**Chapter 4 – Triangles**

As the students have learned that a triangle is a three-sided polygon with three edges and three vertices. A very important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is known as the angle sum property of a triangle. The students will further learn in detail about the definition of a triangle, shape of a triangle, angles of a triangle, properties, types, and perimeter of a triangle, area of a triangle, and area of a triangle using Heron’s formula.

**Chapter 5 – Trigonometric Ratios**

There are a total of six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Trigonometry is the branch of maths that deals with the sides and angles of a right-angled triangle. Hence the trig ratios are evaluated with respect to angles and sides. Here, the students will know the definition, how to find trigonometric ratios, the trigonometric ratios table, and trigonometric applications.

**Chapter 6 – Trigonometric Identities**

The trigonometric identities play an important role in trigonometric functions including expression or an equation. Trigonometric identities are true for every value of variables occurring on both sides of an equation. From this chapter, the students will learn what are trigonometric identities, list of trigonometric identities, reciprocal trigonometric identities, Pythagorean trigonometric identities, ratio trigonometric identities, trigonometric identities of opposite angles, trigonometric identities of complementary angles, trigonometric identities of supplementary angles, sum & difference of angles trigonometric identities, double angle trigonometric identities, half angle identities, and product-sum trigonometric identities.

**Chapter 7 – Statistics**

Statistics is a study of the collection, analysis, interpretation, presentation, and organization of data. Statistics is a branch of applied mathematics. There are two basic and important ideas involved in statistics; uncertainty and variation. Both can be determined only through statistical analysis. The uncertainties are determined by probability which is very important in statistics. The students will learn the basics of statistics, mathematical statistics, types of statistics, formulas, summary, scope, methods, data analysis, measures of dispersion, and application of statistics.

**Chapter 8 – Quadratic Equations**

In this chapter, the students will learn about quadratic polynomial, quadratic equation, the standard form of quadratic equation, solving quadratic equation by factorization, roots of a quadratic equation, solving a quadratic equation by completion of squares method, solving of a quadratic equation using the quadratic formula, discriminant, nature of roots, solving using quadratic formula when D>0, solving quadratic equation when D=0, solving quadratic equation when D<o, graphical representation of quadratic equation, formation of a quadratic equation from its roots, and sum & product of roots of a quadratic equation.

**Chapter 9 – Arithmetic Progressions**

Arithmetic progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. The students will learn what is arithmetic progression, notation in arithmetic progression, the first term of AP, common differences in arithmetic progression, the general form of an AP, arithmetic progression formulas, the nth term of an AP, types of AP, and a sum of N terms of AP.

**Chapter 10 – Circles**

A circle is a close two-dimensional geometrical figure such that all points on the surface of a circle are equidistant from the point called the ‘centre’. The distance from the centre to any point on the surface of a circle is ‘radius’. In this chapter, the students will know about circle & a line in a plane, tangent, secant, tangent as a special case of secant, two parallel tangents at most for a given secant, tangent perpendicular to the radius at the point of contact, the number of tangents drawn from a given point, length of a tangent, and lengths of tangents drawn from an external point.

**Chapter 11 – Constructions**

In this chapter, the students will learn how to construct the division of the line segment, constructions of triangles using scale factor, and construction of tangents to a circle with two different cases.

**Chapter 12 – Some Applications of Trigonometry**

From this chapter, the students will understand the concepts of heights and distances. It consists of a briefing on the technique used by astronomers too. The students can study horizontal level & line of sight, angle of elevation, angle of depression, calculate heights & distances, heights & distance summary, and measure the distances of celestial bodies with the help of trigonometry.

**Chapter 13 – Probability**

The branch of mathematics that measures the uncertainty of the occurrence of an event using numbers is called probability. The chance of an event is expressed on a scale ranging from 0-1. It could also be the percentage. The students will know about event & outcome, experimental probability, theoretical probability, elementary event, a sum of probabilities, impossible event, sure event, range of probability of an event, geometric probability, and complimentary events.

**Chapter 14 – Co-ordinate Geometry**

Co-ordinate geometry is the location of a point on the plane. It is denoted with the help of the ‘x’ and ‘y’ axis. In this chapter, the students will learn the basics of coordinate geometry, points on a Cartesian Plane, the distance between two points on the same coordinate axes, the distance between two points using Pythagoras theorem, distance formula, section formula, finding ratios between given points, midpoint, points of trisection, centroid of a triangle, area of a triangle given its vertices, and collinearity condition.

**Chapter 15 – Areas Related to Circles**

The area of a circle is the region occupied by the circle in a two-dimensional plane. The area of a circle helps to measure the space occupied by a circular plot or field. From this chapter, the students can understand the circle, area of a circle, derivation of an area of a circle, using areas of rectangles, using areas of triangles, the surface area of a circle, and the difference between square area & circle area.

**Chapter 16 – Surface Areas and Volumes**

From this chapter, the students will learn the following topics in detail. Surface area & volume of a cuboid, surface area & volume of a cube, surface area & volume of a cylinder, surface area & volume of a right circular cone, surface area & volume of a sphere, surface area & volume of a hemisphere, surface area & volume of a combination of solids, surface area & volume of a frustum of a cone, and conversion of solid from one shape to another.

**Importance of Mathematics**

All students desire to get good marks but the ambitious students always try to get more study material to look beyond the textbooks. They desire to achieve their goals in life so it is imperative for them to get high scores at the school level. Bright students study hard and make their impression as the first step towards success. **R D Sharma Solutions for Class 10 **will give their confidence a boost as the answers are arranged per the syllabus and in a much easier manner.

If the foundation is made strong by acquiring impressive marks in class 10, the further path becomes nice and easy. The students who rate their career as a top priority cannot miss the handy and helpful solution from R D Sharma.

**Future Opportunities for Maths Students**

Graduating or post-graduating in maths has a high potential to grab a great job with a handsome salary. The banking and financial sectors always welcome the students with excessive and impressive talent as the whole GDP of a country depends on the finance sector. To increase, per capita income, many schemes are launched and these schemes are designed by some great mathematicians. Let us see some of the important jobs maths graduates can seek –

- Statistician
- Mathematician
- Actuary
- Economist
- Data Analyst/Business Analyst/Big Data Analyst
- Operations Research Analyst
- Psychometrician
- Market Researcher

**Conclusion**

Maths is a very vast subject and whatever you learn will be insufficient for a thirsty student. Along with the textbooks, many guides are available that support the basic study of the students. Though the high or low marks in class 10 are not significant to the future success of students, they mark their path. In India, parents are tenser about their studies than their children because of the tradition of the education system. The concept of a high percentage of school and college end years are rated as directly proportional to their future and this is where the actual problem begins.

In a hoard of competition, the parents neglect the real capability of their children and expect too much from them. Bright students by nature do not worry about their studies because of their talent and confidence but expecting improbability from an average student is too much. However, this can be achieved to some extent with the help of R D Sharma Solutions for Class 10. Thereby, it is advisable to use this study material along with the textbooks to reduce the gap.

**FAQs**

**Are R D Sharma’s solutions for class 10 reliable?**

R D Sharma solutions are reliable because of easy readability and arrangement of answers. Sighting the difficulties faced by the students the solutions are structured in an appropriate way.

**Why to refer R D Sharma for class 10 study?**

R D Sharma solutions are tailor-made for the right way of answers. It consists of probable and important questions as well as a practice question sheet.

**How many chapters are covered in R D Sharma solutions for class 10?**

**R D Sharma Solutions for Class 10** covers all 16 chapters included in the syllabus.

**Can a student understand the answers neatly?**

R D Sharma solution set is a well-mannered set of answers. It can be one of the best study materials for class 10 students due to its student-friendly way of elaborative answers.

**Where can a student get R D Sharma solutions for class 10?**

Students can avail of the solutions can be availed from many of the educational websites in PDF format.

**What is the value addition in R D Sharma solutions?**

Wherever needed, the visuals are added for the betterment of students. This will make an average student easily understand the explanation.