We all know that education has the utmost importance as education leads to building a good generation and this education system can spread to all levels of the population through them. Education makes each person well cultured and gives the impetus to build further well-educated generations. As education is very important, Maths and Science are two subjects which are of prime importance.

**R D Sharma Solutions for Class 9** gives the opportunity to the students to improve upon their knowledge base and grow in their careers. Mathematics is a subject of great significance and needs in almost every field. Studying mathematics will be an advantage with a strong base to build a good career.

Table of Contents

**Mathematics**

**Chapter-wise summary**

**Chapter 1 – Number System**

The students will have the knowledge of numbers systems including rational and irrational numbers, representation of the numbers on a number line, real numbers, rationalization, and laws of exponents. The chapter tells the shortcut methods and tricks to solve the problems. The students will get the detailed knowledge of

**Number system **– It is a system of writing in order to express numbers. it is the mathematical notation to represent numbers of a given set consistently using digits or other symbols.

**Rational numbers **– It is defined as a number that is shown as p/q where q is not zero.

**Irrational numbers** – They are the real numbers that cannot be represented as a simple fraction. They cannot be expressed as a ratio and are in contradiction to rational numbers.

**Real numbers** – Real numbers are defined as the union of both rational and irrational numbers. They can be positive and negative and denoted as ‘R’.

**Chapter 2 – Exponents of Real Numbers**

In this chapter, the students will learn about various problems with an integral exponent of a real number, laws of integral exponents, and rational exponents of a real number. Exponents are used to showing the repeated multiplication of a number by itself. The students will also understand the concepts of products with the same bases, quotient with the same bases, power raised to a power, product of a power, quotient to a power, zero power, negative exponent rule, and fractional exponent rule.

**Chapter 3 – Rationalization**

Here, the concepts of rationalization are explained in a step-by-step manner. The chapter consists of problems based on identities and the rationalization of the denominator.

**Chapter 4 – Algebraic Identities**

This chapter contains exercise-wise problems solved based on the concepts like identities, identity for the square of a trinomial, identity for the cube of a binomial, sum & difference of cubes, and another identity. These solutions are algebraic expressions that are well structured in an interactive manner.

**Chapter 5 – Factorization of Algebraic Expressions**

From this chapter, the students will learn the factorization of algebraic expressions, factorization using common factors, factorization by regrouping terms, and factorizing expressions using standard identities.

**Chapter 6 – Factorization of Polynomials**

In this chapter, the students will understand the concepts of polynomials, types of polynomial, the degree of a polynomial, linear polynomial, quadratic polynomial, cubic polynomial, and the value of a polynomial, zeroes of a polynomial, remainder theorem, factor theorem, and algebraic identities.

**Chapter 7 – Introduction to Euclid’s Geometry**

This chapter consists of the details on an introduction to Euclid’s geometry, Euclid’s postulates, Euclid’s axioms, theorem, and equivalent versions of Euclid’s fifth postulate, and important questions.

**Chapter 8 – Lines and Angles**

From this chapter, the students can learn basic terms & definitions of lines & angles, intersecting & non-intersecting lines, pair of angles, axiom linear pair of angles, axiom converse lo linear pair of angles, theorem of vertically opposite angles, parallel lines with a transversal, corresponding angles axiom, the converse of corresponding angles axiom, alternate interior angles theorem, the converse of alternate interior angles theorem, the sum of co-interior angles are supplementary, lines parallel to the same lines, and angle sum property of a triangle.

**Chapter 9 – Triangle, Its Angles, and Congruent Triangles**

This chapter speaks about the congruent triangles, criteria for congruency, SSS criteria for congruency, SAS criteria for congruency, ASA criteria for congruency, AAS criteria for congruency, RHS criteria for congruency, properties of an isosceles triangle, and inequalities in triangles.

**Chapter 10 – Co-ordinate Geometry**

This chapter elaborates on the coordinate geometry, Cartesian system, origin, coordinate axes & quadrants, points in different quadrants, plotting on a graph, plotting a point in the plane if its coordinates are given, and solved examples.

**Chapter 11 – Heron’s Formula**

Triangle is a closed three-dimensional figure. The students will get to know triangles, the area of an equilateral triangle, the area of an isosceles triangle, the area of a triangle by Heron’s formula, and the area of any polygon by Heron’s formula.

**Chapter 12 – Linear Equations in Two Variables**

In this chapter, the students will learn about linear equation in one variable, linear equation in 2 variables, the solution of linear equation in 2 variables, graphical presentation of a linear equation in 2 variables, solutions of linear equation in 2 variables on a graph, lines passing through the origin, and lines parallel to coordinate axes.

**Chapter 13 – Quadrilaterals**

This chapter details the concept of a quadrilateral. A quadrilateral is a shape that has four sides. In this chapter students can learn parallelogram – opposite sides of a parallelogram are equal, opposite angles of a parallelogram are equal, properties of diagonal of a parallelogram, diagonals of a rhombus bisect each other at right angles, diagonals of a rectangle bisect each other & are equal, diagonals of a square bisect each other at right angles & are equal, important results related to a parallelogram, the mid-point theorem, quadrilaterals, angle sum property of quadrilateral, types of quadrilaterals, Venn diagram of different types of quadrilaterals.

**Chapter 14 – Areas of Parallelograms and Triangles**

This chapter talks about the figures on the common base & between the same parallels, the area of a parallelogram, the area of a triangle, triangles on the common base & between the same parallels, two triangles having the common base & equal areas, and a parallelogram & a triangle between the same parallels.

**Chapter 15 – Circles**

This chapter gives students an insight into the introduction of circles, radius, tangent & secant, chord, diameter, circumference, arc, segment & sector, circles & their chords, theorem of equal chords subtending angles at the center, theorem of equal angles subtended by different chords, perpendicular from the center to a chord bisects the chord, a line through the center that bisects the chord is perpendicular to the chord, circle through 3 points, equal chords are at equal distances from the center, chords equidistant from the center are equal, the angle subtended by an arc of a circle on the circle and at the center, the angle subtended by diameter on the circle, a line segment that subtends equal angles at two other points, the sum of opposite angles of a cyclic quadrilateral, and the sum of pair of opposite angles in a quadrilateral.

**Chapter 16 – Constructions**

In this chapter, the students will know about introduction to constructions, linear pair axiom, angle bisector, construction of an angle bisector, construction of a perpendicular bisector, proof of the validity of construction of a perpendicular bisector, construction of an angle of 60 degrees, proof for the validity of construction of an angle of 60 degrees, construction of triangles, given base, base angle, and the sum of other two sides, given base, base angle, and AB-AC, proof for validation for construction of a triangle with given base, base angle, and the difference between two sides, given base, base angle, and AC-AB, given perimeter & two base angles, and proof for validation for construction of a triangle with given perimeter and two base angles.

**Chapter 17 – Surface Areas and Volume of a Cuboid, Cube, Circular Cylinder, Right Circular Cone,** **Sphere**

This chapter details the surface area and volume of different figures. This includes cuboid & cube, circular cylinder, right circular cone, and sphere. The students will learn about the surface area and volume of a cuboid, the lateral surface area of a cuboid, cube, the total surface area of a cube, the lateral surface area of a cube, the right regular cylinder, the curved surface area of a right circular cylinder, the total surface area of a right circular cylinder, right circular cone, the relation between slant height & height of a right circular cone, the curved surface area of a right circular cone, the total surface area of a right circular cone, the surface area of a sphere, volume of a cuboid, cube, right circular cylinder, right circular cone, sphere, and volume & capacity.

**Chapter 18 – Tabular Representation and Graphical Representation of Statistical Data**

This chapter tells the students the introduction to statistics, data, frequency, ungrouped data, grouped data, class interval, frequency table, sorting, ungrouped frequency table, grouped frequency table, bar graphs, variable being a number, histograms, frequency polygon, midpoint of the class interval, equality of areas, average, mean, mode, and median.

**Chapter 19 – Measures of a Central Tendency**

This chapter is about the measures of a central tendency, definition, mean, median, mode, and measures of central tendency & dispersion.

**Chapter 20 – Probability**

This chapter teaches the students about the introduction to probability, experiment, trial, experimental/empirical probability, coin tossing experiment, rolling of dice experiment, and the sum of probabilities of favorable & unfavorable events.

**Importance of Mathematics**

Mathematics is the base of Science and it is needed in many fields too. it is proven from a survey that most students voted Maths as the most difficult subject. As we all know, math is the most significant part of human logic and thoughts. Maths will enable people to understand various transactions and processes. In day-to-day life also Maths is used automatically and small dealings are done with calculations.

Maths is used in several fields and disciplines. Math concepts are used in engineering, economics, and Science. Despite this, the students struggle to cope with the complexity of the subject. Moreover, the answers in Maths cannot be partially wrong or correct; they can either be right or wrong. Another aspect of Maths is that it needs consistent effort to perform well in the subject. R D Sharma Solutions for Class 9 will help students exclusively to score higher marks.

**Interesting uses of Mathematics in daily life**

You will be surprised with the following list but if you think properly, you will agree with each point mentioned –

- Shopping at the most favorable price
- Cooking delicious food
- Playing music
- Making financial decisions
- Estimating the time, distance, and cost of a journey
- Balancing the checkbook
- Understanding sports
- Developing/Enhancing problem-solving skills
- Knowing the process of loans for various purposes

**Conclusion**

Mathematics is a number game and for those who like to play around the number and are willing to understand the subject by heart, the sky is the limit. We know that many great mathematicians have contributed heavily to the nation’s growth. A highly talented batch of mathematicians can change the economy of the country but the hurdle is the availability of such people.

Mathematics is a highly respected branch but because of the complex nature of the subject, most students find it difficult to deal with it. At class 9 level, building a strong base for Maths is a good opportunity for the aspirants provided they get proper guidance. **R D Sharma Solutions for Class 9**, partially, takes this responsibility to build a good generation with its simple yet appropriate way of structuring the solutions.

## FAQs

**Why is R D Sharma’s solution referred by the students?**

**R D Sharma Solutions for Class 9** are designed by experts and professionals. Due to the easy way of answering the description, most students prefer these.

**Why Maths is an important subject?**

Mathematics supports the development and enhances logical and critical thinking hence Maths is an important subject.

**How many chapters are included in the syllabus?**

There are a total of 16 major chapters and topics wise there are 20 descriptions.

**What are the job opportunities for Maths graduates?**

Apart from the banking and financial sectors, Maths graduates can explore opportunities in various organizations and even government sectors.

**Can a student opt for Maths along with a specialization in Statistics?**

Yes, specialization in Statistics can give the candidate bigger chances of high-profile jobs.

**Can a student opt to research Maths?**

Yes, but it is not easy to do research in mathematics unless you are prepared to devote your all time and you have the basic essential knowledge of advanced mathematical tools used in various fields.