Another book on mathematics which I recommend for Class 9-10 CBSE students is MATHEMATICS by R.D Sharma. I will talk about the book for Class 9 now:
Chapter 1 is called NUMBER SYSTEM. It has good explanations on the number line, conversions of rational numbers into decimal form and vice versa, followed by irrational numbers (along with some theorems) and how to represent them on the number line, real numbers and real number line and contains an algorithm on how to find the positive square root of a positive real number and how to represent it on the number line (important).
Chapter 2 is called EXPONENTS OF REAL NUMBERS. It talks about positive and negative integral exponents of a real number along with laws (important) and rational exponents of a real number along with laws (important).
Chapter 3 is called RATIONALISATION. It starts by listing some useful identities (important) and describes rationalisation of denominator (important).
Chapter 4 is called ALGEBRAIC IDENTITIES. It starts with a recap of algebraic identities you have learnt in previous classes and introduces you to new ones along with proofs.
Chapter 5 is called FACTORIZATION OF ALGEBRAIC EXPRESSIONS. It shows you how to factorize different types of algebraic expressions.
Chapter 6 is called FACTORIZATION OF POLYNOMIALS. It defines a polynomial with related concepts, discusses the concept of roots of polynomials with related theorems (important), remainder theorem (very important), factor theorem (very important), factorization of polynomials by using factor theorem (very important).
Chapter 7 is called LINEAR EQUATIONS IN TWO VARIABLES. It starts with a definition, followed by solution of a linear equation in two variables, shows you how to draw graphs of the same (important) and also shows you to draw the equations of lines parallel to the x and y-axes (important). (More in Class 10)
Chapter 8 is called CO-ORDINATE GEOMETRY. It describes the cartesian co-ordinate axes, quadrants, cartesian co-ordinates of a point, sign convention and plotting of points (More in Class 10).
Chapter 9 is called INTRODUCTION TO EUCLID’S GEOMETRY. It mostly explains basic concepts of geometry such as point, plane and line, properties of points and lines, parallel and intersecting lines along with theorems, concepts related to line segments, the concepts of ray, half-line and line separation and half-plane.
Chapter 10 is called LINES AND ANGLES. It describes angles and related concepts, different types of angles, relations between angles along with theorems, different types of angles made by a transversal with two lines along with theorems.
Chapters 9 and 10 are very important chapters which will form the basis of what you will learn later on about geometry.
Chapter 11 is called TRIANGLE AND ITS ANGLES. It talks about the different types of triangles followed by some important theorems and exterior angles of a triangle along with related theorems.
Chapter 12 is called CONGRUENT TRIANGLES. It starts with congruence of line segments and angles and moves on to congruence of triangles followed by different criteria for congruency (very important) and theorems on inequality relations in triangles.
You will learn more about triangles in Class 10.
Chapter 13 is called QUADRILATERALS. It introduces you to quadrilaterals along with related concepts, defines the various types of quadrilaterals, contains a lot of important theorems on parallelograms, important theorems on the rectangle, rhombus and square and ends with a couple of theorems on triangles which are proved by making use of the theorems you learnt on parallelograms.
Chapter 14 is called AREAS OF PARALLELOGRAMS AND TRIANGLES. It contains many theorems involving calculation of areas of different combinations of parallelograms and triangles.
Chapter 15 is called CIRCLES. It starts with some basic concepts related to circles followed by many very important theorems. Then it introduces you to cyclic quadrilaterals followed by many theorems related to the same. (More in Class 10)
Chapter 16 is called Constructions. It starts with some basic constructions followed by constructions involving triangles. Learn and practice all the methods well: they are important for your exams. (More in Class 10)
Chapter 17 is called HERON’S FORMULA. It lists formulae for calculating perimeters and areas of a square, rectangle, certain triangles and a parallelogram, followed by Heron’s formula. You can expect questions from this chapter, so study and practice everything well.
Chapter 18 is called SURFACE AREA AND VOLUME OF A CUBOID AND CUBE. It starts by describing a cuboid and cube and shows you how to calculate the surface area and lateral surface area as well as volume of the same.
Chapter 19 is called SURFACE AREA AND VOLUME OF A RIGHT CIRCULAR CYLINDER. It starts by describing a right circular cylinder along with related terms and derives the formulae for calculation of the surface area of a right circular cylinder and a hollow cylinder as well as the formulae for calculation of the volume of a right-circular cylinder and a hollow cylinder.
Chapter 20 is called SURFACE AREA AND VOLUME OF A RIGHT CIRCULAR CONE. It introduces you to a right circular cone (along with related concepts) and shows you how to calculate the surface area and volume of a right circular cone.
Chapter 21 is called SURFACE AREA AND VOLUME OF A SPHERE. It describes several concepts related to spheres and lists formulae for calculating the surface area and volume of a sphere, hemisphere and spherical shell.
Chapter 22 is called TABULAR REPRESENTATION OF STATISTICAL DATA. It explains primary and secondary data, presentation of data, frequency distributions (very important), contains algorithms on how to construct discrete and grouped frequency distributions and introduces you to cumulative frequency distributions.
Chapter 23 is called GRAPHICAL REPRESENTATION OF STATISTICAL DATA. It talks about bar graphs and shows you how to construct bar graphs, describes histograms and shows you how to construct different kinds of histograms as well as frequency polygons.
Chapter 24 is called MEASURES OF CENTRAL TENDENCY. It discusses arithmetic mean of ungrouped data along with properties (important) as well as describes different methods of calculating the arithmetic mean of grouped data, defines median and shows you how to compute median of ungrouped data and discusses its properties and uses. Similarly defines mode, shows you how to compute mode of ungrouped data and lists uses and properties of mode.
You will learn more about statistics in Class 10.
Chapter 25 is called PROBABILITY. It introduces you to the concept of probability and explains various important terms. Make sure you understand the basics well because you will need these concepts not just for your exams but in higher classes as well (More in Class 10).
Here is a discussion on the Class 10 book:
Chapter 1 is called REAL NUMBERS. It has a brief discussion on divisibility followed by Euclid’s division lemma and division algorithm (along with proof) and the fundamental theorem on arithmetic along with applications.
Chapter 2 is called POLYNOMIALS. It starts with a brief recap followed by graphs of polynomials, some formulae involving roots and coefficients of polynomials and division algorithm for polynomials. Everything in this chapter is very important not just for your exams, but for higher classes also, so study it well.
Chapter 3 is called PAIR OF LINEAR EQUATIONS IN TWO VARIABLES. You started learning about this topic in Class 9. Here you will learn about simultaneous linear equations in two variables along with their graphs and how to solve them graphically and algebraically, conditions for solvability and how to use them to solve different kinds of word problems.
Chapter 4 is called QUADRATIC EQUATIONS. It introduces you to quadratic equations and its roots, formulation of quadratic equations, different methods of solving quadratic equations, concepts involving roots and shows you how to solve different kinds of word problems using quadratic equations.
Chapter 5 is called ARITHMETIC PROGRESSIONS. It starts explaining sequences in general and then talks about Arithmetic Progressions (A.P), how to find the general term of an A.P from the beginning and from the end, middle term of a finite A.P, shows you how to select terms of an A.P to solve problems and derives the formula for the sum to ‘n’ terms of an A.P.
Chapter 6 is called CO-ORDINATE GEOMETRY. There is a recap of what you learnt in Class 9 followed by derivations of the formula of distance between two points, section formulae along with applications and area of a triangle.
Chapter 7 is called TRIANGLES. It introduces you to the concept of similarity and then talks about similar polygons, similar triangles and their properties, followed by basic proportionality theorem and it’s converse, theorems on internal and external bisectors in triangles and more theorems involving proportionality. The second half of the chapter explains criteria for similarity of triangles followed by more theorems related to similarity in triangles and Pythagoras theorem along with important results based on it. This is an extremely important chapter: study it well and practice the problems thoroughly.
Chapter 8 is called CIRCLES. It describes secant and tangent and theorems related to tangents (all very important). This is another very important chapter for your exams, so study everything thoroughly and practice the problems well.
Chapter 9 is called CONSTRUCTIONS. It shows you methods of division of a line segment, how to construct a triangle similar to a given triangle, tangents to a circle at a given point (both when the centre is known and not known) and tangents from an external point (both when the centre is known and not known). You will see questions like the ones in this chapter in your exams, so study it thoroughly.
Chapter 10 is called TRIGONOMETRIC RATIOS. It lists the formulae for trigonometric ratios, relations between trigonometric ratios, derives the values of trigonometric ratios of specific angles as well the formulae for trigonometric ratios of complementary angles.
Chapter 11 is called TRIGONOMETRIC IDENTITIES. It proves some very important trigonometric identities and how to use them.
Chapter 12 is called HEIGHT AND DISTANCE. This chapter teaches you to solve problems regarding heights and distances using trigonometric concepts that you have learnt before. It explains angles of elevation and depression and contains many examples which you should practice again and again until you are comfortable with them because you will see similar problems in your exams.
Study the chapters on trigonometry until they are like second nature to you: many of you will see these concepts in higher classes in much more detail.
Chapter 13 is called AREAS RELATED TO CIRCLES. It starts with the basic formulae for perimeter and area of a circle and shows you how to calculate the area enclosed by two concentric circles, defines a sector and derives the formula for calculating the area of a sector, defines a segment and derives the formula for calculating the area of a segment and shows you through solved examples how to calculate the areas of combinations of plane figures. This is another very important chapter for your exams, so practice the problems thoroughly.
Chapter 14 is called SURFACE AREAS AND VOLUMES. It lists some formulae for cuboid, cube, right circular cylinder, right circular hollow cylinder, right circular cone, sphere and spherical shell. Then it contains solved problems involving conversions of solids into other solids of different shapes and involving surface areas and volumes of combinations of solids. The last part of the chapter explains what the frustum of a right circular cone is and shows you how to calculate its volume and surface area. Study and practice everything well: you will see similar problems in your exams.
Chapter 15 is called STATISTICS. In Class 9 you learnt about the calculation of mean, median and mode of ungrouped data. This chapter discusses different methods of calculating the mean, median and mode of grouped data (both discrete and continuous). It talks about the merits and demerits of median and merits, demerits and uses of mode and relations between mean, median and mode. The last part of the chapter contains two methods for construction of cumulative frequency polygons and cumulative frequency curves or ogives (important).
Chapter 16 is called PROBABILITY. It explains several terms, briefly discusses a couple of formulae related to probability and geometric probability.
All the concepts in the books for both Class 9 and 10 are explained from the basic to the advanced levels in a very detailed, lucid and easy-to-understand manner. There are worked out examples and exercises at the end of each section in each chapter. There are exercises of different types at the end of each chapter as well as answers and hints to some of them. Practice them thoroughly.
