For Class 9 ICSE students, ICSE Concise Mathematics by Selina Publishers is a good book to start with. All the topics you will need to master are well-explained in the book. There a lot of problems for practice as well. It’s a good place to start. I will talk about this book now, so read on!
UNIT 1: Pure Arithmetic
Chapter 1 is called Rational and Irrational Numbers. It covers all concepts you need to know at this stage. Starting with a brief discussion on the number system, it then talks about different aspects of rational and irrational numbers. The theory is brief and to the point and at the same time easy to understand. It also contains a very good discussion on surds. There are worked out problems and exercises which will prepare you how to tackle different types of problems that you might see in your exams.
UNIT 2: Commercial Mathematics
Chapter 2 is called Compound Interest (without using formula). This is an easy topic. The most important part of this chapter are the worked out problems and exercises which will give you excellent practice.
Chapter 3 is called Compound Interest (using formula). It lists all the formula you need to know and shows you how to approach many different kinds of problems which is again the most important part of this chapter. So, practice everything thoroughly.
UNIT 3: Algebra
Chapter 4 is called Expansions. It does a quick recap of the algebra you’ve learnt in earlier classes along with problems which will help brush up your concepts. Then it introduces you to more complex formulae and problems based on those which are important for your exams.
Chapter 5 is called Factorisation. It teaches you how to factorize different kinds of algebraic expressions and has some very good problems for you to practice.
Chapter 6 is called simultaneous equations (linear and including problems). It starts by explaining the three different methods of solving linear simultaneous equations which you need to know at this stage and then shows you how to solve different types of word problems using the same. This is a relatively easy topic and the book deals with it well. Again, solve the exercises for practice.
Chapter 7 is called indices. This chapter is tricky for students new to the topic. Knowing the rules and solving the problems in the chapter will clear any conceptual difficulties that you might have at first.
Chapter 8 is called Logarithms. This topic can appear complicated to beginners but this chapter presents it in a simple and easy-to-understand way. All the laws you need to know are in the book along with many different kinds of problems, so make sure you study it well.
UNIT 4: Geometry
Chapter 9 is called Triangles (Congruency in Triangles). It starts by explaining some basic concepts related to triangles in general and moves onto congruency. All the proofs of the different kinds of congruency of triangles are explained very well and in a very organized manner and there are many different kinds of problems which I highly recommend you practice.
Chapter 10 is called Isosceles Triangles. The two basic theorems are stated and proved at the beginning of the chapter and there some very good problems solving which will give you confidence.
Chapter 11 is called Inequalities. This is a very important topic. Study the theorems and the corollaries at the beginning of the chapter. They are very well-presented. The problems from this are chapter are harder than average and make use of several different concepts. It will take some time to get used to solving these problems. So make sure you start early.
Chapter 12 is called Mid-Point and Its Converse (including Intercept Theorem). It starts with the Mid-Point Theorem and it’s converse and also contains the Equal Intercept Theorem. These are very important topics which will take some time to get used to. Understand the theorems and practice the problems in the chapter again and again until you become comfortable with the material.
Chapter 13 is called Pythagoras Theorem (Proof and Simple Applications with Converse).It starts with a couple of theorems which show two different ways to prove the Pythagoras Theorem and contains some of the best problems on the topic I have seen. So, practice them again and again.
Chapter 14 is called Rectilinear Figures (Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium). It starts with general stuff related to polygons which you should learn well as you might see them in your exams and you will use them in higher classes. Then it talks about different kinds of quadrilaterals and related theorems. The theory in the chapter is well-organized and you should study it well. It contains a lot of very important worked-out problems which are even better.
Chapter 15 is called Construction of Polygons (Using Ruler and Compass Only). It describes the methods of construction of different kinds of polygons: quadrilaterals in general, parallelograms, trapezium, rectangles, rhombus, square and a regular hexagon. The chapter contains everything you need to know for your exams. This is a very important chapter for your exams, so study it well.
Chapter 16 is called Area Theorem (Proof and Use). This chapter talks about comparing the areas of different combinations of parallelograms, rectangles, triangles etc between the same parallels, on the same base and so on. There are a few theorems on these. This topic is extremely important because most of you will keep seeing it again and again through your student lives. So, learn the theory and practice the problems well.
Chapter 17 is called Circle and is another very important topic which you will need to use in higher classes. The theory is brief, clear and to the point. The chapter is long and contains a bunch of theorems and a lot of problems. Study and practice them well.
I have seen similar problems being asked in Class 9 Annual exams as well as in Class 10 Board exams, so make sure you study the material and practice the problems in UNIT 4 thoroughly.
UNIT 5: Statistics and Graph Work
Chapter 18 is called Statistics. This chapter introduces to the basic concepts of statistics. It shows you how to tabulate data in different ways as well as graphically represent data. Learn this chapter and solve the problems thoroughly because not only are the concepts introduced in this chapter important for your exams, but also they will form the foundation of everything you will learn about statistics later on.
Chapter 19 is called Mean and Median (For Ungrouped Data Only). It introduces you to the concept of mean and some of it’s properties followed by a very good discussion on the median. The worked out examples are good and there are some very good end-of-chapter problems which will make you think.
UNIT 6: Mensuration
Chapter 20 is called Area and Perimeter of Plane Figures. It starts by showing you how to calculate the perimeter and area of different kinds of triangles in different ways. Then it lists how to calculate the perimeter and area of all types of quadrilaterals. Then it moves onto circles. Practice all the problems in this chapter because you will see similar stuff not just in your Class 9 exams, but in higher classes as well.
Chapter 21 is called Solids (Surface Area and Volume of 3-D Solids).This is a short and relatively easy chapter which you shouldn’t have much trouble with. The problems in this chapter will require you to use formulae and concepts from the previous chapter, so keep that in mind.
UNIT 7: Trigonometry
Chapter 22 is called Trigonometric Ratios (Sine, Cosine, Tangent of an Angle and Their Reciprocals). This chapter introduces you to the basics of trigonometry and is extremely important not just for your exams but also because a lot of you will use these concepts throughout your student lives. The material and problems in the chapter are good for beginners. You will need to use some of the stuff on geometry you learnt in previous chapters, so keep that in mind.
Chapter 23 is called Trigonometric Ratios of Standard Angles (Including Evaluation of an Expression Involving Trigonometric Ratios). It derives the trigonometric ratios of standard angles and shows you how to evaluate expressions involving them. It also shows you how to solve equations involving trigonometric expressions. Solve the problems, they will
give you excellent practice.
Chapter 24 is called Solution of Right Triangles (Simple 2-D Problems Involving One Right-angled Triangle). This is a very short and simple chapter which shows you how to find the values of other angles and other sides of a right-angled triangle provided: the values of one side and one acute angle are given or two sides are given. The problems are easy, but do not underestimate them. Remember, the more you practice the better. You will use these techniques in later classes as well.
Chapter 25 is called Complementary Angles. It does a good job of introducing you to complementary angles for Sine and Cosine, Tangent and Cotangent and Secant and Cosecant. It contains all that you need to know on the topic at this stage. You will use these concepts again and again and in much more detail in higher classes and maybe even after that, so make sure you build a strong foundation.
UNIT 8: Co-ordinate
Chapter 26 is called Co-ordinate Geometry. It introduces the basics of co-ordinate geometry. I have found the theory to be precise and good. Understanding how to draw the different graphs can take some time, but the explanations and illustrations are good. The parts on inclination, slope and intercepts are explained clearly as well. Studying the chapter and practicing problems will help you get used to dealing with graphs as a beginner.
Chapter 27 is called Graphical Solution (Solution of Simultaneous Linear Equations, Graphically). This chapter shows you how to draw graphs of different kinds of linear equations in two variables on graph paper and how to deal with problems based on that. It also explains and illustrates how to solve simultaneous linear equations graphically. It even includes some word problems which you have to solve using graphs. Everything is explained and illustrated in an organized and methodical way. Practice the exercises as well.
Chapter 28 is called Distance Formula. It explains how to calculate the distance between two points using co-ordinate geometry and the Pythagoras Theorem. It also shows you how to calculate the circumcentre of a triangle using the distance formula. There are a lot different types of problems which you need to practice in order to internalize the formula.
Towards the end of the book you will find a wealth of problems in 3 stages (Stage 1, Stage 2 and Stage 3) arranged in progressive levels of difficulty, which I highly recommend you practice. The book ends with answers to all the unsolved problems in the book.
Good luck!
I will write about ICSE Concise Mathematics by Selina Publishers for Class 10 ICSE students. I recommend you start with this book before moving onto other books.
UNIT 1: Commercial Mathematics
Chapter 1 is called GST (Goods and Services Tax). It contains definitions of everything you need to know on this topic. Once you understand what all the terms mean, the rest will be easy for you. There are a lot of different kinds of problems in this chapter. Practice them thoroughly otherwise you will make mistakes in the exam.
Chapter 2 is called Banking (Recurring Deposit Accounts). This is a very short chapter and contains just one formula. Nevertheless, do not underestimate it and practice the problems.
Chapter 3 is called Shares and Dividends. Again it contains some definitions explained succinctly which you will find very easy to understand. There are a lot of problems which will give you excellent practice.
UNIT 2: Algebra
Chapter 4 is called Linear Inequations (In one variable). At the beginning of the chapter there are general rules which you have to understand. It also introduces you to solutions sets and how to represent solutions on the number line which are very important. Everything, including the problems, are presented in a very organized way which will make learning easy.
Chapter 5 is called quadratic equations which is a very important topic, not just for Class 10, but for later as well. It describes what a quadratic equation is, the nature of it’s roots and how to solve different kinds of quadratic equations. There’s a lot more to it, but the chapter pretty much contains everything you need to know at this stage (most of you will see it in much more detail in higher classes). Solving the problems will prepare you for the next chapter.
Chapter 6 is called Solving (simple) Problems (Based on Quadratic Equations). It shows you how to solve different kinds of word problems using quadratic equations. Practice all the problems in the chapter and you will get used to solving problems of this type.
Chapter 7 is called Ratio and Proportion (Including Properties and Uses). It talks about ratio and proportion in more detail than what you’ve learnt before. It explains some terms that you need to know because you will be required to solve problems which will contain those terms. Also, there are some properties of proportions which are extremely important because you will see problems based on them. There are tons of problems which will give you excellent practice.
Chapter 8 is called Remainder and Factor Theorems. This is a brief but very important chapter. The best part of this chapter are the different kinds of problems. You will see similar stuff in your Class 10 exams. So, practice them well.
Chapter 9 is on Matrices. There’s a lot of theory in this chapter. All the properties of matrices that you need to know at this stage are well-explained. This topic will take some getting used to, but this chapter (including problems) is an excellent place to start. Most of u will have to study this topic in much more depth later on, so keep that in mind.
Chapter 10 is on Arithmetic Progression. This chapter is important not just for your exams, but as foundation for higher classes as well. Understand the formulas, properties and the different methods to solve problems, which are very well-presented in this chapter.
Chapter 11 is on Geometric Progression which is another topic which you will encounter in higher classes. Again the formulae, properties and problem-solving methods are presented in an elegant and organized manner, so make sure you learn and practice them well.
UNIT 3: Co-ordinate Geometry
Chapter 12 is called Reflection (In x-axis, y-axis, x=a, y=a and the origin; Invariant Points). Like the name suggests, the chapter teaches you how to find reflections of a point about different lines as well as talks about invariant points which remain unchanged. It also teaches you how to do the same on graph paper. This topic might appear a little confusing to beginners, but this chapter is where you should start. Practicing the problems will further clear your concepts.
Chapter 13 is called Section and Mid-Point Formula. All the formulae and their proofs and the sample problems are illustrated and explained very clearly which will help build your concepts. Practice them again and again until you are comfortable with the material. Brush up your concepts on geometry from earlier classes if you need to.
Chapter 14 is called Equation of a Line. It introduces you to different concepts related to co-ordinate geometry of straight lines. Again all the formulae and proofs which you will need at this stage are there in this chapter. There’s tons of problems of many different types, both solved and otherwise. Take your time and solve them.
Chapter 15 is called Similarity (With Applications to Maps and Models). This is an extremely important topic which you need to know in and out, not just for your exams but also for higher classes. The chapter starts with basic definitions and then describes conditions for similarity of two triangles, followed by worked out problems and exercises. In the second half of the chapter there are two very important theorems along with their applications which use the concepts of similarity. I have seen similar stuff asked in previous exam papers, so make sure you study them well. The chapter ends with a discussion on size transformation and it’s applications to maps and models. In short, it contains some of the best theory I have seen on the topic. So study it thoroughly and practice the problems.
Chapter 16 is called Loci (Locus and Its Constructions). This is another concept that a lot of you will see in higher classes. This is a short chapter which starts with definitions and illustrations of what a locus is, followed by theorems and applications. Practice these again and again and then attempt the exercises. The chapter ends by listing some important geometrical concepts which you should have at your fingertips.
Chapter 17 is called Circles. The chapter starts with some important definitions and concepts related to circles followed by some extremely important theorems which you will need in your exams. There is a multiple different kinds of problems, all of which you should practice. The chapter ends by listing some important results, followed by more exercises. I have seen similar problems in previous years question papers, so keep that in mind.
Chapter 18 is called Tangents and Intersecting Chords. This chapter again contains some very important theorems which you should thoroughly understand and know how to use to solve problems. Solve the problems, both worked out and otherwise. Similar problems have been asked before, so make sure you get enough practice.
Chapter 19 is called Constructions (Circles). Understand the techniques presented in this chapter. Do not memorize. Practice the problems again and again until you get comfortable with the techniques. You will see questions like these in the exam.
UNIT 4: Mensuration
Chapter 20 is called Cylinder, Cone and Sphere (Surface Area and Volume). This chapter includes formulae and problems on surface areas and volumes of cylinders, hollow cylinders, cones, spheres, spherical shells, hemispheres as well as conversions and combinations of the aforementioned solids. You are bound to see problems like these in your exams, so study the chapter and practice the problems well.
UNIT 5: Trigonometry
Chapter 21 is called Trigonometric Identities (Including Trigonometric Ratios of Complementary Angles and Use of Four Figure Trigonometric Tables). It starts out with the basics of trigonometry and contains a lot of problems on trigonometric identities and trigonometric ratios of complementary angles. Then it shows you how to use trigonometric tables to calculate values of natural sines, cosines and tangents. You have seen some of this material in Class 9, so it shouldn’t be that hard for you. But still, practice the problems because you will see problems like in your exams and this chapter will form the foundation for a lot of stuff you will encounter in higher classes as well.
Chapter 22 is called Heights and Distances. This chapter teaches you how to apply the trigonometry that you’ve learnt to solve problems. This chapter mostly contains problems which will prepare you for what you will see in your exams.
UNIT 6: Statistics
Chapter 23 is called Graphical Representation (Histograms and Ogives). It teaches you to draw histograms for continuous grouped data, discontinuous grouped data and when class marks are given. Then it defines cumulative frequency, shows you how to prepare a cumulative frequency table and teaches you to draw a cumulative frequency curve or an ogive. This is an easy chapter but nevertheless practice the problems, so you don’t have to spend much time solving problems of this type on the exams.
Chapter 24 is called Measures of Central Tendency (Mean, Median, Quartiles and Mode). It starts by introducing you to the concept of arithmetic mean. It then very elegantly shows you with examples different methods of calculating the mean of a discrete frequency distribution. Then it demonstrates how to calculate the mean for grouped data by applying the same methods. After that it introduces you to the concept of median and explains how to calculate the median for tabulated data and grouped data. Then it introduces you to quartiles and related terms and shows you how to solve related problems. The chapter ends by defining mode and shows you how to deal with related problems. You will need to practice the problems, both worked-out and otherwise in order to fully internalize the material in this chapter and as preparation for your exams.
Chapter 25 is called Probability. It starts with introducing you to the basic concepts of probability. Make sure you understand everything from the very beginning. This chapter describes different scenarios tossing coins and throwing dice and includes related problems. It also shows you how to deal with problems involving cards. All these concepts are very important for your exams and similar problems have been asked before. So study everything thoroughly.
The book ends by listing lots of practice problems for revision. It also includes 5 practice tests. Timing yourself while doing them will help you gauge your readiness for the exam. It also contains detailed solutions to the 2019 paper and answers to all the exercises. Good luck!
