# ICSE Maths Class 9

## ICSE CLASS 9: AN OVERVIEW

ICSE Class 9 is one of the most vital grades amongst all the other grades. Students will have to focus on each subject because this grade lays the foundation for higher classes. Those who want to appear for competitive examinations must start preparing from class 9. When it comes to reputation, ICSE ICSE tops the list of boards. The CISCE always believes in giving the best quality of education to the students.

SpeEdLabs has designed the relevant study materials and solutions for ICSE Class 9 strategically so that it becomes easier for the students to grasp the knowledge fast and convey it efficiently. SpeEdLabs strictly follows the curriculum provided by CISCE to offer the perfect study materials for students to excel in their academics efficiently.

Below we have provided all the information regarding ICSE Class 9 exams for the academic years 2021-2022.

### Chapter-1 Rational and Irrational Numbers

This chapter covers topics like definition, properties, and decimal representation of rational numbers, followed with their problems, the meaning of irrational numbers, real numbers, surds, rationalization, simplifying an expression, etc are the topics covered in this chapter along with solved examples for reference and practice purposes.

### Chapter-2 Compound Interest [without using formula]

This is very important and you can expect at least 2-3 questions from an examination point of view. The topics like simple interest, compound interest, their differences, applications, etc are clearly explained here with examples and exercises for better understanding. Also, the relationship between simple interest and compound interest, and explaining each term like rate, principle, are discussed with simple problems.

### Chapter-3 Compound Interest [using formula]

This is a continuation of the previous chapter but here the problems are solved using a definite formula. This is an exclusive problematic chapter where concepts like inverse, miscellaneous problems, problems where the compounded interest is half-yearly or yearly, and their formula-based applications are discussed in this chapter.

### Chapter-4 Expansions

In this chapter topics like identities, expansions of (a+b)3, (x+a)(x+b), (a+b+c)2, problems and solved examples exclusively provided on these modeled expansions for better practice purposes, special products, etc are few discussed under this chapter.

### Chapter-5 Factorization

This chapter is another important one, where topics like grouping, differences of two squares, sum/difference of two cubes, trinomial form splitting, taking out common factors, etc are the various methods of factorization explained here with examples, exercises for better understanding.

### Chapter-6 Simultaneous Equations

This chapter covers topics like various methods of solving simultaneous equations, elimination by substitutions, elimination by equating coefficients, cross-multiplication, equations reducible to linear equations, simultaneous equations, etc followed by example problems for practice purposes.

### Chapter-7 Indices

This chapter covers topics like laws of indices, handling positive, fractional, negative and zero indices, followed by simple problems and exercises. Also, simplification of expressions, exponential equations are discussed here with solved examples for practice purposes.

### Chapter-8 Logarithms

Starting with a general introduction on logarithms, concepts like interchanging, laws of logarithms and its applications, expansion of expressions with respect to laws of logs are discussed here thoroughly followed with exercises for better understanding purposes.

### Chapter-9 Triangles

Beginning with a brief introduction and review of triangles covered in previous years, in addition, the topics covered in this chapter are the relationships between sides and angles of triangles, simple constructions, congruent triangles, and its conditions are discussed here with solved examples for better practice purposes.

### Chapter-10 Isosceles

This is a very small chapter that covers two important theorems with respect to the sides and angles of a triangle and a few simple problems for understanding the concepts thoroughly.

### Chapter-11 Inequalities

This is another simple and theorems-based chapter started with a brief introduction on inequalities followed by three important theorems with respect to sides, angles, and perpendicular lines along with problems are explained here in this chapter.

### Chapter-12 Midpoint and its Converse

The two most important theorems called the Mid-point theorem along with converse of midpoint and equal intercept theorem followed with problems and exercises for better understanding.

### Chapter-13 Pythagoras

Beginning with a general introduction, the explanation of two theorems called area-based, alternating with respect to right-angled triangles are explained here followed by simple problems and exercises for better understanding.

### Chapter-14 Rectilinear Figures

This chapter explains topics like names of the polygon, regular polygon, definition, properties, and types of quadrilaterals, like trapezium, parallelogram, rectangle, rhombus, square, etc, also the various diagonal properties are discussed in detail with examples and solved exercises for practice purposes.

### Chapter-15 Construction of Polygons

This chapter is interesting and simple as it involves the construction of various quadrilaterals, like parallelograms, trapezium, rectangles, rhombus, square, regular hexagon, etc are clearly explained here with a set of exercises.

### Chapter-16 Area Theorems

Starting with the introduction, topics like figures between the same parallels, triangles with the same vertex, and bases along the same line are the theorems covered in this chapter.

### Chapter-17 Circle

Starting with the introduction, topics like a circle, its definition, properties, terms like arc, segment, sector, chord properties, etc their respective properties, solved examples for reference, an ample number of exercises for better understanding and practice purposes are discussed here in this chapter.

### Chapter-18 Statistics

This is the more practical chapter where topics like a variable, tabulation of data, frequency, its definition, applications, frequency distribution table its types, terms like class intervals, class limits, cumulative frequency and its table, graphical representation of data, and graphical representation of data with respect to continuous frequency distribution, etc are covered in this chapter with solved examples and exercises for better understanding the concepts and helps in securing good marks in examination point of view.

### Chapter-19 Mean and Median

The topics like the mean of ungrouped data, properties and application problems of mean, the definition of median, its properties and functionalities and provided with ample set of respective problems for better understanding.

### Chapter-20 Area and Perimeter of Plane Figures

Starting with the basic introduction, concepts like area, perimeter, and special types of triangles, quadrilaterals, are discussed here with exercises for practice purposes, also circle, its area, circumference, special cases, properties, etc are explained here with ample set of examples for thorough understanding.

### Chapter-21 Solids

This chapter covers topics like the cuboid, cube, their respective definitions, properties, and problem applications provided with a set of solved examples for reference purposes and an ample set of exercises after each topic for better understanding purposes. The terms like the cost of an article, cross-section, and flow of water are also discussed here in this chapter.

### Chapter-22 Trigonometrical Ratios

This chapter talks exclusively on the various trigonometric formulas, their applications in problems, formula derivations, etc are discussed here. The topics like perpendicular, base, hypotenuse with res

pect to a right triangle, notation of angles, trigonometric ratios, reciprocal relations are covered here under this chapter.

### Chapter-23 Trigonometrical Ratios of Standard Angles

This chapter is the continuation of the previous chapter in addition to other topics like solving trigonometric equations, trigonometric ratios of angles like 30, 60, 45 degrees respectively. This chapter involves a lot of problem-solving so a deep and better understanding of the concepts is very much required.

### Chapter-24 Solutions of right triangles

The most important concept of solving easy 2-D problems involving one right-angled triangle etc is discussed here with a deep and thorough explanation and understanding provided with solved examples and exercises for practice purposes.

### Chapter-25 Complementary Angles

This chapter also is the continuation of the previous chapters where the concept of complementary angles with respect to trigonometric ratios, sine, and cosine angles are thoroughly explained here followed with examples for practice purposes.

### Chapter-26 Coordinate Geometry

The topics like a dependent and independent variable, ordered pair, how to do plotting of points and read them as coordinates, cartesian plane, quadrants, and sign convention, marking a linear equation, slope, y-intercept on a graph are discussed in detail in this chapter.

### Chapter-27 Graphical Solution

This chapter explains topics like linear equations with two variables, simultaneous equations, their definitions, methods of solving them, and representing them graphically are discussed here in this chapter followed by exercises and solved examples for reference and practice purposes.

### Chapter-28 Distance Formula

The topics like the distance formula, circumcenter of a triangle are covered in this chapter along with a set of exercises for better understanding and practice purposes. Also, from an examination point of view, this chapter is very simple and has good enough weightage to secure better marks.

Solved Examples

Important Questions

Video Solutions

## Solved Examples For Maths Class 9

The ICSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn in a playful way. It makes the process of conveying knowledge to the students efficient and healthy.

*Chapter 1- Rational and Irrational Number**Chapter 2- Compound Interest (without using formula)**Chapter 3- Compound Interest (Using formula)**Chapter 4-Â ExpansionÂ**Chapter 5- Factorisation**Chapter 6- Simultaneous (Linear) Equations (Including Problems)**Chapter 7- Indices (Exponents)Â**Chapter 8- Logarithms**Chapter 9- Triangles (Congruency in Triangles)**Chapter 10-Isosceles TriangleÂ**Chapter 11-InequalitiesÂ**Chapter 12- Midpoint and it’s Converse**Chapter 13-Pythagoras TheoremÂ**Chapter 14-Rectilinear Figures [Parallelogram, Rectangle, Rhombus, Square, and Trapezium]**Chapter 15-Construction of Polygon (Using ruler and compass only)Â**Chapter 16-Area Theorems (Proof and Use)Â**Chapter 17-Circle**Chapter 18-StatisticsÂ**Chapter 19-Mean and MedianÂ**Chapter 20-Area and Perimeter of Plane Figures**Chapter 21-Solids [Surface Area and Volume of 3-DSolids]**Chapter 22-Trigonometrical Ratios**Chapter 23-Trigonometrical Ratios of Standard AnglesÂ**Chapter 24-Solution of Right Triangles**Chapter 25-Complementary Angles**Chapter 26-Coordinate Geometry**Chapter 27-Â Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)Â**Chapter 28-Distance Formula*

## Important Questions For Maths Class 9

The ICSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn in a playful way.

It makes the process of conveying knowledge to the students efficient and healthy.

*Chapter 1- Rational and Irrational Number**Chapter 2- Compound Interest (without using formula)**Chapter 3- Compound Interest (Using formula)**Chapter 4-Â ExpansionÂ**Chapter 5- Factorisation**Chapter 6- Simultaneous (Linear) Equations (Including Problems)**Chapter 7- Indices (Exponents)Â**Chapter 8- Logarithms**Chapter 9- Triangles (Congruency in Triangles)**Chapter 10-Isosceles TriangleÂ**Chapter 11-InequalitiesÂ**Chapter 12- Midpoint and it’s Converse**Chapter 13-Pythagoras TheoremÂ**Chapter 14-Rectilinear Figures [Parallelogram, Rectangle, Rhombus, Square, and Trapezium]**Chapter 15-Construction of Polygon (Using ruler and compass only)Â**Chapter 16-Area Theorems (Proof and Use)Â**Chapter 17-Circle**Chapter 18-StatisticsÂ**Chapter 19-Mean and MedianÂ**Chapter 20-Area and Perimeter of Plane Figures**Chapter 21-Solids [Surface Area and Volume of 3-DSolids]**Chapter 22-Trigonometrical Ratios**Chapter 23-Trigonometrical Ratios of Standard AnglesÂ**Chapter 24-Solution of Right Triangles**Chapter 25-Complementary Angles**Chapter 26-Coordinate Geometry**Chapter 27-Â Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)Â**Chapter 28-Distance Formula*