Concise Mathematics Class 9 ICSE Solutions

Chapter 1 – Rational and Irrational Numbers

Dive deeper into the interesting world of numbers with ICSE Selina Maths solutions Class 9 Chapter 1 Rational and Irrational Numbers. Numbers are the soul in Mathematics. In previous Classes, students would have learned about Natural Numbers, Whole Numbers, Integers, representing the numbers in the number line, etc. This Chapter will help students to understand different sets of numbers like rational and irrational numbers and understand the place of rational and irrational numbers in the number system. Read, practice, and revise the exercise–wise solutions to know more about the concepts effectively. Through the solutions, our experts show you how to simplify a Mathematical expression by rationalizing the denominator. Let us have a look at the topics that are being discussed in this Chapter:

1.1 Introduction

1.2 Rational Numbers

1.3 Properties of Rational Numbers

1.4 Decimal Representation of Rational Numbers

1.5 Irrational Numbers

1.6 Real Numbers

1.7 Surds (Radicals)

1.8 Rationalization

1.9 Simplifying an Expression by Rationalizing its Denominator

Chapter 2 – Compound Interest (Without Using Formula)

In this Chapter Maths ICSE solutions Class 9 Chapter 2 compound Interest, students will learn how interest is calculated when someone borrows or invest money.  Interest is always calculated on the original principal throughout the loan period, irrespective of the length of the period for which money is borrowed. In the same way, compound interest is a difference between the final amount and the original price. If someone has invested a specific amount of money at a particular rate of interest for a particular number of years, then find out how the amount will be compounded annually or semi–annually. Besides, you will also learn how to calculate the outstanding loan amount with the given data, and learn to work with the depreciation value of items to calculate their original cost. Learn the steps for performing this calculation without using a formula and by practising the different kinds of textbook questions with solutions. Practice the application of compound interest in real–life scenarios and solve maximum questions. Topic covered in this unit are:

2.1 Introduction

2.2 Interest (simple interest)

2.3 Compound Interest

2.4 Compound Interest as a Repeated Simple Interest 

2.5 More About Compound interest

2.6 Relation Between Simple Interest And Compound Interest

Chapter 3 – Compound Interest UsingFormula

Selina Class 9 Maths solution Chapter 3 is a continuation of Chapter 2 and will help students to understand the difference between simple interest and compound interest. In the previous unit, students were taught to calculate the compound interest without using a formula. The calculation becomes complicated when the number of conversion periods increases. To make the calculation easier, some formulas are used. Topic covered in this unit are:

3.1 Introduction

3.2 Using Formula

3.3 Inverse Problems

3.4 Miscellaneous Problems

and Other Applications of the Formula

Chapter 4 – Expansions

Selina concise Mathematics Class 9 solutions Chapter 4 – Expansions, This topic helps in finding the product of two positive numbers with the given information about the sum of their squares and the difference between the two numbers. Understand the methods to simplify or expand Mathematical expressions according to the given details. Students can understand the process through which the contents of brackets are evaluated. It helps students to recollect the identities which they had learned in the earlier Classes. Topic covered in this unit are:

4.1 Introduction

4.2 Identities

4.3 Expansions of (a + b)3

4.4 Expansions of (x + a)(x + b)

4.5 Expansions of (a + b + c)2

4.6 Using Expansions

4.7 Special Products

Chapter 5 – Factorisation

ICSE Class 9 Maths Selina solutions Chapter 5 – Factorisation, in this topic you will Learn to factorize the given terms by taking out common factors from those terms. This Chapter mainly deals with the concept of factorization. When a polynomial is expressed as the product of two or more expressions, each of them is called a factor of the polynomial. Students can learn the process of writing an expression in the form of terms of products multiplied together known as factorization. Topic covered in this unit are:

5.1 Introduction

5.2 Methods of Factorization

Type 1: Taking out the common factors

Type 2: Grouping

Type 3: Trinomial in the form of ax2 + bx + c (by splitting method)

Type 4: Difference of two squares

Chapter 6 – Simultaneous Equations

Solution of Selina Maths Class 9, Chapter 6 – Simultaneous Equations deals with different techniques to solve the linear equations. Different methods include the elimination method and the substitution method to solve linear equations Algebraically.

ax + by + c = 0 is a linear equation in which a, b and c are the constants and x and y are the variables. Students can obtain in–depth knowledge about the important concepts covered in this Chapter with the help of PDF solutions. Topic covered in this unit are:

6.1 Introduction

6.2 Methods of solving simultaneous equations.

6.3 Method of elimination by substitutions.

6.4 Method of elimination by equating coefficients.

6.5 Method of cross–multiplication.

6.6 Equations reducible to linear equations.

6.7 Problems based on simultaneous equations.

Chapter 7 – Indices

ICSE Class 9 Maths solutions Chapter 7 – Indices deals with the concept of exponents and indices which are explained by experts of Vedantu in understandable language to make it easier for the students while learning and reviewing step–wise answers for simplifying Mathematical expressions based on exponents. Find answers to problems covering concepts like negative indices, fractional indices, positive indices, and zero indices. Topic covered in this unit are:

7.1 Introduction

7.2 Laws of Indices

Exponents

Exponents.

7.3 Handling positive, fractional, negative, and zero indices.

7.4 Simplification of expressions.

7.5 Solving exponential equations.

Chapter 8 – Logarithms

ICSE solutions for Class 9 Maths Chapter 8 – Logarithms, in this topic students can understand the method of calculation using logarithm. Logarithms are used to make complex calculations easy. These concepts are related to the Indices covered in the previous Chapter. Understanding the various laws and properties of Logarithms through application–type questions and solutions. Topic covered in this unit are:

8.1 Introduction

8.2 Interchanging

8.3 Laws of logarithms with use.

8.4 Expansion of expressions.

8.5 More about logarithms.

Chapter 9 – Triangles

ICSE Class 9 Maths Selina solutions Chapter 9 deals with various terms like centroid, median, orthocentre, altitude, etc. which are important from the exam perspective. Practice more questions to revise the criteria of congruence such as Side-Side-Side (SSS), Angle-Angle-Side (AAS), Side-Angle-Side (SAS), and Right Angle-Hypotenuse-Side (RHS). Topic covered in this unit are:

9.1 Introduction

9.2 Relation between sides and angles of Triangles.

9.3 Some important terms.

9.4 Congruent Triangles.

9.5 Conditions

Chapter 10 – Isosceles Triangle

Selina ICSE solutions for Class 9 Maths Isosceles Triangle, in this Chapter you will come across problems asking to prove that one angle is equal to another angle in a given Triangle. It also provides students with an overview of different properties and problems related to Isosceles Triangles. Topic covered in this unit are:

10.1 Introduction

10.2 Theorems

Chapter 11 – Inequalities

The topic of Inequalities related to Triangles is explained in the Chapter. Students will learn about the properties and problems related to the Isosceles Triangles. The concepts are explained in very simple language to help students score well in the annual exam, irrespective of their intelligence quotient. Try to solve maximum problems by applying the theory that the greater angle is opposite to the greater side if two sides of a Triangle are not equal. Topic covered in this unit are:

11.1 Introduction

11.2 Theorems

Chapter 12 – Midpoint and Its Converse

Solution of Selina Maths Class 9 Chapter 12 – Midpoint and Its Converse, in this Chapter, students will learn the Mid–Point Theorem, its converse, along with the intercept theorem which is important from the exam point of view. Also, go through the solutions to understand the correct application of the intercept theorem to show that two lines that are part of a Triangle bisect each other. Topic covered in this unit are:

12.1 Mid-point theorem

12.2 Equal Intercept Theorem

Chapter 13 – Pythagoras Theorem

Solution of Selina Maths Class 9 Chapter 13 – Pythagoras Theorem helps students to understand the simple applications of the Pythagoras theorem and its converse. Students need to learn all the applications of Pythagoras’ theorem as it is used to solve different types of Mathematical problems. Topic covered in this unit are:

13.1 Introduction

13.2 Pythagoras Theorem

Chapter 14 – Rectilinear Figures

This Chapter explains the various properties and theorems related to polygons like parallelogram, square, rectangle and trapezium, etc. Learn more about the interior angles and exterior angles of polygons. Topic covered in this unit are:

14.1 Introduction

14.2 Names of polygon

14.3 Regular Polygon

14.4 Quadrilaterals

14.5 Types of Quadrilaterals

• Trapezium

• Parallelogram

• Rectangle

• Rhombus

• Square

14.6 Diagonal properties

Chapter 15 – Construction of Polygons

Students will learn about the steps to be followed while constructing polygons in this Chapter. The construction topic is explained in simple language to help students perform well in the Class 9 exams. This topic is quite scoring and students can find the detailed steps to construct diagrams of quadrilaterals such as rhombus, square, etc. according to the given data. Topic covered in this unit are:

15.1 Construction of Quadrilaterals.

15.2 Construction of Parallelograms.

15.3 Construction of Trapezium.

15.4 Construction of Rectangles.

15.5 Construction of Rhombus.

15.6 Construction of Square.

15.7 Construction of Regular Hexagon.

Chapter 16 – Area Theorems (Proof and Use)

Solution of Selina Maths Class 9 Chapter 16 deals with the area theorems based on the latest ICSE syllabus. This Chapter helps students to understand the different theorems related to areas of polygons, learn to give proofs based on area theorems while solving problems related to quadrilaterals. Topic covered in this unit are:

16.1 Introduction

16.2 Figures between the same parallels.

Chapter 17 – Circle

Refer Selina concise Mathematics Class 9 solutions to easily solve simple problems related to circles. Learn to find the length of a chord or the radius of a circle. A figure obtained by joining all those points in a plane at the same fixed distance from a fixed point in the same plane is termed a circle. Topic covered in this unit are:

17.1 Introduction

17.2 Circle

17.3 More about the circle

17.4 Arc, Segment, and Sector

17.5 Chord Properties

Chapter 18 – Statistics

Selina ICSE solutions for Class 9 Chapter 18 learn the steps to draw a cumulative frequency table or a combined histogram as per the information given. The process of collecting, presenting, summarising, and analysis of the given set of data and the conclusion obtained from it is termed statistics. Topic covered in this unit are:

18.1 Introduction

18.2 Variable.

18.3 Tabulation of data.

18.4 Frequency.

18.5 Frequency distribution table.

18.6 Types of frequency distributions.

18.7 Class intervals and Class limits.

18.8 Cumulative frequency and cumulative frequency table.

18.9 Graphical representation of data.

18.10 Graphical representation of continuous frequency distribution.

Chapter 19 – Mean and Median

With Selina Class 9 Maths solution students can learn about the mean and median of the given data and the steps to be followed while calculating them. Understand the approach to work with ungrouped data. Get the model solutions to find the correct mean for observations with a misread number. Topic covered in this unit are:

19.1 Mean of Ungrouped data.

19.2 Properties of mean.

19.3 Median

Chapter 20 – Area and Perimeter

With Selina ICSE solutions for Class 9 Maths learn to find the area of quadrilaterals such as a square, parallelogram, rhombus, trapezium, and rectangle. The area of a plane figure is the measure of the surface enclosed by its boundary and the perimeter of a plane figure is the length of its boundary. The Chapter provides an overview of the area and perimeter of plane figures. Topic covered in this unit are:

20.1 Introduction

20.2 Area and perimeter of Triangles.

20.3 Some special types of Triangles.

20.4 Area and Perimeter of quadrilaterals.

20.5 Some special types of quadrilaterals.

20.6 Circumference of a circle.

20.7 Area of a circle

Chapter 21 – Solids

With Selina ICSE solutions for Class 9 Maths learn more about the volume and surface area of a cube, cylinder, and cuboid, A solid is something that occupies space and has a definite shape. Space that is occupied by the solid is called its volume. The sum of the areas of all the surfaces of the solid is called its surface area or total surface area. Topic covered in this unit are:

21.1 Introduction

21.2 Cuboid.

21.3 Cube.

21.4 Cost of an article.

21.5 Cross-section.

21.6 Flow of water.

Chapter 22 – Trigonometric Ratios

Get step–wise answers to calculate the values of sine, cosine, tangent, cotangent, secant and cosecant of the three sides of a right–angled Triangle. Topic covered in this unit are:

22.1 Introduction

22.2 Concept of perpendicular,  hypotenuse, and base  in a right–angled Triangle.

22.3 Notation of angles.

22.4 Trigonometric Ratios.

22.5 Reciprocal Relations.

Chapter 23 – Trigonometric Ratios of Standard Angles

The Chapter includes the evaluation of an expression involving Trigonometric ratios and problems related to it are explained in this Chapter. Topic covered in this unit are:

23.1 Trigonometrical Ratios of Angles 300 and 600.

23.2 Trigonometrical Ratios of Angle 450.

23.3 Solving a Trigonometric equation.

Chapter 24 – Solutions of Right Triangles

ICSE Class 9 Maths Selina solutions Chapter 24 will help students in finding the values of the remaining sides and remaining angles when two sides of a Triangle are given or one of the sides and one acute angle are given. This Chapter provides students with an overview of various problems related to solutions of right angles and also helps to figure out how to find the magnitude of an angle in a right–angled Triangle with the help of available data. Topic covered in this unit are:

24.1 Introduction

24.2 Simple 2-D problems involving one right–angled Triangle.

Chapter 25 – Complementary Angles

ICSE solutions for Class 9 Maths Chapter 25, Students can also gain knowledge about the concept of Trigonometric ratios of complementary angles along with their applications in daily life. Topic covered in this unit are:

25.1 Introduction

25.2 Concept of Trigonometric ratios of complementary angles.

25.3 Complementary angles for sine and cosine.

Chapter 26 – Coordinate Geometry

The branch of Geometry dealing with the position of points on a plane defined by coordinates is known as coordinate Geometry. This unit will help students understand the Cartesian system. Learn more about the dependent and independent variables in a given equation. Topic covered in this unit are:

26.1 Introduction

26.2 Dependent and Independent Variable.

26.3 Ordered Pair.

26.4 Cartesian Plane.

26.5 Co–ordinates of Points.

26.6 Quadrants and Sign Convention.

26.7 Plotting of Points.

26.8 Graphing a linear equation.

26.10 Inclination and Slope.

26.11 Y-Intercept.

Chapter 27 – Graphical Solution

In this topic, students will learn how to plot graphs for equations given in Maths problems. Revise the concept of simultaneous linear equations, Understand how to state a linear relationship between two variables by using information available after drawing a graph. Topic covered in this unit are:

27.1 Graphs of Linear Equations in Two Variables.

27.2 Solution of Simultaneous Linear Equations, Graphically.

Chapter 28 – Distance Formula

In this topic, understand the method of finding the distance between the given pairs of points. The student will learn to find out the ordinate and abscissa of a given point.  Topic covered in this unit are:

28.1 Introduction

28.2 The distance formula.

28.3 Circumcentre of a Triangle.