from a handpicked tutor in LIVE 1-to-1 classes

# Class 9 Maths

Class 9 Maths is the base of secondary-stage math learning that promotes various computational skills. It solidifies the mathematical understanding of concepts based on coordinate geometry, number system, algebra, trigonometry, mensuration, statistics, graphs, etc. Class 9 math helps students to gradually shift their concrete mathematical knowledge into abstract concepts and topics. Thus, studying each and every topic covered under 9th-class maths is highly important for students.

## Class 9 Maths Syllabus

Class 9 Maths syllabus is thoroughly prepared to help young learners acquire basic mathematical concepts with ease. The syllabus of class 9 comprises topics related to fractions and more. Here is the complete syllabus of 9th class maths.

**Number Systems**

- Recap of representing natural numbers, integers, and rational numbers on the number line.
- Understanding rational numbers as recurring/terminating decimals.
- Operations on real numbers.
- Examples of non-recurring/non-terminating decimals.
- Existence of irrational numbers (numbers that are not rational)
- Recap of laws of exponents with integral powers.
- Rational exponents with positive real bases

**Algebra**

**Polynomials**- polynomials in one variable, with examples and counter-examples
- Coefficients of a polynomial, terms of a polynomial and zero polynomial
- Degree of a polynomial
- Constant, linear, quadratic, and cubic polynomials
- Monomials, binomials, trinomials
- Factors and multiples
- Zeros of a polynomial
- Remainder theorem with examples
- Factor theorem with proof and examples
- Factorization of quadratic polynomials like ax
^{2}+ bx + c, a ≠ 0 where a, b, and c are real numbers, and of cubic polynomials using the factor theorem

**Linear Equations in Two Variables**- Recall of linear equations in one variable
- Introduction to the linear equation in two variables
- Study of linear equations of the form ax + by + c = 0
- Linear equation in two variables with infinitely many solutions and justify using graphs
- Graph of linear equations in two variables - real-life problems with both algebraic and graphical solutions

**Coordinate Geometry**

- cartesian plane
- coordinates of a point
- names and terms associated with the coordinate plane, notations
- plotting points in the plane.

**Geometry**

**Lines and Angles**- If a ray stands on a line, then the sum of the two adjacent angles so formed is 180°and the converse
- If two lines intersect, vertically opposite angles are equal
- Results on angles formed by a transversal and two parallel lines - corresponding angles, alternate angles, and interior angles
- Lines that are parallel to a given line are parallel
- The sum of the angles of a triangle is 180° (Angle sum property)
- If a side of a triangle is produced, the exterior angle thus formed is equal to the sum of the two opposite interior angles (Exterior angle theorem)

**Introduction to Euclid's Geometry**- History - Geometry in India and Euclid's geometry
- Euclid's method of formalizing observed phenomena into axioms, postulates, and theorems.
- The five postulates of Euclid.
- Equivalent versions of the fifth postulate.
- Showing the relationship between axiom and theorem, for example:

(Axiom) Given two distinct points, there exists one and only one line through them.

(Theorem) Two distinct lines cannot have more than one point in common.

**Triangles**- Congruence of triangles
- Congruency rules: SAS Congruence, ASA Congruence, SSS Congruence, RHS Congruence
- Triangle inequalities
- Relation between the angle of a triangle and the facing side

**Quadrilaterals**- A diagonal divides a parallelogram into two congruent triangles
- In a parallelogram opposite sides are equal, and conversely, if the opposite sides of a quadrilateral are equal, then it is a parallelogram
- In a parallelogram, opposite angles are equal, and conversely, if the opposite angles of a quadrilateral are equal, then it is a parallelogram
- A quadrilateral is a parallelogram if a pair of opposite sides are parallel and equal
- In a parallelogram, the diagonals bisect each other and conversely, if the diagonals of a quadrilateral bisect each other, then it is a parallelogram
- In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and in half of it (midpoint theorem) and its converse

**Circles**- Concepts related to circles - radius, circumference, diameter, chord, arcs and subtended angles, secant, sector, segment
- Circle theorems
- Equal chords of a circle subtend equal angles at the centre and its converse
- The perpendicular from the centre of a circle to a chord bisects the chord and its converse
- Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and converse
- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle
- Angles in the same segment of a circle are equal
- The sum of either of the pair of opposite angles of a cyclic quadrilateral is 180° and its converse

**Construction**- Construction of bisectors of line segments and angles of measure 60˚, 90˚, 45˚ etc
- Construction of a triangle given its base, sum/difference of the other two sides, and one of the base angles

**Mensuration**- Heron's formula - Area of a triangle by Heron's formula (no proof)
- Surface areas and volumes - Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/right circular cones

**Statistics and Probability**

**Introduction to Statistics -**Collection of data, presentation of data (tabular form, ungrouped/grouped, bar graphs, histograms)**Probability**- History, repeated experiments and observed frequency approach to finding probability.
- Study of empirical probability using real-life examples and also using examples from the statistics chapter

## Develop 9th Class Maths Skills

9th class maths focuses on developing various real-life skills in students. Students progress their basic mathematical skills related to geometry, statistics, probability, linear equations, polynomials, and so on. A thorough understanding of these 9th maths concepts can be implemented through various interactive activities and visualization. Here are some of the basic class 9 maths skills and concepts that are applicable in further grades.

**Numbers System**

In class 9, students extend their understanding of numbers to rational and irrational numbers and also work with exponents, decimals and various measurement units. 9th maths emphasises using these numbers in algebraic expressions, equations and calculations to define and solve real-life problems.

**Coordinate Geometry**

In 9th class maths, students get a chance to learn more concepts of coordinate geometry like plotting the linear equations in two variables along with plotting points. This knowledge is very helpful for 9th maths students when they enter the higher grades and learn the concepts of straight lines, functions, and so on.

## Class 9 Maths Tips and Tricks

Class 9 maths is an important part of academics that establishes a firm foundation for the following years. Here are some useful tips and tricks for 9th students to learn and score well in exams.

**Follow Daily Practice Routine:**Class 9 maths is the basis for various higher-level maths skills thus students must implement a well-defined preparation strategy. Students should sincerely perform their everyday practice.**Solve Previous Years' Question Papers:**Practicing question papers from previous years will help students to get an idea of the complexity level of the exam. It will also benefit students in enhancing their speed and accuracy**Cover Full Syllabus:**Covering the full syllabus of 9th maths is a must for students to clarify all their doubts before exams.**Refer to Reliable Study material:**Refer to reliable study material like the prescribed textbooks for class 9 maths. These are the best preparation resources as the class 9 maths exam is set according to them.

## Class 9 Maths Worksheets

Class 9 maths worksheets build a strong foundation of concepts as they include extra questions for class 9 maths. They are curated in a way that they include all topics and all difficulty levels. Hence providing worksheets to the students is one of the best teaching strategies. These worksheets help the students to increase their analytical and logical thinking skills. After solving the worksheets, by checking their answers with the answers given at the end of the worksheets, they can analyze their areas of weakness and rework on those areas to build strong conceptual knowledge.

## Class 9 Maths Formulas

For 9th maths students, it is really important to memorize the formulas. Class 9 maths involves several formulas related to algebra, mensuration, statistics, and more. The important formulas are listed below:

- Surface area of cube = 6(side)
^{2} - Surface area of cuboid = 2 (length × width + width × height + height × length)
- Surface area of sphere = 4πr
^{2} - Surface area of cone = πrl + πr
^{2} - Volume of cube = (side)
^{3} - Volume of cuboid = length × width × height
- Volume of sphere = (4/3) πr
^{3} - Volume of cone = 1/3 πr
^{2}h - (a + b)
^{2}= a^{2}+ 2ab + b^{2} - Mean = (sum of observations)/(number of observations)

For more formulas, you can visit our class 9 maths formulas page.

## Solved Examples on Class 9 Maths

**Example 1:** What is the degree of the polynomial 3 - y^{2}?

**Solution:**

To find the degree of the polynomial, first the degree of each term in it should be found. Here:

- degree of 3 is 0 (as it is constant)
- degree of y
^{2}is 2 (as the exponent is 2)

Here, the highest degree is 2 and this is the degree of the given polynomial.

**Answer:** The degree is 2.

**Example 2:** The dimensions of a room are 6 m × 5 m × 4 m. Find the cost of painting its walls at the rate of Rs. 11 per square meter?

**Solution:**

Room is in the shape of a cuboid whose length is, l = 6 m, width is, w = 5m, and height is, h = 4 cm.

Its surface area = 2 (6 × 5 + 5 × 4 + 4 × 6) = 148 m^{2}.

The cost of painting it per square meter is Rs.11. Thus, the total cost = 148 × 11 = Rs. 1628.

**Answer:** The total cost of painting the room is Rs.1,628.

## FAQs on Class 9 Maths

### What are the Topics of Class 9 Maths?

Keeping a copy of **class 9 maths** helps students to have an idea of what they are going to learn in the current academic year. Here is a brief list of 9th class maths topics and for the detailed list, just scroll up.

- Number System with rational and irrational numbers
- Linear equations in two variables and graphing
- Polynomials with remainder theorem and factor theorem
- Coordinate geometry with plotting points and lines
- Lines and angles with properties of angles of transversal and angles of triangles
- Congruence of triangles with rules
- Quadrilaterals with theorems on parallelograms
- Circles and circle theorems
- Mensuration with SA and volume of a cube, cuboid, sphere, cone, and cylinder
- Statistics with finding the mean of grouped data and frequency polygons
- Probability with real life and statistical examples

### What is the Use of Class 9 Maths Solutions?

Class 9 maths solutions have step-by-step solutions for maths problems. Keeping them handy is very useful for the students to refer to when they get stuck solving problems.

### Is 9th Maths Difficult?

No, 9th maths is not very difficult except for a few topics like theorems on parallelograms and circles. Expertise can be achieved even in these difficult topics by constant practice.

### How Do You Get 100% in Class 9 Maths?

To get 100% in 9th class maths, all the topics should be focused on, not only the easier ones. It is advised to have the chapter names according to the weightage allotted to it by the school board. For getting 100%, students should be thorough with all the concepts and not only with solving the questions.

### What is Frequency in 9th Class Maths?

Frequency in class 9 maths is usually seen in the statistics chapter. It is usually the second column of the table of data. It represents the number of data values. For example, if the first column of the table is height of students and the second column is frequency, then the frequency of 10 against the height of students 100-110 cm means that there are 10 students whose height is in between 100 cm to 110 cm.

### What is the Easiest Chapter in Class 9 Maths?

Some chapters of class 9 maths are very easy like number system, polynomials, statistics, etc. But the number system is the one which most of the 9th maths students feel very easier.

### Is Class 9 Maths Easier Compared to Class 10 Maths?

It might be assumed that class 9 maths is easier than 10th maths as it belongs to a lower grade. But in fact, class 9 maths has a few difficult topics such as congruence, quadrilaterals, circles, etc. Hence, class 10 maths is easier.

### Why Should We Practice Extra Questions for Class 9 Maths?

Of course, text book questions and solved examples should be practised first to get an idea of the concept. But to get an in-depth understanding of the concept and to achieve application skills, extra questions for class 9 maths would al

visual curriculum