NCERT Class 9 Mathematics Ganita Manjari: Chapter 2 — Introduction to Linear Polynomials
This chapter, "Introduction to Linear Polynomials" from NCERT Class 9 Mathematics Ganita Manjari, revisits algebraic expressions learned in earlier grades. It introduces the concept of linear polynomials through practical examples. The first example involves calculating the total number of pens and pencils from boxes of different colours, introducing terms, variables, coefficients, and constants. The second example deals with the cost of fencing and decorating a rectangular garden, forming an algebraic expression for the total cost. The third example explores forming rectangles from a wire of fixed length and deriving an expression for their area. Students are encouraged to identify components of these expressions and compare them, fostering a deeper understanding of algebraic structures and their applications in real-world scenarios, crucial for CBSE learning.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 9 |
| Subject | Mathematics |
| Book | Ganita Manjari |
| Chapter | Chapter 2 — Introduction to Linear Polynomials |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 467 |
Learning outcomes
- Identify terms, variables, coefficients, and constants in algebraic expressions.
- Formulate algebraic expressions from given real-world scenarios.
- Differentiate between various types of algebraic expressions.
- Understand the concept of linear polynomials.
- Apply algebraic expressions to solve problems related to geometry and quantities.
Vocabulary
| Word | Meaning |
|---|---|
| Algebraic expression | A combination of variables, constants, and mathematical operations. |
| Terms | Parts of an algebraic expression separated by '+' or '-' signs. |
| Variables | Letter-numbers or symbols that can take any value. |
| Coefficients | The numerical factor multiplying a variable in a term. |
| Constant | A term that does not contain any variables. |
| Linear polynomial | A polynomial of degree one. |
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Practice questions
- In the expression 4x + 5y + 3, identify the terms, variables, and coefficients. Answer: Terms: 4x, 5y, 3. Variables: x, y. Coefficients: 4 (for x), 5 (for y). Constant: 3.
- If a rectangle has length 'l' and width 'w', write an expression for its perimeter. Answer: Perimeter = 2l + 2w.
- What is the degree of a linear polynomial? Answer: The degree of a linear polynomial is one.
Frequently asked questions
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.
What are variables in an algebraic expression?
Variables are symbols, usually letters, that represent unknown values or quantities that can change.
What is a coefficient?
A coefficient is the numerical factor that multiplies a variable in an algebraic term.
What is a constant term?
A constant term is a number in an algebraic expression that does not have a variable attached to it.
How do we form an algebraic expression from a word problem?
We identify the unknown quantities as variables and use the given information and mathematical operations to represent the situation as an expression.
What is the main focus of Chapter 2 in NCERT Class 9 Mathematics?
The chapter focuses on understanding algebraic expressions and introducing the concept of linear polynomials through various examples.
Related resources
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Topics covered
NCERT Class 9 Mathematics — Ganita Manjari — Chapter 2 — Introduction to Linear Polynomials. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.