Summary
Chapter 2 of NCERT Class 9 Maths, "Introduction to Linear Polynomials", introduces univariate polynomials and their degree, then focuses on linear polynomials (degree 1), linear patterns, linear growth and decay, linear relationships of the form y = ax + b, and plotting them as straight lines.
This chapter begins with algebraic expressions and defines one-variable (univariate) polynomials, where the highest power of the variable is the degree. It classifies polynomials as constant (degree 0), linear (degree 1), quadratic (degree 2) and cubic (degree 3), then studies linear polynomials in depth. Students evaluate polynomials by substituting values (input-output process), form linear equations, and explore linear patterns where consecutive terms differ by a constant. The chapter covers linear growth and linear decay, expresses linear relationships as y = ax + b, and teaches plotting these as straight lines, identifying slope a and y-intercept b.
Key points & formulas
- 01The degree of a polynomial is the highest power of its variable
- 02Polynomials by degree: constant 0, linear 1, quadratic 2, cubic 3
- 03A linear polynomial has degree 1, such as 3z + 7 or 2x + 3
- 04Evaluate a polynomial by substituting a value of the variable
- 05A linear pattern has a constant difference between consecutive terms
- 06Linear growth increases and linear decay decreases by a fixed amount
- 07A linear relationship is y = ax + b, where a is slope and b the y-intercept
Frequently asked questions
01What is a linear polynomial in Class 9 Maths?
A linear polynomial is a polynomial of degree 1, meaning the highest power of its variable is one. Examples from the chapter include 3z + 7, 4x, and 2x + 3.
02What is the difference between linear growth and linear decay?
Linear growth describes a pattern where a quantity increases by a constant amount over equal intervals, shown by a line with positive slope. Linear decay describes a pattern where a quantity decreases by a constant amount over equal intervals, shown by a line with negative slope.
03What do a and b represent in the equation y = ax + b?
In y = ax + b, a represents the slope of the line and b represents the y-intercept, the point (0, b) where the line cuts the y-axis. When b = 0, the equation becomes y = ax and the line passes through the origin.
04How do you find the degree of a polynomial?
The degree is the highest power of the variable in the polynomial. For example, 5y^3 + y^2 + 2y - 1 has degree 3, x^2 + 5x + 1 has degree 2, and the constant 8 has degree 0 since it can be written as 8x^0.
More chapters in Ganita Manjari
This is the complete Ganita Manjari Chapter 2 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 9 textbooks.
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