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CBSE Class 9 — Notes, Chapters & Practice Quizzes

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Mathematics · 8 chapters
Summary, key terms, extra questions with answers and a practice quiz with AI diagnosis for each.

Chapter 2: Introduction to Linear PolynomialsClass 9 Mathematics — summary, notes, extra questions & NCERT solutions

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What is the degree of the polynomial \(2x^2 - 5x + 3\)?

Summary

This chapter builds on algebraic expressions to define univariate polynomials — expressions in a single variable such as \(5y^3 + y^2 - 8\) — and their degree, the highest power of the variable. Polynomials of degree \(0,1,2,3\) are called constant, linear, quadratic and cubic respectively. The focus is the linear polynomial, of the form \(ax + b\). A linear pattern is a sequence whose consecutive terms differ by a constant amount, and many real situations (taxi fares, savings, growing tile patterns) follow such patterns. When a linear polynomial is set equal to a constant, a linear equation results. Two variables related linearly satisfy \(y = ax + b\): here \(a\) is the slope and \(b\) the \(y\)-intercept. Plotting two points and joining them graphs the line. Changing \(a\) tilts the line (steeper when \(|a|>1\)); changing \(b\) shifts it up or down, keeping lines of equal slope parallel. Positive slope models linear growth, negative slope models linear decay. The chapter also treats polynomials as input-output (function) machines.

Polynomials and degreeLinear polynomialsLinear patternsGrowth and decayGraphing \(y=ax+b\)

Key terms

Polynomial
An algebraic expression in one variable made of terms with whole-number powers, such as \(x^2 + 5x + 1\).
Degree
The highest power of the variable in a polynomial; e.g. \(3z+7\) has degree \(1\).
Linear polynomial
A polynomial of degree one, of the form \(ax + b\) with \(a \ne 0\).
Slope
The coefficient \(a\) in \(y = ax + b\); it measures the steepness of the line.
\(y\)-intercept
The constant \(b\) in \(y = ax + b\); the point \((0,b)\) where the line meets the \(y\)-axis.
Linear pattern
A sequence in which the difference between consecutive terms is constant.

Extra questions & answers

Think and Reflect

Think and Reflect

Exercise Set 2.1

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Exercise Set 2.2

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Exercise Set 2.3

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Exercise Set 2.4

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Exercise Set 2.5

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Think and Reflect

Exercise Set 2.6

End-of-Chapter Exercises

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Graph a linear polynomial
slope m1
intercept c0
y = m*x + c
Key-term flashcards
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Polynomial
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An algebraic expression in one variable made of terms with whole-number powers, such as \(x^2 + 5x + 1\).
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Practice quiz · Introduction to Linear Polynomials

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Introduction to Linear Polynomials

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