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Quadratic Equations and Linear Inequalities — Concept Maps

NIOS · Class 12 · Mathematics

3 concept maps of Quadratic Equations and Linear Inequalities for NIOS Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards6 formulas & key relations5 concepts

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A labeled diagram illustrating how a straight line divides the Cartesian plane into two distinct half-planes, showing examples of vertical and non-vertical lines.
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One of 4 illustrations for Quadratic Equations and Linear Inequalities in Super Tutor — alongside flashcards, concept maps and practice questions.

3 Concept Maps

Mind map showing the structure, components, and key characteristics of a quadratic equation

Mind map showing the structure, components, and key characteristics of a quadratic equation

The map in words

  • Quadratic Equation
    • Standard Form
      • ax² + bx + c = 0
      • Condition: a ≠ 0
    • Coefficients
      • a: Leading coefficient
      • b: Middle coefficient
      • c: Constant term
    • Characteristics
      • Degree 2
      • Maximum 2 roots
      • Can be real or complex

Step-by-step flowchart showing the factorization method for solving quadratic equations

Step-by-step flowchart showing the factorization method for solving quadratic equations

The map in words

  • Start: ax² + bx + c = 0
    • Identify factors of ac
      • Find two numbers that multiply to ac and add to b
        • Split middle term using these numbers
          • Group and factor out common terms
            • Write as product of two linear factors
              • Set each factor equal to zero
                • Solve each linear equation
                  • Verify solutions
                    • State the roots

Flowchart showing the quadratic formula method and how the discriminant determines root nature

Flowchart showing the quadratic formula method and how the discriminant determines root nature

The map in words

  • Quadratic Equation: ax² + bx + c = 0
    • Identify coefficients a, b, c
      • Calculate Discriminant D = b² - 4ac
        • Value of D?
          • D > 0: Two distinct real roots
            • Apply formula: x = -b ± √D / 2a
              • Calculate the roots
          • D = 0: Two equal real roots
          • D < 0: Two complex conjugate roots

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Frequently Asked Questions

What are the important topics in Quadratic Equations and Linear Inequalities for NIOS Class 12 Mathematics?
Key topics in Quadratic Equations and Linear Inequalities include Quadratic Equations — Basics and Roots, Solving Quadratic Equations by Factorization, Solving Quadratic Equations by Quadratic Formula (Sridharacharya's Formula), Relation Between Roots and Coefficients. Study these first, then practise questions on each for the NIOS Class 12 board exam.
What do the concept maps for Quadratic Equations and Linear Inequalities show?
The 3 maps show how the ideas in Quadratic Equations and Linear Inequalities connect: Mind map showing the structure, components, and key characteristics of a quadratic equation; Step-by-step flowchart showing the factorization method for solving quadratic equations. Each map is also written out as an outline on this page.
How should I revise Quadratic Equations and Linear Inequalities for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Quadratic Equations and Linear Inequalities. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Quadratic Equations and Linear Inequalities

All NIOS Class 12 Mathematics Concept Maps

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