Class 10 Math Quadratic Equations MCQ Test

Class 10 Math Quadratic Equations MCQ Test: Boost your understanding with free online multiple-choice questions for CBSE Class 10 Math Chapter 4. Master the concepts of quadratic equations, their solutions, and applications. Ideal for CBSE exam preparation and competitive tests.

Quadratic Equations MCQ Test Quiz

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10th Math: Quadratic Equations

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About Quadratic Equations MCQ Test

Chapter 4 of the CBSE Class 10 Math curriculum, titled “Quadratic Equations,” covers the fundamental aspects of quadratic equations, including their solutions, properties, and real-life applications. This chapter is crucial for understanding how to solve and apply quadratic equations in various mathematical contexts. The free MCQ quiz provided in this chapter will help students solidify their understanding and prepare effectively for their CBSE examinations.

4. Quadratic Equations
4.1 Introduction
4.2 Quadratic Equations
4.3 Solution of a Quadratic Equation by Factorisation
4.4 Nature of Roots
4.5 Summary

Key Concepts Covered:

Quadratic Equations:
- Definition: A quadratic equation is a second-degree polynomial equation of the form $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are constants, and $a \neq 0$ . The highest power of the variable $x$ is 2.
Standard Form and General Form:
- Standard Form: $ax^2 + bx + c = 0$ .
- General Form: Any quadratic equation that can be converted into the standard form.
Solutions of Quadratic Equations:
- Roots or Solutions: The values of $x$ that satisfy the equation. They can be real or complex.
- Finding Roots:
  - Factoring: Expressing the quadratic equation as a product of linear factors (e.g., $x^2 – 5x + 6 = (x – 2)(x – 3) = 0$ ).
  - Completing the Square: Converting the quadratic equation into a perfect square trinomial (e.g., $x^2 + 6x + 9 = (x + 3)^2$ ).
  - Quadratic Formula: Using the formula $x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$ to find the roots, where $b^2 – 4ac$ is the discriminant.
Discriminant:
- Definition: The part of the quadratic formula under the square root, $b^2 – 4ac$ $b^{2} - 4 a c$ . It determines the nature of the roots:
  - Positive Discriminant: Two distinct real roots.
  - Zero Discriminant: One real root (repeated root).
  - Negative Discriminant: Two complex roots (conjugate pairs).
Nature of Roots:
- Real and Distinct Roots: If the discriminant is positive.
- Real and Equal Roots: If the discriminant is zero.
- Complex Roots: If the discriminant is negative.
Application of Quadratic Equations:
- Word Problems: Translate real-life scenarios into quadratic equations and solve them. Examples include problems related to projectile motion, area, and optimization.
- Example: If the area of a rectangle is 60 square units, and its length is 5 units more than its width, find the dimensions of the rectangle.
Graphical Representation:
- Parabola: The graph of a quadratic equation is a parabola. It opens upwards if $a > 0$ and downwards if $a < 0$ .
- Vertex: The highest or lowest point of the parabola, depending on the direction it opens. The vertex can be found using the formula $x = -\frac{b}{2a}$ .
Vertex Form of a Quadratic Equation:
- Vertex Form: $y = a(x – h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
- Conversion: Convert the standard form $ax^2 + bx + c$ to vertex form by completing the square.

Quiz Structure:

The MCQ quiz for this chapter includes a series of questions designed to test students’ understanding of quadratic equations, their solutions, and applications. These questions cover definitions, methods of solving quadratic equations, the discriminant, and the graphical representation. The interactive format allows students to practice and assess their knowledge effectively.

Conclusion:

Practicing with the Class 10 Math Quadratic Equations MCQ Test Chapter 4 is an excellent way for CBSE students to prepare for their exams. This chapter provides a thorough understanding of quadratic equations, including how to solve them and apply them to various problems. The MCQ quiz helps reinforce these concepts, ensuring students are well-prepared for their academic assessments and competitive exams.

Sanjay Kumar

Math educator (6-12) with an MSc from Delhi University and quiz content creator at QuizRanker.org.