Class 10 Quadratic Equations Case Based Questions

Quadratic Equations Case Study Class 10

Class 10 Quadratic Equations Case Based Questions

Understanding Quadratic Equations Case Study Class 10 is essential for board exam preparation. These case study questions class 10 maths quadratic equations help students connect concepts with real-life problems. Since Class 10 is crucial, solving case study class 10 builds confidence and strengthens problem-solving skills. Moreover, these questions are part of class 10 maths chapter 4 case study questions.

Importance of QClass 10 Quadratic Equations Case Based Questions

Practicing case based questions improves logical thinking. Consequently, students learn to apply formulas beyond textbooks. Teachers often recommend cbse maths quadratic equations case study for revision before exams. In addition, such practice helps identify weak areas. By solving case studies, students enhance their ability to analyze situations effectively.

Preparation with Online Tests

Our free online tests on case study class 10 include detailed explanations. Hence, students can self-assess regularly. The case study questions class 10 maths provided cover diverse scenarios. Therefore, learners can boost their confidence and ensure accuracy in exams.

Case Study 2: Rectangular Flower Garden

Case Study 2

A school is planning to build a rectangular flower garden. The principal wants the garden’s length to be 4 metres more than its width. The area of the garden is expected to be 96 square metres. To find the appropriate dimensions, the students decide to model the situation using a quadratic equation. They learn that converting the geometric condition into an algebraic equation leads to a quadratic expression that can be solved either by factorization or by completing the square. Using both methods allows them to verify their answer. This real-life context helps them understand how quadratic equations can represent physical problems, such as dimensions and area.

Key Concepts and Formulas:

  • Let width be \( x \), then length = \( x + 4 \)
  • Area of rectangle = \( \text{length} \times \text{width} \)
  • Standard form: \( ax^2 + bx + c = 0 \)
  • Factorization and Completing the Square methods: \[ x^2 + 4x – 96 = 0 \]
  • Completing the square: Convert to a perfect square trinomial.

1. What quadratic equation represents the area of the rectangular garden?

  • A) \( x^2 + 4x + 96 = 0 \)
  • B) \( x^2 – 4x – 96 = 0 \)
  • C) \( x^2 + 4x – 96 = 0 \)
  • D) \( x^2 – 4x + 96 = 0 \)
Answer: C) \( x^2 + 4x – 96 = 0 \)
Solution: \[ \text{Let width be } x,\ \text{length is } x + 4,\ \text{area is } 96 \\ \Rightarrow x(x+4) = 96 \Rightarrow x^2 + 4x – 96 = 0 \]

2. Solve the equation using factorization. What is the width of the garden?

  • A) 8 metres
  • B) 12 metres
  • C) 6 metres
  • D) 10 metres
Answer: A) 8 metres
Solution: \[ x^2 + 4x – 96 = 0 \\ \Rightarrow (x + 12)(x – 8) = 0 \Rightarrow x = -12 \text{ or } 8 \\ \text{Negative width is not possible, so width = 8 m} \]

3. What is the corresponding length of the garden?

  • A) 10 metres
  • B) 12 metres
  • C) 8 metres
  • D) 14 metres
Answer: B) 12 metres
Solution: \[ \text{Length} = x + 4 = 8 + 4 = 12 \text{ m} \]

4. Solve the equation \( x^2 + 4x – 96 = 0 \) by completing the square. What value of \( x \) do you get?

  • A) 6
  • B) 8
  • C) 12
  • D) 10
Answer: B) 8
Solution: \[ x^2 + 4x – 96 = 0 \Rightarrow x^2 + 4x = 96 \\ \Rightarrow x^2 + 4x + 4 = 100 \Rightarrow (x + 2)^2 = 100 \\ \Rightarrow x + 2 = \pm10 \Rightarrow x = 8 \text{ or } -12 \] Only positive value accepted: \( x = 8 \)

5. What is the area of the rectangular garden based on the final dimensions?

  • A) 96 square metres
  • B) 104 square metres
  • C) 112 square metres
  • D) 88 square metres
Answer: A) 96 square metres
Solution: \[ \text{Width } = 8,\ \text{Length } = 12,\ \text{Area } = 8 \times 12 = 96\ \text{sq m} \]

Your Results:

Correct Answers: 0

Incorrect Answers: 0

Percentage Score: 0%

Educational Resources Footer

Free Educational Resources

Free Study Material English Vocabulary Tests Grammar for Hearing Impaired Math for Hearing Impaired English Vocabulary Case Study Questions Math GRE Vocabulary Tests LaTeX Tutorial R Programming Tests Online English Games Online Math Games Learn Computer Basics JEE Math Tests CAT Quant Tests Increase Calculation Speed Class 10 Math Tests Prompt Engineering SAT Math Tutorial Logic Quizzes Grade 1 Logic Quizzes Grade 2

© 2023 Udgam Welfare Foundation. All rights reserved.