Last Updated on September 8, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities. It is a part of Case Study Questions for CBSE Class 8 Maths Series.

Chapter | Algebraic Expressions and Identities |

Type of Questions | Case Study Questions |

Nature of Questions | Competency Based Questions |

Board | CBSE |

Class | 8 |

Subject | Maths |

Useful for | Class 8 Studying Students |

Answers provided | Yes |

Difficulty level | Mentioned |

Important Link | Class 8 Maths Chapterwise Case Study |

### Case Study Questions on Algebraic Expressions and Identities

**Questions**

**Passage 1: **

A playground is in shape of a square. The area of the square PQRS is 256 m^{2} with each side (x + 2) m. One day Suraj along with his two friends Ajay and Aman went to play there with bicycle. Someone stole Suraj bicycle, but Ajay and Aman helped him by contributing ₹(4a + 60) and ₹(6a + 10) respectively, to buy a new bicycle. The cost of bicycle was ₹4200.

On basis of this information given in passage answer following questions.

Q. 1. Find the value of x.

(a) 16

(b) 18

(c) 14

(d) 12

**Difficulty Level: **Easy

Ans. Option (c) is correct.

Explanation: Area of square = 256 m^{2}

(x + 2)^{2} = 162

x + 2 = 16

x = 16 – 2

x = 14

Q. 2. Find the side of square quare-shaped ground?

(a) 19

(b) 12

(c) 18

(d) 16

**Difficulty Level: **Easy

Ans. Option (d) is correct.

Explanation: x = 14

Therefore, side of square = (x + 2) = 14 + 2 = 16

Q. 3. What is the value of a?

(a) 410

(b) 403

(c) 413

(d) 423

**Difficulty Level: **Medium

Ans. Option (C) is correct.

Explanation: (4a + 60) + (6a + 10) = 4200

4a + 60 + 6a + 10 = 4200

10a + 70 = 4200

10a = 4130

Hence, a = 413

Q. 4. What was the amount given by Ajay and Aman to Suraj?

**Difficulty Level: **Medium

Sol. Money contributed by Ajay = (4a + 60)

Money contributed by Aman = (6a + 10)

Total amount = ₹4200

4a + 60 + 6a + 10 = 4200

10a + 70 = 4200

a = 413

Money contributed by Ajay = 4 × 413 + 60 = 1652 + 60 = ₹1712

Money contributed by Aman = 6 × 413 + 10 = 2478 + 10 = ₹2488

Q. 5. What is the perimeter of the playground?

**Difficulty Level: **Medium

Sol. Perimeter of square shaped playground = 4 × (x + 2)

x = 14

Substituting value of x inside, we get

= 4 × (14 + 2)

Perimeter = 4 × 16 = 64 m

### Also check

- Exponents and Powers Class 8 Case Study Questions Maths Chapter 10
- Mensuration Class 8 Case Study Questions Maths Chapter 9
- Algebraic Expressions and Identities Class 8 Case Study Questions Maths Chapter 8
- Comparing Quantities Class 8 Case Study Questions Maths Chapter 7
- Cube and Cube Roots Class 8 Case Study Questions Maths Chapter 6
- Square and Square Roots Class 8 Case Study Questions Maths Chapter 5
- Data Handling Class 8 Case Study Questions Maths Chapter 4
- Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3
- Linear Equations in One Variable Class 8 Case Study Questions Maths Chapter 2
- Rational Numbers Class 8 Case Study Questions Maths Chapter 1

### Download eBooks for CBSE Class 8 Maths

- Rational Numbers Topicwise Worksheet for CBSE Class 8 Maths
- Linear Equations in One Variable Worksheet for CBSE Class 8 Maths
- Understanding Quadrilaterals Worksheet for CBSE Class 8 Maths
- Data Handling Worksheet for CBSE Class 8 Maths
- Squares and Square Roots Worksheet for CBSE Class 8 Maths
- Cube and Cube Roots Worksheet for CBSE Class 8 Maths
- Comparing Quantities Worksheet for CBSE Class 8 Maths
- Algebraic Expressions and Identities Worksheet for CBSE Class 8 Maths

### Topics from which case study questions may be asked

- Multiplication of Algebraic Expressions
- Multiplying a Monomial by a Polynomial
- Multiplying a Polynomial by a Polynomial

* Addition and Subtraction of Algebraic Expressions:* While adding or subtracting polynomials, first look for like terms and then add or subtract these terms, then handle the unlike terms.

**Multiplication of Algebraic Expressions**

(i) Multiplying two monomials

(ii) Multiplying three or more monomials

**Multiplying a monomial by a polynomial**

(i) Multiplying a monomial by a binomial

(ii) Multiplying a monomial by a trinomial

**Multiplying a polynomial by a polynomial**

(i) Multiplying a binomial by a binomial

(ii) Multiplying a binomial by a trinomial.

Subtraction of a number is the same as addition of its additive inverse.

Case study questions from the above given topic may be asked.

### Important Keywords

**Like term: **Terms having same literal factors are called like terms e.g., 7ab^{2}, 2ab^{2}, 3b^{2}a are like terms.**Monomial: **An algebraic expression that contains only one term is called monomial. e.g., –6abc, 5xy etc**Binomial: **An algebraic expression that contains two terms are called Binomial. e.g., x + 5 etc**Trinomial: **An algebraic expression that contains three terms are called trinomial. e.g., 2x – 7y + 4 etc**Polynomial: **An algebraic expression that contains one or more terms are called Polynomial. e.g., 7xy + 2z + 3y + 4a

### Frequently Asked Questions (FAQs) on Algebraic Expressions and Identities Case Study

#### Q1: What are algebraic expressions?

A1: Algebraic expressions are mathematical phrases that include numbers, variables (like x, y), and operations (like addition, subtraction, multiplication, and division). They represent a quantity and can include constants, coefficients, and variables. For example, 3x+4 is an algebraic expression.

#### Q2: What is the difference between a term and a coefficient in an algebraic expression?

A2: A term in an algebraic expression is a single part of the expression separated by addition or subtraction signs. A coefficient is the numerical factor of a term.

#### Q3: What are like and unlike terms?

A3: Like terms in an algebraic expression are those that have the same variables raised to the same powers. Unlike terms have different variables or different powers.

#### Q4: What is an identity in algebra, and how is it different from an equation?

A4: An identity is an equation that is true for all values of the variables involved. An equation, on the other hand, is true only for specific values of the variables.

#### Q5: How do you add and subtract algebraic expressions?

A5: To add or subtract algebraic expressions, first identify and group like terms. Then, add or subtract the coefficients of these like terms while keeping the variables and their powers the same.

#### Q6: **How are algebraic identities useful in simplifying expressions?**

A6: Algebraic identities are useful in simplifying complex algebraic expressions by allowing us to replace complicated expressions with simpler, equivalent forms. This makes it easier to perform calculations and solve problems efficiently.

#### Q7: **What is factorization of algebraic expressions, and why is it important?**

A7: Factorization is the process of breaking down an algebraic expression into a product of its factors. It is important because it simplifies expressions and is essential in solving equations, especially quadratic equations.

#### Q8: **Are there any online resources or tools available for practicing comparing quantities case study questions?**

A8: We provide case study questions for CBSE Class 8 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.