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Class 7 Mathematics Chapter 4 Expression Using Latter-Numbers

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I. Chapter Summary:

This chapter introduces algebraic expressions, focusing on the use of letters (variables) to represent numbers. Students learn how to form expressions, understand terms, coefficients, constants, and how to evaluate expressions by substituting values. The chapter also covers the basic operations on algebraic expressions such as addition, subtraction, and multiplication, helping build a foundation for algebraic manipulations.

II. Key Concepts Covered:

• Algebraic Expressions: Combinations of variables, constants, and arithmetic operations.

• Variables: Symbols (usually letters) representing unknown or changing quantities.

• Constants: Fixed numerical values in an expression.

• Terms: Parts of an expression separated by plus (+) or minus (−) signs.

• Coefficients: Numbers multiplying the variables in a term.

• Like Terms: Terms having the same variable(s) raised to the same power(s).

• Evaluating Expressions: Substituting numerical values for variables and simplifying.

• Addition and Subtraction of Algebraic Expressions: Combining like terms.

• Multiplication of Algebraic Expressions: Using distributive property and multiplying coefficients and variables.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which of the following is an algebraic expression?
   a) 5 + 3
   b) 4x + 7
   c) 12 ÷ 3
   d) 8 − 2
   Answer: b) 4x + 7
   (PYQ 2022)

2. What is the coefficient in the term 7y?
   a) 7
   b) y
   c) 1
   d) None
   Answer: a) 7
   (PYQ 2021)

3. Identify the constant in the expression 3a + 5.
   a) 3
   b) a
   c) 5
   d) None
   Answer: c) 5
   (PYQ 2020)

4. Like terms are:
   a) Terms with the same variable part
   b) Terms with the same coefficient
   c) Terms with different variables
   d) None of these
   Answer: a) Terms with the same variable part
   (PYQ 2019)

(B) Short Answer Questions (2/3 Marks):

1. Define algebraic expression and give two examples.

2. What are like terms? Give an example.

3. How do you evaluate the expression 5x − 3 when x = 4?

4. Explain the difference between a constant and a coefficient.

(C) Long Answer Questions (5 Marks):

1. Simplify: 3x + 4 + 5x − 7.

2. Multiply: (2x + 3)(4x − 5).

3. Evaluate and simplify the expression: 2a + 3b − 4 when a = 2 and b = −1.

4. Explain with examples how to add and subtract algebraic expressions.

(D) HOTS (Higher Order Thinking Skills) Questions:

1. If 3x − 5 = 10, find the value of x. Explain your method.

2. Given the expression 4(m + n) − 3(m − n), simplify and explain each step.

IV. Key Formulas/Concepts:

• Addition/Subtraction of Like Terms: Combine coefficients, keep the variable part same.

• Multiplication of Terms: Multiply coefficients and variables separately, use laws of exponents (e.g., xa×xb=xa+bx^a \times x^b = x^{a+b}xa×xb=xa+b).

• Evaluating Expressions: Substitute values and perform arithmetic operations.

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

• 1 Mark: Definitions of terms, identifying constants and coefficients (2018, 2021)

• 2/3 Marks: Simplification, evaluation of expressions (2019, 2020)

• 5 Marks: Multiplication and expansion of algebraic expressions (2018, 2022)

VIII. Real-World Application Examples to Connect with Topics:

• Calculating costs when quantities and prices vary, using expressions to represent total cost.

• Understanding formulas in physics and chemistry where variables denote quantities.

• Programming and algorithms where variables store changing data.

• Financial calculations like interest using algebraic expressions.

IX. Student Tips & Strategies for Success (Class-Specific):

• Practice identifying terms, coefficients, and constants in expressions.

• Memorize basic algebraic identities and rules for operation.

• Work on step-by-step simplification to avoid errors.

• Use substitution to understand and check the correctness of expressions.

• Solve previous year questions regularly for exam readiness.

X. Career Guidance & Exploration (Class-Specific):

• For Classes 9–10:

  • Lays foundation for algebra essential in engineering, computer science, economics, and more.

  • Important for Olympiads and NTSE preparations.

• For Classes 11–12:

  • Prepares students for higher algebra, calculus, and related competitive exams like JEE, NEET (for mathematics-based careers).

  • Useful in fields like data science, analytics, and research.

XI. Important Notes:

• Always stay updated with the latest syllabus from the official CBSE website.

• Focus on conceptual clarity rather than rote memorization.

• Regular practice with varied problems enhances problem-solving skills.