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Class 7 → Mathematics → Chapter 4: Expression Using Letter-Numbers (Algebraic Expressions)
I. Chapter Summary:
The chapter Expression Using Letter-Numbers introduces students to algebra, where letters are used along with numbers to form expressions. These letters are called variables and represent unknown or changing values. Students learn how to form algebraic expressions, understand terms, coefficients, and constants, and simplify expressions. This chapter builds a foundation for algebra and helps students represent real-life situations mathematically.
II. Key Concepts Covered:
1. Variables
Letters (like x, y, a) used to represent unknown values.
2. Constants
Fixed numerical values (e.g., 5, 10, 100).
3. Algebraic Expressions
Combination of variables, constants, and operations.
Example: 3x + 5
4. Terms
Parts of an expression separated by + or −.
Example: In 3x + 5, terms are 3x and 5.
5. Coefficient
The numerical value multiplied with a variable.
Example: In 4x, coefficient is 4.
6. Like and Unlike Terms
- Like terms: Same variables (2x, 5x)
- Unlike terms: Different variables (2x, 3y)
7. Simplification of Expressions
Combine like terms to simplify expressions.
III. Important Questions:
(A) MCQs (1 Mark):
- In the expression 5x, x is called:
(a) Constant
(b) Variable ✅
(c) Coefficient
(d) Term - Which is a constant?
(a) x
(b) y
(c) 10 ✅
(d) z - Like terms are:
(a) 2x and 3y
(b) 5x and 2x ✅
(c) 3 and x
(d) 4y and 5z - Simplify: 2x + 3x
(a) 5x ✅
(b) 6x
(c) x
(d) 2x
(B) Short Answer Questions (2/3 Marks):
- Define variable with an example.
- What are like terms? Give examples.
- Identify terms in the expression 4x + 7.
- Simplify: 3x + 2x + 5
(C) Long Answer Questions (5 Marks):
- Explain algebraic expressions with examples.
- Differentiate between variables, constants, and coefficients.
- Simplify algebraic expressions step-by-step.
- Explain like and unlike terms with examples.
(D) HOTS Questions:
- Why are variables useful in solving real-life problems?
- How can algebraic expressions help in representing patterns?
IV. Key Formulas/Concepts:
Basic Algebraic Expression Form
$ax + b$
Where:
- a = coefficient
- x = variable
- b = constant
Combining Like Terms
$2x + 3x = 5x$
Example:
$3x + 2x + 5 = 5x + 5$
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):
| Unit/Chapter | Estimated Marks | Type of Questions Typically Asked |
|---|---|---|
| Expression Using Letter-Numbers | 5–7 Marks | MCQs, Short Answer, Simplification |
Note: This is an estimate. Actual marks distribution may vary.
VII. Previous Year Questions (PYQs):
1 Mark:
- Identify variable in 3x + 5. (2019)
2/3 Marks:
- Simplify: 2x + 5x (2020)
- Define like terms. (2021)
5 Marks:
- Explain algebraic expressions with examples. (2022)
VIII. Real-World Application Examples:
- Calculating cost: If one pen costs ₹x, then 5 pens cost 5x
- Representing age: If Ravi’s age is x, his father’s age is x + 30
- Distance problems in daily life
- Pattern formation in mathematics
IX. Student Tips & Strategies for Success:
Time Management:
- Practice algebra daily for better understanding.
Exam Preparation:
- Focus on identifying terms and simplifying correctly.
- Practice combining like terms.
Stress Management:
- Solve problems step-by-step.
- Avoid rushing calculations.
X. Career Guidance & Exploration:
- Science Stream: Engineering, Mathematics
- Commerce Stream: Accounting, Economics
- Arts Stream: Statistics, Logical Reasoning
Entrance Exams (Basic Awareness):
- JEE (Engineering)
- CA Foundation
XI. Important Notes:
- Always identify variables, constants, and coefficients clearly.
- Combine only like terms.
- Practice regularly for better clarity.
- Refer to NCERT textbook.
- Revise concepts frequently.