The Class 9 Maths Chapter 2 Introduction to Linear Polynomials Worksheet with Answers PDF is a practice resource for Class 9 students to improve their understanding of linear polynomial concepts. This worksheet includes CBSE Board concept-based questions, application problems, exam-level exercises, and detailed answers to help students learn topics such as polynomial expressions, degree, coefficients, values, zeros of linear polynomials, and graphical representation.
These Worksheets are prepared according to the latest NCERT Class 9 Maths learning approach and focus on building problem-solving skills through regular practice. Students looking for Class 9 Worksheets can use this chapter-wise worksheet for revision, homework practice, and exam preparation.
The Class 9 Maths Worksheets provide structured questions with solutions that help students check their mistakes and understand every step clearly. By solving this worksheet, students can strengthen their basics of Introduction to Linear Polynomials and improve their confidence in Mathematics.
Class 9 Introduction to Linear Polynomials Worksheet with Answers PDF
The Class 9 Introduction to Linear Polynomials worksheet with answers PDF provides chapter-wise practice questions based on important concepts from algebra. Students can solve different types of problems and compare their answers with detailed explanations.
Learning Outcomes
After completing this worksheet, students will be able to:
- Identify linear polynomial expressions correctly.
- Find the degree and coefficient of a polynomial.
- Calculate the value of a polynomial for given variables.
- Find the zero of a linear polynomial.
- Understand the standard form ax + b.
- Apply linear polynomials in real-life problems.
- Represent linear relationships through graphs.
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Introduction to Linear Polynomials Practice Questions
Solve these Chapter 2 Introduction to Linear Polynomials Class 9 worksheet questions to improve your understanding of polynomial concepts.
Level 1: Concept Check
1. Which of the following is a linear polynomial?
a) x² + 5
b) 3x - 2
c) 1/x + 4
d) x³ - x
2. State the degree of the constant polynomial -8.
3. Identify the coefficient of x in the polynomial:
x/3 + 6
4. Write the standard form of a linear polynomial in one variable.
5. Check whether the expression √x + 5 is a polynomial or not. Give reason.
Level 2: Application Practice
6. Find the value of the linear polynomial p(x) = 5x - 4 for:
a) x = 2
b) x = -1
7. Find the zero of the linear polynomial:
q(x) = 3x + 9
8. Identify whether the following expressions are polynomials. Also mention their degree.
a) 7y - 5
b) y + 2/y
9. A shop charges ₹20 as a fixed packing cost and ₹15 per item purchased. Write a linear polynomial to represent the total cost for x items.
Level 3: Exam Practice
10. A pattern follows the linear polynomial:
T(n) = 4n + 2
Find:
a) Value of T(5)
b) Stage number when the value is 42
11. Find the linear polynomial f(x) = ax + b if:
f(0) = 3 and f(2) = 9
12. For the polynomial p(x) = 2x + 5:
a) Find the value at x = 0, 1, and -1.
b) Write the points formed.
c) Identify the type of graph obtained.
Answers and Explanations
Level 1 Answers
1. Answer: b) 3x - 2
Explanation:
A linear polynomial has the highest power of the variable equal to 1. In 3x - 2, the power of x is 1, so it is a linear polynomial.
2. Answer: 0
Explanation:
The degree of every non-zero constant polynomial is 0 because it can be written with the variable having power 0.
3. Answer: 1/3
Explanation:
x/3 can be written as (1/3)x. Therefore, the coefficient of x is 1/3.
4. Answer: ax + b
Explanation:
The standard form of a linear polynomial is ax + b, where a and b are constants and a ≠ 0.
5. Answer: Not a polynomial
Explanation:
√x is equal to x¹/². A polynomial cannot have fractional powers of variables.
Level 2 Answers
6. Given: p(x) = 5x - 4
For x = 2:
p(2) = 5(2) - 4
= 10 - 4
= 6
For x = -1:
p(-1) = 5(-1) - 4
= -5 - 4
= -9
7. Given: q(x) = 3x + 9
For zero of polynomial:
3x + 9 = 0
3x = -9
x = -3
Answer: The zero of the polynomial is -3.
8. Answers:
a) 7y - 5
It is a polynomial.
Degree = 1
b) y + 2/y
It is not a polynomial because 2/y contains a negative power of the variable.
9. Answer:
Total Cost = Item Cost + Fixed Cost
Therefore,
P(x) = 15x + 20
The required linear polynomial is 15x + 20.
Level 3 Answers
10. Given: T(n) = 4n + 2
a) For n = 5:
T(5) = 4(5) + 2
= 20 + 2
= 22
b) For value 42:
4n + 2 = 42
4n = 40
n = 10
Answer: Stage 10
11. Given: f(x) = ax + b
Using f(0) = 3:
a(0) + b = 3
b = 3
Using f(2) = 9:
2a + 3 = 9
2a = 6
a = 3
Therefore,
f(x) = 3x + 3
12. Given: p(x) = 2x + 5
At x = 0:
p(0) = 5 → Point (0,5)
At x = 1:
p(1) = 7 → Point (1,7)
At x = -1:
p(-1) = 3 → Point (-1,3)
The points form a straight-line graph.
Important Topics Covered in Introduction to Linear Polynomials Worksheet
This worksheet on polynomials for Class 9 with answers covers:
- Meaning of polynomial expressions
- Introduction to linear polynomials
- Standard form ax + b
- Degree of a polynomial
- Coefficients and constants
- Value of polynomial
- Zero of linear polynomial
- Linear patterns
- Graphical representation of linear relationships
- Real-life applications of linear polynomials
Common Mistakes Students Should Avoid
While solving the Class 9 polynomials worksheet, students should avoid these common mistakes:
- Considering expressions with variables in denominators as polynomials.
- Confusing coefficients and constants.
- Writing the wrong degree of a polynomial.
- Forgetting that the highest power decides the degree.
- Making sign errors while finding zeros.
- Incorrect substitution of variable values.
- Plotting wrong coordinates while drawing graphs.
