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Short Intro

Exercise 2.2 focuses on evaluating linear and quadratic polynomials and solving real-life word problems using linear equations. These detailed step-by-step solutions help students understand algebra concepts easily and improve their problem-solving skills for school exams and competitive preparation.

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Quick Information Box

Topic	Details
Chapter	Introduction to Linear Polynomials
Exercise	Exercise 2.2
Subject	Mathematics
Class	Grade 9
Main Topics	Polynomial Evaluation & Linear Equations
Difficulty Level	Moderate
Useful For	School Exams & Olympiad Foundation

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Concepts Used (Topics Covered)

• Linear Polynomials
• Quadratic Polynomials
• Polynomial Evaluation
• Substitution Method
• Linear Equations
• Ratio Problems
• Age Problems
• Coin Problems
• Rectangle Problems

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Important Formulas

Linear Polynomial

$ax+b$

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Quadratic Polynomial

$ax^2+bx+c$

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Perimeter of Rectangle

$P=2(l+b)$

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Value of Polynomial

Substitute the given value of the variable into the expression.

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Questions & Step-by-Step Solutions

Question 1

Find the value of the linear polynomial $5x – 3$ if:

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(i) $x = 0$

Solution

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(ii) $x = -1$

Solution

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(iii) $x = 2$

Solution

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Question 2

Find the value of the quadratic polynomial $7s^2 – 4s + 6$ if:

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(i) $s = 0$

Solution

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(ii) $s = -3$

Solution

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(iii) $s = 4$

Solution

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Question 3

The present age of Salil’s mother is three times Salil’s present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Solution

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Question 4

The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Solution

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Question 5

Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total ₹88, how many coins does she have of each type?

Solution

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Question 6

A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

Solution

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Question 7

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

Solution

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Common Mistakes

❌ Forgetting brackets during substitution
❌ Wrong sign handling for negative numbers
❌ Using incorrect perimeter formula
❌ Confusing ratio with difference

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Exam Tips

✔ Write variables clearly before solving
✔ Substitute values carefully
✔ Always verify final answers
✔ Practice word problems regularly

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Practice MCQs

1. Find value of $3x + 2$ when $x = 4$

A) 10
B) 12
C) 14
D) 16

Answer

✅ C) 14

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2. Which is a quadratic polynomial?

A) $2x+1$
B) $x^2+5x+1$
C) $7$7
D) $5x^3$

Answer

✅ B) $x^2+5x+1$

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3. Perimeter of rectangle formula is:

A) $l+b$
B) $2l+b$
C) $2(l+b)$
D) $lb$

Answer

✅ C) $2(l+b)$

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4. If ratio is 2:5, numbers can be written as:

A) $2+x$ and $5+x$
B) $2x$ and $5x$
C) $x/2$ and $x/5$
D) None

Answer

✅ B) $2x$ and $5x$

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FAQ Section

Q1. What is polynomial evaluation?

It means finding the value of a polynomial after substituting a variable value.

Q2. What is a linear polynomial?

A polynomial having degree 1 is called a linear polynomial.

Q3. What is a quadratic polynomial?

A polynomial having degree 2 is called a quadratic polynomial.

Q4. Why are word problems important?

They improve logical thinking and real-life mathematical understanding.

Q5. Can negative numbers be substituted in polynomials?

Yes, negative values can also be substituted.

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