Exercise 2.2 Class 9 Maths Solutions | Introduction to Linear Polynomials (Ganita Manjari)

by

Exercise 2.2 from Introduction to Linear Polynomials focuses on evaluating polynomials and solving real-life problems using algebraic expressions. This exercise strengthens the understanding of linear and quadratic polynomials along with their applications. Below are step-by-step solutions to all questions.

Exercise 2.2 Solutions

Question 1

Find the value of the linear polynomial 5x−3 if:
(i) x=0 (ii) x=−1 (iii) x=2

✏️ Solution

(i) When x=0

=5(0)−3

=−3

(ii) When x=−1

=5(−1)−3

=−5−3

=−8

(iii) When x=2

=5(2)−3

=10−3

=7

Question 2

Find the value of the quadratic polynomial 7s²−4s+6 if:
(i) s=0 (ii) s=−3 (iii) s=4

Solution

(i) s=0:

7(0)2−4(0)+6

=6

(ii) s=−3

7(9)+12+6

=63+12+6

=81

(iii) s=4

7(16)−16+6

=112−16+6

=102

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

Let Salil’s present age be x years

And his Mother’s present age be 3x years

After 5 years:

Age of Salil= (x+5) yrs

Age of his mother= (3x+5)yrs

According to question:

(x+5)+(3x+5)=70

4x+10=70

4x=60

⇒x=15

So Salil’s present age = 15 years
Mother’s present age = 45 years

Question 4

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

Solution

Let numbers be 2x and 5x

5x−2x=63

3x=63

⇒x=21

So Numbers are

2x=42

5x=105

Question 5

Ruby has 3 times as many two-rupee coins as five-rupee coins. Total amount is ₹88. Find number of coins.

Solution

Let number of ₹5 coins = x
Then ₹2 coins = 3x

Value of ₹5 notes=₹5x

Value of ₹3 notes=₹6x

Total money=88

5x+6x=88

11x=88

x=8

So number of ₹5 coins = 8
Number of ₹2 coins = 24

Question 6

A farmer cuts a 300 feet fence into two pieces. The longer piece is four times the shorter piece. Find lengths.

✏️ Solution

Let shorter piece = x feet
Longer piece = 4x feet

x+4x=300

5x=300

⇒x=60

Shorter piece = 60 ft
Longer piece = 240 ft

Question 7

Length of rectangle is three more than twice its width. Perimeter = 24 cm. Find dimensions.

✏️ Solution

Let width = x cm
Length = (2x+3)cm

Perimeter: 2(L+W)=24

L+W=12

(2x+3)+x=12

3x+3=12

⇒3x=9

⇒x=3

Width = 3 cm
Length = 9 cm

🟢 Conclusion

This exercise builds a strong base in polynomials and algebraic thinking. Students learn how to evaluate expressions and solve real-life problems using equations.

Other important posts