Q1. Page 21: Find the value of the linear polynomial 5x - 3 if: (i) x = 0 (ii) x = -1 (iii) x = 2
Answer:
(i) 5(0) - 3 = -3
(ii) 5(-1) - 3 = -5 - 3 = -8
(iii) 5(2) - 3 = 10 - 3 = 7
Q2. Page 21: Find the value of the quadratic polynomial 7s² - 4s + 6 if: (i) s = 0 (ii) s = -3 (iii) s = 4
Answer:
(i) 7(0)² - 4(0) + 6 = 6
(ii) 7(-3)² - 4(-3) + 6 = 7(9) + 12 + 6 = 63 + 18 = 81
(iii) 7(4)² - 4(4) + 6 = 7(16) - 16 + 6 = 112 - 10 = 102
Q3. Page 21: 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.
Answer:
Let Salil's present age be x years.
Then his mother's present age is 3x years.
After 5 years:
- Salil's age = x + 5
- Mother's age = 3x + 5
Sum of their ages after 5 years = 70:
(x + 5) + (3x + 5) = 70
4x + 10 = 70
4x = 60
x = 15
Salil's present age = 15 years.
Mother's present age = 45 years.
Q4. Page 21: The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.
Answer:
Let the two integers be 2x and 5x (since their ratio is 2:5).
Their difference is 63:
5x - 2x = 63
3x = 63
x = 21
The integers are:
2x = 42 and 5x = 105
Q5. Page 21: 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?
Answer:
Let the number of five-rupee coins be x.
Then the number of two-rupee coins is 3x.
Total value of coins:
5x + 2(3x) = 88
5x + 6x = 88
11x = 88
x = 8
Number of five-rupee coins = 8.
Number of two-rupee coins = 3x = 24.
Q6. Page 21: 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?
Answer:
Let the length of the shorter piece be x feet.
Then the longer piece is 4x feet.
The total length is 300 feet:
x + 4x = 300
5x = 300
x = 60
Shorter piece = 60 feet.
Longer piece = 4x = 240 feet.
Q7. Page 21: 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?
Answer:
Let the width of the rectangle be w cm.
Then the length is 2w + 3 cm.
Perimeter = 2(length + width) = 24 cm
2(2w + 3 + w) = 24
2(3w + 3) = 24
6w + 6 = 24
6w = 18
w = 3 cm
Length = 2(3) + 3 = 6 + 3 = 9 cm
The dimensions are width = 3 cm and length = 9 cm.