Q1. Page 23: A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the n^th month.

Answer:

Money at the end of each month:

• End of 1st month: ₹500 + ₹150 = ₹650
• End of 2nd month: ₹650 + ₹150 = ₹800
• End of 3rd month: ₹800 + ₹150 = ₹950

Linear Expression: The amount in the savings account at the end of the nth month is:

A(n) = 500 + 150n

where n is the number of months.

Q2. Page 24: A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1, 2, 3, ... hours? Find a linear expression to represent the number of members at the end of the n^th hour.

Answer:

Members remaining after each hour:

• After 1 hour: 120 - 9 = 111
• After 2 hours: 120 - 18 = 102
• After 3 hours: 120 - 27 = 93

Linear Expression: The number of members remaining after n hours is:

M(n) = 120 - 9n

where n is the number of hours.

Q3. Page 24: Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.

Answer:

Area for each breadth:

• (i) Breadth = 12 cm, Area = 13 × 12 = 156 cm²
• (ii) Breadth = 10 cm, Area = 13 × 10 = 130 cm²
• (iii) Breadth = 8 cm, Area = 13 × 8 = 104 cm²

Linear Pattern: Let the breadth be 'b' cm. The area A is given by:

A = 13b

This is a linear pattern where the area increases by 13 cm² for every 1 cm increase in breadth.

Q4. Page 24: Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern representing the volume of the rectangular box.

Answer:

Volume for each height:

• (i) Height = 5 cm, Volume = 7 × 11 × 5 = 385 cm³
• (ii) Height = 9 cm, Volume = 7 × 11 × 9 = 693 cm³
• (iii) Height = 13 cm, Volume = 7 × 11 × 13 = 1001 cm³

Linear Pattern: Let the height be 'h' cm. The volume V is given by:

V = 7 × 11 × h = 77h

This is a linear pattern where the volume increases by 77 cm³ for every 1 cm increase in height.

Q5. Page 24: Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.

Answer:

Pages read in 15 days:

20 pages/day × 15 days = 300 pages

Pages left after 15 days:

500 - 300 = 200 pages

Linear Pattern: Let the number of days be 'd'. The number of pages left L is:

L(d) = 500 - 20d

This is a linear pattern representing linear decay (pages decrease by 20 each day).