Students can practice TS SCERT Class 6 Maths Solutions Chapter 9 Introduction to Algebra Ex 9.1 to get the best methods of solving problems.

## TS 6th Class Maths Solutions Chapter 9 Introduction to Algebra Exercise 9.1

Question 1.

Find the rule which gives the number of matchsticks required to make the following matchsticks patterns.

(i) A pattern of letter ‘T’

Answer:

The rule which gives the number of sticks required to make the pattern T is 2n.

(ii) A pattern of letter ‘E’

Answer:

The rule which gives the number of sticks required to make the pattern E is 5n.

(iii) A pattern of letter ‘Z’

Answer:

The rule which gives the number of sticks required to make the pattern Z is 3n.

Question 2.

Make a rule between the number of blades required and the number of fans (say n) in a hall ?

Answer:

The number of blades that a fan has = 3

Number of fans = n (say)

∴ The number of blades for ‘n’ fans = 3 × n = 3n

The required rule is 3n.

Question 3.

Find a rule for the following patterns between number of shapes formed and number of matchsticks required.

(a)

Answer:

The first shape has 2 matchsticks, the second shape 4 and the third shape 6.

∴ The required rule 2s.

(‘s’ stands for number of shapes.)

(b)

Answer:

The first shape has 3 matchsticks, the second shape 6 and the third shape 9.

∴ The required rule is 3s.

(‘s’ stands for number of shapes.)

Question 4.

The cost of one pen is ₹ 7 then what is the rule for the cost of ‘n’ pens.

Answer:

Cost of one pen is Rs. 7.

Cost of ‘n’ pens = 7 × n = 7n

The rule for cost of n’ pens is 7n.

Question 5.

The cost of one bag is ₹ 90, what is the rule for the cost of ‘m’ bags ?

Answer:

The cost of one bag = Rs. 90.

Cost of ‘m’ bags = 90 × m = 90m

The rule for the cost of ‘m’ bags is 90m.

Question 6.

The rule for purchase of books is-that the cost of q books is ₹ 23; then find the price of one book ?

Answer:

Cost of ‘q’ books = Rs. 23

∴ Cost of one book = \(\frac{23}{q}\)

The rule for the price of one book is \(\frac{23}{q}\).

Question 7.

John says that he has two books less than Gayathri. Write the relationship using letter x.

Answer:

Let the number of books that Gayathri has be x.

Then the number of books that John has = (x – 2)

(∵ John says that he has two books less than Gayathri)

The required relationship is (x – 2).

Question 8.

Rekha has 3 books more than twice the books with Suresh. Write the relationship using letter y.

Answer:

Let the number of books with Suresh be ‘y’.

Twice the number of books with Suresh = 2 × y – 2y.

As per the problem, the number of ‘ books that Rekha has = (2y + 3)

The required relationship is 2y + 3.

Question 9.

A teacher distributes 6 pencils per student. Can you find how many pencils are needed for the given number of students (use V for the number of students).

Answer:

Let the number of students be ’z’.

The teacher gives 6 pencils to each student.

The number of pencils that are given to ‘z’ students = 6 × z = 6z

The rule that is required is 6z.

Question 10.

Complete each table to generate the given functional relationship.

Answer:

Question 11.

Observe the following pattern.

Count the number of line segments in each shape.

(i) How many line segments will the 9th shape contain ?

(ii) Write the rule for the above pattern.

Answer:

(i) Shape – 1 contains 3 line segments.

Shape – 2 contains 5 line segments.

Shape – 3 contains 7 line segments.

Shape – 4 contains 9 line segments.

Shape – 5 contains 11 line segments.

Shape – 6 contains 13 line segments.

Shape – 7 contains 15 line segments.

Shape – 8 contains 17 line segments.

Shape – 9 contains 19 line segments.

The number of line segments that 9 such shapes contains is 99.

(∵ 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)

(ii) The rule for the above pattern is 3 + 2(n – 1).