Exercise 9.1

1. Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

Solution:

Let the variable be m

The rule which gives the number of sticks required to make the pattern are.

(i) A pattern of letter T :

(ii) A pattern of letter E :

(iii) A pattern of letter Z :

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

Solution:

Instruction

The number of blades that a fan has =

Number of fans = n (say)

Therefore the number of blades for ‘n’ fans = × n =

The required rule is 3n..

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

(a)

Solution:

The first shape has matchsticks, the second shape and the third shape .

Therefore the required rule .(‘s’ stands for number of shapes.)

(b)

Solution:

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

Therefore The required rule is .(‘s’ stands for number of shapes.)

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

Solution:

Instruction

Cost of one pen is Rs. .

Cost of n pens = 7 × n =

The rule for cost of n pens is 7n.

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

Solution:

Instruction

The cost of one bag = Rs. .

Cost of ‘m’ bags = 90 × m =

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

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

Solution:

Instruction

Cost of ‘q’ books = Rs.

Cost of one book =

Therefore the rule for the price of one book is 23q.

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

Solution:

Instruction

Let the number of books that Gayathri has be .

Then the number of books that John has = x−

John says that he has two books less than Gayathri)

Therefore the required relationship is (x – 2).

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

Solution :

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

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

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

Therefore the required relationship is 2y + 3.

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).

Solution:

Let the number of students be z.

The teacher gives pencils to each student.

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

The rule that is required is 6z.

10. Complete each table to generate the given functional relationship.

(i)

x	1	2	3	4	5	9
3x + 2	5						38

(ii)

x	1	3	6	7	9	8
5a - 1	4						49

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.

Solution:

(i) Number of line segments in each shape:

Shape – 1 contains line segments.

Shape – 2 contains line segments.

Shape – 3 contains line segments.

Shape – 4 contains line segments.

Shape – 5 contains line segments.

Shape – 6 contains line segments.

Shape – 7 contains line segments.

Shape – 8 contains line segments.

Shape – 9 contains line segments.

The total number of line segments in 9 such shapes is .

(ii) The rule for the above pattern is:

+ n−

Chapter 9: Introduction to Algebra

Glossary

Exercise 9.1

(a)

(b)

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Chapter 9: Introduction to Algebra

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Glossary

Exercise 9.1

(a)

(b)