Q: In the figure, let x denotes the number of steps and y denotes the number of matchsticks used. Find the relationship between Y and y by tabulation.

Let x denote the number of steps and y denote the number of matchsticks used. In step 1, x = 1 ⇒ y = number of mathsticks used is 1 In step 2, x = 2 ⇒ y = number of mathsticks used is 4 In step 3, x = 3 ⇒ y = number of mathsticks used is 7 and so on. The values of v andy are tabulated as x = 1 ⇒ y = 1 = 3(1) – 2 x = 2 ⇒ y = 4 = 3(2) – 2 x = 3 ⇒ y = 7 = 3(3) – 2 x = 4 ⇒ y = 10 = 3(4) – 2 From the t

Question 1

Observe the pattern given below. Continue the pattern for three more steps. Let, ‘x’ be the number of steps and ‘y’ be the number of match sticks. Tabulate the values of ‘x’ and ‘y’ and verify the relationship y = 7x + 5.

Accepted Answer

Three more patterns are From the table y = 7x + 5 is verified. Try These (Text book Page No. 92)

Question 2

In the given figure, let Y denote the number of steps and y denote its area. Find the relationship between x and y by tabulation.

Accepted Answer

Let x denote the number of steps and y denote the area.
In the first shape let x = 1 and the area be 1 cm 2
when x = 2 : Area = 22 = 4 cm 2
whenx = 3 : Area = 32 = 9 cm 2 and so on.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions 4

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions 4

From the table:
x = 1 ⇒ y = 1 2
x = 2 ⇒ y = 2 2
x = 4 ⇒ y = 4 2
x = 5 ⇒ y = 5 2
Hence the relationship between x and y is y = x 2
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions

Question 3

In the figure, let x denotes the number of steps and y denotes the number of matchsticks used. Find the relationship between Y and y by tabulation.

Accepted Answer

Let x denote the number of steps and y denote the area.
In the first shape let x = 1 and the area be 1 cm 2
when x = 2 : Area = 22 = 4 cm 2
whenx = 3 : Area = 32 = 9 cm 2 and so on.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions 4

From the table:
x = 1 ⇒ y = 1 2
x = 2 ⇒ y = 2 2
x = 4 ⇒ y = 4 2
x = 5 ⇒ y = 5 2
Hence the relationship between x and y is y = x 2
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions

Question 4

Observe the above completed and r find the sequence that you see in it and complete them. (i) 1,2, 3, 4, 5, 6, 7. (ii) 1, 3, _____, _____, _____, _____. (iii) 1, _____, _____, _____, _____, (iv) _____, _____, _____, _____.

Accepted Answer

(i) 1,2, 3, 4, 5, 6, 7. (ii) 1,3,6,10,15,21. (iii) 1,4,10,20,35. (iv) 1,5,15,35.

Question 5

Observe the sequence of numbers obtained in the 3rd and 4th slanting rows of Pascal’s Triangle and find the difference between the consecutive numbers and complete the table given below.

Accepted Answer

Try These (Text book Page No. 96)

Question 6

Complete the given Pascal’s Triangle. Find the common property of the numbers filled by you. Can you relate this pattern with the pattern discussed in situation 2. Discuss.

Accepted Answer

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Intext Questions 16

Common Properties:
The numbers filled by me are even numbers. Also they make triangular shape.
Yes, this pattern and the pattern given in situation 2 have the same properties.
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Question 7

Match the given patterns of shapes with the appropriate number pattern and its generalization.

Accepted Answer

(i) (d) (ii) (a) (iii) (c) (iv) (c) (v) (b) Objective Type Questions

Question 8

The elements along the sixth row of the Pascal’s Triangle is (i) 1,5,10,5,1 (ii) 1,5,5,1 (iii) 1,5,5,10,5,5,1 (iv) 1,5,10,10,5,1

Accepted Answer

(iv) 1,5,10,10,5,1

Question 9

The difference between the consecutive terms of the fifth slanting row containing four elements of a Pascal’s Triangle is (i) 3,6,10,… (ii) 4,10,20,… (iii) 1,4,10,… (iv) 1,3,6,…

Accepted Answer

(ii) 4,10,20,…

Question 10

What is the sum of the elements of ninth row in the Pascal’s Triangle? (i) 128 (ii) 254 (iii) 256 (iv) 126

Accepted Answer

Question 11

Write the first five numbers in the third slanting row of the Pascal’s Triangle and find their squares. What do you infer?

Accepted Answer

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 4

Numbers in the 3rd slanding row are 1, 3, 6, 10, 15, 21,….
The squares are 1 2 , 3 2 , 6 2 , 10 2 . 15 2 , 21 2 ,…. = 1, 9, 36, 100, 225, 441,…
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 5

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 5

From the above table we can conclude that the squares of the triangular numbers are the sum of cubes of natural numbers.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3

Challenge Problems

Question 12

Tabulate and find the relationship between the variables (x and y) for the following patterns.

Accepted Answer

(i) Let the number of steps be x and the number of shapes be y.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 7

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 7

From the table
x = 1 ⇒ y = 1 = 12
x = 2 ⇒ y = 4 = 22
x = 3 ⇒ y = 9 = 32
x = 4 ⇒ y = 16 = 42
Hence the relationship between x and y is y = x2.
(ii) Let the number of steps be x and the number of shapes be y.
Tabulating the values of x and y
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 8

Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3 8

From the table x = 1 ⇒ y = 1 = 1
x = 2 ⇒ y = 2 + 1 = 3
x = 3 ⇒ y = 3 + 2 = 5
x = 4 ⇒ y = 4 + 3 = 7
x = 5 ⇒ y = 5 + 4 = 9
Hence the relationship between x and y is y = 2x-1.
Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 5 Information Processing Ex 5.3