Well-designed AP 6th Class Maths Guide Chapter 11 Algebra Exercise 11.1 offers step-by-step explanations to help students understand problem-solving strategies.
Algebra Class 6 Exercise 11.1 Solutions – 6th Class Maths 11.1 Exercise Solutions
Question 1.
Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
a) A pattern of letter T as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 2 × 1 = 2
n = 2, the number of matchsticks required = 2 × 2 = 4
n = 3, the number of matchsticks required = 2 × 3 = 6
∴ The rule = 2 × n = 2 n, where n is number of Ts.
b) A pattern of letter Z as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 3 × 1 = 3
n = 2, the number of matchsticks required = 3 × 2 = 6
n = 3, the number of matchsticks required = 3 × 3 = 9
∴ The rule = 3 × n = 3n, where n is number of Zs .
c) A pattern of letter U as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 3 × 1 = 3
n = 2, the number of matchsticks required = 3 × 2 = 6
n = 3, the number of matchsticks required = 3 × 3 = 9
∴ The rule = 3 × n = 3n, where n is number of Us .
d) A pattern of letter V as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 2 × 1 = 2
n = 2, the number of matchsticks required = 2 × 2 = 4
n = 3, the number of matchsticks required = 2 × 3 = 6
n = 4, the number of matchsticks required = 2 × 4 = 8
∴ The rule = 2 × n = 2n, where n is number of Vs.
e) A pattern of letter E as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 5 × 1 = 5
n = 2, the number of matchsticks required = 5 × 2 = 10
n = 3, the number of matchsticks required = 5 × 3 = 15
∴ The rule = 5 × n = 5n, where n is number of Es.
f) A pattern of letter S as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 5 × 1 = 5
n = 2, the number of matchsticks required = 5 × 2 = 10
n = 3, the number of matchsticks required = 5 × 3 = 15
∴ The rule = 5 × n = 5n, where n is number of Ss.
g) A pattern of letter A as
Solution:
Number of matchsticks required to make the pattern
For n = 1, the number of matchsticks required = 6 × 1 = 6
n = 2, the number of matchsticks required = 6 × 2 = 12
n = 3, the number of matchsticks required = 6 × 3 = 18
∴ The rule = 6 × n = 6n, where n is number of As.
Question 2.
We already know the rule for the pattern of letters L, C and F. Some of the letters from Q. 1 (given above) give us the same rule as that given by L. Which are these ? Why does this happen ?
Solution:
Rule for the following letters.
Letter | Rule |
L | 2n |
V | 2n |
T | 2n |
Letter | Rule |
C | 3n |
F | 3n |
U | 3n |
From the above tables,
i) We obseerve that the rule is same of L,V and T i.e. 2n as they are required only two matchsticks.
ii) Letters C, F and U have the same rule i.e. 3n, as they required only 3 matchsticks.
Question 3.
Cadets are marching in a parade. There are 5 cadets in a row. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows.)
Solution:
Number of cadets in a row = 5
Number of rows = n
Number of cadets = n
For n = 1 is 5 × 1 = 5
n = 2 is 5 × 2 = 10
n = 3 is 5 × 3 = 15
∴ Rule is 5n, where n represents the number of rows.
Question 4.
If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
Solution:
Number of boxes = b
Number of mangoes in a box = 50
Number of unangoes
For n – 1 is 50 × 1 = 50
For n = 2 is 50 × 2 = 100
For n = 3 is 50 × 3 = 150
∴ Rule is 50 b, where b represents the number of boxes.
Question 5.
The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Solution:
Number of students = s
Number of pencils ditributed per student = 5
Number of pencils required
For n = 1 is 5 × 1 = 5
For n =2 is 5 × 2 = 10
For n = 3 is 5 × 3 = 15
∴ Rule is 5s, where s represents the number of students.
Question 6.
A bird files 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes.)
Solution:
Distance covered in 1 minute = 1 km
The flying time = t
Distance covered
For n = 1 is 1 × 1 = 1 km
For n = 2 is 1× 2 = 2 km
For n = 3 is 1 × 3 = 3 km
∴ Rule is 1 × t km, where t represents, the flying time.
Question 7.
Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 dots in a row. How many dots will her Rangoll have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Solution:
Number of rows = 9
Number of dots in a row drawn by Radha = 8
∴ The number of dots required
For r = 1 is 9 × 1 = 9
For r = 2 is 9 × 2 = 18
For r = 3 is 9 × 3 = 27
∴ Rule is 9r, where r represents the number of rows.
If r = 8 (i.e. 8 rows), the number of dots = 9 × 8 = 72
r = 10 (i.e. 10 rows), the number of dots = 9 × 10 = 90
Question 8.
Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age ? Take Radha’s age to be x years.
Solution:
Radha’s age = x years
Given that Leela’s age = Radha’s age – 4 years
= x years – 4 years
= (x – 4) years
Question 9.
Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Solution:
Given that the number of laddus given away = l
Number of laddus left = 5
∴ Number of laddus made by mother = l + 5
Question 10.
Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be x, what is the number of oranges in the larger box ?
Solution:
Given that, the number of oranges in smaller box = x
∴ Number of oranges in bigger box = 2 (number of oranges in small box) + Number of oranges remain outside)
So, the number of oranges in bigger box = 2x + 10
Question 11.
a) Look at the following matchstick pattern of squares (Figure). The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint : If you remove the vertical stick at the end, you will get a pattern of Cs.)
Solution:
Let n be the number of squares.
∴ Number of matchsticks required.
For n = 1 = 3n + 1 = 3 × 1 + 1 = 4
For n = 2 = 3n + 1 = 3 × 2 + 1 = 7
For n = 3 = 3n + 1 = 3 × 3 + 1 = 10
For n = 4 = 3n + 1 = 3 × 4 + 1 = 13
For n, 3 × n + 1 = 3n + 1
∴ Rule is 3n + 1, where n represents the number of squares.
b) Following figure gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
Solution:
Let n be the number of triangles.
∴ Number of matchsticks required.
For n = 1 = 2 × 1 = 1
For n = 2 = 2 × 2 = 1
For n = 3 = 2 × 3 + 1
For n = 4 = 2 × 4 + 1
For n, 2 × n + 1 = 2n + 1
∴ Rule is 2n + 1, where n represents the number of matchsticks.