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Chapter 11: Algebra

    Introduction

    Matchstick Patterns

    The Idea of a Variable

    More Matchstick Patterns

    More Examples of Variables

    Exercise 11.1

    What Have We Discussed

    Enhanced Curriculum Support

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Chapter 11: Algebra > Exercise 11.1

Exercise 11.1

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

(a) A pattern of letter T :

(b) A pattern of letter Z :

(c) A pattern of letter U :

(d) A pattern of letter V :

(e) A pattern of letter E :

(f) A pattern of letter S :

(g) A pattern of letter A :

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:

Instruction

We know that T require only matchsticks.
So, the pattern for the letter T is n.
Among all the letters given in question 1, only and are the letters which require two matchsticks.
Hence, (a) and (d).

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:

Instruction

Let n be the number of rows.
Number of cadets in a row =
Total number of cadets = number of cadets in a row × number of rows = n

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:

Instruction

Let n be the number of boxes.
Number of mangoes in a box =
Total number of mangoes = number of mangoes in a box × number of boxes = n

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:

Instruction

Let s be the number of students.
Penclis given to each student =
Total number of penclis = number of penclis giveb to each student × number of students = s

6. A bird flies 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:

Instruction

Let t minutes be the flying times.
Distance covered in one minute = km
Distance covered in t minutes = Distance covered in one minute × flying time
= × t = km

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 Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?

Solution:

Instruction

Number of dots in a rows =
Number of rows =
Total number of dots in r rows = Number of dots in a row × number of rows = r
Number of dots in 8 rows = × 9 =
Number of dots in 10 rows = × 9 =

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 :

Let radha's age be x years.

Leela's age = years younger than radha

= (x - ) years

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:

Number of laddus mother gave = l

Remaining laddus =

Total number of laddus = number of laddus given away by mother + number of laddus remanining

= (l + ) laddus

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:

Number of oranges in a small box =

Number of oranges in two small boxes = x

Number of oranges remaining =

Number of oranges in large box = number of oranges in two small boxes + number of oranges remained

= x +

11. (a) Look at the following matchstick pattern of squares. 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:

Instruction

Let the variable for the number of squares made be n.
In the first iteration we have, matchsticks making the square.
Upon observing the pattern, we can see that we need to add matchsticks to make the second iteration.
Similarly, we need to add matchsticks to make the third iteration.
Thus, the equation for the pattern above is:

(b) Fig 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:

Instruction

Let the variable for the number of triangles made be n.
In the first iteration we have, matchsticks making the triangle.
Upon observing the pattern, we can see that we need to add matchsticks to make the second iteration.
Similarly, we need to add matchsticks to make the third iteration.
Thus, the equation for the pattern above is: