Updated By SaraNextGen

On April 21, 2024, 11:35 AM

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 T

(b) A pattern of letter Z as Z

(c) A pattern of letter U as U

(d) A pattern of letter V as V

(e) A pattern of letter E as E

(f) A pattern of letter S as S

(g) A pattern of letter A as A

Answer:

(a)

From the figure, it can be observed that it will require two matchsticks to make a T. Therefore, the pattern is 2n.

(b)

From the figure, it can be observed that it will require three matchsticks to make a Z. Therefore, the pattern is 3n.

(c)

From the figure, it can be observed that it will require three matchsticks to make a U. Therefore, the pattern is 3n.

(d)

From the figure, it can be observed that it will require two matchsticks to make a V. Therefore, the pattern is 2n.

(e)

From the figure, it can be observed that it will require five matchsticks to make an E. Therefore, the pattern is 5n.

(f)

From the figure, it can be observed that it will require five matchsticks to make a S. Therefore, the pattern is 5n.

(g)

From the figure, it can be observed that it will require six matchsticks to make an A. Therefore, the pattern is 6n.

Question 2:

We already know the rule for the pattern of letters L, C and F. Some of the letters from some of the letters out of (a) T, (b) Z, (c) U, (d) V, (e) E, (f) S, (g) R give us the same rule as that given by L. Which are these? Why does this happen?

Answer:

It is known that L requires only two matchsticks. Therefore, the pattern for L is 2n. Among all the letters given above in Question 1, only T and V are the two letters which require two matchsticks.

Hence, (a) and (d)

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.)

Answer:

Let number of rows be n.

Number of cadets in one row = 5

Total number of cadets = Number of cadets in a row × Number of rows

= 5n

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.)

Answer:

Let the number of boxes be b.

Number of mangoes in a box = 50

Total number of mangoes = Number of mangoes in a box × Number of boxes

= 50b

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.)

Answer:

Let the number of students be s.

Pencils given to each student = 5

Total number of pencils

= Number of pencils given to each student × Number of students

= 5s

Question 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.)

Answer:

Let the flying time be t minutes.

Distance covered in one minute = 1 km

Distance covered in t minutes = Distance covered in one minute × Flying time

= 1 × t = t km

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

Answer:

Number of dots in 1 row = 9

Number of rows = r

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

= 9r

Number of dots in 8 rows = 8 × 9 = 72

Number of dots in 10 rows = 10 × 9 = 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.

Answer:

Let Radha’s age be x years.

Leela’s age = Radha’s age − 4

= (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?

Answer:

Number of laddus given away = l

Number of laddus remaining = 5

Total number of laddus = Number of laddus given away + Number of laddus

remaining

= 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?

Answer:

Number of oranges in one small box = x

Number of oranges in two small boxes = 2x

Number of oranges left = 10

Number of oranges in the large box = Number of oranges in two small boxes

+ Number of oranges left

= 2x + 10

Question 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.)

(b) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.

Answer:

(a) It can be observed that in the given matchstick pattern, the number of

matchsticks are 4, 7, 10, and 13, which is 1 more than thrice of the number of squares in the pattern.

Hence, the pattern is 3n + 1, where n is the number of squares.

(b) It can be observed that in the given matchstick pattern, the number of

matchsticks are 3, 5, 7, and 9, which is 1 more than twice of the number of triangles in the pattern.

Hence, the pattern is 2n + 1, where n is the number of triangles.