Understanding Algebra with the Help of Patterns

Q.

Question 1(i)

Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
A pattern of letter T as

Q.

if $0.6x+0.8=.28x+1.16$ then the value of $x$ ?

Q. 6, 13, 20, 27 .......

What are the next two terms in the given sequence?

1. 30, 40
2. 31, 41
3. 34, 41
4. 35, 42

Q.

How many matchsticks are needed to make six 8s?

1. 40

2. 42

3. 44

4. 46

Q. Good evening mam/sir
my query to you is that......add the following
(i) 0+y
(ii)1/2ax+1/2ax
thank you

Q.

If 5 letters are taken out of 5 different envelopes. In how many ways, can they be reinserted in the envelopes so that no letter goes to its original envelopes?

1. 9

2. 44

3. 120

4. 24

Q. 24, 21, 18, 15 .......

What are the next two terms in the given sequence?

1. 12, 9
2. 10, 9
3. 11, 8
4. 12, 7

Q. Simplify each of the following algebraic expressions by removing grouping symbols.
2x + (5x − 3y)

Q.

Santosh wishes to arrange books in a bookshelf in rows of $6$ books each. Find the rule that gives number of books that can be put in the bookshelf.

Q. The number of matchsticks required to make the given pattern can be given by (2n + 1).

1. True
2. False

Q. The number of matchsticks required to make the given pattern can be given by (2n + 1).

1. True
2. False

Q. Match the figures to their corresponding algebraic representation (where n > 0).

1. $n^2$
2. $n+1$
3. $2n-1$

Q. A total of 100 match sticks were used in making a number 20 times, then with 10 match sticks the number can be made .

1. once
2. twice
3. thrice

Q.

Look at the pattern given:


If we consider a single figure, then what pattern does the number of squares in each row follow?

1. Perfect squares

2. Prime numbers

3. Even numbers

4. Odd numbers

Q. If 8 matchsticks are used to make the number 75, then matchsticks will be required to make it 6 times.

1. 48
2. 36
3. 42

Q.

Match the following figures according to the number of matchsticks required to make them.

1. 1-c; 2-b; 3-a

2. 1-a; 2-d; 3-c

3. 1-a; 2-b; 3-c

4. 1-c; 2-a; 3-d

Q.

Given below is a pattern made using squares. Observe the pattern and tell the number of squares in the next figure in the sequence. Also find the general form which represents the number of squares in the sequence.

1. The pattern doesn’t follow with the next set of squares

2. $16,n^2$

3. $25,2n+1$
4. $25,n^2$

Q. 6, 13, 20, 27 .......

What are the next two terms in the given sequence?

1. 31, 41
2. 34, 41
3. 35, 42
4. 30, 40

Q.

Match the following figures according to the number of matchsticks required to make them, where n > 0.

1. 5n + 1
2. 2n + 1
3. 4n + 1