Exercise 10.1

(1) An algebraic expression is a single term or a combination of terms connected by the symbols '+' (plus) or '–' (minus).

(2) If every term of an expression is a constant term, then the expression is called a expression. If an expression has at least one algebraic term, then the expression is called an expression.

(3) An algebraic expression containing term is called a monomial. An algebraic expression containing unlike terms is called a binomial. An algebraic expression containing unlike terms is called a trinomial. An algebraic expression containing more than three unlike terms is called a multinomial.

(4) The of all the exponents of the variables in a monomial is called the degree of the term or degree of monomial.

(5) The degree of any constant term is .

(6) The of the degrees of all the terms of the expression is called the degree of the expression.

(7) If no two terms of an expression are alike then the expression is said to be in its form.

(8) In an expression, if the terms are arranged in a manner such that the degrees of the terms are in descending order then the expression is said to be in form.

(9) The sum of two or more like terms is a like term with a numerical coefficient equal to the of the numerical coefficients of all the like terms.

(10) The difference between two like terms is a like term with a numerical coefficient equal to the between the numerical coefficients of the two like terms.

1. Find the rule which gives the number of matchsticks required to make the following patterns-

(i) A pattern of letter 'H'

Answer:

Here we have to find rule for pattern of letter 'H'

Let, the number of matchsticks =

We required matchsticks.

Rule for pattern of letter 'H' = 3

(ii) A pattern of letter 'V'

Answer:

Here we have to find rule for pattern of letter 'V'

Let, the number of matchsticks = m

We required matchsticks.

Rule for pattern of letter 'V' = 2

2. Given below is a pattern made from coloured tiles and white tiles.

(i) Draw the next two figures in the pattern above.

Answer:

Figure 4: The cross shape extends, each arm has 4 tiles (including the center), so the cross is larger.

Figure 5: The cross shape extends further, each arm has 5 tiles (including the center).

(Drawings to be done by student in notebook or on paper.)

(ii) Fill the table given below and express the pattern in the form of an algebraic expression.

Figure Number	1	2	3	4	5
Number of coloured tiles	4

Answer:

Here we have to express the pattern in the form of an algebraic expression.

For Figure 1, the number of coloured tiles = .

Let the figure number be n.

Rule for number of coloured tiles = n, where n = 1, 2, 3, ….

The pattern in the form of an algebraic expression:

Now, let's fill the table:

When n = 1: 4n = 4 × 1 =

When n = 2: 4n = 4 × 2 =

When n = 3: 4n = 4 × 3 =

When n = 4: 4n = 4 × 4 =

When n = 5: 4n = 4 × 5 =

Figure Number	1	2	3	4	5
No. of coloured tiles	4	8	12	16	20

(iii) Fill the table given below and express the pattern in the form of an algebraic expression.

Figure Number	1	2	3	4	5
No. of total tiles	5

Answer:

Here we have to express the pattern in the form of an algebraic expression.

For Figure 1, the number of total tiles = .

Let the figure number be n.

Rule for number of total tiles = , where n = 1, 2, 3, …

The pattern in the form of an algebraic expression:

Now, let's fill the table:

When n = 1: 4n + 1 = 4 × 1 + 1 =

When n = 2: 4n + 1 = 4 × 2 + 1 =

When n = 3: 4n + 1 = 4 × 3 + 1 =

When n = 4: 4n + 1 = 4 × 4 + 1 =

When n = 5: 4n + 1 = 4 × 5 + 1 =

Figure Number	1	2	3	4	5
No. of total tiles	5	9	13	17	21

3. Write the following statements using variables, constants and arithmetic operations.

(i)

6 more than p

Answer:

6 more than p = +

(ii)

‘x' is reduced by 4

Answer:

‘x' is reduced by 4 = -

(iii)

8 subtracted from y

Answer:

8 subtracted from y = -

(iv)

q multiplied by ‘-5'

Answer: {.reveal(when="blank-2")}q multiplied by ‘-5' =

(v)

y divided by 4

Answer: {.reveal(when="blank-3")}y divided by 4 = /

(vi)

One-fourth of the product of 'p' and 'q'

Answer: {.reveal(when="blank-4")}One-fourth of the product of 'p' and 'q' = /

(vii)

5 added to the three times of 'z'

Answer: {.reveal(when="blank-5")}5 added to the three times of 'z' = +

(viii)

x multiplied by 5 and added to '10'

Answer: {.reveal(when="blank-6")}x multiplied by 5 and added to 10 = +

(ix)

5 subtracted from two times of 'y'

Answer: {.reveal(when="blank-7")}5 subtracted from two times of 'y' = -

(x)

y multiplied by 10 and added to 13

Answer: {.reveal(when="blank-8")}y multiplied by 10 and added to 13 = +

4. Write the following expressions in statements.

(i)

x + 3

Answer: {.reveal(when="blank-0")}x + 3 = +

(ii)

y - 7

Answer: {.reveal(when="blank-1")}y - 7 = -

(iii)

10l

Answer: {.reveal(when="blank-2")}10l =

(iv)

x/5

Answer: {.reveal(when="blank-3")}x/5 = /

(v)

3m + 11

Answer: {.reveal(when="blank-4")}3m + 11 = +

(vi)

2y - 5

Answer: {.reveal(when="blank-5")}2y - 5 = -

5. Some situations are given below. State the number in situations is a variable or constant?

Example: Our age – its value keeps on changing so it is an example of a variable quantity.

(i)

The number of days in the month of January

Answer: {.reveal(when="blank-0")}The number in this situation is

(ii)

The temperature of a day

Answer: {.reveal(when="blank-1")}The number in this situation is

(iii)

Length of your classroom

Answer: {.reveal(when="blank-2")}The number in this situation is

(iv)

Height of the growing plant

Answer: {.reveal(when="blank-3")}The number in this situation is

Algebraic Expressions

Glossary

Exercise 10.1

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)

(ii)

(iii)

(iv)

Sign in to Innings2

Algebraic Expressions

Reset Progress

Glossary

Exercise 10.1

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)

(ii)

(iii)

(iv)