## Selina Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)

**Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 11 Fundamental Concepts (Including Fundamental Operations)**

### Fundamental Concepts Exercise 11A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.

Separate constant terms and variable terms from tile following :

Solution:

Question 2.

Constant is only 8 others are variables

(i) 2x ÷ 15

(ii) ax+ 9

(iii) 3x^{2} × 5x

(iv) 5 + 2a-3b

(v) 2y – \(\frac { 7 }{ 3 }\) z÷x

(vi) 3p x q ÷ z

(vii) 12z ÷ 5x + 4

(viii) 12 – 5z – 4

(ix) a^{3} – 3ab^{2} x c

Solution:

Question 3.

Write the coefficient of:

(i) xy in – 3axy

(ii) z^{2} in p^{2}yz^{2}

(iii) mn in -mn

(iv) 15 in – 15p^{2
}Solution:

Question 4.

For each of the following monomials, write its degree :

(i) 7y

(ii) – x^{2}y

(iii) xy^{2}z

(iv) – 9y^{2}z^{3}

(v) 3 m^{3}n^{4}

(vi) – 2p^{2}q^{3}r^{4
}Solution:

Question 5.

Write the degree of each of the following polynomials :

(i) 3y^{3}-x^{2}y^{2} + 4x

(ii) p^{3}q^{2} – 6p^{2}q^{5} + p^{4}q^{4}

(iii) – 8mn^{6}+ 5m^{3}n

(iv) 7 – 3x^{2}y + y^{2}

(v) 3x – 15

(vi) 2y^{2}z + 9yz^{3
}Solution:

Question 6.

Group the like term together :

(i) 9x^{2}, xy, – 3x^{2}, x^{2} and – 2xy

(ii) ab, – a^{2}b, – 3ab, 5a^{2}b and – 8a^{2}b

(iii) 7p, 8pq, – 5pq – 2p and 3p

Solution:

Question 7.

Write numerical co-efficient of each of the followings :

(i) y

(ii) -y

(iii) 2x^{2}y

(iv) – 8xy^{3}

(v) 3py^{2}

(vi) – 9a^{2}b^{3
}Solution:

Question 8.

In -5x^{3}y^{2}z^{4}; write the coefficient of:

(i) z^{2}

(ii) y^{2}

(iii) yz^{2}

(iv) x^{3}y

(v) -xy^{2}

(vi) -5xy^{2}z

Also, write the degree of the given algebraic expression.

Solution:

**EXERCISE 11 (B)**

Question 1.

Fill in the blanks :

(i) 8x + 5x = ………

(ii) 8x – 5x =……..

(iii) 6xy^{2} + 9xy^{2} =……..

(iv) 6xy^{2} – 9xy^{2} = ………

(v) The sum of 8a, 6a and 5b = ……..

(vi) The addition of 5, 7xy, 6 and 3xy = …………

(vii) 4a + 3b – 7a + 4b = ……….

(viii) – 15x + 13x + 8 = ………

(ix) 6x^{2}y + 13xy^{2} – 4x^{2}y + 2xy^{2} = ……..

(x) 16x^{2} – 9x^{2} = and 25xy^{2} – 17xy^{2}=………

Solution :

Question 2.

Add :

(i)- 9x, 3x and 4x

(ii) 23y^{2}, 8y^{2} and – 12y^{2}

(iii) 18pq – 15pq and 3pq

Solution:

Question 3.

Simplify :

(i) 3m + 12m – 5m

(ii) 7n^{2} – 9n^{2} + 3n^{2}

(iii) 25zy—8zy—6zy

(iv) -5ax^{2} + 7ax^{2} – 12ax^{2}

(v) – 16am + 4mx + 4am – 15mx + 5am

Solution:

Question 4.

Add :

(i) a + b and 2a + 3b

(ii) 2x + y and 3x – 4y

(iii)- 3a + 2b and 3a + b

(iv) 4 + x, 5 – 2x and 6x

Solution:

Question 5.

Find the sum of:

(i) 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z

(ii) 3a + 5b + 2c, 2a + 3b-c and a + b + c.

(iii) 4x^{2}+ 8xy – 2y^{2} and 8xy – 5y^{2} + x^{2}

(iv) 9x^{2} – 6x + 7, 5 – 4x and 6 – 3x^{2}

(v) 5x^{2} – 2xy + 3y^{2} and – 2x^{2} + 5xy + 9y^{2}

and 3x^{2} -xy- 4y^{2}

(vi) a^{2} + b^{2} + 2ab, 2b^{2} + c^{2} + 2bc

and 4c^{2}-a^{2} + 2ac

(vii) 9ax – 6bx + 8, 4ax + 8bx – 7

and – 6ax – 46x – 3

(viii) abc + 2 ba + 3 ac, 4ca – 4ab + 2 bca

and 2ab – 3abc – 6ac

(ix) 4a^{2} + 5b^{2} – 6ab, 3ab, 6a^{2} – 2b^{2}

and 4b^{2} – 5 ab

(x) x^{2} + x – 2, 2x – 3x^{2} + 5 and 2x^{2} – 5x + 7

(xi) 4x^{3} + 2x^{2} – x + 1, 2x^{3} – 5x^{2}– 3x + 6, x^{2} + 8 and 5x^{3} – 7x

Solution:

Question 6.

Find the sum of:

(i) x and 3y

(ii) -2a and +5

(iii) – 4x^{2 }and +7x

(iv) +4a and -7b

(v) x^{3}+3x^{2}y and 2y^{2}

(vi) 11 and -by

Solution:

Question 7.

The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.

Solution:

Question 8.

The two adjacent sides of a rectangle are 6a + 96 and 8a – 46. Find its, perimeter.

Solution

Question 9.

Subtract the second expression from the first:

Solution:

Question 10.

Subtract:

Solution:

Question 11.

Subtract – 5a^{2} – 3a + 1 from the sum of 4a^{2} + 3 – 8a and 9a – 7.

Solution:

Question 12.

By how much does 8x^{3} – 6x^{2} + 9x – 10 exceed 4x^{3} + 2x^{2} + 7x -3 ?

Solution:

Question 13.

What must be added to 2a^{3} + 5a – a^{2} – 6 to get a^{2} – a – a^{3} + 1 ?

Solution:

Question 14.

What must be subtracted from a^{2} + b^{2} + lab to get – 4ab + 2b^{2} ?

Solution:

Question 15.

Find the excess of 4m^{2} + 4n^{2} + 4p^{2 }over m^{2}+ 3n^{2} – 5p^{2
}Solution:

Question 16.

By how much is 3x^{3} – 2x^{2}y + xy^{2} -y^{3} less than 4x^{3} – 3x^{2}y – 7xy^{2} +2y^{3
}Solution:

Question 17.

Subtract the sum of 3a^{2} – 2a + 5 and a^{2} – 5a – 7 from the sum of 5a^{2} -9a + 3 and 2a – a^{2} – 1

Solution:

Question 18.

The perimeter of a rectangle is 28x^{3}+ 16x^{2} + 8x + 4. One of its sides is 8x^{2} + 4x. Find the other side

Solution:

Question 19.

The perimeter of a triangle is 14a^{2} + 20a + 13. Two of its sides are 3a^{2} + 5a + 1 and a^{2} + 10a – 6. Find its third side.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Simplify:

Solution:

**EXERCISE 11 (C)**

Question 1.

Multiply:

Solution:

Question 2.

Copy and complete the following multi-plications :

Solution:

Question 3.

Evaluate :

Solution:

Question 4.

Evaluate:

Solution:

Question 5.

Evaluate :

Solution:

Question 6.

Multiply:

Solution:

Question 7.

Multiply:

Solution:

**EXERCISE 11 (D)**

Question 1.

Divide:

Solution:

Question 2.

Divide :

Solution:

Question 3.

The area of a rectangle is 6x^{2}– 4xy – 10y^{2} square unit and its length is 2x + 2y unit. Find its breadth

Solution:

Question 4.

The area of a rectangular field is 25x^{2} + 20xy + 3y^{2} square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.

Solution:

Question 5.

Divide:

Solution:

**EXERCISE 11 (E)**

Simplify

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Question 26.

Solution:

**EXERCISE 11 (F)**

Enclose the given terms in brackets as required :

Question 1.

x – y – z = x-{…….)

Solution:

Question 2.

x^{2} – xy^{2} – 2xy – y^{2} = x^{2} – (…….. )

Solution:

Question 3.

4a – 9 + 2b – 6 = 4a – (…….. )

Solution:

Question 4.

x^{2} -y^{2} + z^{2} + 3x – 2y = x^{2} – (…….. )

Solution:

Question 5.

– 2a^{2} + 4ab – 6a^{2}b^{2} + 8ab^{2} = – 2a (……… )

Solution:

Simplify :

Question 6.

2x – (x + 2y- z)

Solution:

Question 7.

p + q – (p – q) + (2p – 3q)

Solution:

Question 8.

9x – (-4x + 5)

Solution:

Question 9.

6a – (- 5a – 8b) + (3a + b)

Solution:

Question 10.

(p – 2q) – (3q – r)

Solution:

Question 11.

9a (2b – 3a + 7c)

Solution:

Question 12.

-5m (-2m* + 3*n – 7p)

Solution:

Question 13.

-2x (x + y) + x^{2
}Solution:

Question 14.

Solution:

Question 15.

8 (2a + 3b – c) – 10 (a + 2b + 3c)

Solution:

Question 16.

Solution:

Question 17.

5 x (2x + 3y) – 2x (x – 9y)

Solution:

Question 18.

a + (b + c – d)

Solution:

Question 19.

5 – 8x – 6 – x

Solution:

Question 20.

2a + (6- \(\overline { a-b }\) )

Solution:

Question 21.

3x + [4x – (6x – 3)]

Solution:

Question 22.

5b – {6a + (8 – b – a)}

Solution:

Question 23.

2x-[5y- (3x -y) + x]

Solution:

Question 24.

6a – 3 (a + b – 2)

Solution:

Question 25.

8 [m + 2n-p – 7 (2m -n + 3p)]

Solution:

Question 26.

{9 – (4p – 6q)} – {3q – (5p – 10)}

Solution:

Question 27.

2 [a – 3 {a + 5 {a – 2) + 7}]

Solution:

Question 28.

5a – [6a – {9a – (10a – \(\overline { 4a-3a }\) )}]

Solution:

Question 29.

9x + 5 – [4x – {3x – 2 (4x – 3)}]

Solution:

Question 30.

(x + y – z)x + (z + x – y)y – (x + y – z)z

Solution:

Question 31.

-1 [a-3 {b -4 (a-b-8) + 4a} + 10]

Solution:

Question 32.

Solution:

Question 33.

10 – {4a – (7 – \(\overline { a-5 }\)) – (5a – \(\overline { 1+a }\))}

Solution:

Question 34.

7a- [8a- (11a-(12a- \(\overline { 6a-5a }\))}]

Solution:

Question 35.

Solution:

Question 36.

x-(3y- \(\overline { 4z-3x }\) +2z- \(\overline { 5y-7x }\))

Solution: