## 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) 3x2 × 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) a3 – 3ab2 x c
Solution:

Question 3.
Write the coefficient of:
(i) xy in – 3axy
(ii) z2 in p2yz2
(iii) mn in -mn
(iv) 15 in – 15p2
Solution:

Question 4.
For each of the following monomials, write its degree :
(i) 7y
(ii) – x2y
(iii) xy2z
(iv) – 9y2z3
(v) 3 m3n4
(vi) – 2p2q3r4
Solution:

Question 5.
Write the degree of each of the following polynomials :
(i) 3y3-x2y2 + 4x
(ii) p3q2 – 6p2q5 + p4q4
(iii) – 8mn6+ 5m3n
(iv) 7 – 3x2y + y2
(v) 3x – 15
(vi) 2y2z + 9yz3
Solution:

Question 6.
Group the like term together :
(i) 9x2, xy, – 3x2, x2 and – 2xy
(ii) ab, – a2b, – 3ab, 5a2b and – 8a2b
(iii) 7p, 8pq, – 5pq – 2p and 3p
Solution:

Question 7.
Write numerical co-efficient of each of the followings :
(i) y
(ii) -y
(iii) 2x2y
(iv) – 8xy3
(v) 3py2
(vi) – 9a2b3
Solution:

Question 8.
In -5x3y2z4; write the coefficient of:
(i) z2
(ii) y2
(iii) yz2
(iv) x3y
(v) -xy2
(vi) -5xy2z
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) 6xy2 + 9xy2 =……..
(iv) 6xy2 – 9xy2 = ………
(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) 6x2y + 13xy2 – 4x2y + 2xy2 = ……..
(x) 16x2 – 9x2 = and 25xy2 – 17xy2=………

Solution :

Question 2.
(i)- 9x, 3x and 4x
(ii) 23y2, 8y2 and – 12y2
(iii) 18pq – 15pq and 3pq

Solution:

Question 3.
Simplify :
(i) 3m + 12m – 5m
(ii) 7n2 – 9n2 + 3n2
(iii) 25zy—8zy—6zy
(iv) -5ax2 + 7ax2 – 12ax2
(v) – 16am + 4mx + 4am – 15mx + 5am
Solution:

Question 4.
(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) 4x2+ 8xy – 2y2 and 8xy – 5y2 + x2
(iv) 9x2 – 6x + 7, 5 – 4x and 6 – 3x2
(v) 5x2 – 2xy + 3y2 and – 2x2 + 5xy + 9y2
and 3x2 -xy- 4y2
(vi) a2 + b2 + 2ab, 2b2 + c2 + 2bc
and 4c2-a2 + 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) 4a2 + 5b2 – 6ab, 3ab, 6a2 – 2b2
and 4b2 – 5 ab
(x) x2 + x – 2, 2x – 3x2 + 5 and 2x2 – 5x + 7
(xi) 4x3 + 2x2 – x + 1, 2x3 – 5x2– 3x + 6, x2 + 8 and 5x3 – 7x
Solution:

Question 6.
Find the sum of:
(i) x and 3y
(ii) -2a and +5
(iii) – 4xand +7x
(iv) +4a and -7b
(v) x3+3x2y and 2y2
(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 – 5a2 – 3a + 1 from the sum of 4a2 + 3 – 8a and 9a – 7.
Solution:

Question 12.
By how much does 8x3 – 6x2 + 9x – 10 exceed 4x3 + 2x2 + 7x -3 ?
Solution:

Question 13.
What must be added to 2a3 + 5a – a2 – 6 to get a2 – a – a3 + 1 ?
Solution:

Question 14.
What must be subtracted from a2 + b2 + lab to get – 4ab + 2b2 ?
Solution:

Question 15.
Find the excess of 4m2 + 4n2 + 4pover m2+ 3n2 – 5p2
Solution:

Question 16.
By how much is 3x3 – 2x2y + xy2 -y3 less than 4x3 – 3x2y – 7xy2 +2y3
Solution:

Question 17.
Subtract the sum of 3a2 – 2a + 5 and a2 – 5a – 7 from the sum of 5a2 -9a + 3 and 2a – a2 – 1
Solution:

Question 18.
The perimeter of a rectangle is 28x3+ 16x2 + 8x + 4. One of its sides is 8x2 + 4x. Find the other side
Solution:

Question 19.
The perimeter of a triangle is 14a2 + 20a + 13. Two of its sides are 3a2 + 5a + 1 and a2 + 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 6x2– 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth
Solution:

Question 4.
The area of a rectangular field is 25x2 + 20xy + 3y2 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.
x2 – xy2 – 2xy – y2 = x2 – (…….. )
Solution:

Question 3.
4a – 9 + 2b – 6 = 4a – (…….. )
Solution:

Question 4.
x2 -y2 + z2 + 3x – 2y = x2 – (…….. )
Solution:

Question 5.
– 2a2 + 4ab – 6a2b2 + 8ab2 = – 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 + 3n – 7p)
Solution:

Question 13.
-2x (x + y) + x2
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: