Selina solutions concise mathematica class 7 icse Solutions for Chapter 11 fundamental concepts including fundamental operations

Q1) 1. Separate constant terms and variable terms from the following:

(i) 8, x, 6xy, 6 + x, -5xy^2, 15az^2, \frac{32z}{xy}, \frac{y^2}{3x}

Q2)

(i) 2x\div15

(ii) ax + 9

(iii) 3x^2\times5x\

(iv) 5+2a-3b

(v) 2y\ -\frac{7}{3}z\div x

(vi) 3pxq\ \div z

(vii) 12z\div5x\ +4

(viii) 12-5z-4

(ix) a^3-3ab^2xc

Q3)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

Q4) For each of the following monomials, write its degree : (i) 7y (ii) – x^2 y (iii) xy^2 z (iv) -9y^2z^3 (v) 3m^3n^4 (vi) -2p^2q^3r^4

Q5) Write the degree of each of the following polynomials :

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

(ii) p^3q^3-6p^2q^5+p^4q^4

(iii) -8mn^6+5m^3n

(iv)7-3x^2y+y^2

(v)3x\ -15

(vi) 2y^2z\ +\ 9yz^3

Q6) 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

Q7) Write numerical coefficient of each of the followings :

(i) y

(ii) -y

(iii) 2x^2y

(iv) -8xy^3

(v) 3py^2

(vi) -9a^2b^3

Q8) In -5x^3y^2z^4; write the coefficient of:

(i)\ z^2\

(ii)y^2

(iii)yz^{2\ }

(iv)x^3y

(v)-xy^2

(vi)-5xy^2z

Also, write the degree of the given algebraic expression.

Q1) 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^2y+13xy^2-4x^2y\ +2xy^2= ………..

(x) 16x^2-9x^2\ =\ ……….. and 25xy^2-17xy^2\ =\ ………..

Q3) 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

Q4) 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

Q5) 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^2-5ab

(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

Q6) 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^2y\ and\ 2y^2

(vi) 11 and -by

Q7) The sides of a triangle are 2x + 3y, x + 5y and 7x – 2y, find its perimeter.

Q8) The two adjacent sides of a rectangle are 6a + 96 and 8a – 46. Find its, perimeter.

Q9) Subtract the second expression from the first:

(i) 2a + b, a + b

(ii) -2b + 2c, b + 3c

(iii) 5a + b, -6b + 2a

(iv) a^3-1+a,\ 3a-2a^2

(v) p + 2, 1

(vi) x + 27 + z, -x – y – 3z

(vii) 3a^2-8ab-2b^2,\ 3a^2-4ab+6b^2

(viii) 4pq-6p^2-2q^2,\ 9p^2

(ix)10abc,\ 2a^2+2abc-4b^2

(x) a^2+ab+c^2,\ a^2-d^2

Q10) Subtract:

(i) 4x from 8 – x

(ii) -8c from c + 3d

(iii) -5a – 2b from b + 6c

(iv) 4p+p^2\ from\ 3p^2-8p

(v) 5a – 3b + 2c from 4a – b – c

(vi) – xy + yz – zx from xy – yz + xz

(vii) 2x^2-7xy-y^2\ from\ 3x^3-5xy+3y^2

(viii) a^2-3ab-6b^2\ from\ 2b^2-a^2+2ab

(ix) 4x^2-5x^2y+y^2\ from\ 3y^2+5xy^2-7x^2-9x^2y

(x) 6m^3+4m^2+7m-3\ from\ 3m^3+4

Q11) Subtract -5a^2-3a+1 from the sum of 4a^2+3-8a\ and\ 9a-7.

Q12) By how much does 8x^3-6x^2+9x-10 exceed 4x^3+2x^2+7x-3 ?

Q13) What must be added to 2a^3+5a-a^2-6\ to get a^2-a-a^3+1?

Q14) What must be subtracted from a^2+b^2+2ab\ to get -4ab+2b^2?

Q15) Find the excess of 4m^2+4n^2+4p^2 over m^2+3n^2-5p^2.

Q16) By how much is 3x^3-2x^2y\ +xy^2-y^3\ less than 4x^3-3x^2y-7xy^2+2y^3?

Q17) 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.

Q18) The perimeter of a rectangle is 28x^3+16x^2+8x+4. One of its sides is 8x^2+4x. Find the other side.

Q19) 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.

Q20) If x = 4a^2+b^2-6ab, y = 3b^2-2a^2+8ab and z = 6a^2+8b^2-6ab, find:

(i) x + y + z (ii) x – y – z

Q21) If m = 9x^2-4xy+5y^2 and n = -3x^2+2xy-y^2, find:

(i) 2m – n

(ii) m + 2n

(iii) m – 3n

Q22) Simplify:

(i) 3x + 5(2x + 6) – 7x

(ii) 3(4y – 10) + 2(y – 1)

(iii) – (7 + 6x) – 7(x + 2)

(iv) x – (x – y) – y – (y – x)

(v) 4x + 7y – [[5y – 8]] – 2x

(vi) -2m + 5 + 4(m – 3)

(vii) 2x – y + 5 – (x – y)

(viii) 2(x – y) – (x – 8)

(ix) 4(3x – 8) – 3(5x + 3) – 2(6x – 8)

(x) 5(x – 4) – 3(x – 4) + 7(x – 4)

Q1) Multiply:

(i) 3x,\ 5x^2y\ and\ 2y

(ii) 5,\ 3a\ and\ 2ab^2

(iii) (iii) 5x + 2y and 3xy

(iv) 6a – 5b and – 2a

(v) 4a + 5b and 4a – 5b (vi) 9xy+2y^2\ and\ 2x-3y

(vii) -3m^2n\ +5mn-4mn^2and\ 6m^2n

(viii) 6xy^2-7x^2y^2+10x^3and\ -3x^2y^3

Q2) Copy and complete the following multiplications :

Q3) Evaluate:

(i) (c + 5)(c – 3)

(ii) (3c – 5d)(4c – 6d)

(iii) \left(\frac{1}{2}a+\frac{1}{2}b\right)\left(\frac{1}{2}a-\frac{1}{2}b\right)

(iv) \left(a^2+2ab+b^2\right)\left(a+b\right)

(v) \left(3x-1\right)\left(4x^3-2x^2+6x-3\right)

(vi) \left(4m-2\right)\left(m^2+5m-6\right)

(vii) \left(8-12x+7x^2-6x^3\right)\left(5-2x\right)

(viii) \left(4x^2-4x+1\right)\left(2x^3-3x^2+2\right)

(ix) \left(6p^2-8pq+2q^2\right)\left(-5p\right)

(x) -4y\left(15x+12y-8z\right)\left(x-2y\right)

(xi) \left(a^2+b^2+c^2-ab-bc-ca\right)\left(a+b+c\right)

Q4) Evaluate:

(i) (a + b)(a – b)

(ii) \left(a^2+b^2\right)(a + b)(a – b) ; using the result of (i)

(iii) \left(a^4+b^4\right)(a + b)(a – b) ; using the result of (ii)

Q5) Evaluate:

(i) (3x – 2y)(4x + 3y)

(ii) (3x – 2y)(4x + 3y)(8x – 5y)

(iii) (a + 5)(3a – 2)(5a + 1)

(iv) \left(a+1\right)\left(a^2-a+1\right)\ and\ \left(a-1\right)\left(a^2+a+1\right) and then \left(a+1\right)\left(a^2-a+1\right)\ +\left(a-1\right)\left(a^2+a+1\right)

(v) \left(5m-2n\right)\left(5m+2n\right)\left(25m^2+4n^2\right)

Q6) Multiply:

(i) mn^4,\ m^3n\ and\ 5m^2n

(ii) 2mnpq, 4mnpq and 5mnpq

(iii) pq-pm\ and\ p^2m

(iv) x^3-3y^3\ and\ 4x^2y^2

(v) a^3-4ab\ and\ 2a^2b

(vi) x^2+5xy-3y^2\ and\ 2x^2y

Q7) (i) (2x + 3y)(2x + 3y)

(ii) (2x – 3y)(2x + 3y)

(iii) (2x + 3y)(2x – 3y)

(iv) (2x – 3y)(2x – 3y)

(v) (-2x + 3y)(2x – 3y)

(vi) (xy + 2b)(xy – 2b)

(vii) (x – a)(x + 3b)

(viii) (2x + 5y + 6)(3x + y – 8)

(ix) (3x – 5y + 2)(5x – 4y – 3)

(x) (6x – 2y)(3x – y)

(xi) \left(1+6x^2-4x^3\right)\left(-1+3x-3x^2\right)

Q1) Divide:

(i) -16ab^2c\ by\ 6abc

(ii) 25x^2y\ by\ -5y^2

(iii) 8x\ +\ 24\ by\ 4

(iv) 4a^2-a\ by\ a

(v) 8m-16\ by\ -8

(vi) -50+40p\ by\ 10p

(vii) 4x^3-2x^2\ by\ -x

(viii) 10a^3-15a^2b\ by\ -5a^2

(ix) 12x^3y-8x^2y^2+4x^2y^3\ \div4xy

(x) 9a^4b-15a^3b^2+12a^2b^3\ \div-3a^2b

Q3) The area of a rectangle 6x^2-4xy-10y^2 square unit and its length is 2x + 2y unit. Find its breadth.

Q4) The area of a rectangular field is 25x^2+20xy+3y^2square unit. If its length is 5x + 3y unit, find its breadth, Hence find its perimeter.

Q1) Simplify:

\frac{x}{2}+\frac{x}{4}

Q2) Simplify:

\frac{a}{10}+\frac{2a}{5}

Q3) Simplify:

\frac{y}{4}+\frac{3y}{5}

Q4) Simplify:

\frac{x}{2}-\frac{x}{8}

Q5) Simplify:

\frac{3y}{4}-\frac{y}{5}

Q6) Simplify:

\frac{2p}{3}-\frac{3p}{5}

Q7) Simplify:

\frac{k}{2}+\frac{k}{3}+\frac{2k}{5}

Q8) Simplify:

\frac{2x}{5}+\frac{3x}{4}-\frac{3x}{5}

Q9) Simplify:

\frac{4a}{7}-\frac{2a}{3}+\frac{a}{7}

Q10) Simplify:

\frac{2b}{5}-\frac{7b}{15}+\frac{13b}{3}

Q11) Simplify:

\frac{6k}{7}-\left(\frac{8k}{9}-\frac{k}{3}\right)

Q12) Simplify:

\frac{3a}{8}+\frac{4a}{5}-\left(\frac{a}{2}+\frac{2a}{5}\right)

Q13) Simplify:

x+\frac{x}{2}+\frac{x}{3}

Q14) Simplify:

\frac{y}{5}+y-\frac{19y}{15}

Q15) Simplify:

\frac{x}{5}+\frac{x+1}{2}

Q16) Simplify:

x+\frac{x+2}{3}

Q17) Simplify:

\frac{3y}{5}-\frac{y+2}{2}

Q18) Simplify:

\frac{2a+1}{3}+\frac{3a-1}{2}

Q19) Simplify:

\frac{k+1}{2}+\frac{2k-1}{3}-\frac{k+3}{4}

Q20) Simplify:

\frac{m}{5}-\frac{m-2}{3}+m

Q21) Simplify:

\frac{5\left(x-4\right)}{3}+\frac{2\left(5x-3\right)}{5}+\frac{6\left(x-4\right)}{7}

Q22) Simplify:

\left(p+\frac{p}{3}\right)\left(2p+\frac{p}{2}\right)\left(3p-\frac{2p}{3}\right)

Q23) Simplify:

\frac{7}{30}of\left(\frac{p}{3}+\frac{7p}{15}\right)

Q24) Simplify:

\left(2p+\frac{p}{7}\right)\div\left(\frac{9p}{10}+4p\right)

Q25) Simplify:

\left(\frac{5k}{8}-\frac{3k}{5}\right)\div\frac{k}{4}

Q26) Simplify:

\left(\frac{y}{6}+\frac{2y}{3}\right)\div\left(y+\frac{2y-1}{3}\right)

Q1) Enclose the given terms in brackets as required :

x – y – z = x-{…….)

Q2) Enclose the given terms in brackets as required : x^2-xy^2-2xy-y^2=x^2-\left(……\right)

Q3) Enclose the given terms in brackets as required :

4a – 9 + 2b – 6 = 4a – (…….. )

Q4) Enclose the given terms in brackets as required :

x^2-y^2+z^2+3x-2y=x^2-\left(……\right)

Q6) Simplify :

2x – (x + 2y- z)

Q7) Simplify :

p + q – (p – q) + (2p – 3q)

Q8) Simplify :

9x – (-4x + 5)

Q9) Simplify :

6a – (- 5a – 8b) + (3a + b)

Q10) Simplify :(p – 2q) – (3q – r)

Q11) Simplify : 9a (2b – 3a + 7c)

Q12) Simplify :-5m (-2m + 3n – 7p)

Q13) Simplify :

-2x\left(x+y\right)+x^2

Q14) Simplify :

b\left(2b-\frac{1}{b}\right)-2b\left(b-\frac{1}{b}\right)

Q15) Simplify :

8(2a+3b-c)-10(a+2b+3c)

Q16) Simplify :

a\left(a+\frac{1}{a}\right)-b\left(b-\frac{1}{b}\right)-c\left(c+\frac{1}{c}\right)

Q17) Simplify :

5x(2x+3y)-2x(x-9y)

Q18) Simplify :

a+(b+c-d)

Q19) Simplify :

5 – 8x – 6 – x

Q20) Simplify :

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

Q21) Simplify :

3x + \left[4x-\left(6x-3\right)\right]

Q22) Simplify :

5b – {6a + (8 – b – a)}

Q23) Simplify :

2x – {5y – (3x – y) + x}

Q24) Simplify :

6a – 3 (a + b – 2)

Q25) Simplify :

8{m + 2n-p – 7 (2m -n + 3p)}

Q26) Simplify :

{9 – (4p – 6q)} – {3q – (5p – 10)}

Q27) Simplify :

2 \left[a-3\left\{a+5\left(a-2\right)+7\right\}\right]

Q28) Simplify :

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

Q29) Simplify :

9x+5-[4x-3x-2(4x-3)]

Q30) Simplify :

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

Q31) Simplify :

-1\left[a-3b-4(a-b-8)+4a+10\right]

Q32) Simplify :

p^2-\left[x^2-\left\{x^2-\left(q^2-\overline{x^2-q^2}\right)-2y^2\right\}\right]

Q33) Simplify :

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

Q34) Simplify :

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

Q35) Simplify :

8x-\left[4y-\left\{4x+\left(2x-\overline{2y-2x}\right)\right\}\right]

Q36) Simplify :

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