Selina solutions for Concise Mathematics [English] Class 7 ICSE chapter 11 - Fundamental Concepts (Including Fundamental Operations) [Latest edition]

Separate constant terms and variable terms from tile following:

8, x, 6xy, 6 + x, - 5xy² , 15az² , `(32"z")/"xy", "y"^2/"3x"`

For the expression, given below, state whether it is a monomial, binomial or trinomial:

2x ÷ 15

Constant is only 8 other is variable ax + 9

Constant is only 8 other is variable 3x² × 5x

Constant is only 8 other is variable 5 + 2a - 3b

Constant is only 8 other is variable 2y –`7/3` z ÷ x

Constant is only 8 other is variable 3p x q ÷ z

Constant is only 8 other is variable 12z ÷ 5x + 4

Constant is only 8 other is variable 12 – 5 z – 4

Constant is only 8 other is variable a³ – 3ab² x c 

Write the coefficient of: xy in – 3axy

Write the coefficient of: z² in p²yz 

Write the coefficient of: mn in -mn

Write the coefficient of: 15 in – 15p² 

For the following monomials, write its degree: 7y

For the following monomials, write its degree: – x²y 

For the following monomials, write its degree: xy²z 

For the following monomials, write its degree: – 9y²z³ 

For the following monomials, write its degree: 3m³n⁴ 

For the following monomials, write its degree: – 2p²q³r⁴ 

Write the degree of the following polynomial:

3y³ − x²y² + 4x

Write the degree of the following polynomial: p³q² – 6p²q⁵ + p⁴q⁴ 

Write the degree of the following polynomial: – 8mn⁶+ 5m³n 

Write the degree of the following polynomial: 7 – 3x²y + y² 

Write the degree of the following polynomial: 3x – 15

Write the degree of the following polynomial: 2y²z + 9yz³ 

Group the like term together: 9x², xy, – 3x², x² and – 2xy

Group the like term together: ab, – a²b, – 3ab, 5a²b and – 8a²b 

Group the like term together: 7p, 8pq, – 5pq – 2p and 3p

Write numerical co-efficient of the following: y

Write numerical co-efficient of the following: - y

Write numerical co-efficient of the following: 2 x²y

Write numerical co-efficient of the following: – 8xy³ 

Write numerical co-efficient of the following: 3py² 

Write numerical co-efficient of the following: – 9a²b³ 

In -5x³y²z⁴ ; write the coefficient of: z² Also, write the degree of the given algebraic expression.

In -5x³y²z⁴ ; write the coefficient of y² Also, write the degree of the given algebraic expression. 

In -5x³y²z⁴ ; write the coefficient of yz². Also, write the degree of the given algebraic expression. 

In -5x³y²z⁴ ; write the coefficient of x³y.  Also, write the degree of the given algebraic expression. 

In -5x³y²z⁴ ; write the coefficient of -xy².  Also, write the degree of the given algebraic expression.

In -5x³y²z⁴ ; write the coefficient of -5xy²z. Also, write the degree of the given algebraic expression.

Fill in the blank:

8x + 5x = ________

Fill in the blank:

8x - 5x = ________

Fill in the blank:

6xy² + 9xy² = _____. 

Fill in the blank:

6xy² – 9xy² = ______

Fill in the blank:

The sum of 8a, 6a and 5b = _______.

Fill in the blank:

The addition of 5, 7xy, 6 and 3xy = _____

Fill in the blank:

4a + 3b – 7a + 4b = _____

Fill in the blank:

- 15x + 13x + 8 = ______

Fill in the blank:

6x²y + 13xy² – 4x²y + 2xy² = _______ 

Fill in the blank:

16x² – 9x² = and 25xy² – 17xy² = _______.

Add : - 9x, 3x and 4x

Add : 23y² , 8y² and – 12y² 

Add : 18pq – 15pq and 3pq

Simplify : 3m + 12m – 5m

Simplify: 7n² – 9n² + 3n² 

Simplify: 25zy—8zy—6zy

Simplify: -5ax² + 7ax² – 12ax² 

Simplify: – 16am + 4mx + 4am – 15mx + 5am

Add : a + b and 2a + 3b

Add : 2x + y and 3x – 4y

Add : - 3a + 2b and 3a + b

Add : 4 + x, 5 – 2x and 6x

Find the sum of: 3x + 8y + 7z, 6y + 4z- 2x and 3y – 4x + 6z

Find the sum of: 3a + 5b + 2c, 2a + 3b-c and a + b + c.

Find the sum of: 4x²+ 8xy – 2y² and 8xy – 5y² + x² 

Find the sum of: 9x² – 6x + 7, 5 – 4x and 6 – 3x² 

Find the sum of: 5x² – 2xy + 3y² and – 2x² + 5xy + 9y² and 3x² -xy- 4y² 

Find the sum of: a² + b² + 2ab, 2b² + c² + 2bc and 4c² -a² + 2ac 

Find the sum of:

9ax – 6bx + 8, 4ax + 8bx – 7 and – 6ax – 4bx – 3

Find the sum of: abc + 2ba + 3ac + 4ca – 4ab + 2bca + 2ab – 3abc – 6ac

Find the sum of: 4a² + 5b² – 6ab, 3ab, 6a² – 2b² and 4b² – 5 ab 

Find the sum of: x² + x – 2, 2x – 3x² + 5 and 2x² – 5x + 7

Find the sum of: 4x³ + 2x² – x + 1, 2x³ – 5x² – 3x + 6, x2 + 8 and 5x³ – 7x 

Find the sum of: x and 3y

Find the sum of: -2a and +5

Find the sum of: – 4x² and +7x

Find the sum of: + 4a and -7b

Find the sum of: x³+3x²y and 2y² 

Find the sum of: 11 and -by

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

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

Subtract the second expression from the first:

2a + b, a + b

Subtract the second expression from the first:

−2b + 2c, b + 3c

Subtract the second expression from the first:

5a + b, - 6b + 2a

Subtract the second expression from the first:

a³ - 1 + a, 3a - 2a² 

Subtract the second expression from the first:

p + 2, 1

Subtract the second expression from the first:

x + 2y + z, - x - y - 3z

Subtract the second expression from the first:

3a² - 8ab - 2b² , 3a² - 4ab + 6b² 

Subtract the second expression from the first:

4pq - 6p² - 2q² , 9p² 

Subtract the second expression from the first:

10abc, 2a² + 2abc - 4b² 

Subtract the second expression from the first:

a² + ab + c², a² - d² 

Subtract: 4x from 8 - x

Subtract: - 8c from c + 3d

Subtract: - 5a - 2b from b + 6c

Subtract: 4p + p² from 3p² - 8p 

Subtract: 5a - 3b + 2c from 4a - b - 2c

Subtract: −xy + yz − zx from xy − yz + xz

Subtract: 2x² - 7xy - y² from 3x² - 5xy + 3y² 

Subtract: a² - 3ab - 6b² from 2b² - a² + 2ab

Subtract: 4x² - 5x²y + y² from - 3y² + 5xy² - 7x² - 9x²y 

Subtract: 6m³ + 4m² + 7m - 3 from 3m³ + 4 

Subtract – 5a² – 3a + 1 from the sum of 4a² + 3 – 8a and 9a – 7. 

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

What must be added to 2a³ + 5a – a² – 6 to get a² – a – a³ + 1?

What must be subtracted from a² + b² + lab to get – 4ab + 2b²? 

Find the excess of 4m² + 4n² + 4p² over m²+ 3n² – 5p² 

By how much is 3x³ – 2x²y + xy² -y³ less than 4x³ – 3x²y – 7xy² +2y³ 

Subtract the sum of 3a² – 2a + 5 and a² – 5a – 7 from the sum of 5a² -9a + 3 and 2a – a² – 1 

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

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. 

If x = 4a² + b² - 6ab; y = 3b² - 2a² + 8ab and z = 6a² + 8b² - 6ab find: x + y + z

If x = 4a² + b² - 6ab; y = 3b² - 2a² + 8ab and z = 6a² + 8b² - 6ab find: x - y - z

If m = 9x² - 4xy + 5y² and n = - 3x² + 2xy - y² find: 2m - n

If m = 9x² - 4xy + 5y² and n = - 3x² + 2xy - y² find: m + 2n

If m = 9x² - 4xy + 5y² and n = - 3x² + 2xy - y² find: m - 3n

Simplify: 3x + 5(2x + 6) - 7x

Simplify: 3(4y - 10)  2(y - 1)

Simplify: - (7 + 6x) - 7(x + 2)

Simplify: x - (x - y) - y - (y - x)

Simplify: 4x + 7y - (5y - 8) - 2x

Simplify: - 2m + 5 + 4(m - 3)

Simplify: 2x - y + 5 - (x - y)

Simplify: 2(x - y) - (x - 8)

Simplify: 4(3x - 8) - 3(5x + 3) - 2(6x - 8)

Simplify: 5(x − 4) − 3(x − 4) + 7(x − 4)

Multiply: 3x, 5x²y and 2y 

Multiply: 5, 3a and 2ab² 

Multiply: 5x + 2y and 3xy

Multiply: 6a - 5b and - 2a

Multiply: 4a + 5b and 4a - 5b

Multiply: 9xy + 2y² and 2x - 3y 

Multiply: - 3m²n + 5mn - 4mn² and 6m²n 

Multiply: 6xy² - 7x²y² + 10x³ and - 3x²y³ 

Copy and complete the following multi-plication:

3a + 2b
× - 3xy  

Copy and complete the following multi-plication:

9x + 5y
× - 3xy   

Copy and complete the following multi-plication:

3xy - 2x² - 6x
×     -5x²y      

Copy and complete the following multi-plication:

a + b
× a + b 

Copy and complete the following multi-plication:

ax - b
× 2ax + 2b²  

Copy and complete the following multi-plication:

2a - b + 3c
× 2a - 4b   

Copy and complete the following multi-plication:

3m² + 6m - 2n
× 5n - 3m           

Copy and complete the following multi-plication:

6 - 3x + 2x² 
× 1 + 5x - x²  

Copy and complete the following multiplication:

4x³ − 10x² + 6x − 8
× 3 + 2x − x²        

Evaluate: (c + 5)(c - 3)

Evaluate: (3c - 5d)(4c - 6d)

Evaluate: `(1/2 "a" + 1/2 "b") (1/2 "a" - 1/2 "b")`

Evaluate: (a² + 2ab + b²)(a + b)

Evaluate: (3x - 1)(4x³ - 2x² + 6x - 3) 

Evaluate: (4m - 2)(m² + 5m - 6) 

Evaluate: (8 - 12x + 7x² - 6x³)(5 - 2x)

Evaluate: (4x² - 4x + 1)(2x³ - 3x² + 2) 

Evaluate: (6p² - 8pq + 2q²) (- 5p)

Evaluate: - 4y (15 + 12y - 8z) (x - 2y)

Evaluate: (a² + b² + c² - ab - bc - ca)(a + b + c) 

Evaluate:

(i) (a + b)(a - b)

(ii) (a² + b²)(a + b)(a - b); using the result of (i).

(iii) (a⁴ + b⁴)(a² + b²)(a + b)(a - b); using the result of (ii).

Evaluate: (3x - 2y)(4x + 3y)

Evaluate: (3x - 2y)(4x + 3y) (8x - 5y)

Evaluate: (a + 5)(3a - 2)(5a + 1)

Evaluate: (a + 1)(a² - a + 1) and (a - 1)(a² + a + 1) 

Evaluate: (5m - 2n)(5m + 2n)(25m² + 4n²) 

Multiply: mn⁴, m³n and 5m²n³ 

Multiply: 2mnpq, 4mnpq and 5 mnpq

Multiply: pq - pm and p²m 

Multiply: x³ - 3y³ and 4x²y² 

Multiply: a³ - 4ab and 2a²b 

Multiply: x² + 5yx - 3y² and 2x²y 

Multiply: (2x + 3y)(2x + 3y)

Multiply: (2x - 3y)(2x + 3y)

Multiply: (2x + 3y)(2x - 3y)

Multiply: (2x - 3y)(2x - 3y)

Multiply: (-2x + 3y)(2x - 3y)

Multiply: (xy + 2b)(xy - 2b)

Multiply: (x - a)(x + 3b)

Multiply: (2x + 5y + 6)(3x + y - 8)

Multiply: (3x - 5y + 2)(5x - 4y - 3)

Multiply: (6x - 2y)(3x - y)

Multiply: (1 + 6x² - 4x³)(-1 + 3x - 3x²) 

Divide: - 16ab²c by 6abc

Divide: 25x²y by - 5y² 

Divide: 8x + 24 by 4

Divide: 4a² - a by - a 

Divide: 8m - 16 by - 8

Divide: - 50 + 40p by 10p

Divide: 4x³ - 2x² by - x 

Divide: 10a³ - 15a²b by - 5a² 

Divide: 12x³y - 8x²y² + 4x²y³ by 4xy 

Divide: 9a⁴b - 15a³b² + 12a²b³ by - 3a²b 

Divide:

n² − 2n + 1 by n − 1 

Divide: m² − 2mn + n² by m − n

Divide: 4a² + 4a + 1 by 2a + 1

Divide: p² + 4p + 4 by p + 2

Divide: x² + 4xy + 4y² by x + 2y 

Divide: 2a² - 11a + 12 by a - 4 

Divide: 6x² + 5x - 6 by 2x + 3

Divide: 8a² + 4a - 60 by 2a - 5 

Divide: 9x² - 24xy + 16y² by 3x- 4y 

Divide: 15x² + 31xy + 14y² by 5x + 7y 

Divide: 35a³ + 3a²b - 2ab² by 5a - b 

Divide: 6x³ + 5x² − 21x + 10 by 3x − 2 

The area of a rectangle is 6x² – 4xy – 10y² square unit and its length is 2x + 2y unit. Find its breadth.

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.

Divide: 2m³n⁵ by - mn 

Divide: 5x² - 3x by x

Divide: 10x³y - 9xy² - 4x²y² by xy 

Divide: 3y³ - 9ay² - 6ab²y by -3y 

Divide: x⁵ - 15x⁴ - 10x² by -5x² 

Divide: 12a² + ax - 6x² by 3a - 2x 

Divide: 6x² - xy - 35y² by 2x - 5y 

Divide: x³ − 6x² + 11x − 6 by x² − 4x + 3 

Divide: m³ − 4m² + m + 6 by m² − m − 2 

Simplify: `"x"/2+"x"/4`

Simplify: `"a"/10+"2a"/5`

Simplify: `"y"/4 +"3y"/5`

Simplify: `"x"/2 -"x"/8`

Simplify: `"3y"/4 -"y"/5`

Simplify: `"2p"/3 -"3p"/5`

Simplify: `"k"/2 + "k"/3 + "2k"/5`

Simplify: `"2x"/5 + "3x"/4 - "3x"/5` 

Simplify: `"4a"/7 + "2a"/3 - "a"/7` 

Simplify: `"2b"/5 - "7b"/15 + "13b"/3` 

Simplify: `"6k"/7 - ("8k"/9 - "k"/3)`

Simplify: `"3a"/8 + "4a"/5 - ("a"/2 + "2a"/5)`

Simplify: `"x" + "x"/2 + "x"/3`

Simplify: `"y"/5 + "y" - "19y"/15`

Simplify: `"x"/5 + "x + 1"/2`

Simplify: `"x" + "x + 2"/3`

Simplify: `"3y"/5 - "y + 2"/2`

Simplify: `"2a + 1"/3 + "3a - 1"/2`

Simplify: `"k + 1"/2 + "2k - 1"/3 - "k + 3"/4`

Simplify: `"m"/5 - "m - 2"/3 + "m"`

Simplify: `(5 ("x" - 4))/3 + (2(5x - 3))/5 + (6(x - 4))/7`

Simplify: `("p" + "p"/3)("2p" + "p"/2)("3p" - "2p"/3)`

Simplify: `7/30  "of" ("p"/3 + "7p"/15)`

Simplify: `(2"p" + "p"/7) div ("9p"/10 + "4p")`

Simplify: `("5k"/8 - "3k"/5) div "k"/4`

Simplify: `("y"/6 + "2y"/3) div ("y" + ("2y" - 1)/3)`

Enclose the given term in bracket as required:

x – y – z = x - {…….)

Enclose the given term in bracket as required:

x² – xy² – 2xy – y² = x² – (……..)

Enclose the given term in bracket as required:

4a – 9 + 2b – 6 = 4a – (……..)

Enclose the given term in bracket as required:

x² -y² + z² + 3x – 2y = x² – (……..)

Enclose the given term in bracket as required:

– 2a² + 4ab – 6a²b² + 8ab² = – 2a (………)

Simplify: 2x – (x + 2y- z)

Simplify: p + q – (p – q) + (2p – 3q)

Simplify: 9x – (- 4x + 5)

Simplify: 6a – (- 5a – 8b) + (3a + b)

Simplify: (p – 2q) – (3q – r)

Simplify: 9a (2b – 3a + 7c)

Simplify: -5m (-2m + 3n – 7p)

Simplify: - 2x (x + y) + x² 

Simplify: `"b"("2b" - 1/"b") - "2b"("b" - 1/"b")`

Simplify: 8 (2a + 3b – c) – 10 (a + 2b + 3c)

Simplify: 

`a(a + 1/a) - b(b - 1/b) - c(c + 1/c)`

Simplify: 5 x (2x + 3y) – 2x (x – 9y)

Simplify: a + (b + c – d)

Simplify: 5 − 8x − 6 − x

Simplify: `2"a" +(6 - bar("a" - "b"))`

Simplify: 3x + [4x – (6x – 3)]

Simplify: 5b – {6a + (8 – b – a)}

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

Simplify: 6a – 3 (a + b – 2)

Simplify: 8 [m + 2n-p – 7 (2m -n + 3p)]

Simplify: {9 – (4p – 6q)} – {3q – (5p – 10)}

Simplify: 2 [a – 3 {a + 5 {a – 2) + 7}]

Simplify: 5a – [6a – {9a – (10a – `bar("4a" - "3a"))}]`

Simplify: 9x + 5 – [4x – {3x – 2 (4x – 3)}]

Simplify: (x + y – z)x + (z + x – y)y – (x + y – z)z

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

Simplify: `"p"^2 - ["x"^2 - {"x"^2 - ("q"^2 - bar("x"^2 - "q"^2)) - "2y"^2}]`

Simplify: `10  – {4"a" – (7 – bar ("a" - 5) - (5"a" - bar(1 + "a")))`

Simplify: `7"a" ["8a" - (11"a" - (12"a" - bar"6a - 5a"))]`

Simplify: `8"x" - ["4y" - {"4x" + ("2x" - bar"2y - 2x")}]`

Simplify: `"x" - ("3y" - bar"4x - 3x" + 2z - bar"5y - 7x")`