Selina solutions concise mathematics class 6 icse Solutions for Chapter 18 fundamental concepts algebra

Q1) Express each of the following statements in algebraic form :

(i) The sum of 8 and x is equal to y.

(ii) x decreased by 5 is equal to y.

(iii) The sum of 2 and x is greater than y.

(iv) The sum of x and y is less than 24.

(v) 15 multiplied by m gives 3n.

(vi) Product of 8 and y is equal to 3x.

(vii) 30 divided by b is equal to p.

(viii) z decreased by 3x is equal to y.

(ix) 12 times of x is equal to 5z.

(x) 12 times of x is greater than 5z.

(xi) 12 times of x is less than 5z.

(xii) 3z subtracted from 45 is equal to y.

(xiii) 8x divided by y is equal to 2z.

(xiv) 7y subtracted from 5x gives 8z.

(xv) 7y decreased by 5x gives 8z.

Q2) For each of the following algebraic expressions, write a suitable statement in words:

(i) 3x + 8=15

(ii) 7 – y > x

(iii) 2y – x < 12

(iv) 5 ÷ z = 5

(v) a + 2b > 18

(vi) 2x – 3y= 16

(vii) 3a – 4b > 14

(viii) b + 7a < 21

(ix) (16 + 2a) – x > 25

(x) (3x + 12) – y < 3a

Q1) Separate the constants and the variables from each of the following:

6,\ 4y,\ -3x,\ \frac{5}{4},\ \frac{4}{5}xy,\ az,\ 7p,\ 0,\frac{9x}{y},\ \frac{3}{4x},\ -\frac{xz}{3y}

Q2) Separate the constants and the variables from each of the following:

\left(i\right)\ 4x,\ -3y,\ -x,\ \frac{2}{3}x,\ \frac{4}{5}y\ and\ y

\left(ii\right)\ \frac{2}{3}xy,\ -4yx,\ 2yz,\ \frac{-2}{3}yz,\ \frac{zy}{3}and\ yx

\left(iii\right)\ -ab^2,\ b^2a^2,\ 7b^2a,\ -3a^2b^2\ and\ 2ab^2

\left(iv\right)\ 5ax,\ -5by,\ \frac{by}{7},\ 7xa\ and\ \frac{2ax}{3}

Q3) State whether true or false :

(i) 16 is a constant and y is a variable but 16y is variable.

(ii) 5x has two terms 5 and x.

(iii) The expression 5 + x has two terms 5 and x

(iv) The expression 2x^2+x is a trinomial.

(v) ax^2+bx+c is a trinomial.

(vi) 8 x ab is a binomial.

(vii) 8 + ab is a binomial.

(viii) x^3-5xy+6x+7 is a polynomial.

(ix) x^3-5xy+6x+7 is a multinomial.

(x) The coefficient of x in 5x is 5x.

(xi) The coefficient of ab in – ab is – 1.

(xii) The coefficient of y in – 3xy is – 3

Q4) State the number of terms in each of the following expressions :

(i) 2a – b

(ii) 3\times x+\frac{a}{2}

(iii) 3x-\frac{x}{p}

(iv) a\div x\times b+c

(v) 3x\div2+y+4

(vi) xy\div2

(vii) x+y\div a

(viii) 2x+y+8\div y

(ix) 2\times a+3\div b+4

Q5) State whether true or false:

(i) xy and – yx are like terms.

(ii) 3\times x+\frac{a}{2} are like terms.

(iii) a and – a are like terms.

(iv) – ba and 2ab are unlike terms.

(v) 5 and 5x are like terms.

(vi) 3xy and 4xyz are unlike terms.

Q6) For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

(i) xy

(ii) xy + x

(iii) 2x\div y

(iv) -a

(v) ax^2-x+5

(vi) -3bc + d

(vii) 1 + x + y

(viii) 1+x\div y

(ix) x+xy-y^2

Q7) Write down the coefficient of x in the following monomial :

(i) x

(ii) – x

(iii) – 3x

(iv) – 5ax

(v) \frac{3}{2}xy

(vi) \frac{ax}{y}

Q8) Write the coefficient of:

(i) x\ in\ -3xy^2

(ii) x in – ax

(iii) y in – y

(iv) y\ in\ \frac{2}{a}y

(v) xy in – 2xyz

(vi) ax\ in\ -axy^2

(vii) x^2y\ in\ -3ax^2y

(viii) xy^2\ in\ 5axy^2

Q9) State the numeral coefficient of the following monomials :

(i) 5xy

(ii) abc

(iii) 5pqr

(iv) \frac{-2x}{y}

(v) \frac{2}{3}xy^2

(vi) \frac{-15xy}{az}

(vii) -7x\div y

(viii) -3x\div\left(2y\right)

Q10) Write the degree of each of the following polynomials :

(i) x+x^2

(ii) 5x^2-7x+2

(iii) x^3-x^8+x^{10}

(iv) 1-100x^{20}

(v) 4+4x-4x^3

(vi) 8x^2y-3y^2+x^2y^5

(vii) 8z^3-8y^2z^3+7yz^5

(viii) 4y^2-3x^3+y^2x^7

Q1) Express each of the following statements in algebraic form :

(i) The sum of 3x and 4y is 8.

(ii) 5x decreased by 7 gives y.

(iii) 31 added to 4x gives 6x.

(iv) 3x subtracted from 89 gives 44.

Q2) Group the like terms :

(i) 7y,\ 3x,\ -8y,\ -x\ and\ \frac{x}{5}

(ii) 3x^2,\ -5x^3,\ -x^2,\ 5x^2\ and\ 8x^3

(iii) x^2y^3,\ -5x^3y^2,\ 8x^3y^2,\ -4x^2y^3\ and\ -x^2y^3

Q3) Write the number of terms in each of the following polynomials :

(i) 5+4x\div2

(ii) 5+4x+2y

(iii) 8x^2-4x+7

(iv) \frac{x}{5}+\frac{x^2}{7}-\frac{x^3}{8}-\frac{1}{4}

(v) 6x^2\div x-18\div9+x^2

Q4) For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:

(i) x + y

(ii) 5x – 4y

(iii) 7 × 2 + 5x + 8

(iv) 64 + 3 ÷ b

(v) 9 ÷ a × b

(vi) 8a ÷ b

Q5) Write the coefficient of x^2y:

(i) -7x^2yz

(ii) 8abx^2y

(iii) -x^2y

Q6) Write the coefficient of:

(i) x^2\ in\ -8x^2y

(ii) y\ in\ 4y

(iii) x\ in\ -xy^2

Q7) Write the numeral coefficient of:

(i) 7x^2y

(ii) \frac{2x}{3}

(iii) -\frac{5}{4}xy^2z

Q8) Write the degree of each of the following polynomials :

(i) x^5-6x^8+x

(ii) 4x^3-x^4

(iii) 4-x^2

(iv) x-1

(v) x^2+x-x^3

(vi) x^3-8xy^2+x^3y^3

(vii) x^7-6y^4

(viii) 3y^3-2y^2z^4

(ix) 100x^8-8x^{100}

Q9) Write each statement, given below in algebraic form :

(i) 28 more than twice of x is equal to 45.

(ii) 3y reduced by 5z is greater than 8x.

(iii) 6x divided by 13y is less than 17.

(iv) 9 multiplied by 5x is equal to 2y.

Q10) State whether true or false :

(i) If 23 is a constant and x is a variable, 23 + x is constant.

(ii) If 23 is a constant and x is a variable, 23x is a variable.

(iii) If y is a variable and 57 is a constant, y – 57 is a variable.

(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x × 2y is a variable.