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

Exercises in Chapter 18 fundamental concepts algebra Grade 6

Exercise 18(A)

Exercise 18(B)

Revision Exercise

Questions in Exercise 18(A)

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

Questions in Exercise 18(B)

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) $4y^2-3x^3+y^2x^7$

Questions in Revision Exercise

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.

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Chapters in this book

Number System (Consolidating the Sense of Numberness)

Estimation

Numbers in India and International System (With Comparison)

Place Value

Natural Numbers and Whole Numbers (Including Patterns)

Negative Numbers and Integers

Number Line

HCF and LCM

Playing with Numbers

Sets

Ratio

Proportion (Including Word Problems)

Unitary Method

Fractions

Decimal Fractions

Percent (Percentage)

Idea of Speed, Distance and Time

Fundamental Concepts (Algebra)

Fundamental Operations (Related to Algebraic Expressions)

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Simple (Linear) Equations (Including Word Problems)

Fundamental Concepts (Geometry)

Angles (With their Types)

Properties of Angles and Lines (Including Parallel Lines)

Triangles (Including Types, Properties and Construction)

Quadrilateral

Polygons

The Circle

Revision Exercise on Symmetry (Including Constructions on Symmetry)

Recognition of Solids

Perimeter and Area of Plane Figures

Data Handling (Including Pictograph and Bar Graph)

Mean and Median