ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.1

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.1

Question 1.
From the algebraic expressions using variables, constants, and arithmetic operations:
(i) 6 more than thrice a number x.
(ii) 5 times x is subtracted from 13.
(iii) The numbers x and y both squared and added.
(iv) Number 7 is added to 3 times the product of p and q.
(v) Three times of x is subtracted from the product of x with itself.
(vi) Sum of the numbers m and n is subtracted from their product.
Solution:

Question 2.
A taxi charges ₹ 9 per km and a fixed charge of ₹ 50. If the taxi is hired for x km, write an algebraic expression for this situation.
Solution:

Question 3.
Write down the algebraic expression whose terms are:
(i) 5a, -3b, c
(ii) x², -5x, 6
(iii) x²y, xy, -xy²
Solution:

Question 4.
Write all the terms of each of the following algebraic expressions:
(i) 3 – 7x
(ii) 2 – 5a + \(\frac { 1 }{ 2 }\) b
(iii) 3x⁵ + 4y³ – 7xy² + 3
Solution:

Question 5.
Identify the terms and their factors in the algebraic expressions given below:
(i) -4x + 5y
(ii) xy + 2x²y²
(iii) 1.2ab – 2.4b + 3.6a
Solution:

Question 6.
Show the terms and their factors by tree diagrams of the following algebraic expressions:
(i) 8x + 3y²
(ii) y – y³
(iii) 5xy² + 7x²y
(iv) -ab + 2b² – 3a²
Solution:

Question 7.
Write down the numerical coefficient of each of the following:
(i) -7x
(ii) -2x³y²
(iii) 6abcd²
(iv) \(\frac { 2 }{ 3 }\) pq²
Solution:

Question 8.
Write down the coefficient of x in the following:
(i) -4bx
(ii) 5xyz
(iii) -x
(iv) -3x²y
Solution:

Question 9.
In -7xy²z³, write down the coefficient of:
(i) 7x
(ii) -xy²
(iii) xyz
(iv) 7yz²
Solution:

Question 10.
Identify the terms (other than constants) and write their numerical coefficients in each of the following algebraic expressions:
(i) 3 – 7x
(ii) 1 + 2x – 3x²
(iii) 1.2a + 0.8b
Solution:

Question 11.
Identify the terms which contain x and write the coefficient of x in each of the following expressions:
(i) 13y² – 8xy
(ii) 7x – xy²
(iii) 5 – 7xyz + 4x²y
Solution:

Question 12.
Identify the term which contain y2 and write the coefficient of y2 in each of the following expressions:
(i) 8 – xy²
(ii) 5y² + 7x – 3xy²
(iii) 2x²y – 15xy² + 7y²
Solution:

Question 13.
Classify into monomials, binomials and trinomials:
(i) 4y – 7z
(ii) -5xy²
(iii) x + y – xy
(iv) ab² – 5b -3a
(v) 4p²q – 5pq²
(vi) 2017
(vii) 1 + x + x²
(viii) 5x² – 7 + 3x + 4
Solution:

Question 14.
State whether the given pair of terms is of like or unlike terms:
(i) -7x, \(\frac { 5 }{ 2 }\) x
(ii) -29x, -29y
(iii) 2xy, 2xyz
(iv) 4m²p, 4mp²
(v) 12xz, 12x²z²
(vi) -5pq, 7qp
Solution:

Question 15.
Identify like terms in the following:
(i) x²y, 3xy², -2x²y, 4x²y²
(ii) 3a²b, 2abc, -6a²b, 4abc
(iii) 10pq, 7p, 8q – p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Solution:

Question 16.
Write down the degree of following polynomials in x:
(i) x² – 6x⁷ + x⁸
(ii) 3 – 2x
(iii) -2
(iv) 1 – x²
Solution:

Question 17.
Write the degree of the following polynomials:
(i) 3x² – 5xy² + 7
(ii) xy² – y³ + 3y⁴ – 2
(iii) 7 – 2x³ – 5xy³ + 9y⁵
Solution:

Question 18.
State true or false:
(i) If 5 is constant andy is variable, then 5y and 5 + y are variables
(ii) 7x has two terms, 7 and x
(iii) 5 + xy is a trinomial
(iv) 7a × bc is a binomial
(v) 7x³ + 2x² + 3x – 5 is a polynomial
(vi) 2x² – \(\frac { 3 }{ x }\) is a polynomial
(vii) Coefficient of x in -3xy is -3
Solution: