Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions Chapter-8. We provide step by step Solutions of Exercise / lesson-8 Algebraic Expression ICSE Class-7th ML Aggarwal Mathematics .
Our Solutions contain all type Questions with Exe-8.1 , Exe-8.2, Exe-8.3 , Exe-8.4, Objective Type Questions ( including Mental Maths Multiple Choice Questions Value Based Questions, HOT) and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.
Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions Chapter-8
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Objective Type Questions, Mental Maths,
Multiple Choice Questions ,(MCQ)
Exercise-8.1, Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions
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.
Answer-1
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.
Answer-2
Question 3.
Write down the algebraic expression whose terms are:
(i) 5a, -3b, c
(ii) x2, -5x, 6
(iii) x2y, xy, -xy2
Answer-3
Question 4.
Write all the terms of each of the following algebraic expressions:
(i) 3 – 7x
(ii) 2 – 5a + 12 b
(iii) 3x5 + 4y3 – 7xy2 + 3
Answer-4
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
Answer-5
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
Answer-6
Question 7.
Write down the numerical coefficient of each of the following:
(i) -7x
(ii) -2x3y2
(iii) 6abcd2
(iv) 2⁄3 pq2
Answer-7
Question 8.
Write down the coefficient of x in the following:
(i) -4bx
(ii) 5xyz
(iii) -x
(iv) -3x2y
Answer-8
Question 9.
In -7xy2z3, write down the coefficient of:
(i) 7x
(ii) -xy2
(iii) xyz
(iv) 7yz2
Answer-9
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
Answer-10
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
Answer-11
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
Answer-12
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
Answer-13
Question -14.
State whether the given pair of terms is of like or unlike terms:
(i) -7x, 5⁄2 x
(ii) -29x, -29y
(iii) 2xy, 2xyz
(iv) 4m2p, 4mp2
(v) 12xz, 12x2z2
(vi) -5pq, 7qp
Answer-14
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
Answer-15
Question 16.
Write down the degree of following polynomials in x:
(i) x2 – 6x7 + x8
(ii) 3 – 2x
(iii) -2
(iv) 1 – x2
Answer-16
Question 17.
Write the degree of the following polynomials:
(i) 3x2 – 5xy2 + 7
(ii) xy2 – y3 + 3y4 – 2
(iii) 7 – 2x3 – 5xy3 + 9y5
Answer-17
Question 18.
State true or false:
(i) If 5 is constant and y 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 – 3⁄x is a polynomial
(vii) Coefficient of x in -3xy is -3
Answer-18
Class-7 ML Aggarwal ICSE Maths Solutions Exercise- 8.2, Algebraic Expression
Question 1.
Add:
(i) 7x, -3x
(ii) 6x, -11x
(iii) 5x2, -9x2
(iv) 3ab2, -5ab2
(v) 1⁄2 pq, -1⁄3 pq
(vi) 5x3y, -2⁄3 x3y
Answer-1
Question 2.
Add:
(i) 3x, -5x, 7x
(ii) 7xy, 2xy, -8xy
(iii) -2abc, 3abc, abc
(iv) 3mn, -5mn, 8mn, -4mn
(v) 2x3, 3x3, -4x3, -5x3
Answer-2
Question 3.
Simplify the following combining like terms:
(i) 21b – 32 + 7b – 20b
(ii) 12m2 – 9m + 5m – 4m2 – 7m + 10
(iii) -z2 + 13z2 – 5z + 7z2 – 15z
(iv) 5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2
(v) p – (p – q) – (q – p) – q
(vi) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
(vii) (3y2 + 5y – 4) – (8y – y2 – 4)
Answer-3
Question 4.
Find the sum of the following algebraic expressions:
(i) 5xy, -7xy, 3x2
(ii) 4x2y, -3xy2, -5xy2, 5x2y
(iii) -7mn + 5, 12mn + 2, 8mn – 8, -2mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
(vii) 3x3 – 5x2 + 2x + 1, 3x – 2x2 – x3, 2x2 – 7x + 9
(viii) 7a2 – 5a + 2, 3a2 – 7, 2a + 9, 1 + 2a – 5a2
Answer-4
Question 5.
Simplify the following:
(i) 2x2 + 3y2 – 5xy + 5x2 – y2 + 6xy – 3x2
(ii) 3xy2 – 5x2y + 7xy – 8xy2 – 4xy + 6x2y
(iii) 5x4 – 7x2 + 8x – 1 + 3x3 – 9x2 + 7 – 3x4 + 11x – 2 + 8x2
Answer-5
Question 6.
Subtract:
(i) -5y2 from y2
(ii) -7xy from -2xy
(iii) a(b – 5) from b(5 – a)
(iv) -m2 + 5mn from 4m2 – 3mn + 8
(v) 5a2 – 7ab + 5b2 from 3ab – 2b – 2b2
(vi) 4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq
(vii) 7xy + 5x2 – 7y2 + 3 from 7x2 – 8xy + 3y2 – 5
(viii) 2x4 – 7x2 + 5x + 3 from x4 – 3x3 – 2x2 + 3
Answer-6
Question 7.
Subtract p – 2q + r from the sum of 10p – r and 5p + 2q.
Answer-7
Question 8.
From the sum of 4 + 3x and 5 – 4x + 2x2, subtract the sum of 3x2 – 5x and -x2 + 2x + 5.
Answer-8
Question 9.
What should be added to x2 – y2 + 2xy to obtain x2 + y2 + 5xy?
Answer-9
Question 10.
What should be subtracted from -7mn + 2m2 + 3n2 to get m2 + 2mn + n2?
Answer-10
Question 11.
How much is y4 – 12y2 + y + 14 greater than 17y3 + 34y2 – 51y + 68?
Answer-11
Question 12.
How much does 93p2 – 55p + 4 exceed 13p3 – 5p2 + 17p – 90?
Answer-12
Question 13.
What should be taken away from 3x2 – 4y2 + 5xy + 20 to obtain -x2 – y2 + 6xy + 20?
Answer-13
Question 14.
From the sum of 2y2 + 3yz, -y2 – yz – z2 and yz + 2z2, subtract the sum of 3y2 – z2 and -y2 + yz + z2.
Answer-14
Exercise- 8.3, Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions
Question 1.
If m = 2, find the value of:
(i) 3m – 5
(ii) 9 – 5m
(iii) 3m2 – 2m – 1
(iv) 5⁄2 m – 4
Answer-1
Question 2.
If p = – 2, find the value of:
(1) 4p + 7
(ii) -3p2 + 4p + 7
(iii) -2p3 – 3p2 + 4p + 7
Answer-2
Question 3.
If a = 2, b = -2, find the value of:
(i) a2 + b2
(ii) a2 + ab + b2
(iii) a2 – b2
Answer-3
Question 4.
When a = 0, b = -1, find the value of the given expressions:
(i) 2a2 + b2 + 1
(ii) a2 + ab + 2
(iii) 2a2b + 2ab2 + ab
Answer-4
Question 5.
If p = -10, find the value of p2 – 2p – 100.
Answer-5
Question 6.
If z = 10, find the value of z3 – 3(z – 10).
Answer-6
Question 7.
Simplify the following expressions and find their values when x = 2:
(i) x + 7 + 4(x – 5)
(ii) 3(x + 2) + 5x – 7
(iii) 6x + 5(x – 2)
(iv) 4(2x – 1) + 3x + 11
Answer-7
Question 8.
Simplify the following expressions and find their values when a = -1, b = -2:
(i) 2a – 2b – 4 – 5 + a
(ii) 2(a2 + ab) + 3 – ab
Answer-8
Exercise- 8.4, Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions
Question 1
Observe the pattern ……….. equal length
If n shape …………. each case
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Question 2
Observe the pattern ……….. equal length
If n shape …………. each case
Answer
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Question 3
If a pattern ………… expression
(i)……….
(ii)……….
(iii)………
(iv)…………
(v)………..
(vi)……….
Answer
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Objective Type Questions
Mental Maths, Chapter-8 Algebraic Expression Class-7 ML Aggarwal ICSE Maths Solutions
Question 1.
Fill in the blanks:
(i) The terms with different algebraic factors are called ……….
(ii) The number of terms in a monomial is ………
(iii) An algebraic expression having two unlike terms is called a ……..
(iv) 3a2b and -7ba2 are ……….. terms.
(v) -6a2b and -6ab2 are ……… terms.
(vi) The number of unlike terms in the algebraic expression 3x2 – 2xy + 5x2 is ………
(vii) The factors of the term -3p2q2 are ……..
(viii) The perimeter of a triangle whose sides measure 2a, b and a + b is ………
(ix) The value of the expression 2x3 – 7x2 + 5x – 3 when x = 1 is ………..
(x) In the term -7a2bc, the coefficient of a is ……..
(xi) The degree of the polynomial 3 – 5x2 + 7x3 – x4 is ……….
(xii) The degree of the polynomial 3x2 – 2xy2 + 5 is ………
Answer-1
Question 2.
State whether the following statements are true (T) or false (F).
(i) The expression 5x + 7 – 2x is a trinomial.
(ii) (7x – 10) – (3x – 5) = 4x – 15.
(iii) The coefficient of 3x in -3x3y is -xy.
(iv) The constant term in the expression 2x2 – 3xy – 7 is 7.
(v) If x = 3 and y = 1⁄3 then the value of xy (x2 + y2) is 91⁄9.
(vi) (3x – y + 5) – (x + y) is a binomial.
(vii) Sum of 2 and p is 2p.
(viii) Sum of x2 + x and y2 + y is 2x2 + 2y2.
(ix) In like terms, variables and their powers are the same.
(x) Every polynomial is a monomial.
(xi) If we add a monomial and a binomial, then answer can never be a monomial.
(xii) If we subtract a monomial from a binomial, then the answer is at least a binomial.
(xiii) if we add a monomial and a trinomial, then the answer can be a monomial.
(xiv) If we add a monomial and a binomial, then the answer can be a trinomial.
Answer-2
Multiple Choice Question (MCQ)
Choose the correct answer from the given four options (3 to 16)
Question 3.
The algebraic expression for the statement ‘Thrice square of a number x subtracted from five times the sum of y and 2’ is
(a) 5y + 2 – 3x2
(b) 3x2 – (5y + 2)
(c) 5(y + 2) – 3x2
(d) 5(y + 2) – (3x)2
Answer-3
Question 4.
The expression 7x – 5(x2 + y2) is a
(a) monomial
(b) binomial
(c) trinomial
(d) none of these
Answer-4
Question 5.
The coefficient of 5a2 in -5a3bc is
(a) -bc
(b) a2bc
(c) -a2bc
(d) -abc
Answer-5
Question -6.
Which of the following is a pair of like terms?
(a) -5xy, 5x
(b) -5xy, 3yz
(c) -5xy, -5y
(d) -5xy, 7yx
Answer-6
Question 7.
The like terms is the expressions 3x(3 – 2y) and 2(xy + x2) are
(a) 9x and 2x2
(b) -6xy and 2xy
(c) 9x and 2xy
(d) -6xy and 2x2
Answer-7
Question 8.
Identify the binomial out of the following:
(a) 3xy2 + 5y – x2y
(b) 2x2y – 5y – 2x2y
(c) 3xy2 + 5y – xy2
(d) xy + yz + zx
Answer-8
Question- 9.
The number of (unlike) terms in the expression 3xy2 + 2y2z – y2x + y(xz + yz) – 5
(a) 3
(b) 4
(c) 5
(d) 6
Answer-9
Question 10.
The value of the expression x3 + y3 when x = 2 and y = -2 is
(a) 0
(b) 8
(c) 16
(d) -16
Answer-10
Question 11.
-xy – (-5xy) is equal to
(a) -6xy
(b) 6xy
(c) -4xy
(d) 4xy
Answer-11
Question 12.
On subtracting 7x + 5y – 3 from 5y – 3x – 9, we get
(a) 10x + 6
(b) -10x – 6
(c) 10x + 10y – 12
(d) -10x – 12
Answer-12
Question 13.
The value of the expression 5⁄3 x2 + 1 when x = -2 is
(a) −17/3
(b) −7/3
(c) 21/3
(d) 23/3
Answer-13
Question 14.
The number of sides in a pattern having 3 hexagons arranged in a row as shown in the given figure is
(a) 18
(b) 17
(c) 16
(d) 15
Answer-14
Question 15.
The degree of the polynomial 3x3y – 5xy4 – 2x + 1 is
(a) 5
(b) 4
(c) 3
(d) 2
Answer-15
Higher Order Thinking Skills ( HOTS )
Question 1.
The length of a rectangle is 3x – 4y + 6z and the perimeter is 7x + 8y + 17z, find the breadth of the rectangle.
Answer-1
Question 2.
Answer-2
Question 3.
If a = 3, b = -1, then find the value of each of the following:
Answer-3
Check Your Progress
Question 1
Consider the expression 3⁄2 x2y – 1⁄2 xy2 + 6x2y2.
(i) How many terms are there? What do you call such an expression?
(ii) List out the terms.
(iii) In the term −1⁄2 xy2, write down the numerical coefficient and the literal coefficient.
(iv) In the term −1⁄2 xy2, what is the coefficient of x?
Answer-1
Question 2.
Write the Degree of the following polynomials:
(i) 2⁄5 x3 – 7x2 – 1⁄2 x + 3
(ii) 2⁄3 xy2 – 5xy + 3⁄5 y2x2 + 2x
Answer-2
Question 3.
Identify monomials, binomials and trinomials from the following algebraic expressions:
(i) 5x × y
(ii) 3 – 5x
(iii) 1⁄2 (7x – 3y + 5z)
(iv) 3x2 – 1.2xy
(v) -3x3y4z5
(vi) 5x(2x – 3y) + 7x2
Answer-2
Question 4.
Using horizontal method:
(i) Add x2 + y2 – 2xy, -2x2 – y2 – 2xy and 3x2 + y2 + xy
(ii) Subtract -x2 + y2 + 2xy from 2x2 – 3y2.
Answer-4
Question 5.
Using column method, add ab + 2bc – ca and 2ab – bc – ca and subtract 4ab + 5bc – 3ca.
Answer-5
Question 6.
The sides of a triangle are 5a – 3b, 3a + 2b and 5b – 2a, find its perimeter.
Answer-6
Question 7.
If two adjacent sides of a rectangle are 4x +7y and 3y – x, find its perimeter.
Answer-7
Question 8.
Subtract the sum of 3x2 + 2xy – 2y2 and 5y2 – 7xy from 5x2 + 2y2 – 3xy.
Answer-8
Question 9.
What must be added to 5x3 – 2x2 + 3x + 7 to get 7x3 + 7x – 5?
Answer-9
Question 10.
How much is 3p – 4q + r less than 4p + 3q – 5r?
Answer-10
Question 11.
How much is 3a2 – 5ab + 7b2 + 3 greater than 2a2 + 2ab + 5?
Answer-11
Question 12.
How much should 5x3 + 3x2 – 2x + 1 be increased to get 6x2 + 7?
Answer-12
Question 13.
Subtract the sum of 12ab – 10b2 – 18a2 and 9ab + 12b2 + 14a2 from the sum of ab + 2b2 and 3b2 – a2.
Answer-13
Question 14.
when a = 3, b = 0, c = -2, find the values of:
(i) ab + 2bc + 3ca + 4abc
(ii) a3 + b3 + c3 – 3abc
Answer-14
Question 15.
Write the algebraic expression for the nth term of the number pattern 13, 23, 33, 43, ………..
Answer-15
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