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ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Objective Type Questions 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 Objective Type Questions

Mental Maths

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 ………
Solution:

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 = \(\frac { 1 }{ 3 }\) then the value of xy (x² + y²) is 9\(\frac { 1 }{ 9 }\).
(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.
Solution:

Multiple Choice Questions

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
Solution:

Question 4.
The expression 7x – 5(x² + y²) is a
(a) monomial
(b) binomial
(c) trinomial
(d) none of these
Solution:

Question 5.
The coefficient of 5a² in -5a³bc is
(a) -bc
(b) a²bc
(c) -a²bc
(d) -abc
Solution:

Question 6.
Which of the following is a pair of like terms?
(a) -5xy, 5x
(b) -5xy, 3yz
(c) -5xy, -5y
(d) -5xy, 7yx
Solution:

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
Solution:

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
Solution:

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
Solution:

Question 10.
The value of the expression x³ + y³ when x = 2 and y = -2 is
(a) 0
(b) 8
(c) 16
(d) -16
Solution:

Question 11.
-xy – (-5xy) is equal to
(a) -6xy
(b) 6xy
(c) -4xy
(d) 4xy
Solution:

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
Solution:

Question 13.
The value of the expression \(\frac { 5 }{ 3 }\) x² + 1 when x = -2 is
(a) \(\frac { -17 }{ 3 }\)
(b) \(\frac { -7 }{ 3 }\)
(c) \(\frac { 21 }{ 3 }\)
(d) \(\frac { 23 }{ 3 }\)
Solution:

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
Solution:

Question 15.
The degree of the polynomial 3x³y – 5xy⁴ – 2x + 1 is
(a) 5
(b) 4
(c) 3
(d) 2
Solution:

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.
Solution:

Question 2.

Solution:

Question 3.
If a = 3, b = -1, then find the value of each of the following:

Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.4 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 8.4

Question 1.
Observe the patterns of shapes of letters formed from line segments of equal lengths:

If n shapes of letters are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.
Solution:

Question 2.
Observe the pattern of shapes of digits formed from line segment of equal lengths:

If n shapes of digits are formed, then write the algebraic expression for the number of line segments required for making these n shapes in each case.
Solution:

Question 3.
If a pattern consists of n shapes formed by line segments of equal lengths and the number of line segments required to make n shapes is given by the algebraic expression:
(i) 2n + 1
(ii) 3n + 1
(iii) 3n + 2
(iv) 5n + 1
(v) 5n + 2
(vi) 4n + 3
then find the number of line segments required to form 5, 10 and 100 shapes in each case.
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.3 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 8.3

Question 1.
If m = 2, find the value of:
(i) 3m – 5
(ii) 9 – 5m
(iii) 3m² – 2m – 1
(iv) \(\frac { 5 }{ 2 }\) m – 4
Solution:

Question 2.
If p = – 2, find the value of:
(1) 4p + 7
(ii) -3p² + 4p + 7
(iii) -2p³ – 3p² + 4p + 7
Solution:

Question 3.
If a = 2, b = -2, find the value of:
(i) a² + b²
(ii) a² + ab + b²
(iii) a² – b²
Solution:

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
Solution:

Question 5.
If p = -10, find the value of p² – 2p – 100.
Solution:

Question 6.
If z = 10, find the value of z³ – 3(z – 10).
Solution:

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
Solution:

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
Solution:

ML Aggarwal Class 7 Solutions Chapter 8 Algebraic Expressions Ex 8.2 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 8.2

Question 1.
Add:
(i) 7x, -3x
(ii) 6x, -11x
(iii) 5x², -9x²
(iv) 3ab², -5ab²
(v) \(\frac { 1 }{ 2 }\) pq, \(\frac { -1 }{ 3 }\) pq
(vi) 5x³y, \(\frac { -2 }{ 3 }\) x³y
Solution:

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
Solution:

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)
Solution:

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
Solution:

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
Solution:

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
Solution:

Question 7.
Subtract p – 2q + r from the sum of 10p – r and 5p + 2q.
Solution:

Question 8.
From the sum of 4 + 3x and 5 – 4x + 2x², subtract the sum of 3x² – 5x and -x² + 2x + 5.
Solution:

Question 9.
What should be added to x² – y² + 2xy to obtain x² + y² + 5xy?
Solution:

Question 10.
What should be subtracted from -7mn + 2m² + 3n² to get m² + 2mn + n²?
Solution:

Question 11.
How much is y⁴ – 12y² + y + 14 greater than 17y³ + 34y² – 51y + 68?
Solution:

Question 12.
How much does 93p² – 55p + 4 exceed 13p³ – 5p² + 17p – 90?
Solution:

Question 13.
What should be taken away from 3x² – 4y² + 5xy + 20 to obtain -x² – y² + 6xy + 20?
Solution:

Question 14.
From the sum of 2y² + 3yz, -y² – yz – z² and yz + 2z², subtract the sum of 3y² – z² and -y² + yz + z².
Solution:

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: