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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:

ML Aggarwal Class 7 Solutions Chapter 7 Percentage and Its Applications Check Your Progress 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 7 Percentage and Its applications Check Your Progress

Question 1.
Convert the following percentages into fractions in the simplest form:
(i) 12\(\frac { 1 }{ 2 }\) %
(ii) 66\(\frac { 2 }{ 3 }\) %
(iii) 8\(\frac { 1 }{ 3 }\) %
Solution:

Question 2.
Express each of the following fractions as a percentage:
(i) \(\frac { 5 }{ 8 }\)
(ii) \(\frac { 13 }{ 40 }\)
(iii) \(\frac { 7 }{ 6 }\)
Solution:

Question 3.
Express each of the following percentages as a decimal:
(i) 122%
(ii) 2.2%
(iii) 3\(\frac { 1 }{ 8 }\) %
Solution:

Question 4.
Express 0.0345 as a percentage.
Solution:

Question 5.
Convert each part of the ratio 5 : 6 : 9 to a percentage.
Solution:

Question 6.
(i) What percent of a day is half an hour?
(ii) What percent is \(\frac { 3 }{ 4 }\) metres of 4\(\frac { 1 }{ 2 }\) metres?
Solution:

Question 7.
The population of a town decreased from 25000 to 24500. Find the percentage decrease.
Solution:

Question 8.
Arun bought a car for ₹ 350000. The next year, the price went upto ₹ 370000. What was the precentage increase in the price?
Solution

Question 9.
The population of a village has decreased by 6%. If the original population was 3650, find the population after decrease.
Solution:

Question 10.
43% of the students in a school are girls. If the number of boys is 1482, find:
(i) the total strength of the school
(ii) number of girls in the school.
Solution:

Question 11.
Rohan bought a calculator for ₹ 760 and sold it for ₹ 874. Find his profit and profit percentage.
Solution:

Question 12.
On selling an article for ₹ 1027, Meena suffered a loss of ₹ 273. Find her loss percentage.
Solution:

Question 13.
By selling a fan for ₹ 710, a trader suffers a loss of ₹ 40. Find the cost price of the fan. At what price this fan should be sold in order to gain 10%?
Solution:

Question 14.
A shopkeeper sells an article at ₹ 300, thus earning a profit of 20%. Find the cost price of the article.
Solution:

Question 15.
A shopkeeper sells an article at ₹ 320, thus suffering a loss of 20%. Find the cost price of the article.
Solution:

Question 16.
If ₹ 6000 is borrowed at 6.5% per annum simple interest, find the interest and the amount to be paid at the end of 3 years.
Solution:

Question 17.
How long will it take for ₹ 1860 invested at the rate of 9.5% per annum simple interest to amount to ₹ 2449?
Solution:

Question 18.
At what rate will ₹ 7200 fetch a simple interest of ₹ 3024 in 4 years?
Solution:

Question 19.
What sum of money will yield a simple interest of ₹ 1155in 3 years 6 months at 11% p.a.?
Solution:

ML Aggarwal Class 7 Solutions Chapter 7 Percentage and Its Applications 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 7 Percentage and Its Applications Objective Type Questions

Question 1.
Fill in the blanks:
(i) 6% of ₹ 50 = ……….
(ii) If 25% of a number is 12, then the number is ……….
(iii) The mixed fraction 1\(\frac { 3 }{ 4 }\) converted to percentage form is
(iv) If a number increases from 20 to 28, then the increasing percentage is ………
(v) If cost price is ₹ 400 and loss is 15%, then the selling price is ……..
(vi) The profit or loss percentage is always calculated on ……….
(vii) The simple interest on a sum of ₹ 5600 at 8% p.a. for one year is ……….
(viii) 135% converted to decimal is ………
(ix) ……… is 50% more than 60.
(x) 25 mL is ………… percent of 5 litres.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) 20% more than 30 is 36.
(ii) The ratio 2 : 5 converted to percentage is 60%.
(iii) 6\(\frac { 1 }{ 4 }\) % expressed as a fraction is \(\frac { 1 }{ 16 }\).
(iv) 80% of 450 m is equal to 360 m.
(v) If a number decreases from 20 to 15, then the decrease is 25%.
(vi) If Feroz obtains 336 marks out of600 marks, then the percentage of marks obtained by him is 33.6.
(vii) 0.018 is equivalent to 8%.
(viii) 250 cm is 4% of 1 km.
(ix) If S.P. of an article is ₹ 540 and loss is ₹ 40, then its C.P. is ₹ 500.
(x) By selling a book for ₹ 50, a shopkeeper suffers a loss of 10%. The cost price of the books is ₹ 60.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 16):
Question 3.
The ratio 2 : 3 expressed as percent is
(a) 40%
(b) 60%
(c) 66\(\frac { 2 }{ 3 }\) %
(d) 33\(\frac { 1 }{ 3 }\) %
Solution:

Question 4.
The ratio of Fatima’s income to her saving is 4 : 1. The percentage of money saved by her is
(a) 20%
(b) 25%
(c) 40%
(d) 80%
Solution:

Question 5.
225% is equal to
(a) 2 : 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4
Solution:

Question 6.
If 30% of x is 72, then x is equal to
(a) 120
(b) 240
(c) 360
(d) 480
Solution:

Question 7.
If x% of 80 = 12, then x is equal to
(a) 15
(b) 20
(c) 25
(d) 30
Solution:

Question 8.
0.025 when expressed as a percent is
(a) 250%
(b) 25%
(c) 4%
(d) 2.5%
Solution:

Question 9.
In class, 45% of students are girls. If there are 22 boys in the class, then the total number of students in the class is
(a) 30
(b) 36
(c) 40
(d) 44
Solution:

Question 10.
What percent of \(\frac { 1 }{ 7 }\) is \(\frac { 2 }{ 35 }\) ?
(a) 20%
(b) 25%
(c) 30%
(d) 40%
Solution:

Question 11.
If a man buys an article for ₹ 80 and sells it for ₹ 100, then gain percentage is
(a) 20%
(b) 25%
(c) 40%
(d) 125%
Solution:

Question 12.
If a man buys an article for ₹ 120 and sells it for ₹ 100, then his loss percentage is
(a) 10%
(b) 20%
(c) 25%
(d) 16\(\frac { 2 }{ 3 }\)%
Solution:

Question 13.
The salary of a man is ₹ 24000 per month. If he gets an increase of 25% in the salary, then the new salary per month is
(a) ₹ 2500
(b) ₹ 28000
(c) ₹ 30000
(d) ₹ 36000
Solution:

Question 14.
On selling an article for ₹ 100, Renu gains ₹ 20. Her gain percentage is
(a) 25%
(b) 20%
(c) 15%
(d) 40%
Solution:

Question 15.
The simple interest on ₹ 6000 at 8% p.a. for one year is
(a) ₹ 600
(b) ₹ 480
(c) ₹ 400
(d) ₹ 240
Solution:

Question 16.
If Rohit borrows ₹ 4800 at 5% p.a. simple interest, then the amount he has to return at the end of 2 years is
(a) ₹ 480
(b) ₹ 5040
(c) ₹ 5280
(d) ₹ 5600
Solution:

Value Based Questions

Question 1.
One bad apple is accidentally mixed with some good apples in a basket. As a result of which 25% of the total apples go bad. Now the number of good apples in the basket is 30. Find the number of good apples kept in the basket previously. What will happen if one bad person is mixed with some good ones?
Solution:

Question 2.
There is a group of 50 people who are patriotic out of which 40% believe in non-violence. Find the number of persons who believe in non-violence. Explain the importance of non-violence in patriotism.
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
A person preparing medicine wants to convert 15% alcohol solution into 32% alcohol solution. Find how much pure alcohol should he mix with 400 mL of 15% alcohol solution to obtain it.
Solution:

Question 2.
A manufacturer sells an item to an agency at a profit of 25%. The agency sells the item to a shopkeeper at 10% profit and shopkeeper sells the item at a profit of 20%. If the selling price of the item is ₹ 594, find the manufacturing price.
Solution: