ICSE

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Ex 9.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.4

Question 1.
Find the value of the following:
(i) 4³
(ii) (-6)⁴
(iii) \(\left(\frac{2}{3}\right)^{4}\)
(iv) (-2)³ × 5²
Solution:

Question 2.
Find the value of:
(i) 3x + 2y when x = 3 and y – 2
(ii) 5x – 3y when x = 2 and y = -5
(iii) a + 2b – 5c when a = 2, b = -3 and c = 1
(iv) 2p + 3q + 4r + pqr when p = -1, q = 2 and r = 3
(v) 3ab + 4bc – 5ca when a = 4, 6 = 5 and c = -2.
Solution:

Question 3.
Find the value of:
(i) 2x² – 3x + 4 when × = 2
(ii) 4x³ – 5x² – 6x + 7 when x = 3
(iii) 3x³ + 9x² – x + 8 when x = -2
(iv) 2x⁴ – 5x³ + 7x – 3 when x = -3
Solution:

Question 4.
If x = 5, find the value of:
(i) 6 – 7x²
(ii) 3x² + 8x – 10
(iii) 2x³ – 4x² – 6x + 25
Solution:

Question 5.
If x = 2, y = 3 and z = -1, find the values of:
(i) x + y
(ii) \(\frac{x y}{z}\)
(iii) \(\frac{2 x+3 y-4 z}{3 x-z}\)
Solution:

Question 6.
If a = 2, b = 3 and c = -2, find the value of a² + b² + c² – 2ab – 2bc – 2ca + 3abc.
Solution:

Question 7.
If p = 4, q = -3 and r = 2, find the value of: p³ + q³ – r³ – 3pqr.
Solution:

Question 8.
If m = 1, n = 2 and p = -3, find the value of 2mn⁴ – 15m²n + p.
Solution:

Question 9.
State true or false:
(i) The value of 3x – 2 is 1 when x = 0.
(ii) The value of 2x² – x – 3 is 0 when x = -1.
(iii) p² + q² – r² when p = 5, q = 12 and r = 13.
(iv) 16 – 3x = 5x when x = 2.
Solution:

Question 10.
For x = 2 and y = -3, verify the following:
(i) (x + y)² = x² + 2xy + y²
(ii) (x – y)² = x² – 2xy + y²
(iii) x² – y² = (x + y) (x – y)
(iv) (x + y)² = (x – y)² + 4xy
(v) (x + y)³ = x³ + y³ + 3x²y + 3xy²
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Ex 9.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.3

Question 1.
Form four expressions with numbers 7, 5 and 8 (no variables) using operations of addition, subtraction or multiplication with the condition that every number should be used but not more than once.
Solution:

Question 2.
Which out of following are expressions with numbers only?
(i) 2y + 3
(ii) (7 × 20) – 82
(iii) 5 × (21 – 7) + 9 x 2
(iv) 5 -11 n
(v) (5 × 4) – 45 + p
(vi) 3 × (11 + 7) – 24 + 3
Solution:

Question 3.
Identify the operations (addition, subtraction, multiplication, division) in forming the following expressions and tell how the expressions have been formed:
(i) x + 5
(ii) y – 7
(iii) 3z
(iv) \(\frac{p}{5}\)
(v) 2x + 17
(vi) 3y – 5
(vii) \(-7 m+\frac{2}{3}\)
(viii) \(\frac{x}{3}-15\)
Solution:

Question 4.
Write expression for the following:
(i) 7 added to p
(ii) p subtracted from 7
(iii) p multiplied by 7
(iv) p divided by 7
(v) 7 divided by p
(vi) 7 subtracted from -m
(vii) p multiplied by -5
(viii) -p divided by 5
Solution:

Question 5.
Write expression for the following:
(i) 11 added to 2 m
(ii) 11 subtracted from 2 m
(iii) 3 added to 5 times y
(iv) 3 subtracted from 5 times y
(v) y is multiplied by -8 and then 5 is added to the result
(vi) y is multiplied by 5 and then the result is subtracted from 16.
Solution:

Question 6.
Write the following in mathematical form using signs and symbols:
(i) 6 more than thrice a number x.
(ii) 7 taken away from y.
(iii) 3 less than quotient of x by y.
Solution:

Question 7.
Form six expressions using t and 4. Use not more than one number operation and every expression must have t in it.
Solution:

Question 8.
Form expressions using y, 2 and 7. Use only two different number operations and every expression must have y in it.
Solution:

Question 9.
A student scored x marks in English but the teacher deducted 5 marks for bad handwriting. What was the student’s final score in English?
Solution:

Question 10.
Raju’s father’s age is 2 years more than 3 times Raju’s age. If Raju’s present age is y years, then what is his father’s age?
Solution:

Question 11.
Mohini is x years old. Express the following in algebraic form:
(i) three times Mohini’s age next year.
(ii) four times Mohini’s age 3 years ago.
(iii) the present age of Mohini’s uncle, if his uncle is 5 times as old as Mohini will be two years from now.
(iv) the present age of Mohini’s cousin, if her cousin is two years less than one-third of Mohini’s age five years ago.
Solution:

Question 12.
A cuboidal box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
Solution:

Question 13.
A bus travels at v km per hour. It is going from Delhi to Jaipur. After the bus has travelled 5 hours, Jaipur is still 20 km away. What is the distance from Delhi to Jaipur?
Solution:

Question 14.
Change the following statements using expressions into statements in ordinary language:
(i) A notebook cost ₹ p. A book costs ₹ 3p.
(ii) The cost of rice per kg is ₹ p. The cost of oil per litre is ₹5p.
(iii) The speed of a truck is v km per hour. The speed of a bus is (v + 10) km per hour.
(iv) Tony’s box contains 8 times the marbles he puts on the table.
(v) The total number of students in the school is 20 times that of our class.
(vi) Raju is x years old. His uncle is 4x years old and his aunt is (4x – 3) years old.
(vii) In arrangement of dots there are r rows. Each row contains 5 dots.
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Ex 9.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.2

Question 1.
If the side of an equilateral triangle is l, then express the perimeter of the triangle in terms of l.
Solution:

Question 2.
The side of a regular hexagon is l. Express its perimeter in terms of l.
Solution:

Question 3.
The length of an edge of a cube is l. Find the formula for the sum of lengths of all the edges of the cube.

Solution:

Question 4.
If the radius of a circle is r units, then express the length of a diameter of the circle in terms of r.
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Ex 9.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.1

Question 1.
Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.

Solution:

Question 2.
If there are 24 mangoes in a box, how will you write the number of mangoes in terms of the number of boxes? (use b for the number of boxes.)
Solution:

Question 3.
Anuradha is drawing a dot Rangoli (a beautiful pattern of lines joining dots). She has 8 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 12 rows?
Solution:

Question 4.
Anu and Meenu are sisters. Anu is 5 years younger than Meenu. Can you write Anu’s age in terms of Meenu’s age? Take Meenu’s age as x years.
Solution:

Question 5.
Oranges are to be transferred from larger boxes to smaller boxes. When a larger box is empited, the oranges from it fill 3 samller boxes and still 7 oranges are left. If the number of oranges in a small box are taken to be x, then what is the number of oranges in the larger box?
Solution:

Question 6.
Harsha’s score in Mathematics is 15 more than three-fourth of her score in Science. If she scores x marks in Science, find her score in Mathemstics?
Solution:

Question 7.
Look at the following matchstick pattern of equilateral triangles. The triangles are not separate. Two neighbouring triangles have a common matchstick. Observe the pattern and find the rule that gives the number of matchsticks.

Solution:

Question 8.
Look at the following matchstick pattern of letter A. The A’s are not separate. Two neighbouring A’s have two common matchsticks. Observe the pattern and find the rule that gives the number of matchsticks.

Solution:

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion 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 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Check Your Progress

Question 1.
From the given figure, find the ratio of

(i) Number of triangles to the number of circles inside the rectangle.
(ii) Number of squares to the number of all the figures inside the rectangle.
(iii) Number of circles to the number of remaining figures inside the rectangle.
Solution:

Question 2.
The length of a pencil is 16 cm and its diameter is 6 mm. What is the ratio of the diameter of the pencil to that of its length?
Solution:

Question 3.
A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any game. Find the ratio of number of members who play
(i) badminton to the number of those who play chess.
(ii) badminton to the number of those who do not play any game.
(iii) tennis to the number of those who do not play any game.
(iv) tennis to the number of those who play either badminton or chess.
Solution:

Question 4.
Do the ratios 15 cm to 3 m and 25 seconds to 3 minutes from a proportion?
Solution:

Question 5.
Divide ₹500 among Suresh and Awanti in the ratio 3 : 7.
Solution:

Question 6.
The ratio of the number of girls to that of boys in a school is 9 : 11. If the number of boys in the school is 2035, find:
(i) the number of girls in the school,
(ii) the number of students in the school.
Solution:

Question 7.
The ratio of income to expenditure of a family is 7 : 6. Find the savings if the income of family is ₹42000.
Solution:

Question 8.
An employee earns ₹72,000 in 3 months.
(i) How much does he earn in 7 months?
(ii) In how many months will he earn ₹3,60,000?
Solution:

Question 9.
A train travels 110 km in 2 hours and a car travels 245 km in \(3 \frac{1}{2}\) hours. What is the ratio of the speed of the train to that of the car?
Solution: