Cambridge Math's Milestone Class 6th

Cambridge Math's Milestone 

CHAPTER REVIEW PAGE NO-106 ANSWER

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Multiple Choice Questions

1. Letters used along with numbers in algebra are called:
   Answer: (a) Variables
   Reason: Letters in algebra represent variables.

2. _________ have a fixed numerical value.
   Answer: (d) Constants
   Reason: Constants are numbers that do not change in value.

3. Variables:
   Answer: (b) Literals
   Reason: Variables are often called literals.

4. 5 times x can be written as:
   Answer: (c) 5x
   Reason: Multiplication of 5 and x is written as 5x in algebra.

5. Name the property: (a × b) × c = a × (b × c):
   Answer: (b) Associative property
   Reason: This property deals with the grouping of numbers in multiplication.

6. 10 added to a number can be written as:
   Answer: (c) 10 + x
   Reason: "10 added to a number" is represented as 10 + x.

7. The general rule to find the perimeter of a square if one side of the square is ‘a’ is given by:
   Answer: (c) 4a
   Reason: Perimeter of a square = 4 × side length = 4a.

8. The general rule to find the perimeter of a rectangle if length and breadth are l and b, respectively, is:
   Answer: (d) 2(l + b)
   Reason: Perimeter of a rectangle = 2 × (length + breadth).

9. The algebraic expression for 8 subtracted from the product of x and y is:
   Answer: (d) 8 – xy
   Reason: First multiply x and y, then subtract 8.

10. If x = 5, then x – 3 + 2 is:

    • Substitute x = 5 into the expression:
      $5 - 3 + 2 = 4$.
      Answer: (a) 4

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Subjective Questions

1. Find the value of the algebraic equation: $20y + 30x - 10$ for $x = 4$ and $y = 3$.

   • Substitute $x = 4$ and $y = 3$:
     $20(3) + 30(4) - 10 = 60 + 120 - 10 = 170.$
     Answer: 170

2. Savitha is half the age of her mother. Find the age of both after 10 years.

   • Let Savitha’s current age = $x$.
     Her mother’s current age = $2x$.
   • After 10 years:
     Savitha’s age = $x + 10$, her mother’s age = $2x + 10$.

3. Write the algebraic statement for $10 - 2x$.
   Answer: $10 - 2x$: Ten minus twice a number x.

4. If the perimeter of a regular heptagon is $x \, \text{m}$, then write the general rule for the length of each side.

   • A heptagon has 7 equal sides.
     Length of each side = $\frac{x}{7}$.

5. Convert these expressions into statements in ordinary language:

   • Cost of 1 kg oranges = $x$.
     Ordinary language: The cost of 1 kg of oranges is $x$ rupees.
   • Cost of 1 kg apples = $5x$.
     Ordinary language: The cost of 1 kg of apples is 5 times the cost of 1 kg of oranges.

6. 14 is subtracted from twice a number. Write the algebraic expression and find the value of the expression by taking the number to be 8.

   • Algebraic expression: $2x - 14$.
   • Substitute $x = 8$:
     $2(8) - 14 = 16 - 14 = 2.$
     Answer: 2.

7. Express $z$ exceeds $y$ in algebraic form.
   Answer: $z - y$.

8. Express the number of days in $y$ years.

   • Number of days in $y$ years = $365y$.
     Answer: $365y$.

9. Using any variable, write the algebraic expression for two consecutive odd integers.

   • Let the first odd integer = $x$.
     The next consecutive odd integer = $x + 2$.
     Answer: $x$ and $x + 2$.

10. Using any variable, write the algebraic expression for two consecutive even integers.

    • Let the first even integer = $x$.
      The next consecutive even integer = $x + 2$.
      Answer: $x$ and $x + 2$.

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CHAPTER REVIEW PAGE NO-107 ANSWER

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Reasoning

11. Anil’s monthly salary is $s$ rupees. Find his salary in one year.

• There are 12 months in a year.
  Anil’s salary in one year = $12s$.
  Answer: $12s$.

12. Rahul’s weight is 30 kg. His weight increases by $x$ kg every year. What will be his weight after 5 years?

• Increase in weight in 5 years = $5x$.
  Total weight = $30 + 5x$.
  Answer: $30 + 5x$.

13. If $x$ students plan a one-day tour and $₹150$ is collected from each student, out of which $₹1500$ is paid in advance as a bus fee. Find the money left with $x$ students.

• Total amount collected = $150x$.
  Money left = $150x - 1500$.
  Answer: $150x - 1500$.

14. Justify each of the following situations using one of the rules from arithmetic (commutative property of addition, distributive property of multiplication, distributive property of multiplication over addition):

a. Lohitha and Bavya are two sisters. On Monday, Lohitha bought 3 cupcakes and Bavya bought 6 cupcakes as evening snacks. Next day, Lohitha bought 6 cupcakes and Bavya bought 3 cupcakes as evening snacks. Find out the total number of cupcakes they bought on each day and identify the rule being justified.

• Total cupcakes bought on Monday = $3 + 6 = 9$.
  Total cupcakes bought on Tuesday = $6 + 3 = 9$.
  This shows $3 + 6 = 6 + 3$, which is an example of the commutative property of addition.
  Answer: Commutative property of addition.

b. Two friends order breakfast from a food court. They order a combo pack of 2 sandwiches and a glass of juice each. Write an expression using distributivity of numbers for the total quantity of food they purchased.

• Total quantity of food = $2 \times (2 + 1) = 2 \times 3 = 6$.
  This shows the distributive property of multiplication over addition.
  Answer: Distributive property of multiplication over addition.

c. Rema and Seema are friends. Rema has 3 boxes with her and each box carries 8 apples. Seema has a total of 8 boxes which have 3 apples each. Calculate how many apples each has in total and identify the arithmetic rule applied to find this.

• Apples with Rema = $3 \times 8 = 24$.
  Apples with Seema = $8 \times 3 = 24$.
  This shows $3 \times 8 = 8 \times 3$, which is an example of the commutative property of multiplication.
  Answer: Commutative property of multiplication.

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Analysis & Creating

15. Frame 5 situations and write algebraic expressions to express them.

• A box contains $x$ pencils. The total number of pencils in 5 boxes = $5x$.
• A person’s age is $y$. Their age 10 years ago = $y - 10$.
• The cost of $n$ books, each priced at $₹50$, = $50n$.
• A vehicle travels $d$ km in one hour. Distance traveled in 4 hours = $4d$.
• A fruit basket has $m$ apples and $n$ oranges. Total fruits = $m + n$.

16. Draw any regular polygon and find the general rule for calculating its perimeter.

• For a regular polygon with $n$ sides and side length $a$, the perimeter = $n \times a$.

17. Complete the table by taking 5 different values for $x$.

• Table completion requires specific data, but the steps involve substituting different $x$-values into the given expression.

18. Matchstick Pattern (Letter E):

a. Observe the patterns and find the rule that gives the total number of matchsticks.

• Number of matchsticks increases by 3 for every new “E.”
  Rule: $3n + 2$, where $n$ is the number of “E”s.

b. If we remove a horizontal stick from the middle, what is the pattern obtained? Find a rule for the new pattern.

• Removing one stick reduces the count by 1.
  New rule: $3n + 1$.

19. Matchstick Triangle Path:

a. If you continue this same pattern, how many extra matchsticks would be needed to make a 6-triangle path?

• Each new triangle adds 2 matchsticks.
  For 6 triangles, additional matchsticks = $6 \times 2 = 12$.

b. In the same way, how many matchsticks would be required for arranging an 8-triangle path?

• Total matchsticks = $3 + (8 \times 2) = 3 + 16 = 19$.

c. Find a rule to obtain the number of matchsticks required to make an $n$-triangle path.

• Rule: $2n + 1$.

d. If you create a 6-triangle path, how many extra matchsticks would be needed for 4 types of such triangular paths?

• For each 6-triangle path, matchsticks = $2(6) + 1 = 13$.
  For 4 paths: $4 \times 13 = 52$.

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Let me know if you need detailed clarifications! tudy kunji  by Prem Sir