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Algebraic Expressions & Identities Test - 5

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Algebraic Expressions & Identities Test - 5
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  • Question 1
    1 / -0

    Suhail is a postman. He receive money for his work based on a formula, which is 3l(4l - 5) + 3 and is calculated in rupees, where l is the number of letters he delivers. If he delivers 5 letters on Monday, then how much amount of money will he be paid?

    Solution

    The given formula is:
    3l(4l - 5) + 3
    ⇒ 12l2 - 15l + 3 ... (1)

    According to the question,

    Put l = 5 in equation (1).
    ⇒ 12(5)2 - 15(5) + 3
    ⇒ 12(25) - 75 + 3

    ⇒ 300 - 75 + 3
    ⇒ Rs. 228

     

  • Question 2
    1 / -0

    Sumit opened a new account in ABS bank. In the first month, he deposited Rs. p in his account. In the second month, he deposited Rs. p2 money in his account. In the third month, he deposited the cube of the amount deposited by him in the first month. In the fourth month, he deposited money equal to the product of amounts deposited by him in the last three months. The amount deposited in the fourth month is

    Solution

    Amount deposited in the first month = Rs. p

    Amount deposited in the second month = Rs. p2

    Amount deposited in the third month = Rs. (p × p × p) = Rs. p3

    Total amount deposited in the fourth month = Rs. (p × p2 × p3)

    = p1 + 2 + 3

    = Rs. p6

     

  • Question 3
    1 / -0

    In an electronics shop, a refrigerator costs 3a - 7b + 6, a television costs 5a + 2b + 8 and a music system costs a + 5b + 6. If a customer pays (2)2a + (4)2 to the shopkeeper for all of these, how much amount does he need to pay more?

    Solution

    Given:
    Cost of a refrigerator = 3a - 7b + 6.

    Cost of a television = 5a + 2b + 8.

    Cost of a music system = a + 5b + 6.

    Total billing amount = 3a - 7b + 6 + 5a + 2b + 8 + a + 5b + 6 = 9a + 20.

    Since the customer has already paid (2)2a + (4)2;

    (9a + 20) - ((2)2a + (4)2) = 9a + 20 - 4a - 16 = 5a + 4.

    He needs to pay 5a + 4 more to the shopkeeper.

     

  • Question 4
    1 / -0

    Fill in the blanks.

    (A) A factor which occurs in each term is called the ____ factor.
    (B) The representation of an expression as the product of its factors is called ____.
    (C) (y + a)(y + b) = y2 + (a + b)y + ____
    (D) A/An ____ is formed by the product of variables and constants.

    Solution

    (A) A factor which occurs in each term is called the common factor.
    (B) The representation of an expression as the product of its factors is called factorisation.

    (C) (y + a)(y + b) = y2 + (a + b)y + ab.

    (D) A/An term is formed by the product of variables and constants.

     

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