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Algebraic Expressions & Identities Test - 7

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Algebraic Expressions & Identities Test - 7
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  • Question 1
    1 / -0
    What is the result when we multiply by ?
    Solution
    ()()

    = () + y()

    =
  • Question 2
    1 / -0
    If 4p + 5q = 24 and pq = 8, find the value of 16p2 + 25q2.
    Solution
    We have 4p + 5q = 24 and pq = 8
    Squaring both sides,
    (4p + 5q)2 = (24)2
    (4p)2 + (5q)2 + 2 (4p) (5q) = (24)2
    16p2 + 25q2 + 40pq = 576
    16p2 + 25q2 + 40 × 8 = 576
    16p2 + 25q2 = 576 – 320
    16p2 + 25q2 = 256
  • Question 3
    1 / -0
    Simplify the following expression:

    Solution


    =

    =

    =

    =

    ==
  • Question 4
    1 / -0
    The square of (5xy - 7x) is equal to
    Solution

    =
    =
  • Question 5
    1 / -0
    If y2 + = 79, find the value of .
    Solution
    + 2

    = 79 + 2

    = 81

     = 9
  • Question 6
    1 / -0
    If 2m - 9n = 12 and mn = -2, then the value of 4m2 + 81n2 is
    Solution
    We have 2m - 9n = 12 and mn = -2
    Squaring both sides,
    (2m - 9n)2 = (12)2
    (2m)2 + (9n)2 - 36mn = 144
    4m2 + 81n2 - 36 x (-2) = 144
    4m2 + 81n2 + 72 = 144
    4m2 + 81n2 = 144 - 72 = 72
  • Question 7
    1 / -0
    The product of and gives
    Solution


    = + 1

    =

    =
  • Question 8
    1 / -0
    Find the missing term in the following problem.

    = + _______
    Solution
    =
    = + 2xy
    Therefore, the missing term is 2xy.
  • Question 9
    1 / -0
    What should be added to to get ?
    Solution
    Let the expression to be added be m.
    + m =
    m = - ()
    m =
    m =

  • Question 10
    1 / -0
    Simplify the following expression:


    Solution


    =

    =

    =
  • Question 11
    1 / -0
    What must be added to 16y2 - 4y + 8 to get 6y2 - 2y - 4?
    Solution
    Let the term added be 'a'.
    16y2 - 4y + 8 + a = 6y2 - 2y - 4
    a = 6y2 - 2y - 4 - (16y2 - 4y + 8)
    a = 6y2 - 2y - 4 - 16y2 + 4y - 8
    a = -10y2 + 2y - 12
  • Question 12
    1 / -0
    If , find the value of .
    Solution


    Squaring both sides,





    From the question,



  • Question 13
    1 / -0
    Multiply and .
    Solution


    =


  • Question 14
    1 / -0
    Simplify the following expression:

    Solution


    =

    =
  • Question 15
    1 / -0
    Find the value of 'a' if and xy = 2.
    Solution






    Given: xy = 2

    a = 5 × 2

    So, a = 10
  • Question 16
    1 / -0
    Thomas is making a cuboidal box in his craft class at the school whose length and breadth are 7ab and 4a2b2c2. If the volume of the box is 84a3b4c5, find the height of the box.
    Solution
    Volume of the cuboid = l × b × h

    84a3b4c5 = 7ab × (4a2b2c2) × h

    h =

    h = 3bc3
  • Question 17
    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 18
    1 / -0
    Nikkie is making two rectangular boxes of length, breadth and height as 5a, 3a2, 7a4 and xy, 2x2y, 2xy2, respectively. If she joins them together to make another rectangular box, then what will be the volume of the new box?
    Solution
    Volume of the new box = Volume of the first box + Volume of the second box

    Volume of the first box = 5a × 3a2 × 7a4 ... (1)

    5 × 3 × 7 × a × a2 × a4 = 105a7

    Volume of the second box = xy × 2x2y × 2xy2

     2 × 2 × xy × x2y × xy2

    4x4y4 ... (2)

    Volume of the new box = [Add (1) and (2)] = 105a7 + 4x4y4
  • Question 19
    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 20
    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 21
    1 / -0
    Directions: Study the following statements and choose the correct option.

    Statement I: The value of the product at m = -1 and n = 3 is -432

    Statement II: The value of is 1.
    Solution
    Statement I:



    =

    =

    As m = -1 and n = 3;



    = 9 - 441 = -432

    Statement II:



    =

    =

    = 1
  • Question 22
    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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