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Lecture 2: Properties of Integers

  • Integers Assignments 1

    In a test (+5) marks are given for every correct answer and (–2) marks
    are given for every incorrect answer. (i) Radhika answered all the questions
    and scored 30 marks though she got 10 correct answers. (ii) Jay also
    TRY THESE
    Is (i) 1 ÷ a = 1?
    (ii) a ÷ (–1) = – a? for any integer a.
    Take different values of a and check.
    answered all the questions and scored (–12) marks though he got 4
    correct answers. How many incorrect answers had they attempted?

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  • Integers Assignments 2

    Suppose we represent the distance above the ground by a positive integer
    and that below the ground by a negative integer, then answer the following:
    (i) An elevator descends into a mine shaft at the rate of 5 metre per minute. What will
    be its position after one hour?
    (ii) If it begins to descend from 15 m above the ground, what will be its position after 45
    minutes?

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  • Integers Assignments 3

    In a class test containing 15 questions, 4 marks are given for every
    correct answer and (–2) marks are given for every incorrect answer.
    (i) Gurpreet attempts all questions but only 9 of her answers are correct.
    What is her total score? (ii) One of her friends gets only 5 answers
    correct. What will be her score?

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  • Integers Assignments 4

    Verify (–30) × [13 + (–3)] = [(–30) × 13] + [(–30) × (–3)]

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  • Integers Assignments 5

    Find each of the following products:
    (i) (–18) × (–10) × 9 (ii) (–20) × (–2) × (–5) × 7
    (iii) (–1) × (–5) × (– 4) × (– 6)

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  • Integers Assignments 6

    An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach - 350 m.

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  • Integers Assignments 7

    In a class test (+ 3) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores - 5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly? (iii) Rakesh scores 18 marks by attempting 16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly?

     

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  • Integers Assignments 8

    The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?

     

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  • Integers Assignments 9

    Write five pairs of integers (a, b) such a ÷ b = - 3. One such pair is (6, - 2) because 6 ÷ (- 2) = (- 3).

     

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  • Integers Assignments 10

    Verify that a ÃƒÂ· (b + c) ≠ (a ÃƒÂ· b) + (a ÃƒÂ· c) for each of the following values of a, b and c.

    (a) a = 12, b = -4, c = 2

    (b) a = (- 10), b = 1, c = 1

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  • Integers Assignments 11

    Evaluate each of the following:

    (a)  (b) 

    (c)  (d) 

    (e)  (f) 

    (g) 

    (h)  (i) 

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  • Integers Assignments 12

     

    Replace the blank with an integer to make it a true statement.

    (a) 

    (b) 

    (c) 

    (d) 

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  • Integers Assignments 13

     

    A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.

    (a) The company sells 3, 000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

    (b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.

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  • Integers Assignments 14

     

    In a class test containing 10 questions, 5 marks are awarded for every correct answer and (- 2) marks are awarded for every incorrect answer and 0 for questions not attempted.

    (i) Mohan gets four correct and six incorrect answers. What is his score?

    (ii) Reshma gets five correct answers and five incorrect answers, what is her score?

    (iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

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  • Integers Assignments 15

    A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

     

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  • Integers Assignments 16

     

    Find the product, using suitable properties:

    (a) 26 x (- 48) + (- 48) x (- 36) (b) 8 x 53 x (-125)

    (c) 15 x (- 25) x (- 4) x (- 10) (d) (- 41) x 102

    (e) 625 x (- 35) + (- 625) x 65 (f) 7 x (50 - 2)

    (g) (- 17) x (- 29) (h) (- 57) x (- 19) + 57

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  • Integers Assignments 17

    Starting from (- 1) x 5, write various products showing some pattern to show (- 1) x (- 1) =1.

     

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  • Integers Assignments 18

    i) For any integer a, what is (- 1) x a equal to?

    (ii) Determine the integer whose product with (- 1) is

    (a) - 22 (b) 37 (c) 0

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  • Integers Assignments 19

     

    Verify a - (-b) = a + b for the following values of a and b.

    (i) a = 21, b = 18

    (ii) a = 118, b = 125

    (iii) a = 75, b = 84

    (iv) a = 28, b = 11

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  • Integers Assignments 20

    In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

    5

    - 1

    - 4

    		    

    1

    - 10

    0

    - 5

    - 2

    7

    		    

    - 4

    - 3

    - 2

    0

    3

    - 3

    		    

    - 6

    4

    - 7

    (i)

    		    

    (ii)

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  • Integers Assignments 21

     

    A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?

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    • Description:-

    Lecture 2:

    Today, we will discuss the second topics, i.e; Properties of Integers respectively of Chapter 1 Integers.

    OBJECTIVES:

    1. Basic concept about Properties of Integers

    .2.Problems on Properties of Integers.

    Important Tip: 

    This lecture about Integers is base for the further chapters. These topics help in many ways as how the properties of Integers are related to each other. Multiplication and Division of Integers, it help you in further studies also.Please go through the topic, their notes. Properly do the assignments, watch videos of the concerned topics. If you any doubt about any topic/point please submit it in the discussion section... it will be answered as soon as possible.After all of this...when you fell confident about the particular topic/chapter then take the quiz. 

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