#### Subject:

mathematics

#### Class:

class VII

#### Key Concepts

Various types of numbers, Operations of Integers, Properties of Integers when various operations are used

#### essential questions

1. How do integers give me an understanding of situations in my life?

2. What is the best way to illustrate integer operations?

#### Remembering:

**MCQ on Integers**

- -11,-8,-5,-2, the next number in the series is: a) -1 b) 0 c)1 d) -4
- What is the value of the expression { (-10) ÷2}× (-4)? a) 20 b) 2 c) -9 d) -12
- On a number line, when we add a positive integer we move a) to right b) to left c) do not move at all d) none of these
- On a number line, when we add a negative integer we move a) to right b) to left c) do not move at all d) none of these
- On a number line, when we subtract a positive integer, we move a) to right b) to left c) do not move at all d) none of these
- What will be additive inverse of -5 :a) -6 b) -4 c) 3 d) 5
- What will be additive inverse of 7 : a) – 7 b) -6 c) 1/7 d) -1/7
- Sum of two negative number is always: a) positive b) negative c) zero d) one
- Which property is reflected in the following 7× 5 = 5× 7 a) closure b) commutative c) associative d) distributive
- 0÷ 10 gives a) 0 b) 10 c) 1 d)-10
- On dividing a negative integers by other negative integer the quotient will be a) always negative b) always positive c) either positive or negative d) 1
- How is withdrawal of Rs 200 represented : a) 200 b) -200 c) depositing Rs 200
- What is the nature of the product of a negative integer by itself, odd number of times a) positive b) negative c) non negative d) cannot be determined?
- For any two integer number a and b, a + b is an ____ a) None of these b) Whole number c) Integer d) natural number
- True or false: a) Integers are closed under multiplication. b) -1 is not a multiplicative identity of integers c) If a, b,c are integer and its additive inverse is zero d) Successor of 0 × (-25) is 1 × (-25)

#### understanding:

**MCQ on Integers**

- The Sum of two integers is -112. If one of them is -109 the other is: a) -121 b) -3 c) 3 d) none of the these
- Which of the following is a false: a) -7 + (-6) = -13 b) -5+1 =4 c) 2+(-1)= 1 d) 8+(-9)= -1
- Which of the following is true with respect to -28 and -32? a) -28< -32 b) -28= -32 c) -32 > -28 d) -28 > -32
- An integer when divided by -3 gives quotient 35 and leaves remainder 2. The integer is : a) 32 b) 31 c) -34 d) -103
- The product of two integers is 4 less than 49. If one of the integer is -9 then other integer is: a) 43 b) 40 c) -44 d) -5
- The Sum of two integers is -112. If one of them is -109 the other is: a) -121 b) -3 c) 3 d) none of the these
- what should be added to -5 to get 4: a) 1 b) -1 c)-9 d) 9

- A place is 45 m above sea level and another place is 25 m below sea level. What is the difference between two places?
- Find the product of : a) (-4) × (-5) ×(-8) ×(-10) b) (-6) × (-5) × (-7) × (-2) × (-3) c) (-7) ×(-9) × 0
- Find the sum of: a) 153 and -302 b) -2035 and 1206 c) 28 and -42
- Write a pair of integers whose sum gives: a) zero b) a negative integer c) an integer smaller than both the integers c) an intger greater than both the integers d) an integer smaller than only one of the integers

#### Application:

- At Shimla temperature was – 5° C on Monday and then it dropped by 2° C on Tuesday. What was the temperature of Shimla on Tuesday?
- Predecessor of successor of -21 is_____
- Predecessor of successor of -49 is____
- A gardener plans to plant 630 trees in 21 rows each containing the same number of tree, then how many tree will be there in each row?
- The difference of sum of even numbers and sum of odd numbers between 10 and 20 is _____
- A tanker contains 500 litre of water. Due to a small hole in the tanker, the quantity of water is decreasing at a rate of 9 litres per hour. What will be the quantity of water in litres in the tank after 10 hours.

**MCQ Integers:**

- If the expression [ ( -430 × 109] can also be written as [ a + (-387)], what is the value of ‘a’? a) -4687 b) -4300 c) -3586 d) -3200
- (? -2) × ( 3+5) =24

#### Analysis:

- A person gains Rs 2 on product X and losses Rs 3 on product Y. If he sells 8 items of X and 5 items of Y his profit or loss is a) Profit Rs 1 b) Loss Rs 1 c) -2 d) none of these
- An insect crawls up 5 cm every second on a 60 cm vertical rod and then falls down 2 cm over the next second. How many seconds will it take to climb the rod?
- In a class test containing 20 questions 4 marks are given for every correct answer and (-2) marks are given for every incorrect answer. Ranjita attempts all questions and 12 of her answers are correct. What is her total score?
- A certain freezing process requires that room temperature be lowered from 40° C at the rate of 5 º C per hour. What wil be the room temperature 12 hours after the process begins?
- An elevator descends into a mine shaft at the rate of 6 m/ min. If the descent starts from 20 m above the ground level, how long will it take to reach -370 m?
- A multistory building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement each of height 5 m. A lift in building moves at a rate of 1 m/s. If a man starts from 50 m above the ground, how long will it take him to reach at 2nd floor of basement?

#### Evaluation:

- ramu evaluated an expression -7- (-3). What dod Ramu do wrong?
- Taking today as zero on the number line if the day before yesterday is 17 Jan, what is the date 3 days after tomorrow?
- If ◊ is an operation such that for integers a and b we have: a◊ b = a× b -2 × a × b + b× b(-a) × b + b × b then find i) 4◊ (-3) ii) (-7) ◊ (-1) Also show that i) 4 ◊ (-3) ≠ (-3) ◊ 4 and ii) (-7 ) ◊ (-1) ≠ (-1) ◊ (-7)
- Below u , v, w and x represent different integers where u= -4 and x≠ 1. By using following equation find the value of each: i) u × v= u ii) x × w = w iii) u + x = w Give reasons for your answers.