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mathematics

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

1. -11,-8,-5,-2, the next number in the series is: a) -1  b) 0  c)1  d) -4
2. What is the value of the expression { (-10) ÷2}× (-4)? a) 20  b) 2  c) -9  d) -12
3. 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
4. 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
5. 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
6. What will be additive inverse of -5 :a) -6  b) -4  c) 3  d) 5
7. What will be additive inverse of 7 : a) – 7  b) -6  c) 1/7  d) -1/7
8. Sum of two negative number is always: a) positive b) negative  c) zero  d) one
9. Which property is reflected in the following 7× 5 = 5× 7  a) closure  b) commutative  c) associative  d) distributive
10. 0÷ 10 gives a) 0  b) 10  c) 1  d)-10
11. 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
12. How is withdrawal of Rs 200 represented : a) 200 b) -200 c) depositing Rs 200
13. 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?
14.  For any two integer number a and b, a + b is an ____ a) None of these  b) Whole number  c) Integer  d) natural number
15. 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

1. 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
2. Which of the following is a false: a) -7 + (-6) = -13  b) -5+1 =4   c) 2+(-1)= 1  d) 8+(-9)= -1
3. Which of the following is true with respect to -28 and -32?  a) -28< -32   b) -28= -32   c) -32 > -28  d) -28 > -32
4. An integer when divided by -3 gives quotient 35 and leaves remainder 2. The integer is : a) 32  b) 31  c) -34  d) -103
5. 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
6. 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
7. what should be added to -5 to get 4: a) 1  b) -1  c)-9  d) 9
1. A place is 45 m above sea level and another place is 25 m below sea level. What is the difference between two places?
2. Find the product of : a) (-4) × (-5) ×(-8) ×(-10)  b) (-6) × (-5) × (-7) × (-2) × (-3)  c) (-7) ×(-9) × 0
3. Find the sum of: a) 153 and -302  b) -2035 and 1206  c) 28 and -42
4. 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:

1. 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?
2. Predecessor of successor of -21 is_____
3. Predecessor of successor of -49 is____
4. 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?
5. The difference of sum of even numbers and sum of odd numbers between 10 and 20 is _____
6. 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:

1. 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. (? -2) × ( 3+5) =24

Analysis:

1. 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
2. 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?
3. 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?
4. 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?
5. 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?
6. 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:

1. ramu evaluated an expression -7- (-3). What dod Ramu do wrong?
2. Taking today as zero on the number line if the day before yesterday is 17 Jan, what is the date 3 days after tomorrow?
3. 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)
4. 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.