Free Integers Subjective Test 01 Practice Test - 6th grade 

Question 1

Define Integers? [1 MARK]

SOLUTION

Solution : Definition: 1 Mark

Integers are a collection of natural numbers, zero and negative of natural numbers. 
e.g. ....-3,-2,-1,0,1,2,3.........

Question 2

The temperature of a body first rises by 25∘C and then falls by  32∘C. Find the final temperature of the body, if its initial temperature is : [2 MARKS]
(i) 0∘C
(ii) −20∘C

SOLUTION

Solution : Each option: 1 Mark

(i) Final temperature
⇒0∘C+(+25∘C)+(−32∘C)
⇒0∘C+25∘C−32∘C
⇒−7∘C

(ii) Final temperature
⇒−20∘C+(+25∘C)+(−32∘C)
⇒−20∘C+25∘C−32∘C
⇒−27∘C

Question 3

What is additive inverse of a number? What is the additive inverse of  7 and −5?

SOLUTION

Solution : Definition: 1 Mark
Inverse of 7 and -5: 1 Mark

The additive inverse of a number is what you add to the number to get zero. i.e. additive inverse of 5 is −5 as 5+(−5)=0
Additive inverse of 7 is −7 and  additive inverse of −5 is 5.

Question 4

If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, represent the following using integers with the appropriate signs. [3 MARKS]

a. 200m above sea level

b. Sea level

c.100m below sea level

SOLUTION

Solution :

Each option:1 Mark

a. +200m

b. 0

c. -100m

Question 5

Write the opposite of the each of the following statements? [3 MARKS]

(i) Earning of  Rs 1000

(ii) Gaining a weight of 5 kg

(iii) A deposit of Rs 500 in the bank

SOLUTION

Solution :

Each option: 1Mark

(i) Loss of Rs 1000

(ii) Losing a weight of 5 kg

(iii) Withdrawal of Rs 500

Question 6

Using the number line find the integer in the following cases : [3 MARKS]

(a) Sum of 5 and -3

(b) 5 less than 3

(c) 4 more than -1

SOLUTION

Solution :

Each option: 1 Mark

(a) We first move to the right of 0 by 5 steps reaching 5. Then we move 3 steps to the left of 5 reaching 2.
 
 We get, (+5)+(−3)=2

(b) We want to know an integer which is 5 less than 3 for that we need to start from 3 and move to the left by 5 steps and obtain –2 as shown below:
 

(c) We want to know the integer which is 4 more than –1. So, we start from –1 and proceed 4 steps to the right of –1 to reach 3 as shown below:
   

Question 7

Represent the following in the form of Integers:  [4 MARKS]

(a). 10 below zero

(b). 5 cm above ground level

(c). Earning Rs 500  from some source

(d) A loss of Rs 200 in the shop

 

SOLUTION

Solution :

Each option: 1 Mark

(a). −10

(b). +5

(c). +500

(d). −200

Question 8

(a) The sum of two integers is 94. If one of them is -25, find the other?

(b) The sum of two integers is -320. If one of them is +80, find the other?

(c) The sum of two integers is 100. If one of them is -50, find the other?

(d) The sum of two integers is -660. If one of them is -70, find the other?  [4 MARKS]

SOLUTION

Solution :

Each option: 1 Mark

(a). Let the integer be x⇒−25+x=94⇒x=94+25⇒x=119

(b). Let the integer be x⇒80+x=−320⇒x=−320−80⇒x=−400

(c). Let the integer be x⇒−50+x=100⇒x=100+50⇒x=150

(d). Let the integer be x⇒−70+x=−660⇒x=−660+70⇒x=−590

Question 9

Compute each of the following: [4 MARKS]

 (a) 15+(−5)+15+(−7)

 (b) 34+(−20)+16+(−10)

(c) 32+16+9+(−70)

 (d) −3+(−2)+(−5)+7

SOLUTION

Solution :

Each option: 1 Mark

(a). [15+(−5)]+[15+(−7)]
 ⇒10+8
 ⇒18
 

(b). [34+(−20)]+[16+(−10)]
 ⇒14+6
 ⇒20
 

(c). [32+16]+[9+(−70)]
 ⇒[48+(−61)]
 ⇒48−61
 ⇒−13
 

(d). [−3+(−2)]+[(−5)+7]
 ⇒−5+2
 ⇒−3

Question 10

Evaluate: [4 MARKS]

(a). (−3)×(−3)×(−3)

(b). (32)×(−3)×(2)×(−10)

(c). (−8)×(0)×(−4)×(18)

(d). (−2)×(−3)×(−4)×(−5)

SOLUTION

Solution : Each option: 1 Mark

(a). (−3)×(−3)×(−3)
⇒9×(−3)
 ⇒−27


(b). (32)×(−3)×(2)×(−10)
 ⇒(−96)×2×(−10)
⇒(−192)×(−10)
⇒1920


(c). (−8)×(0)×(−4)×(18)=0


(d). (−2)×(−3)×(−4)×(−5)
⇒6×20
 ⇒120
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