# Free Integers Subjective Test 01 Practice Test - 7th grade

### Question 1

Define Integers. [1 MARK]

#### SOLUTION

Solution :Definition: 1 Mark

Integers are the set of whole numbers and their negatives. Integers greater than zero are called positive integers while integers less than zero are called negative integers.

### Question 2

Define additive identity and additive inverse. Give an example.

[2 MARKS]

#### SOLUTION

Solution :Definition: 1 Mark

Example: 1 Mark

When we add zero to any whole number, we will get the same whole number as result. Hence, zero is known as additive identity.

For example, 5 + 0 = 0, here 0 is the additive identity

The additive inverse of a number is the number that when added, yields zero. To find the additive inverse of a number, we multiply the given number by -1.

For example, if we want to find the additive inverse of the number 5 we multiply it by -1.

5×(−1)=(−5)

So, -5 is the additive inverse of the number 5.

### Question 3

In how many ways can -12 be written as a product of two integers? [2 MARKS]

#### SOLUTION

Solution :Writing the factors: 1 Mark

Answer: 1 Mark

Here, -12 can be written as (−1×12), (−2×6), (−3×4), (−4×3), (−6×2) and (−12×1).

So, -12 can be written in 6 ways as a product of two integers.

### Question 4

Andy has Rs.1540 in his pocket and he spent Rs.250 on his hair cutting and Rs.115 on his face wash. Find the amount left with him. [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Result: 1 Mark

Given: Total Amount Andy had = Rs. 1540

Total amount spend by him

= Rs. 250 + Rs. 115 = Rs. 365

Total amount left = (Total Amount Andy had) - (Total amount spend by him)

⇒Total amount left = Rs. 1540 - Rs. 365

= Rs. 1175

Hence, the total amount left with Andy is Rs.1175.

### Question 5

The marks obtained by a student in a subject in three different tests were 20, 12, (-4). What are the total marks obtained by the student in that subject? What is the minimum number of marks he needs to score in the 4th test if the passing marks are 40?

[2 MARKS]

#### SOLUTION

Solution :Total Marks: 1 Mark

Minimum Marks:1 Mark

The marks obtained by the student are

= 20, 12, (-4)

The total overall marks = 20 + 12 + (-4)

= 20 + 12 - 4

= 32 - 4

= 28

Given that

A student needs to score 40 in order to pass.

So, the number of marks the student needs to get on the 4th test to pass = 40 - 28 = 12

The student needs to score 12 marks in the 4th test to pass.

### Question 6

Arrange the following marks obtained by students in ascending order and represent them on the number line 12, 4, 6, (-1), (-3 ). What is the difference between the student who scored the highest mark and the one who scored the lowest? [3 MARKS]

#### SOLUTION

Solution :Ascending order : 1 Mark

Number Line : 1 Mark

Difference: 1 Mark

Marks obtained by the students = 12, 4, 6 , (-1), (-3 )Marks arranged in ascending order = (-3) , (-1), 4, 6, 12

So, the difference between the highest scorer and the lowest scorer=12-(-3)=12+3=15.

Hence, the difference between the highest scorer and the lowest scorer is 15.

### Question 7

After walking 20km towards North Ram starts walking towards South and walks 45km. How far is Ram now from the starting point? What is the total distance travelled by Ram? [3 MARKS]

#### SOLUTION

Solution :

Distance and direction: 2 Marks

Total Distance: 1 Mark

Distance travelled by Ram in the north direction = 20km

Distance travelled in the south direction = 45km

Ram's distance from the initial point = (45 - 20 ) = 25km

Ram is 25km in the south direction from his starting point.

The total distance travelled by Ram = 20 + 45 = 65km

### Question 8

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? [3 MARKS]

#### SOLUTION

Solution :Application: 1 Mark

Steps: 1 Mark

Result: 1 Mark

(i) Marks given for one correct answer = 4

So, marks given for 9 correct answers

= 4 × 9 = 36

Marks given for one incorrect answer = – 2

So, marks for 6 (15 – 9) incorrect answers

= (–2) × 6 = –12

Therefore, Gurpreet’s total score

= 36 + ( –12) = 24

(ii) Marks given for one correct answer = 4

So, marks given for 5 correct answers

= 4 × 5 = 20

Marks given for one incorrect answer

= (–2)

So, marks for 10 (15 – 5) incorrect answers = (–2) × 10 = –20

Therefore, her friend’s total score

= 20 + ( –20) = 0

### Question 9

A rock climber climbs a hill of height 200m at the rate of 3 m/s. If he starts climbing from 20m above the ground, then find the following :

(i) What is the total distance he needs to trek to climb to the top of the hill?

(ii) What is the time taken by him to reach the hilltop?

(iii) If he covered half of the distance at 3 m/s and remaining distance at 2 m/s, find the total time taken by him to climb the hill. [3 MARKS]

#### SOLUTION

Solution :Each question: 1 Mark

Rate at which climber climbs the hill = 3 m/s

Total distance to be climbed by the climber = 200m - 20m = 180m

The time required by the climber to reach the top of the hill is

=1803

= 60 seconds

Hence, the climber will climb the hill in 60 seconds.

It is given that he covered half of the distance at 3 m/s and the remaining half at 2 m/s.

Total distance to be covered = 180m

Distance covered with speed 3 m/s = 1802

= 90m

Distance covered with speed 2 m/s

= 180-90 = 90m

Time taken to cover the first 90m = 903

= 30 seconds

Time taken to cover the last 90m = 902

= 45 seconds

The total time taken to climb to the top of the hill = 30 + 45 = 75 seconds

### Question 10

A bird is flying at a height of 1200 m from the ground. A hunter shot the bird standing on a hill of height 600m. If the height from which he fired is 1 meter above the hill, find the distance travelled by the bullet to reach the bird? He missed in the first attempt and fired again but by then the bird was 1300 m from the ground. Find the distance travelled by the bullet in the second attempt.

[4 MARKS]

#### SOLUTION

Solution :First attempt: 2 Marks

Second Attempt: 2 Marks

Distance of the bird from the ground surface in the first attempt = 1200mDistance of the hunter from the ground surface = 600m

Distance of the bird from the hunter

= 1200m - 600m = 600mBut, when the hunter stands, the height of the gun from ground = 600 + 1 = 601m

So, distance traveled by bullet in the first attempt= 1200 - 601= 599m

Distance of the bird from the ground surface in the second attempt = 1300m

Distance traveled by the bullet in the second attempt= 1300 - 601 = 699m

### Question 11

Which rule is used to prove {10 × (5 + 2)} = {(10 × 5) + (10 × 2)} ? Using the same rule find the value of 99×101. [4 MARKS]

#### SOLUTION

Solution :Rule: 1 Mark

Value: 3 Mark

LHS = {10 × (5 + 2)}

= 10 × (7)

= 70

RHS = {(10 × 5 ) + (10 × 2 )}

= {50 + 20}

= 70

Hence , LHS = RHS

This rule is known as Distributivity of multiplication over addition.

We have to find out the value of

99×101 = 99×(100+1) = 9900 + 99 = 9999

### Question 12

In a test, +2 marks are given for each correct answer and ( - 1 ) for each wrong answer. A student scored 21 and answered 12 questions correctly. How many questions did he answer incorrect? How many questions did he attempt in total? [4 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

Result: 1 Mark

It is given that, in a test

Marks given for each correct answer = +2Marks given for each wrong answer = ( -1 )

Marks obtained by 12 correct questions = 12 × 2 = 24

Marks obtained by student = 21

So, total negative marks = 24 - 21 = 3

So,the total number of incorrect questions = 3÷1 = 3

Total number of questions he attempted= Number of correct questions + number of incorrect question

= 12 + 3 = 15

So, the total number of questions the student attempted is 15.

### Question 13

Find the product, using suitable properties:

(a) 625 × (− 35) + (− 625) × 65

(b) (− 17) × (− 29)

[4 MARKS]

#### SOLUTION

Solution :

Each option: 2 Marks

a) 625 × (−35) + (−625) × 65

= 625 × [(−35) + (−65)]

(∵ (a × b) + (a × c) = a × (b + c))

= 625 × (−100) = −62500

b) (−17) × (−29)

= (−17) × [−30 + 1]

= [(−17) × (−30)] + [(−17) × 1]

(∵ a × (b + c) = (a × b) + (a × c)

= (510) + (−17) = 493

### Question 14

In a quiz, team A scored - 40, 10, 0 and team B scored 20, 0, - 40 in three successive rounds, team C scored 30,30,20 and team D scored 80, -20, 10.

(i) Which team scored the highest?

(ii) Which team scored the lowest?

(ii) What is the difference between the teams which scored the highest and the team which scored lowest?

(iii) Can we say that we can add integers in any order?

[4 MARKS]

#### SOLUTION

Solution :Each question - 1 Mark

Team A - 40, 10, 0.

Total score = - 40 + 10 + 0 = - 30

Team B - 20, 0,- 40.

Total score = 20 + 0 +(- 40) = - 20

Team C - 30, 30, 20

Total score = 30 + 30 + 20 = 80

Team D - 80, -20, 10

Total score = 80 - 20 + 10 = 90

(i) So, team D scored the highest = 90

(ii) Team A scored the lowest =-30

(iii) The difference between the highest scorer and the lowest scorer

= 90 - (-30) = 90 + 30 = 120

(iv)Yes, we can add integers in any order. We had observed that the scores obtained by both teams in successive rounds were numerically equal but different in order. Yet, the total score of both teams was equal. It is the associative property of addition of integers.

### Question 15

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 a question. Rakesh scores 18 marks by attempting 16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly? [4 MARKS]

#### SOLUTION

Solution :Writing the equation: 1 Mark

Steps: 2 Marks

Result: 1 Mark

Marks obtained for 1 right answer = +3

Marks obtained for 1 wrong answer = −2

Total marks scored by Rakesh = 18

Number of questions attempted = 16

(No. of correct ans)(3) + (No. of incorrect ans)(-2)

= 18

⇒ (No. of correct ans)(3) + (16 - No. of correct ans)(-2)

= 18

⇒ (No. of correct ans)(3) + -32 + 2(No. of correct ans)

= 18

⇒ (No. of correct ans)(5) + -32 = 18

⇒ (No. of correct ans)(5) = 18 + 32 = 50

⇒ No. of correct ans = 10

∴ No. of incorrect ans = 16 - 10 = 6

∴ Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively.