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Mathematics

Integers Mastery: Number Line, Opposites, and Operations (Grade 6)

Integers: order, number line, opposites, absolute value, addition and subtraction
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False Zero is its own additive inverse.
1 pt
True
False
Answer: True
2.
True / False The opposite of a negative integer is a positive integer.
1 pt
True
False
Answer: True
3.
True / False The absolute value of −9 is greater than the absolute value of 7.
1 pt
True
False
Answer: True
4.
True / False Moving left on the number line increases the value of an integer.
1 pt
True
False
Answer: False
5.
True / False The sum of two integers with the same sign has the same sign as the addends.
1 pt
True
False
Answer: True
6.
True / False The difference of any integer and zero is the integer itself.
1 pt
True
False
Answer: True
7.
True / False Subtraction of integers is commutative.
1 pt
True
False
Answer: False
8.
True / False There are exactly four integers strictly between −2 and 3.
1 pt
True
False
Answer: True
9.
True / False The absolute value of any integer is never negative.
1 pt
True
False
Answer: True
10.
True / False Adding −5 to an integer always makes it larger.
1 pt
True
False
Answer: False
11.
Multiple Choice Which integer is 6 units to the left of 3 on the number line?
2 pts
A. 9
B. −3
C. 0
D. 6
Answer: B. −3
12.
Multiple Choice What is the successor of −7?
2 pts
A. −8
B. −6
C. 6
D. 8
Answer: B. −6
13.
Multiple Choice Which comparison is correct?
2 pts
A. −12 > −9
B. −9 > −7
C. −5 < −2
D. 0 < −1
Answer: C. −5 < −2
14.
Multiple Choice Which integer has the least value?
2 pts
A. −4
B. −15
C. 0
D. 7
Answer: B. −15
15.
Multiple Choice If you start at −2 and move 9 steps to the right, where do you land?
2 pts
A. −11
B. 11
C. 7
D. −7
Answer: C. 7
16.
Multiple Choice Which pair of integers are additive inverses?
2 pts
A. −8 and 8
B. 5 and 5
C. 0 and 1
D. −3 and −3
Answer: A. −8 and 8
17.
Multiple Choice Which expression is equal to −14?
2 pts
A. (−9) + (−5)
B. (−10) + 3
C. 20 − 7
D. (−6) − 5
Answer: A. (−9) + (−5)
18.
Multiple Choice The absolute value of −11 is
2 pts
A. −11
B. 11
C. −1
D. 0
Answer: B. 11
19.
Multiple Choice Which situation represents a negative integer?
2 pts
A. A balloon rises 12 meters
B. A bank balance increases by 150 rupees
C. A hiker descends 40 meters
D. A temperature rises by 3°C
Answer: C. A hiker descends 40 meters
20.
Multiple Choice How many integers are there from −2 to 4 inclusive?
2 pts
A. 5
B. 6
C. 7
D. 8
Answer: C. 7
21.
Fill in the Blank The opposite of −13 is _____ .
2 pts
Answer: 13
22.
Fill in the Blank The integer 0 has an absolute value of _____ .
2 pts
Answer: 0
23.
Fill in the Blank Moving 7 units to the left from 5 lands on _____ .
2 pts
Answer: -2
24.
Fill in the Blank The sum of −4 and 9 is _____ .
2 pts
Answer: 5
25.
Fill in the Blank The additive inverse of 26 is _____ .
2 pts
Answer: -26
26.
Fill in the Blank The integer that is 3 more than −12 is _____ .
2 pts
Answer: -9
27.
Fill in the Blank The result of 18 − (−5) is _____ .
2 pts
Answer: 23
28.
Fill in the Blank The distance between −8 and 3 on the number line is _____ units.
2 pts
Answer: 11
29.
Fill in the Blank The predecessor of 0 is _____ .
2 pts
Answer: -1
30.
Fill in the Blank The value of (−7) + (−6) + 4 is _____ .
2 pts
Answer: -9
31.
Word Problem A city's temperature at 6 PM is −3°C. By midnight, it drops by 5°C. What is the temperature at midnight? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Compute change: −3 − 5 = −8
Step 2: Interpret result as the midnight temperature
Answer: −8°C
32.
Word Problem A bank account has a balance of ₹120. Then ₹150 is withdrawn, and later ₹40 is deposited. What is the final balance? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Net change = −150 + 40 = −110
Step 2: Final balance = 120 + (−110) = 10
Answer: ₹10
33.
Word Problem An elevator is on floor 2 (ground is 0). It goes down 5 floors and then up 3 floors. Which floor is it on now? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Position after moves = 2 − 5 + 3
Step 2: Calculate: 2 − 5 = −3; −3 + 3 = 0
Answer: Floor 0
34.
Word Problem A submarine is at a depth of −150 m. It dives 85 m more and then rises 120 m. What is its final depth? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Depth change = −85 + 120 = 35
Step 2: Final depth = −150 + 35 = −115
Answer: −115 m
35.
Word Problem In a game, a team earns 6 points, then loses 10 points, then earns 8 points. What is the net score change? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Net change = 6 − 10 + 8
Step 2: Calculate: 6 − 10 = −4; −4 + 8 = 4
Answer: +4 points
36.
Word Problem A hiker starts at sea level (0 m), climbs 35 m, descends 60 m, and then climbs 20 m. What is the final elevation relative to sea level? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Net elevation = 35 − 60 + 20
Step 2: Compute: 35 − 60 = −25; −25 + 20 = −5
Answer: −5 m
37.
Word Problem On a number line, you start at −9, move 12 units right, then 7 units left. Where do you end up? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Final position = −9 + 12 − 7
Step 2: Calculate: −9 + 12 = 3; 3 − 7 = −4
Answer: −4
38.
Word Problem A stock changes by +3, −5, −4, and +6 points in one day. What is the overall change by the end of the day? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Net change = 3 − 5 − 4 + 6
Step 2: Compute: 3 − 5 = −2; −2 − 4 = −6; −6 + 6 = 0
Answer: 0 points
39.
Word Problem A mountain peak is at an elevation of +2,345 m, and a nearby valley is at −1,280 m. What is the difference in elevation between them? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Difference = 2,345 − (−1,280)
Step 2: Compute: 2,345 + 1,280 = 3,625
Answer: 3,625 m
40.
Word Problem City X is 4°C in the afternoon and falls by 11°C by dawn. City Y is −2°C at 10 PM and falls by 6°C by dawn. Which city is colder at dawn, and by how many degrees? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: City X dawn temp = 4 − 11 = −7°C; City Y dawn temp = −2 − 6 = −8°C
Step 2: Compare: −8°C is 1°C lower than −7°C
Answer: City Y is colder by 1°C
40
Total Questions
100
Total Points
~35
Minutes