StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1.
Word Problem
(3 pts)
A bank account is overdrawn by $85. It receives deposits of $140 and $35 on two successive days, then a withdrawal of $96 and a monthly fee of $12. What is the final balance?
✎ Worked Solution
Step 1: Start at −85.
Step 2: Add 140 and 35: −85 + 140 + 35 = 90.
Step 3: Subtract 96 and 12: 90 − 96 − 12 = −18.
Answer: −$18
2.
Word Problem
(3 pts)
A city’s temperature is −7°C at dawn. It warms by 9°C, cools by 4°C, drops another 5°C, and then rises by 6°C. What is the final temperature?
✎ Worked Solution
Step 1: −7 + 9 = 2.
Step 2: 2 − 4 = −2.
Step 3: −2 − 5 = −7.
Step 4: −7 + 6 = −1.
Answer: −1°C
3.
Word Problem
(3 pts)
An elevator starts at level B3 (count this as −3). It rises 7 floors, then descends 11 floors, then rises 5 floors. Which floor does it stop on?
✎ Worked Solution
Step 1: −3 + 7 = 4.
Step 2: 4 − 11 = −7.
Step 3: −7 + 5 = −2.
Answer: Level −2 (B2)
4.
Word Problem
(3 pts)
A submarine is at a depth of 120 m below sea level. It dives 65 m, ascends 150 m, then dives 48 m. What is its final depth relative to sea level?
✎ Worked Solution
Step 1: Start at −120.
Step 2: Dive 65: −120 − 65 = −185.
Step 3: Ascend 150: −185 + 150 = −35.
Step 4: Dive 48: −35 − 48 = −83.
Answer: −83 m
5.
Word Problem
(3 pts)
A hiker begins at 1,240 m above sea level, descends 180 m, climbs 360 m, then descends 95 m. What is the hiker’s final altitude?
✎ Worked Solution
Step 1: 1240 − 180 = 1060.
Step 2: 1060 + 360 = 1420.
Step 3: 1420 − 95 = 1325.
Answer: 1,325 m
6.
Word Problem
(3 pts)
Two integers x and y satisfy x + y = −11 and x − y = 7. What is the smaller integer?
✎ Worked Solution
Step 1: Add equations: (x + y) + (x − y) = −11 + 7 → 2x = −4.
Step 2: Solve for x: x = −2.
Step 3: Use x − y = 7 → −2 − y = 7 → y = −9.
Answer: −9
7.
Word Problem
(3 pts)
The sum of three consecutive integers is −30. What is the greatest of the three?
✎ Worked Solution
Step 1: Let the integers be n − 1, n, n + 1 → sum = 3n.
Step 2: 3n = −30 → n = −10.
Step 3: Greatest is n + 1 = −9.
Answer: −9
8.
Word Problem
(3 pts)
A robot on a number line starts at −12. It moves right 15 units, then left 19 units, then right 8 units. Where does it end?
✎ Worked Solution
Step 1: −12 + 15 = 3.
Step 2: 3 − 19 = −16.
Step 3: −16 + 8 = −8.
Answer: −8
9.
Word Problem
(3 pts)
A helicopter is at 1,250 m altitude, and a submarine is at −380 m. The helicopter descends 420 m while the submarine ascends 95 m. After these changes, what is the vertical distance between them?
✎ Worked Solution
Step 1: Helicopter: 1250 − 420 = 830 m.
Step 2: Submarine: −380 + 95 = −285 m.
Step 3: Separation: 830 − (−285) = 1115.
Answer: 1,115 m
10.
Word Problem
(3 pts)
An integer n satisfies |n| + 5 = 2n − 3. Find n.
✎ Worked Solution
Step 1: Consider n ≥ 0: |n| = n → n + 5 = 2n − 3 → n = 8.
Step 2: Consider n < 0: |n| = −n → −n + 5 = 2n − 3 → 3n = 8 (not integer).
Answer: 8
11.
Word Problem
(3 pts)
A team’s score changes by +7, −12, +9, −5, and +4 over five rounds. Starting from 0, what is the final score?
✎ Worked Solution
Step 1: 0 + 7 − 12 = −5.
Step 2: −5 + 9 − 5 = −1.
Step 3: −1 + 4 = 3.
Answer: 3
12.
Word Problem
(3 pts)
A day starts at 6°C. Over four intervals, the temperature changes by −11°C, +4°C, −9°C, and +7°C. What is the final temperature?
✎ Worked Solution
Step 1: 6 − 11 = −5.
Step 2: −5 + 4 = −1.
Step 3: −1 − 9 = −10.
Step 4: −10 + 7 = −3.
Answer: −3°C
13.
Word Problem
(3 pts)
Solve for the integer k: −4 + k − 7 + 3k = 9.
✎ Worked Solution
Step 1: Combine like terms: (k + 3k) + (−4 − 7) = 4k − 11.
Step 2: 4k − 11 = 9 → 4k = 20.
Step 3: k = 20 ÷ 4 = 5.
Answer: 5
14.
Word Problem
(3 pts)
In a parking structure, ground is 0. A car starts at level −2, goes up 5 levels, then down 3, then up 4. Which level is the car on?
✎ Worked Solution
Step 1: −2 + 5 = 3.
Step 2: 3 − 3 = 0.
Step 3: 0 + 4 = 4.
Answer: Level 4
15.
Word Problem
(3 pts)
A walker starts at 0 on a number line and makes moves of +8, −13, +7, −4, and +10. What is the final position?
✎ Worked Solution
Step 1: 0 + 8 − 13 = −5.
Step 2: −5 + 7 − 4 = −2.
Step 3: −2 + 10 = 8.
Answer: 8
16.
Word Problem
(3 pts)
You start at −20 on a number line, add an integer x, then subtract 9, and arrive at −12. Find x.
✎ Worked Solution
Step 1: Equation: −20 + x − 9 = −12.
Step 2: Combine constants: x − 29 = −12.
Step 3: x = −12 + 29 = 17.
Answer: 17
17.
Word Problem
(3 pts)
Path A moves +18, −25, +14 from 0. Path B moves −9, +22, −5 from 0. What is the absolute difference between their final positions?
✎ Worked Solution
Step 1: Path A: 0 + 18 − 25 + 14 = 7.
Step 2: Path B: 0 − 9 + 22 − 5 = 8.
Step 3: Difference: |7 − 8| = 1.
Answer: 1
18.
Word Problem
(3 pts)
An integer is such that its opposite is 6 more than the integer itself. What is the integer?
✎ Worked Solution
Step 1: Let the integer be n; then −n = n + 6.
Step 2: 2n = −6 → n = −3.
Answer: −3
19.
Word Problem
(3 pts)
Starting at −2°C, the temperature changes every hour by −3°C, then +5°C, then −4°C, repeating this three-step cycle twice. What is the final temperature?
✎ Worked Solution
Step 1: One cycle change: −3 + 5 − 4 = −2.
Step 2: Two cycles: −2 × 2 = −4.
Step 3: Start at −2: −2 + (−4) = −6.
Answer: −6°C
20.
Word Problem
(3 pts)
Start with the integer 9. First take its opposite, then add −7, then subtract the opposite of −4. What integer do you get?
✎ Worked Solution
Step 1: Opposite of 9 is −9.
Step 2: Add −7: −9 + (−7) = −16.
Step 3: Opposite of −4 is 4; subtract it: −16 − 4 = −20.
Answer: −20
21.
Fill in the Blank
(3 pts)
If integers x and y satisfy x + y = −17 and x − y = 3, the smaller integer is _____
22.
Fill in the Blank
(3 pts)
Evaluate: 4 − { −3 − [2 − (−5)] } = _____
23.
Fill in the Blank
(3 pts)
If |m − 6| = 11 and m is an integer, the smaller solution is _____
24.
Fill in the Blank
(3 pts)
The distance between −17 and 8 on the number line is _____
25.
Fill in the Blank
(3 pts)
The opposite of the sum (−12) + 7 + (−5) is _____
26.
Fill in the Blank
(3 pts)
Compute: (−6) × [ (−3) + 5 ] − { (−4) × [ 2 − (−1) ] } = _____
27.
Fill in the Blank
(3 pts)
If the sum of three consecutive integers is −21, the middle integer is _____
28.
Fill in the Blank
(3 pts)
Solve for n: −3 + 2n = 11 → n = _____
29.
Fill in the Blank
(3 pts)
Starting at −14, moving 6 units right and then 9 units left lands at _____
30.
Fill in the Blank
(3 pts)
The sum of all integers from −12 to 5 inclusive is _____
31.
Fill in the Blank
(3 pts)
Evaluate: |−18| − |5 − (−9)| = _____
32.
Fill in the Blank
(3 pts)
The integer closest to zero among { −17, 9 − 12, (−3) × 2 } is _____
33.
Fill in the Blank
(3 pts)
If 4 + [−2 − (q)] = −5, then q = _____
34.
Fill in the Blank
(3 pts)
Compute: 50 − (−40) − (−2) − 7 = _____
35.
Fill in the Blank
(3 pts)
If |r| + |r − 4| = 10 and r ≤ 4, then r = _____
36.
Fill in the Blank
(3 pts)
The number of integers strictly between −13 and 6 is _____
37.
Fill in the Blank
(3 pts)
Evaluate: (−2) × (−7) + (−3) × 5 − [−4 × (−2)] = _____
38.
Fill in the Blank
(3 pts)
The smaller integer n satisfying |n + 5| = 14 is _____
39.
Fill in the Blank
(3 pts)
Subtracting the opposite of −27 from −8 gives _____
40.
Fill in the Blank
(3 pts)
Solve for t: t − [−(t − 9)] = −3 → t = _____