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Answer Key — Teacher Copy
Mathematics

Advanced Order of Operations Challenge

Order of Operations (BADMAS)
Date: May 31, 2026  •  40 questions  •  Total: 120 points
StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1. Word Problem (3 pts)
Simplify the expression: (8 + 2) * (3^2 - 4) + 7. Show your working.
✎ Worked Solution
Step 1: Calculate inside the brackets: (8 + 2) = 10 and (3^2 - 4) = 9 - 4 = 5
Step 2: Multiply: 10 * 5 = 50
Step 3: Add 7: 50 + 7 = 57
2. Word Problem (3 pts)
Solve the expression: [(15 - 5) / 2] * (2^3 + 9) - 8. Show your working.
✎ Worked Solution
Step 1: Compute (15 - 5) = 10, then 10 / 2 = 5
Step 2: Calculate 2^3 = 8, then 8 + 9 = 17
Step 3: Multiply: 5 * 17 = 85
Step 4: Subtract 8: 85 - 8 = 77
3. Word Problem (3 pts)
Evaluate the expression: 2 * (7 + 3^2) - (14 / 2) + 6. Show your working.
✎ Worked Solution
Step 1: Compute 3^2 = 9, then 7 + 9 = 16
Step 2: Multiply by 2: 2 * 16 = 32
Step 3: Compute 14 / 2 = 7
Step 4: Perform subtraction and addition: 32 - 7 + 6 = 31
4. Word Problem (3 pts)
Find the result of: [(20 / 4)^2 - 5] * (3 + 2). Show your working.
✎ Worked Solution
Step 1: Compute 20 / 4 = 5, then square it: 5^2 = 25
Step 2: Subtract 5: 25 - 5 = 20
Step 3: Compute (3 + 2) = 5
Step 4: Multiply: 20 * 5 = 100
5. Word Problem (3 pts)
Compute: 6 + (12 - 3^2) * (8 / 4). Show your working.
✎ Worked Solution
Step 1: Calculate 3^2 = 9
Step 2: Compute inside the brackets: 12 - 9 = 3
Step 3: Compute 8 / 4 = 2
Step 4: Multiply: 3 * 2 = 6
Step 5: Add 6: 6 + 6 = 12
6. Word Problem (3 pts)
Simplify the expression: [(9 + 6) - 2^2] * (6 + 4) + 15. Show your working.
✎ Worked Solution
Step 1: Compute inside the first bracket: (9 + 6) = 15, and 2^2 = 4
Step 2: Subtract: 15 - 4 = 11
Step 3: Compute (6 + 4) = 10
Step 4: Multiply: 11 * 10 = 110
Step 5: Add 15: 110 + 15 = 125
7. Word Problem (3 pts)
Evaluate: (5^2 - 3 * 4) + [(24 / 3) * (2 + 3)]. Show your working.
✎ Worked Solution
Step 1: Compute 5^2 = 25 and 3 * 4 = 12, then subtract: 25 - 12 = 13
Step 2: Compute 24 / 3 = 8 and (2 + 3) = 5
Step 3: Multiply: 8 * 5 = 40
Step 4: Add the two results: 13 + 40 = 53
8. Word Problem (3 pts)
Simplify the expression: (18 - (3^2 + 2)) / 2 + 7 * (4 - 1). Show your working.
✎ Worked Solution
Step 1: Compute inside the parentheses: 3^2 = 9, then 9 + 2 = 11, and 18 - 11 = 7
Step 2: Divide: 7 / 2 = 3.5
Step 3: Compute (4 - 1) = 3 and then 7 * 3 = 21
Step 4: Add: 3.5 + 21 = 24.5
9. Word Problem (3 pts)
Solve the expression: 3 * (2^3) + (14 - 6) / 2 - 5. Show your working.
✎ Worked Solution
Step 1: Compute 2^3 = 8, then 3 * 8 = 24
Step 2: Compute (14 - 6) = 8 and then 8 / 2 = 4
Step 3: Add and subtract: 24 + 4 - 5 = 23
10. Word Problem (3 pts)
Find the result of the expression: (16 / 4) * (3^2 + 1) - (7 + 3). Show your working.
✎ Worked Solution
Step 1: Compute 16 / 4 = 4 and 3^2 + 1 = 9 + 1 = 10
Step 2: Multiply: 4 * 10 = 40
Step 3: Compute (7 + 3) = 10
Step 4: Subtract: 40 - 10 = 30
11. Word Problem (3 pts)
Simplify: (10 + 5) * (2^3 - 3) / (8 / 2). Show your working.
✎ Worked Solution
Step 1: Compute (10 + 5) = 15 and 2^3 = 8, then 8 - 3 = 5
Step 2: Multiply: 15 * 5 = 75
Step 3: Compute (8 / 2) = 4
Step 4: Divide: 75 / 4 = 18.75
12. Word Problem (3 pts)
Compute the expression: 4 * (6 + 2^2) - (3 + 7) + 10 / 2. Show your working.
✎ Worked Solution
Step 1: Calculate 2^2 = 4, then (6 + 4) = 10
Step 2: Multiply: 4 * 10 = 40
Step 3: Compute (3 + 7) = 10 and 10 / 2 = 5
Step 4: Combine: 40 - 10 + 5 = 35
13. Word Problem (3 pts)
Evaluate: (14 + 2^3) - (9 / 3) * (5 - 2). Show your working.
✎ Worked Solution
Step 1: Compute 2^3 = 8, so (14 + 8) = 22
Step 2: Compute (9 / 3) = 3 and (5 - 2) = 3
Step 3: Multiply: 3 * 3 = 9
Step 4: Subtract: 22 - 9 = 13
14. Word Problem (3 pts)
Simplify: [(18 / 3) + (4^2 - 6)] * 2 - 5. Show your working.
✎ Worked Solution
Step 1: Compute 18 / 3 = 6 and 4^2 = 16, then 16 - 6 = 10
Step 2: Add: 6 + 10 = 16
Step 3: Multiply: 16 * 2 = 32
Step 4: Subtract: 32 - 5 = 27
15. Word Problem (3 pts)
Solve the expression: 7 + 3 * (5^2 - 8) / 2. Show your working.
✎ Worked Solution
Step 1: Compute 5^2 = 25, then subtract 8 to get 17
Step 2: Multiply by 3: 3 * 17 = 51
Step 3: Divide: 51 / 2 = 25.5
Step 4: Add 7: 25.5 + 7 = 32.5
16. Word Problem (3 pts)
Find the result of: [(12 - 4) * (3^2 + 1)] / (10 / 2) + 8. Show your working.
✎ Worked Solution
Step 1: Compute (12 - 4) = 8 and (3^2 + 1) = 9 + 1 = 10
Step 2: Multiply: 8 * 10 = 80
Step 3: Compute (10 / 2) = 5 and divide: 80 / 5 = 16
Step 4: Add 8: 16 + 8 = 24
17. Word Problem (3 pts)
Simplify: (9 * 2^2 - 5) + ((16 / 2) + 3). Show your working.
✎ Worked Solution
Step 1: Compute 2^2 = 4, then 9 * 4 = 36, and subtract 5: 36 - 5 = 31
Step 2: Compute 16 / 2 = 8, then add 3: 8 + 3 = 11
Step 3: Add the two results: 31 + 11 = 42
18. Word Problem (3 pts)
Evaluate: [4 * (9 - 3) + 2^3] - (12 / 4 + 5). Show your working.
✎ Worked Solution
Step 1: Compute (9 - 3) = 6, then 4 * 6 = 24
Step 2: Compute 2^3 = 8, add: 24 + 8 = 32
Step 3: Compute 12 / 4 = 3, then (3 + 5) = 8
Step 4: Subtract: 32 - 8 = 24
19. Word Problem (3 pts)
Solve: (20 - 3^2) * (8 / 2) + 7. Show your working.
✎ Worked Solution
Step 1: Compute 3^2 = 9, then 20 - 9 = 11
Step 2: Compute 8 / 2 = 4
Step 3: Multiply: 11 * 4 = 44
Step 4: Add 7: 44 + 7 = 51
20. Word Problem (3 pts)
Simplify the expression: (15 + 10 / 2) * (2^3 - 4) - 6. Show your working.
✎ Worked Solution
Step 1: Compute 10 / 2 = 5, then 15 + 5 = 20
Step 2: Compute 2^3 = 8, then 8 - 4 = 4
Step 3: Multiply: 20 * 4 = 80
Step 4: Subtract 6: 80 - 6 = 74
21. Fill in the Blank (3 pts)
Fill in the blank: After applying BADMAS, the result of (6 + 4) * (3^2 - 1) is _____ .
✓ Answer
80
22. Fill in the Blank (3 pts)
Fill in the blank: Simplify 20 - (5^2 - 10) * 1 to find the result _____ .
✓ Answer
5
23. Fill in the Blank (3 pts)
Fill in the blank: Evaluating 2 * (5 + 2^3) - 6 gives the final result _____ .
✓ Answer
20
24. Fill in the Blank (3 pts)
Fill in the blank: Simplify [(18 / 3) + (4^2 - 9)] * 2 to obtain _____ .
✓ Answer
26
25. Fill in the Blank (3 pts)
Fill in the blank: The expression 3 * (10 - 2^2) + 4 simplifies to _____ .
✓ Answer
22
26. Fill in the Blank (3 pts)
Fill in the blank: When simplifying (14 + 6) / 2 + 2^3, the final answer is _____ .
✓ Answer
18
27. Fill in the Blank (3 pts)
Fill in the blank: Compute the result of (9 + 3) * (2^2) - 5, which equals _____ .
✓ Answer
43
28. Fill in the Blank (3 pts)
Fill in the blank: Simplifying [8 * (7 - 3^2 / 2) + 5] gives the result _____ .
✓ Answer
25
29. Fill in the Blank (3 pts)
Fill in the blank: The result of (12 * 2 + 3^2) - 10 is _____ .
✓ Answer
23
30. Fill in the Blank (3 pts)
Fill in the blank: Evaluating 4 * (8 - 2) + 2^3 results in _____ .
✓ Answer
32
31. Fill in the Blank (3 pts)
Fill in the blank: The value of [(5 + 7) * (3^2 - 4)] / 2 is _____ .
✓ Answer
30
32. Fill in the Blank (3 pts)
Fill in the blank: Simplify 9 + (16 / 4) * (2^2 - 1) to obtain _____ .
✓ Answer
21
33. Fill in the Blank (3 pts)
Fill in the blank: After using BADMAS, (10 + 2^3) - (18 / 3) evaluates to _____ .
✓ Answer
12
34. Fill in the Blank (3 pts)
Fill in the blank: The expression (15 - 7) * (2^3) + 4 simplifies to _____ .
✓ Answer
68
35. Fill in the Blank (3 pts)
Fill in the blank: Simplify (25 / 5) + (3 * (4^2) - 10) to obtain _____ .
✓ Answer
43
36. Fill in the Blank (3 pts)
Fill in the blank: Applying BADMAS to 2 * (9 + 4) - 3^2 results in _____ .
✓ Answer
17
37. Fill in the Blank (3 pts)
Fill in the blank: The final result of (30 - 2^3) / 2 + 7 is _____ .
✓ Answer
18
38. Fill in the Blank (3 pts)
Fill in the blank: Evaluate (8 + 12) - (2^3) + (16 / 4) to get _____ .
✓ Answer
16
39. Fill in the Blank (3 pts)
Fill in the blank: Simplify 5 * (6 + 2^2) - (14 - 4) to obtain _____ .
✓ Answer
40
40. Fill in the Blank (3 pts)
Fill in the blank: The expression [(18 / 2) + (7 - 3)] * 2 results in _____ .
✓ Answer
26