Datasets:
| {"instruction": "The temperature in a greenhouse, in degrees Celsius, is modelled by 9*t + 19, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature 109 degrees? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10", "id": "algebra-L1-a46cd3b8f4d8844641b4-word", "source_id": "algebra-a46cd3b8f4d8844641b4", "topic": "algebra", "level": 1, "kind": "solve", "question": "The temperature in a greenhouse, in degrees Celsius, is modelled by 9*t + 19, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature 109 degrees?", "answer": "10", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-a46cd3b8f4d8844641b4", "attack": "word_problem", "target": "algebra", "question_original": "Solve 9*x + 19 = 109 for x.", "variable": "t", "underlying_expression": "9*t + 19 = 109", "answer_in_variable": "10", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A submarine's depth gauge shows -6*n + 20 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of 68? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -8", "id": "algebra-L1-7951ce54fcc19f98319f-word", "source_id": "algebra-7951ce54fcc19f98319f", "topic": "algebra", "level": 1, "kind": "solve", "question": "A submarine's depth gauge shows -6*n + 20 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of 68?", "answer": "-8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-7951ce54fcc19f98319f", "attack": "word_problem", "target": "algebra", "question_original": "Solve -6*x + 20 = 68 for x.", "variable": "n", "underlying_expression": "-6*n + 20 = 68", "answer_in_variable": "-8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The change in a savings account, in dollars, after k standard adjustments is -3*k + 17; a negative k means the adjustments were reversed. Find k if the change equals -1 dollars. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 6", "id": "algebra-L1-de62a3a282eca6f95c7d-word", "source_id": "algebra-de62a3a282eca6f95c7d", "topic": "algebra", "level": 1, "kind": "solve", "question": "The change in a savings account, in dollars, after k standard adjustments is -3*k + 17; a negative k means the adjustments were reversed. Find k if the change equals -1 dollars.", "answer": "6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-de62a3a282eca6f95c7d", "attack": "word_problem", "target": "algebra", "question_original": "Solve -3*x + 17 = -1 for x.", "variable": "k", "underlying_expression": "-3*k + 17 = -1", "answer_in_variable": "6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "On a number line, a robot's stopping point after a command with parameter p is 4*p + 10. For which parameter p does the robot stop at -18? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -7", "id": "algebra-L1-aaba0923f4300c5f1624-word", "source_id": "algebra-aaba0923f4300c5f1624", "topic": "algebra", "level": 1, "kind": "solve", "question": "On a number line, a robot's stopping point after a command with parameter p is 4*p + 10. For which parameter p does the robot stop at -18?", "answer": "-7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-aaba0923f4300c5f1624", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x + 10 = -18 for x.", "variable": "p", "underlying_expression": "4*p + 10 = -18", "answer_in_variable": "-7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A spring scale shows 8*s - 20 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -20 grams. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 0", "id": "algebra-L1-bcbd0c6f1a9cc85a77e3-word", "source_id": "algebra-bcbd0c6f1a9cc85a77e3", "topic": "algebra", "level": 1, "kind": "solve", "question": "A spring scale shows 8*s - 20 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -20 grams.", "answer": "0", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-bcbd0c6f1a9cc85a77e3", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x - 20 = -20 for x.", "variable": "s", "underlying_expression": "8*s - 20 = -20", "answer_in_variable": "0", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The elevation of a hiking marker, in meters relative to a lake surface, is 3*m + 16, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation -17? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -11", "id": "algebra-L1-7b597970eb0d709adb92-word", "source_id": "algebra-7b597970eb0d709adb92", "topic": "algebra", "level": 1, "kind": "solve", "question": "The elevation of a hiking marker, in meters relative to a lake surface, is 3*m + 16, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation -17?", "answer": "-11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-7b597970eb0d709adb92", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x + 16 = -17 for x.", "variable": "m", "underlying_expression": "3*m + 16 = -17", "answer_in_variable": "-11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An oven program sets the temperature to 3*w - 6 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 9 degrees above base? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-d0e496a6ddbeadd57d53-word", "source_id": "algebra-d0e496a6ddbeadd57d53", "topic": "algebra", "level": 1, "kind": "solve", "question": "An oven program sets the temperature to 3*w - 6 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 9 degrees above base?", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-d0e496a6ddbeadd57d53", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x - 6 = 9 for x.", "variable": "w", "underlying_expression": "3*w - 6 = 9", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A stock's price change, in cents, t days after a news release is predicted to be -8*t + 16, where negative t refers to days before the release. On which day t is the predicted change 96 cents? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -10", "id": "algebra-L1-9ce1898a0987a65beb2b-word", "source_id": "algebra-9ce1898a0987a65beb2b", "topic": "algebra", "level": 1, "kind": "solve", "question": "A stock's price change, in cents, t days after a news release is predicted to be -8*t + 16, where negative t refers to days before the release. On which day t is the predicted change 96 cents?", "answer": "-10", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-9ce1898a0987a65beb2b", "attack": "word_problem", "target": "algebra", "question_original": "Solve -8*x + 16 = 96 for x.", "variable": "t", "underlying_expression": "-8*t + 16 = 96", "answer_in_variable": "-10", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a board game, a player's score after landing on square n is 9*n - 5 points; squares behind the start are numbered negatively. Which square n yields a score of -86 points? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -9", "id": "algebra-L1-c1cb192ee38649d657dc-word", "source_id": "algebra-c1cb192ee38649d657dc", "topic": "algebra", "level": 1, "kind": "solve", "question": "In a board game, a player's score after landing on square n is 9*n - 5 points; squares behind the start are numbered negatively. Which square n yields a score of -86 points?", "answer": "-9", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-c1cb192ee38649d657dc", "attack": "word_problem", "target": "algebra", "question_original": "Solve 9*x - 5 = -86 for x.", "variable": "n", "underlying_expression": "9*n - 5 = -86", "answer_in_variable": "-9", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A drone's altitude, in meters relative to a rooftop, is 8*z + 19 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 75 meters. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 7", "id": "algebra-L1-fa571a2d89e8499f13d1-word", "source_id": "algebra-fa571a2d89e8499f13d1", "topic": "algebra", "level": 1, "kind": "solve", "question": "A drone's altitude, in meters relative to a rooftop, is 8*z + 19 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 75 meters.", "answer": "7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-fa571a2d89e8499f13d1", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x + 19 = 75 for x.", "variable": "z", "underlying_expression": "8*z + 19 = 75", "answer_in_variable": "7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An electrician measures -3*u - 11 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives -8 volts? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -1", "id": "algebra-L1-ac400409c17f447a4289-word", "source_id": "algebra-ac400409c17f447a4289", "topic": "algebra", "level": 1, "kind": "solve", "question": "An electrician measures -3*u - 11 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives -8 volts?", "answer": "-1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-ac400409c17f447a4289", "attack": "word_problem", "target": "algebra", "question_original": "Solve -3*x - 11 = -8 for x.", "variable": "u", "underlying_expression": "-3*u - 11 = -8", "answer_in_variable": "-1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 2*r - 10; riding the loop backwards counts as negative r. For which r is the net gain -14 meters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -2", "id": "algebra-L1-8913ad723df2f00e9e5c-word", "source_id": "algebra-8913ad723df2f00e9e5c", "topic": "algebra", "level": 1, "kind": "solve", "question": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 2*r - 10; riding the loop backwards counts as negative r. For which r is the net gain -14 meters?", "answer": "-2", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-8913ad723df2f00e9e5c", "attack": "word_problem", "target": "algebra", "question_original": "Solve 2*x - 10 = -14 for x.", "variable": "r", "underlying_expression": "2*r - 10 = -14", "answer_in_variable": "-2", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A warehouse's net inventory change after q shipments is 5*q + 3 boxes, where returned shipments count as negative q. Find q when the net change is 13 boxes. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 2", "id": "algebra-L1-db19c1b5762ae2878648-word", "source_id": "algebra-db19c1b5762ae2878648", "topic": "algebra", "level": 1, "kind": "solve", "question": "A warehouse's net inventory change after q shipments is 5*q + 3 boxes, where returned shipments count as negative q. Find q when the net change is 13 boxes.", "answer": "2", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-db19c1b5762ae2878648", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x + 3 = 13 for x.", "variable": "q", "underlying_expression": "5*q + 3 = 13", "answer_in_variable": "2", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The water level of a canal lock, in centimeters relative to its normal mark, follows 5*h + 1, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level -54 centimeters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -11", "id": "algebra-L1-f60f5fa7b84cfcdf2759-word", "source_id": "algebra-f60f5fa7b84cfcdf2759", "topic": "algebra", "level": 1, "kind": "solve", "question": "The water level of a canal lock, in centimeters relative to its normal mark, follows 5*h + 1, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level -54 centimeters?", "answer": "-11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-f60f5fa7b84cfcdf2759", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x + 1 = -54 for x.", "variable": "h", "underlying_expression": "5*h + 1 = -54", "answer_in_variable": "-11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A scheduling rule sets a meeting's start to 7*d - 14 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -49 minutes after nine o'clock? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -5", "id": "algebra-L1-160c1da09ac1892f426d-word", "source_id": "algebra-160c1da09ac1892f426d", "topic": "algebra", "level": 1, "kind": "solve", "question": "A scheduling rule sets a meeting's start to 7*d - 14 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -49 minutes after nine o'clock?", "answer": "-5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-160c1da09ac1892f426d", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x - 14 = -49 for x.", "variable": "d", "underlying_expression": "7*d - 14 = -49", "answer_in_variable": "-5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A game designer sets a character's health modifier to -3*g + 4 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of -17? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 7", "id": "algebra-L1-91215e1ded8d58efa47c-word", "source_id": "algebra-91215e1ded8d58efa47c", "topic": "algebra", "level": 1, "kind": "solve", "question": "A game designer sets a character's health modifier to -3*g + 4 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of -17?", "answer": "7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-91215e1ded8d58efa47c", "attack": "word_problem", "target": "algebra", "question_original": "Solve -3*x + 4 = -17 for x.", "variable": "g", "underlying_expression": "-3*g + 4 = -17", "answer_in_variable": "7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The temperature in a greenhouse, in degrees Celsius, is modelled by -7*t + 1, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -83 degrees? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12", "id": "algebra-L1-a1e36d4d0ec68c9e9442-word", "source_id": "algebra-a1e36d4d0ec68c9e9442", "topic": "algebra", "level": 1, "kind": "solve", "question": "The temperature in a greenhouse, in degrees Celsius, is modelled by -7*t + 1, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -83 degrees?", "answer": "12", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-a1e36d4d0ec68c9e9442", "attack": "word_problem", "target": "algebra", "question_original": "Solve -7*x + 1 = -83 for x.", "variable": "t", "underlying_expression": "-7*t + 1 = -83", "answer_in_variable": "12", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A submarine's depth gauge shows 7*n + 16 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of -68? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -12", "id": "algebra-L1-3ca6384f2f5cbfd2c2aa-word", "source_id": "algebra-3ca6384f2f5cbfd2c2aa", "topic": "algebra", "level": 1, "kind": "solve", "question": "A submarine's depth gauge shows 7*n + 16 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of -68?", "answer": "-12", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-3ca6384f2f5cbfd2c2aa", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x + 16 = -68 for x.", "variable": "n", "underlying_expression": "7*n + 16 = -68", "answer_in_variable": "-12", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The change in a savings account, in dollars, after k standard adjustments is -4*k - 12; a negative k means the adjustments were reversed. Find k if the change equals 12 dollars. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -6", "id": "algebra-L1-8ab56c0d99d3f1d03334-word", "source_id": "algebra-8ab56c0d99d3f1d03334", "topic": "algebra", "level": 1, "kind": "solve", "question": "The change in a savings account, in dollars, after k standard adjustments is -4*k - 12; a negative k means the adjustments were reversed. Find k if the change equals 12 dollars.", "answer": "-6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-8ab56c0d99d3f1d03334", "attack": "word_problem", "target": "algebra", "question_original": "Solve -4*x - 12 = 12 for x.", "variable": "k", "underlying_expression": "-4*k - 12 = 12", "answer_in_variable": "-6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "On a number line, a robot's stopping point after a command with parameter p is 2*p - 4. For which parameter p does the robot stop at 10? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 7", "id": "algebra-L1-92dd71649ab4988c0188-word", "source_id": "algebra-92dd71649ab4988c0188", "topic": "algebra", "level": 1, "kind": "solve", "question": "On a number line, a robot's stopping point after a command with parameter p is 2*p - 4. For which parameter p does the robot stop at 10?", "answer": "7", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-92dd71649ab4988c0188", "attack": "word_problem", "target": "algebra", "question_original": "Solve 2*x - 4 = 10 for x.", "variable": "p", "underlying_expression": "2*p - 4 = 10", "answer_in_variable": "7", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A spring scale shows 7*s - 18 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -53 grams. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -5", "id": "algebra-L1-380ff0d10a75a93a0191-word", "source_id": "algebra-380ff0d10a75a93a0191", "topic": "algebra", "level": 1, "kind": "solve", "question": "A spring scale shows 7*s - 18 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -53 grams.", "answer": "-5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-380ff0d10a75a93a0191", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x - 18 = -53 for x.", "variable": "s", "underlying_expression": "7*s - 18 = -53", "answer_in_variable": "-5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The elevation of a hiking marker, in meters relative to a lake surface, is 4*m - 5, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation 39? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11", "id": "algebra-L1-867f69314a98742d05a0-word", "source_id": "algebra-867f69314a98742d05a0", "topic": "algebra", "level": 1, "kind": "solve", "question": "The elevation of a hiking marker, in meters relative to a lake surface, is 4*m - 5, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation 39?", "answer": "11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-867f69314a98742d05a0", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x - 5 = 39 for x.", "variable": "m", "underlying_expression": "4*m - 5 = 39", "answer_in_variable": "11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An oven program sets the temperature to 5*w + 12 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 17 degrees above base? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 1", "id": "algebra-L1-b698ffdcb237114b6a86-word", "source_id": "algebra-b698ffdcb237114b6a86", "topic": "algebra", "level": 1, "kind": "solve", "question": "An oven program sets the temperature to 5*w + 12 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 17 degrees above base?", "answer": "1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-b698ffdcb237114b6a86", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x + 12 = 17 for x.", "variable": "w", "underlying_expression": "5*w + 12 = 17", "answer_in_variable": "1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A stock's price change, in cents, t days after a news release is predicted to be 3*t + 2, where negative t refers to days before the release. On which day t is the predicted change 26 cents? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8", "id": "algebra-L1-982ac2f67f4f1472aa2a-word", "source_id": "algebra-982ac2f67f4f1472aa2a", "topic": "algebra", "level": 1, "kind": "solve", "question": "A stock's price change, in cents, t days after a news release is predicted to be 3*t + 2, where negative t refers to days before the release. On which day t is the predicted change 26 cents?", "answer": "8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-982ac2f67f4f1472aa2a", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x + 2 = 26 for x.", "variable": "t", "underlying_expression": "3*t + 2 = 26", "answer_in_variable": "8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a board game, a player's score after landing on square n is 4*n + 8 points; squares behind the start are numbered negatively. Which square n yields a score of 48 points? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10", "id": "algebra-L1-5d450dc0af6ae3f6edfc-word", "source_id": "algebra-5d450dc0af6ae3f6edfc", "topic": "algebra", "level": 1, "kind": "solve", "question": "In a board game, a player's score after landing on square n is 4*n + 8 points; squares behind the start are numbered negatively. Which square n yields a score of 48 points?", "answer": "10", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-5d450dc0af6ae3f6edfc", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x + 8 = 48 for x.", "variable": "n", "underlying_expression": "4*n + 8 = 48", "answer_in_variable": "10", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A drone's altitude, in meters relative to a rooftop, is -8*z + 2 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 34 meters. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -4", "id": "algebra-L1-5066c59697a3d420929f-word", "source_id": "algebra-5066c59697a3d420929f", "topic": "algebra", "level": 1, "kind": "solve", "question": "A drone's altitude, in meters relative to a rooftop, is -8*z + 2 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at 34 meters.", "answer": "-4", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-5066c59697a3d420929f", "attack": "word_problem", "target": "algebra", "question_original": "Solve -8*x + 2 = 34 for x.", "variable": "z", "underlying_expression": "-8*z + 2 = 34", "answer_in_variable": "-4", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An electrician measures 2*u - 19 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives 5 volts? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12", "id": "algebra-L1-6fd287aaf62bdac0c5fd-word", "source_id": "algebra-6fd287aaf62bdac0c5fd", "topic": "algebra", "level": 1, "kind": "solve", "question": "An electrician measures 2*u - 19 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives 5 volts?", "answer": "12", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-6fd287aaf62bdac0c5fd", "attack": "word_problem", "target": "algebra", "question_original": "Solve 2*x - 19 = 5 for x.", "variable": "u", "underlying_expression": "2*u - 19 = 5", "answer_in_variable": "12", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 3*r + 18; riding the loop backwards counts as negative r. For which r is the net gain -6 meters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -8", "id": "algebra-L1-f063b75875268032074c-word", "source_id": "algebra-f063b75875268032074c", "topic": "algebra", "level": 1, "kind": "solve", "question": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 3*r + 18; riding the loop backwards counts as negative r. For which r is the net gain -6 meters?", "answer": "-8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-f063b75875268032074c", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x + 18 = -6 for x.", "variable": "r", "underlying_expression": "3*r + 18 = -6", "answer_in_variable": "-8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A warehouse's net inventory change after q shipments is -8*q + 10 boxes, where returned shipments count as negative q. Find q when the net change is -30 boxes. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-41e90820203e3f734cac-word", "source_id": "algebra-41e90820203e3f734cac", "topic": "algebra", "level": 1, "kind": "solve", "question": "A warehouse's net inventory change after q shipments is -8*q + 10 boxes, where returned shipments count as negative q. Find q when the net change is -30 boxes.", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-41e90820203e3f734cac", "attack": "word_problem", "target": "algebra", "question_original": "Solve -8*x + 10 = -30 for x.", "variable": "q", "underlying_expression": "-8*q + 10 = -30", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The water level of a canal lock, in centimeters relative to its normal mark, follows 6*h + 18, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level 84 centimeters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11", "id": "algebra-L1-f0ae23126569bd5d17c7-word", "source_id": "algebra-f0ae23126569bd5d17c7", "topic": "algebra", "level": 1, "kind": "solve", "question": "The water level of a canal lock, in centimeters relative to its normal mark, follows 6*h + 18, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level 84 centimeters?", "answer": "11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-f0ae23126569bd5d17c7", "attack": "word_problem", "target": "algebra", "question_original": "Solve 6*x + 18 = 84 for x.", "variable": "h", "underlying_expression": "6*h + 18 = 84", "answer_in_variable": "11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A scheduling rule sets a meeting's start to -7*d - 18 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -74 minutes after nine o'clock? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8", "id": "algebra-L1-4c1d72307f21b4381278-word", "source_id": "algebra-4c1d72307f21b4381278", "topic": "algebra", "level": 1, "kind": "solve", "question": "A scheduling rule sets a meeting's start to -7*d - 18 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -74 minutes after nine o'clock?", "answer": "8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-4c1d72307f21b4381278", "attack": "word_problem", "target": "algebra", "question_original": "Solve -7*x - 18 = -74 for x.", "variable": "d", "underlying_expression": "-7*d - 18 = -74", "answer_in_variable": "8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A game designer sets a character's health modifier to -6*g + 13 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of 31? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -3", "id": "algebra-L1-93c000467383a1754bec-word", "source_id": "algebra-93c000467383a1754bec", "topic": "algebra", "level": 1, "kind": "solve", "question": "A game designer sets a character's health modifier to -6*g + 13 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of 31?", "answer": "-3", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-93c000467383a1754bec", "attack": "word_problem", "target": "algebra", "question_original": "Solve -6*x + 13 = 31 for x.", "variable": "g", "underlying_expression": "-6*g + 13 = 31", "answer_in_variable": "-3", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The temperature in a greenhouse, in degrees Celsius, is modelled by 6*t + 0, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -30 degrees? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -5", "id": "algebra-L1-61d5cb42d55762c51116-word", "source_id": "algebra-61d5cb42d55762c51116", "topic": "algebra", "level": 1, "kind": "solve", "question": "The temperature in a greenhouse, in degrees Celsius, is modelled by 6*t + 0, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -30 degrees?", "answer": "-5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-61d5cb42d55762c51116", "attack": "word_problem", "target": "algebra", "question_original": "Solve 6*x + 0 = -30 for x.", "variable": "t", "underlying_expression": "6*t + 0 = -30", "answer_in_variable": "-5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A submarine's depth gauge shows -5*n + 19 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of 29? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -2", "id": "algebra-L1-da9e44e741bb62f7f2a0-word", "source_id": "algebra-da9e44e741bb62f7f2a0", "topic": "algebra", "level": 1, "kind": "solve", "question": "A submarine's depth gauge shows -5*n + 19 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of 29?", "answer": "-2", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-da9e44e741bb62f7f2a0", "attack": "word_problem", "target": "algebra", "question_original": "Solve -5*x + 19 = 29 for x.", "variable": "n", "underlying_expression": "-5*n + 19 = 29", "answer_in_variable": "-2", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The change in a savings account, in dollars, after k standard adjustments is -2*k + 16; a negative k means the adjustments were reversed. Find k if the change equals 8 dollars. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4", "id": "algebra-L1-7d0944d7edde24347b36-word", "source_id": "algebra-7d0944d7edde24347b36", "topic": "algebra", "level": 1, "kind": "solve", "question": "The change in a savings account, in dollars, after k standard adjustments is -2*k + 16; a negative k means the adjustments were reversed. Find k if the change equals 8 dollars.", "answer": "4", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-7d0944d7edde24347b36", "attack": "word_problem", "target": "algebra", "question_original": "Solve -2*x + 16 = 8 for x.", "variable": "k", "underlying_expression": "-2*k + 16 = 8", "answer_in_variable": "4", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "On a number line, a robot's stopping point after a command with parameter p is 8*p - 7. For which parameter p does the robot stop at 81? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11", "id": "algebra-L1-ef51474656050bfddf98-word", "source_id": "algebra-ef51474656050bfddf98", "topic": "algebra", "level": 1, "kind": "solve", "question": "On a number line, a robot's stopping point after a command with parameter p is 8*p - 7. For which parameter p does the robot stop at 81?", "answer": "11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-ef51474656050bfddf98", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x - 7 = 81 for x.", "variable": "p", "underlying_expression": "8*p - 7 = 81", "answer_in_variable": "11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A spring scale shows 8*s - 9 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -33 grams. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -3", "id": "algebra-L1-2151e1bc46365280a2e1-word", "source_id": "algebra-2151e1bc46365280a2e1", "topic": "algebra", "level": 1, "kind": "solve", "question": "A spring scale shows 8*s - 9 grams when its slider sits s notches from the centre mark (notches left of centre count as negative). Find s when the scale shows -33 grams.", "answer": "-3", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-2151e1bc46365280a2e1", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x - 9 = -33 for x.", "variable": "s", "underlying_expression": "8*s - 9 = -33", "answer_in_variable": "-3", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The elevation of a hiking marker, in meters relative to a lake surface, is -3*m + 14, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation -13? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9", "id": "algebra-L1-9df43a71541db80c4267-word", "source_id": "algebra-9df43a71541db80c4267", "topic": "algebra", "level": 1, "kind": "solve", "question": "The elevation of a hiking marker, in meters relative to a lake surface, is -3*m + 14, where m is the marker's index counted from the trailhead (markers before the trailhead have negative index). Which marker m is at elevation -13?", "answer": "9", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-9df43a71541db80c4267", "attack": "word_problem", "target": "algebra", "question_original": "Solve -3*x + 14 = -13 for x.", "variable": "m", "underlying_expression": "-3*m + 14 = -13", "answer_in_variable": "9", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An oven program sets the temperature to 8*w - 14 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 82 degrees above base? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12", "id": "algebra-L1-7f64c5ae35745bc1bb75-word", "source_id": "algebra-7f64c5ae35745bc1bb75", "topic": "algebra", "level": 1, "kind": "solve", "question": "An oven program sets the temperature to 8*w - 14 degrees above its base setting when the dial is turned w clicks (counter-clockwise clicks are negative). How many clicks w give 82 degrees above base?", "answer": "12", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-7f64c5ae35745bc1bb75", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x - 14 = 82 for x.", "variable": "w", "underlying_expression": "8*w - 14 = 82", "answer_in_variable": "12", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A stock's price change, in cents, t days after a news release is predicted to be -2*t - 10, where negative t refers to days before the release. On which day t is the predicted change 12 cents? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -11", "id": "algebra-L1-583f2bbf5e5fb12115fe-word", "source_id": "algebra-583f2bbf5e5fb12115fe", "topic": "algebra", "level": 1, "kind": "solve", "question": "A stock's price change, in cents, t days after a news release is predicted to be -2*t - 10, where negative t refers to days before the release. On which day t is the predicted change 12 cents?", "answer": "-11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-583f2bbf5e5fb12115fe", "attack": "word_problem", "target": "algebra", "question_original": "Solve -2*x - 10 = 12 for x.", "variable": "t", "underlying_expression": "-2*t - 10 = 12", "answer_in_variable": "-11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a board game, a player's score after landing on square n is 6*n + 16 points; squares behind the start are numbered negatively. Which square n yields a score of 10 points? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -1", "id": "algebra-L1-051d902a627b665c021f-word", "source_id": "algebra-051d902a627b665c021f", "topic": "algebra", "level": 1, "kind": "solve", "question": "In a board game, a player's score after landing on square n is 6*n + 16 points; squares behind the start are numbered negatively. Which square n yields a score of 10 points?", "answer": "-1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-051d902a627b665c021f", "attack": "word_problem", "target": "algebra", "question_original": "Solve 6*x + 16 = 10 for x.", "variable": "n", "underlying_expression": "6*n + 16 = 10", "answer_in_variable": "-1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A drone's altitude, in meters relative to a rooftop, is -8*z + 5 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at -27 meters. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4", "id": "algebra-L1-a49915d720ec70f3379d-word", "source_id": "algebra-a49915d720ec70f3379d", "topic": "algebra", "level": 1, "kind": "solve", "question": "A drone's altitude, in meters relative to a rooftop, is -8*z + 5 when its control lever is at position z (pulling the lever back gives negative z). Find the lever position z that puts the drone at -27 meters.", "answer": "4", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-a49915d720ec70f3379d", "attack": "word_problem", "target": "algebra", "question_original": "Solve -8*x + 5 = -27 for x.", "variable": "z", "underlying_expression": "-8*z + 5 = -27", "answer_in_variable": "4", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An electrician measures 3*u - 13 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives 2 volts? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-58e3d6bbab89b21e638f-word", "source_id": "algebra-58e3d6bbab89b21e638f", "topic": "algebra", "level": 1, "kind": "solve", "question": "An electrician measures 3*u - 13 volts on a test circuit when the offset knob is at setting u (u can be negative). What knob setting u gives 2 volts?", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-58e3d6bbab89b21e638f", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x - 13 = 2 for x.", "variable": "u", "underlying_expression": "3*u - 13 = 2", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 7*r + 14; riding the loop backwards counts as negative r. For which r is the net gain 35 meters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3", "id": "algebra-L1-d0ffc064f6298ffea91e-word", "source_id": "algebra-d0ffc064f6298ffea91e", "topic": "algebra", "level": 1, "kind": "solve", "question": "A cyclist's net gain in height, in meters, after riding r laps of a hilly loop is 7*r + 14; riding the loop backwards counts as negative r. For which r is the net gain 35 meters?", "answer": "3", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-d0ffc064f6298ffea91e", "attack": "word_problem", "target": "algebra", "question_original": "Solve 7*x + 14 = 35 for x.", "variable": "r", "underlying_expression": "7*r + 14 = 35", "answer_in_variable": "3", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A warehouse's net inventory change after q shipments is -4*q + 15 boxes, where returned shipments count as negative q. Find q when the net change is -5 boxes. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-090c384b202875c5c5ee-word", "source_id": "algebra-090c384b202875c5c5ee", "topic": "algebra", "level": 1, "kind": "solve", "question": "A warehouse's net inventory change after q shipments is -4*q + 15 boxes, where returned shipments count as negative q. Find q when the net change is -5 boxes.", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-090c384b202875c5c5ee", "attack": "word_problem", "target": "algebra", "question_original": "Solve -4*x + 15 = -5 for x.", "variable": "q", "underlying_expression": "-4*q + 15 = -5", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The water level of a canal lock, in centimeters relative to its normal mark, follows 5*h + 13, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level -37 centimeters? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -10", "id": "algebra-L1-6d0630a6ebc2166a4a51-word", "source_id": "algebra-6d0630a6ebc2166a4a51", "topic": "algebra", "level": 1, "kind": "solve", "question": "The water level of a canal lock, in centimeters relative to its normal mark, follows 5*h + 13, where h is the time in hours since pumping began (negative h is before pumping). At which time h is the level -37 centimeters?", "answer": "-10", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-6d0630a6ebc2166a4a51", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x + 13 = -37 for x.", "variable": "h", "underlying_expression": "5*h + 13 = -37", "answer_in_variable": "-10", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A scheduling rule sets a meeting's start to 8*d + 6 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -82 minutes after nine o'clock? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -11", "id": "algebra-L1-43501982dbccd16ec2c8-word", "source_id": "algebra-43501982dbccd16ec2c8", "topic": "algebra", "level": 1, "kind": "solve", "question": "A scheduling rule sets a meeting's start to 8*d + 6 minutes after nine o'clock when the meeting is moved by d days (moving it earlier gives negative d). For which d does the meeting start -82 minutes after nine o'clock?", "answer": "-11", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-43501982dbccd16ec2c8", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x + 6 = -82 for x.", "variable": "d", "underlying_expression": "8*d + 6 = -82", "answer_in_variable": "-11", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A game designer sets a character's health modifier to 8*g - 13 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of 27? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5", "id": "algebra-L1-e940b0e2a2c97abf67e1-word", "source_id": "algebra-e940b0e2a2c97abf67e1", "topic": "algebra", "level": 1, "kind": "solve", "question": "A game designer sets a character's health modifier to 8*g - 13 at difficulty level g, where easier-than-normal levels are negative and normal is level zero. Which difficulty level g has a modifier of 27?", "answer": "5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-e940b0e2a2c97abf67e1", "attack": "word_problem", "target": "algebra", "question_original": "Solve 8*x - 13 = 27 for x.", "variable": "g", "underlying_expression": "8*g - 13 = 27", "answer_in_variable": "5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The temperature in a greenhouse, in degrees Celsius, is modelled by -5*t - 20, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -40 degrees? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4", "id": "algebra-L1-eb1ed622099c3639cbcb-word", "source_id": "algebra-eb1ed622099c3639cbcb", "topic": "algebra", "level": 1, "kind": "solve", "question": "The temperature in a greenhouse, in degrees Celsius, is modelled by -5*t - 20, where t is the time in hours measured from noon (negative t means before noon). At what time t is the temperature -40 degrees?", "answer": "4", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-eb1ed622099c3639cbcb", "attack": "word_problem", "target": "algebra", "question_original": "Solve -5*x - 20 = -40 for x.", "variable": "t", "underlying_expression": "-5*t - 20 = -40", "answer_in_variable": "4", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A submarine's depth gauge shows -9*n - 9 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of -9? Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 0", "id": "algebra-L1-1458af6d0101c7c6e3ac-word", "source_id": "algebra-1458af6d0101c7c6e3ac", "topic": "algebra", "level": 1, "kind": "solve", "question": "A submarine's depth gauge shows -9*n - 9 units when its dial is set to position n (positions can be negative or zero). Which dial position n gives a reading of -9?", "answer": "0", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L1-1458af6d0101c7c6e3ac", "attack": "word_problem", "target": "algebra", "question_original": "Solve -9*x - 9 = -9 for x.", "variable": "n", "underlying_expression": "-9*n - 9 = -9", "answer_in_variable": "0", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A rectangular banner is designed so that its area, in square centimeters, is (9*x + 7)*(x - 23), where x is a design length in centimeters. Write the area as an expanded polynomial in x. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*x**2 - 200*x - 161", "id": "algebra-L2-e72390e4439ee860aff3-word", "source_id": "algebra-e72390e4439ee860aff3", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A rectangular banner is designed so that its area, in square centimeters, is (9*x + 7)*(x - 23), where x is a design length in centimeters. Write the area as an expanded polynomial in x.", "answer": "9*x**2 - 200*x - 161", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-e72390e4439ee860aff3", "attack": "word_problem", "target": "algebra", "question_original": "Expand (9*x + 7)*(x - 23).", "variable": "x", "underlying_expression": "(9*x + 7)*(x - 23)", "answer_in_variable": "9*x**2 - 200*x - 161", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a rectangular field, in square meters, is 3*x**2 + 72*x - 3036, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*(x - 22)*(x + 46)", "id": "algebra-L2-89a2e08c3a386d6be3c2-word", "source_id": "algebra-89a2e08c3a386d6be3c2", "topic": "algebra", "level": 2, "kind": "factor", "question": "The area of a rectangular field, in square meters, is 3*x**2 + 72*x - 3036, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths.", "answer": "3*(x - 22)*(x + 46)", "expr": "3*x**2 + 72*x - 3036", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-89a2e08c3a386d6be3c2", "attack": "word_problem", "target": "algebra", "question_original": "Factor 3*x**2 + 72*x - 3036 over the integers.", "variable": "x", "underlying_expression": "3*x**2 + 72*x - 3036", "answer_in_variable": "3*(x - 22)*(x + 46)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An accountant's profit formula for t units sold is 3*t**2 - 24*t dollars. Rewrite the formula in fully factored form over the integers, so the break-even points can be read off. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*x*(x - 8)", "id": "algebra-L2-1c50be5bd65a0fcc5ba2-word", "source_id": "algebra-1c50be5bd65a0fcc5ba2", "topic": "algebra", "level": 2, "kind": "factor", "question": "An accountant's profit formula for t units sold is 3*t**2 - 24*t dollars. Rewrite the formula in fully factored form over the integers, so the break-even points can be read off.", "answer": "3*x*(x - 8)", "expr": "3*x**2 - 24*x", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-1c50be5bd65a0fcc5ba2", "attack": "word_problem", "target": "algebra", "question_original": "Factor 3*x**2 - 24*x over the integers.", "variable": "t", "underlying_expression": "3*t**2 - 24*t", "answer_in_variable": "3*t*(t - 8)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A shop's revenue after a price change of t dollars is (-8*t + 39)*(t - 20) dollars. Expand this expression into standard form so it can be entered into a spreadsheet. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -8*x**2 + 199*x - 780", "id": "algebra-L2-603f33bd92b02066336d-word", "source_id": "algebra-603f33bd92b02066336d", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A shop's revenue after a price change of t dollars is (-8*t + 39)*(t - 20) dollars. Expand this expression into standard form so it can be entered into a spreadsheet.", "answer": "-8*x**2 + 199*x - 780", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-603f33bd92b02066336d", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-8*x + 39)*(x - 20).", "variable": "t", "underlying_expression": "(-8*t + 39)*(t - 20)", "answer_in_variable": "-8*t**2 + 199*t - 780", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An engineer models a cable whose height above a bridge deck vanishes exactly where 11*x**2 + 495*x + 5236 = 0, with x the horizontal position in meters from the central pylon (negative to the west). Find all such positions x and list them in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-28, -17]", "id": "algebra-L2-cb917b1f4a24381b0fc4-word", "source_id": "algebra-cb917b1f4a24381b0fc4", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "An engineer models a cable whose height above a bridge deck vanishes exactly where 11*x**2 + 495*x + 5236 = 0, with x the horizontal position in meters from the central pylon (negative to the west). Find all such positions x and list them in increasing order.", "answer": "[-28, -17]", "expr": "11*x**2 + 495*x + 5236", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-cb917b1f4a24381b0fc4", "attack": "word_problem", "target": "algebra", "question_original": "Solve 11*x**2 + 495*x + 5236 = 0 for x. List all roots in increasing order.", "variable": "x", "underlying_expression": "11*x**2 + 495*x + 5236 = 0", "answer_in_variable": "[-28, -17]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A break-even analysis for a product launch leads to the condition 4*t**2 - 104*t - 2028 = 0, where t is the number of weeks from the launch date (negative t is before launch). Find every t that satisfies the condition, listed in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-13, 39]", "id": "algebra-L2-329aa9e2436836fc3a98-word", "source_id": "algebra-329aa9e2436836fc3a98", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A break-even analysis for a product launch leads to the condition 4*t**2 - 104*t - 2028 = 0, where t is the number of weeks from the launch date (negative t is before launch). Find every t that satisfies the condition, listed in increasing order.", "answer": "[-13, 39]", "expr": "4*x**2 - 104*x - 2028", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-329aa9e2436836fc3a98", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x**2 - 104*x - 2028 = 0 for x. List all roots in increasing order.", "variable": "t", "underlying_expression": "4*t**2 - 104*t - 2028 = 0", "answer_in_variable": "[-13, 39]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of seats in a stadium section with n rows is modelled by (-10*n + 9)*(n + 14). Multiply out this expression and write it as a polynomial in n. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -10*x**2 - 131*x + 126", "id": "algebra-L2-e9602add0f4d4cad2f52-word", "source_id": "algebra-e9602add0f4d4cad2f52", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The number of seats in a stadium section with n rows is modelled by (-10*n + 9)*(n + 14). Multiply out this expression and write it as a polynomial in n.", "answer": "-10*x**2 - 131*x + 126", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-e9602add0f4d4cad2f52", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-10*x + 9)*(x + 14).", "variable": "n", "underlying_expression": "(-10*n + 9)*(n + 14)", "answer_in_variable": "-10*n**2 - 131*n + 126", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two tuning dials agree exactly when 6*k**2 - 168*k - 4968 = 0 for the integer setting k (settings may be negative). Find all such values of k, from smallest to largest. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-18, 46]", "id": "algebra-L2-b0f809ba8ae903693faf-word", "source_id": "algebra-b0f809ba8ae903693faf", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "Two tuning dials agree exactly when 6*k**2 - 168*k - 4968 = 0 for the integer setting k (settings may be negative). Find all such values of k, from smallest to largest.", "answer": "[-18, 46]", "expr": "6*x**2 - 168*x - 4968", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-b0f809ba8ae903693faf", "attack": "word_problem", "target": "algebra", "question_original": "Solve 6*x**2 - 168*x - 4968 = 0 for x. List all roots in increasing order.", "variable": "k", "underlying_expression": "6*k**2 - 168*k - 4968 = 0", "answer_in_variable": "[-18, 46]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of tiles needed for a patio design of size n is 9*n**2 - 360*n + 2700. Factor this expression completely over the integers. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*(x - 30)*(x - 10)", "id": "algebra-L2-d054b73ab2ce0c3b84d2-word", "source_id": "algebra-d054b73ab2ce0c3b84d2", "topic": "algebra", "level": 2, "kind": "factor", "question": "The number of tiles needed for a patio design of size n is 9*n**2 - 360*n + 2700. Factor this expression completely over the integers.", "answer": "9*(x - 30)*(x - 10)", "expr": "9*x**2 - 360*x + 2700", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-d054b73ab2ce0c3b84d2", "attack": "word_problem", "target": "algebra", "question_original": "Factor 9*x**2 - 360*x + 2700 over the integers.", "variable": "n", "underlying_expression": "9*n**2 - 360*n + 2700", "answer_in_variable": "9*(n - 30)*(n - 10)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A physics lab models the energy stored in a system at setting k as 8*k**2 - 456*k + 6448 joules. Express this model as a product of irreducible factors with integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8*(x - 31)*(x - 26)", "id": "algebra-L2-cefd817a50c0eb582eee-word", "source_id": "algebra-cefd817a50c0eb582eee", "topic": "algebra", "level": 2, "kind": "factor", "question": "A physics lab models the energy stored in a system at setting k as 8*k**2 - 456*k + 6448 joules. Express this model as a product of irreducible factors with integer coefficients.", "answer": "8*(x - 31)*(x - 26)", "expr": "8*x**2 - 456*x + 6448", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-cefd817a50c0eb582eee", "attack": "word_problem", "target": "algebra", "question_original": "Factor 8*x**2 - 456*x + 6448 over the integers.", "variable": "k", "underlying_expression": "8*k**2 - 456*k + 6448", "answer_in_variable": "8*(k - 31)*(k - 26)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A puzzle asks for the whole numbers n for which 9*n**2 - 9*n - 17820 = 0. Find all solutions n and list them in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-44, 45]", "id": "algebra-L2-16bcefa33687de08b9fb-word", "source_id": "algebra-16bcefa33687de08b9fb", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A puzzle asks for the whole numbers n for which 9*n**2 - 9*n - 17820 = 0. Find all solutions n and list them in increasing order.", "answer": "[-44, 45]", "expr": "9*x**2 - 9*x - 17820", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-16bcefa33687de08b9fb", "attack": "word_problem", "target": "algebra", "question_original": "Solve 9*x**2 - 9*x - 17820 = 0 for x. List all roots in increasing order.", "variable": "n", "underlying_expression": "9*n**2 - 9*n - 17820 = 0", "answer_in_variable": "[-44, 45]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The volume of a container, in cubic centimeters, works out to 7*s**2 - 217*s - 4004 for a design parameter s. Factor the expression fully, using integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 7*(x - 44)*(x + 13)", "id": "algebra-L2-7af459b6687bcbc4d8d8-word", "source_id": "algebra-7af459b6687bcbc4d8d8", "topic": "algebra", "level": 2, "kind": "factor", "question": "The volume of a container, in cubic centimeters, works out to 7*s**2 - 217*s - 4004 for a design parameter s. Factor the expression fully, using integer coefficients.", "answer": "7*(x - 44)*(x + 13)", "expr": "7*x**2 - 217*x - 4004", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-7af459b6687bcbc4d8d8", "attack": "word_problem", "target": "algebra", "question_original": "Factor 7*x**2 - 217*x - 4004 over the integers.", "variable": "s", "underlying_expression": "7*s**2 - 217*s - 4004", "answer_in_variable": "7*(s - 44)*(s + 13)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An engineer writes the power of a circuit at setting k as (-18*k - 5)*(k + 27) watts. Expand the product so that the formula has no parentheses. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -18*x**2 - 491*x - 135", "id": "algebra-L2-95cf16751d459bbb135f-word", "source_id": "algebra-95cf16751d459bbb135f", "topic": "algebra", "level": 2, "kind": "algebra", "question": "An engineer writes the power of a circuit at setting k as (-18*k - 5)*(k + 27) watts. Expand the product so that the formula has no parentheses.", "answer": "-18*x**2 - 491*x - 135", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-95cf16751d459bbb135f", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-18*x - 5)*(x + 27).", "variable": "k", "underlying_expression": "(-18*k - 5)*(k + 27)", "answer_in_variable": "-18*k**2 - 491*k - 135", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A garden's planting area, in square feet, is 12*m**2 - 204*m + 864, where m is the width of a path in feet. Write the area completely factored over the integers. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12*(x - 9)*(x - 8)", "id": "algebra-L2-d0674fb32ba1552d4ddf-word", "source_id": "algebra-d0674fb32ba1552d4ddf", "topic": "algebra", "level": 2, "kind": "factor", "question": "A garden's planting area, in square feet, is 12*m**2 - 204*m + 864, where m is the width of a path in feet. Write the area completely factored over the integers.", "answer": "12*(x - 9)*(x - 8)", "expr": "12*x**2 - 204*x + 864", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-d0674fb32ba1552d4ddf", "attack": "word_problem", "target": "algebra", "question_original": "Factor 12*x**2 - 204*x + 864 over the integers.", "variable": "m", "underlying_expression": "12*m**2 - 204*m + 864", "answer_in_variable": "12*(m - 9)*(m - 8)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A radar tracker reports that an object is at ground level when 3*s**2 + 51*s - 504 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-24, 7]", "id": "algebra-L2-ce0e6d7cbd3d676f4ccd-word", "source_id": "algebra-ce0e6d7cbd3d676f4ccd", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A radar tracker reports that an object is at ground level when 3*s**2 + 51*s - 504 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order.", "answer": "[-24, 7]", "expr": "3*x**2 + 51*x - 504", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-ce0e6d7cbd3d676f4ccd", "attack": "word_problem", "target": "algebra", "question_original": "Solve 3*x**2 + 51*x - 504 = 0 for x. List all roots in increasing order.", "variable": "s", "underlying_expression": "3*s**2 + 51*s - 504 = 0", "answer_in_variable": "[-24, 7]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a picture frame, in square inches, is (16*s - 2)*(s - 39), where s is a border width in inches. Write this area in expanded form. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 16*x**2 - 626*x + 78", "id": "algebra-L2-352770bdb6255350f22d-word", "source_id": "algebra-352770bdb6255350f22d", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The area of a picture frame, in square inches, is (16*s - 2)*(s - 39), where s is a border width in inches. Write this area in expanded form.", "answer": "16*x**2 - 626*x + 78", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-352770bdb6255350f22d", "attack": "word_problem", "target": "algebra", "question_original": "Expand (16*x - 2)*(x - 39).", "variable": "s", "underlying_expression": "(16*s - 2)*(s - 39)", "answer_in_variable": "16*s**2 - 626*s + 78", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A farmer computes the yield of a field as (16*m - 18)*(m + 42) kilograms when m extra rows are planted. Expand the expression into a polynomial in m. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 16*x**2 + 654*x - 756", "id": "algebra-L2-dc6774c498ea8b0b67dd-word", "source_id": "algebra-dc6774c498ea8b0b67dd", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A farmer computes the yield of a field as (16*m - 18)*(m + 42) kilograms when m extra rows are planted. Expand the expression into a polynomial in m.", "answer": "16*x**2 + 654*x - 756", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-dc6774c498ea8b0b67dd", "attack": "word_problem", "target": "algebra", "question_original": "Expand (16*x - 18)*(x + 42).", "variable": "m", "underlying_expression": "(16*m - 18)*(m + 42)", "answer_in_variable": "16*m**2 + 654*m - 756", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A tank's cross-sectional area, in square meters, is (-1*w + 8)*(w + 25), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -x**2 - 17*x + 200", "id": "algebra-L2-6ce26043535832bd990f-word", "source_id": "algebra-6ce26043535832bd990f", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A tank's cross-sectional area, in square meters, is (-1*w + 8)*(w + 25), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out.", "answer": "-x**2 - 17*x + 200", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-6ce26043535832bd990f", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-1*x + 8)*(x + 25).", "variable": "w", "underlying_expression": "(-1*w + 8)*(w + 25)", "answer_in_variable": "-w**2 - 17*w + 200", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A company's profit at production level p is (-13*p + 28)*(p - 49) dollars. Expand the profit formula completely. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -13*x**2 + 665*x - 1372", "id": "algebra-L2-fd335cef1ee795db3d12-word", "source_id": "algebra-fd335cef1ee795db3d12", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A company's profit at production level p is (-13*p + 28)*(p - 49) dollars. Expand the profit formula completely.", "answer": "-13*x**2 + 665*x - 1372", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-fd335cef1ee795db3d12", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-13*x + 28)*(x - 49).", "variable": "p", "underlying_expression": "(-13*p + 28)*(p - 49)", "answer_in_variable": "-13*p**2 + 665*p - 1372", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a rectangular field, in square meters, is 12*x**2 - 420*x + 3168, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12*(x - 24)*(x - 11)", "id": "algebra-L2-5056a22b36b12f35bf6b-word", "source_id": "algebra-5056a22b36b12f35bf6b", "topic": "algebra", "level": 2, "kind": "factor", "question": "The area of a rectangular field, in square meters, is 12*x**2 - 420*x + 3168, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths.", "answer": "12*(x - 24)*(x - 11)", "expr": "12*x**2 - 420*x + 3168", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-5056a22b36b12f35bf6b", "attack": "word_problem", "target": "algebra", "question_original": "Factor 12*x**2 - 420*x + 3168 over the integers.", "variable": "x", "underlying_expression": "12*x**2 - 420*x + 3168", "answer_in_variable": "12*(x - 24)*(x - 11)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A rectangular banner is designed so that its area, in square centimeters, is (4*x + 17)*(x - 45), where x is a design length in centimeters. Write the area as an expanded polynomial in x. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4*x**2 - 163*x - 765", "id": "algebra-L2-e8e882444332d7a2cefd-word", "source_id": "algebra-e8e882444332d7a2cefd", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A rectangular banner is designed so that its area, in square centimeters, is (4*x + 17)*(x - 45), where x is a design length in centimeters. Write the area as an expanded polynomial in x.", "answer": "4*x**2 - 163*x - 765", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-e8e882444332d7a2cefd", "attack": "word_problem", "target": "algebra", "question_original": "Expand (4*x + 17)*(x - 45).", "variable": "x", "underlying_expression": "(4*x + 17)*(x - 45)", "answer_in_variable": "4*x**2 - 163*x - 765", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A shop's revenue after a price change of t dollars is (1*t + 9)*(t + 39) dollars. Expand this expression into standard form so it can be entered into a spreadsheet. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: x**2 + 48*x + 351", "id": "algebra-L2-16c6132b0ce30b9316f7-word", "source_id": "algebra-16c6132b0ce30b9316f7", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A shop's revenue after a price change of t dollars is (1*t + 9)*(t + 39) dollars. Expand this expression into standard form so it can be entered into a spreadsheet.", "answer": "x**2 + 48*x + 351", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-16c6132b0ce30b9316f7", "attack": "word_problem", "target": "algebra", "question_original": "Expand (1*x + 9)*(x + 39).", "variable": "t", "underlying_expression": "(1*t + 9)*(t + 39)", "answer_in_variable": "t**2 + 48*t + 351", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a pricing study, the revenue difference between two plans is zero when 4*p**2 + 48*p - 3456 = 0, where p is the price change in dollars (negative for discounts). Find all values of p, listed from smallest to largest. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-36, 24]", "id": "algebra-L2-7566e987a0e255d1c8c1-word", "source_id": "algebra-7566e987a0e255d1c8c1", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "In a pricing study, the revenue difference between two plans is zero when 4*p**2 + 48*p - 3456 = 0, where p is the price change in dollars (negative for discounts). Find all values of p, listed from smallest to largest.", "answer": "[-36, 24]", "expr": "4*x**2 + 48*x - 3456", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-7566e987a0e255d1c8c1", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x**2 + 48*x - 3456 = 0 for x. List all roots in increasing order.", "variable": "p", "underlying_expression": "4*p**2 + 48*p - 3456 = 0", "answer_in_variable": "[-36, 24]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of seats in a stadium section with n rows is modelled by (-3*n - 21)*(n - 40). Multiply out this expression and write it as a polynomial in n. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -3*x**2 + 99*x + 840", "id": "algebra-L2-3396b5230efde401775d-word", "source_id": "algebra-3396b5230efde401775d", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The number of seats in a stadium section with n rows is modelled by (-3*n - 21)*(n - 40). Multiply out this expression and write it as a polynomial in n.", "answer": "-3*x**2 + 99*x + 840", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-3396b5230efde401775d", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-3*x - 21)*(x - 40).", "variable": "n", "underlying_expression": "(-3*n - 21)*(n - 40)", "answer_in_variable": "-3*n**2 + 99*n + 840", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A carpenter finds that a frame fits exactly when 4*m**2 - 92*m - 96 = 0, where m is the offset in millimeters from the template (negative means shorter). List all offsets m that work, in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-1, 24]", "id": "algebra-L2-770365cd9fea4442e383-word", "source_id": "algebra-770365cd9fea4442e383", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A carpenter finds that a frame fits exactly when 4*m**2 - 92*m - 96 = 0, where m is the offset in millimeters from the template (negative means shorter). List all offsets m that work, in increasing order.", "answer": "[-1, 24]", "expr": "4*x**2 - 92*x - 96", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-770365cd9fea4442e383", "attack": "word_problem", "target": "algebra", "question_original": "Solve 4*x**2 - 92*x - 96 = 0 for x. List all roots in increasing order.", "variable": "m", "underlying_expression": "4*m**2 - 92*m - 96 = 0", "answer_in_variable": "[-1, 24]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An accountant's profit formula for t units sold is 4*t**2 - 196*t + 720 dollars. Rewrite the formula in fully factored form over the integers, so the break-even points can be read off. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4*(x - 45)*(x - 4)", "id": "algebra-L2-57797df36fe3d426a64c-word", "source_id": "algebra-57797df36fe3d426a64c", "topic": "algebra", "level": 2, "kind": "factor", "question": "An accountant's profit formula for t units sold is 4*t**2 - 196*t + 720 dollars. Rewrite the formula in fully factored form over the integers, so the break-even points can be read off.", "answer": "4*(x - 45)*(x - 4)", "expr": "4*x**2 - 196*x + 720", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-57797df36fe3d426a64c", "attack": "word_problem", "target": "algebra", "question_original": "Factor 4*x**2 - 196*x + 720 over the integers.", "variable": "t", "underlying_expression": "4*t**2 - 196*t + 720", "answer_in_variable": "4*(t - 45)*(t - 4)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An engineer writes the power of a circuit at setting k as (14*k - 35)*(k + 43) watts. Expand the product so that the formula has no parentheses. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 14*x**2 + 567*x - 1505", "id": "algebra-L2-1a618fa178dd3fd6c4fd-word", "source_id": "algebra-1a618fa178dd3fd6c4fd", "topic": "algebra", "level": 2, "kind": "algebra", "question": "An engineer writes the power of a circuit at setting k as (14*k - 35)*(k + 43) watts. Expand the product so that the formula has no parentheses.", "answer": "14*x**2 + 567*x - 1505", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-1a618fa178dd3fd6c4fd", "attack": "word_problem", "target": "algebra", "question_original": "Expand (14*x - 35)*(x + 43).", "variable": "k", "underlying_expression": "(14*k - 35)*(k + 43)", "answer_in_variable": "14*k**2 + 567*k - 1505", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The net force on a bead sliding along a wire vanishes where 11*w**2 + 220*w + 1001 = 0, with w its position in centimeters from the midpoint (negative to the left). Find all such positions w, in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-13, -7]", "id": "algebra-L2-a090c599814bae1ff0e9-word", "source_id": "algebra-a090c599814bae1ff0e9", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "The net force on a bead sliding along a wire vanishes where 11*w**2 + 220*w + 1001 = 0, with w its position in centimeters from the midpoint (negative to the left). Find all such positions w, in increasing order.", "answer": "[-13, -7]", "expr": "11*x**2 + 220*x + 1001", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-a090c599814bae1ff0e9", "attack": "word_problem", "target": "algebra", "question_original": "Solve 11*x**2 + 220*x + 1001 = 0 for x. List all roots in increasing order.", "variable": "w", "underlying_expression": "11*w**2 + 220*w + 1001 = 0", "answer_in_variable": "[-13, -7]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An engineer models a cable whose height above a bridge deck vanishes exactly where 5*x**2 - 425*x + 8750 = 0, with x the horizontal position in meters from the central pylon (negative to the west). Find all such positions x and list them in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [35, 50]", "id": "algebra-L2-febeb848d527bfc44ae5-word", "source_id": "algebra-febeb848d527bfc44ae5", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "An engineer models a cable whose height above a bridge deck vanishes exactly where 5*x**2 - 425*x + 8750 = 0, with x the horizontal position in meters from the central pylon (negative to the west). Find all such positions x and list them in increasing order.", "answer": "[35, 50]", "expr": "5*x**2 - 425*x + 8750", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-febeb848d527bfc44ae5", "attack": "word_problem", "target": "algebra", "question_original": "Solve 5*x**2 - 425*x + 8750 = 0 for x. List all roots in increasing order.", "variable": "x", "underlying_expression": "5*x**2 - 425*x + 8750 = 0", "answer_in_variable": "[35, 50]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A break-even analysis for a product launch leads to the condition t**2 + 16*t + 55 = 0, where t is the number of weeks from the launch date (negative t is before launch). Find every t that satisfies the condition, listed in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-11, -5]", "id": "algebra-L2-b6d214c0d0236c5eaa12-word", "source_id": "algebra-b6d214c0d0236c5eaa12", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A break-even analysis for a product launch leads to the condition t**2 + 16*t + 55 = 0, where t is the number of weeks from the launch date (negative t is before launch). Find every t that satisfies the condition, listed in increasing order.", "answer": "[-11, -5]", "expr": "x**2 + 16*x + 55", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-b6d214c0d0236c5eaa12", "attack": "word_problem", "target": "algebra", "question_original": "Solve x**2 + 16*x + 55 = 0 for x. List all roots in increasing order.", "variable": "t", "underlying_expression": "t**2 + 16*t + 55 = 0", "answer_in_variable": "[-11, -5]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a picture frame, in square inches, is (-12*s + 46)*(s - 38), where s is a border width in inches. Write this area in expanded form. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -12*x**2 + 502*x - 1748", "id": "algebra-L2-0cfa75fb92322c9d5fe0-word", "source_id": "algebra-0cfa75fb92322c9d5fe0", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The area of a picture frame, in square inches, is (-12*s + 46)*(s - 38), where s is a border width in inches. Write this area in expanded form.", "answer": "-12*x**2 + 502*x - 1748", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-0cfa75fb92322c9d5fe0", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-12*x + 46)*(x - 38).", "variable": "s", "underlying_expression": "(-12*s + 46)*(s - 38)", "answer_in_variable": "-12*s**2 + 502*s - 1748", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A farmer computes the yield of a field as (10*m + 13)*(m - 42) kilograms when m extra rows are planted. Expand the expression into a polynomial in m. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*x**2 - 407*x - 546", "id": "algebra-L2-97d9804eaccac6aafe42-word", "source_id": "algebra-97d9804eaccac6aafe42", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A farmer computes the yield of a field as (10*m + 13)*(m - 42) kilograms when m extra rows are planted. Expand the expression into a polynomial in m.", "answer": "10*x**2 - 407*x - 546", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-97d9804eaccac6aafe42", "attack": "word_problem", "target": "algebra", "question_original": "Expand (10*x + 13)*(x - 42).", "variable": "m", "underlying_expression": "(10*m + 13)*(m - 42)", "answer_in_variable": "10*m**2 - 407*m - 546", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of tiles needed for a patio design of size n is 10*n**2 - 590*n + 4500. Factor this expression completely over the integers. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*(x - 50)*(x - 9)", "id": "algebra-L2-8fd688cea01b0b79d083-word", "source_id": "algebra-8fd688cea01b0b79d083", "topic": "algebra", "level": 2, "kind": "factor", "question": "The number of tiles needed for a patio design of size n is 10*n**2 - 590*n + 4500. Factor this expression completely over the integers.", "answer": "10*(x - 50)*(x - 9)", "expr": "10*x**2 - 590*x + 4500", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-8fd688cea01b0b79d083", "attack": "word_problem", "target": "algebra", "question_original": "Factor 10*x**2 - 590*x + 4500 over the integers.", "variable": "n", "underlying_expression": "10*n**2 - 590*n + 4500", "answer_in_variable": "10*(n - 50)*(n - 9)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A physics lab models the energy stored in a system at setting k as k**2 - 9*k - 136 joules. Express this model as a product of irreducible factors with integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (x - 17)*(x + 8)", "id": "algebra-L2-9edcc3d157280a0eb421-word", "source_id": "algebra-9edcc3d157280a0eb421", "topic": "algebra", "level": 2, "kind": "factor", "question": "A physics lab models the energy stored in a system at setting k as k**2 - 9*k - 136 joules. Express this model as a product of irreducible factors with integer coefficients.", "answer": "(x - 17)*(x + 8)", "expr": "x**2 - 9*x - 136", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-9edcc3d157280a0eb421", "attack": "word_problem", "target": "algebra", "question_original": "Factor x**2 - 9*x - 136 over the integers.", "variable": "k", "underlying_expression": "k**2 - 9*k - 136", "answer_in_variable": "(k - 17)*(k + 8)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A tank's cross-sectional area, in square meters, is (4*w + 42)*(w + 11), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4*x**2 + 86*x + 462", "id": "algebra-L2-571e6cffef0129a46d1e-word", "source_id": "algebra-571e6cffef0129a46d1e", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A tank's cross-sectional area, in square meters, is (4*w + 42)*(w + 11), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out.", "answer": "4*x**2 + 86*x + 462", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-571e6cffef0129a46d1e", "attack": "word_problem", "target": "algebra", "question_original": "Expand (4*x + 42)*(x + 11).", "variable": "w", "underlying_expression": "(4*w + 42)*(w + 11)", "answer_in_variable": "4*w**2 + 86*w + 462", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A company's profit at production level p is (6*p - 37)*(p + 33) dollars. Expand the profit formula completely. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 6*x**2 + 161*x - 1221", "id": "algebra-L2-a63c1893a5d15986ac34-word", "source_id": "algebra-a63c1893a5d15986ac34", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A company's profit at production level p is (6*p - 37)*(p + 33) dollars. Expand the profit formula completely.", "answer": "6*x**2 + 161*x - 1221", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-a63c1893a5d15986ac34", "attack": "word_problem", "target": "algebra", "question_original": "Expand (6*x - 37)*(x + 33).", "variable": "p", "underlying_expression": "(6*p - 37)*(p + 33)", "answer_in_variable": "6*p**2 + 161*p - 1221", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A rectangular banner is designed so that its area, in square centimeters, is (-12*x - 47)*(x - 5), where x is a design length in centimeters. Write the area as an expanded polynomial in x. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -12*x**2 + 13*x + 235", "id": "algebra-L2-3f4399e7e6c3b1c76602-word", "source_id": "algebra-3f4399e7e6c3b1c76602", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A rectangular banner is designed so that its area, in square centimeters, is (-12*x - 47)*(x - 5), where x is a design length in centimeters. Write the area as an expanded polynomial in x.", "answer": "-12*x**2 + 13*x + 235", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-3f4399e7e6c3b1c76602", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-12*x - 47)*(x - 5).", "variable": "x", "underlying_expression": "(-12*x - 47)*(x - 5)", "answer_in_variable": "-12*x**2 + 13*x + 235", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A shop's revenue after a price change of t dollars is (5*t + 47)*(t + 30) dollars. Expand this expression into standard form so it can be entered into a spreadsheet. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x**2 + 197*x + 1410", "id": "algebra-L2-d95dede0d1e694b3943a-word", "source_id": "algebra-d95dede0d1e694b3943a", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A shop's revenue after a price change of t dollars is (5*t + 47)*(t + 30) dollars. Expand this expression into standard form so it can be entered into a spreadsheet.", "answer": "5*x**2 + 197*x + 1410", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-d95dede0d1e694b3943a", "attack": "word_problem", "target": "algebra", "question_original": "Expand (5*x + 47)*(x + 30).", "variable": "t", "underlying_expression": "(5*t + 47)*(t + 30)", "answer_in_variable": "5*t**2 + 197*t + 1410", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of seats in a stadium section with n rows is modelled by (20*n - 20)*(n - 44). Multiply out this expression and write it as a polynomial in n. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 20*x**2 - 900*x + 880", "id": "algebra-L2-dbedbf9028fcd02a52d0-word", "source_id": "algebra-dbedbf9028fcd02a52d0", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The number of seats in a stadium section with n rows is modelled by (20*n - 20)*(n - 44). Multiply out this expression and write it as a polynomial in n.", "answer": "20*x**2 - 900*x + 880", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-dbedbf9028fcd02a52d0", "attack": "word_problem", "target": "algebra", "question_original": "Expand (20*x - 20)*(x - 44).", "variable": "n", "underlying_expression": "(20*n - 20)*(n - 44)", "answer_in_variable": "20*n**2 - 900*n + 880", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The volume of a container, in cubic centimeters, works out to 9*s**2 - 171*s - 1350 for a design parameter s. Factor the expression fully, using integer coefficients. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*(x - 25)*(x + 6)", "id": "algebra-L2-6b397f9c2788fae99d92-word", "source_id": "algebra-6b397f9c2788fae99d92", "topic": "algebra", "level": 2, "kind": "factor", "question": "The volume of a container, in cubic centimeters, works out to 9*s**2 - 171*s - 1350 for a design parameter s. Factor the expression fully, using integer coefficients.", "answer": "9*(x - 25)*(x + 6)", "expr": "9*x**2 - 171*x - 1350", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-6b397f9c2788fae99d92", "attack": "word_problem", "target": "algebra", "question_original": "Factor 9*x**2 - 171*x - 1350 over the integers.", "variable": "s", "underlying_expression": "9*s**2 - 171*s - 1350", "answer_in_variable": "9*(s - 25)*(s + 6)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A garden's planting area, in square feet, is 12*m**2 - 28812, where m is the width of a path in feet. Write the area completely factored over the integers. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12*(x - 49)*(x + 49)", "id": "algebra-L2-54b76b40f2f3a91ed93c-word", "source_id": "algebra-54b76b40f2f3a91ed93c", "topic": "algebra", "level": 2, "kind": "factor", "question": "A garden's planting area, in square feet, is 12*m**2 - 28812, where m is the width of a path in feet. Write the area completely factored over the integers.", "answer": "12*(x - 49)*(x + 49)", "expr": "12*x**2 - 28812", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-54b76b40f2f3a91ed93c", "attack": "word_problem", "target": "algebra", "question_original": "Factor 12*x**2 - 28812 over the integers.", "variable": "m", "underlying_expression": "12*m**2 - 28812", "answer_in_variable": "12*(m - 49)*(m + 49)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An engineer writes the power of a circuit at setting k as (-7*k - 50)*(k - 23) watts. Expand the product so that the formula has no parentheses. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -7*x**2 + 111*x + 1150", "id": "algebra-L2-a6db297886a6f4da1716-word", "source_id": "algebra-a6db297886a6f4da1716", "topic": "algebra", "level": 2, "kind": "algebra", "question": "An engineer writes the power of a circuit at setting k as (-7*k - 50)*(k - 23) watts. Expand the product so that the formula has no parentheses.", "answer": "-7*x**2 + 111*x + 1150", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-a6db297886a6f4da1716", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-7*x - 50)*(x - 23).", "variable": "k", "underlying_expression": "(-7*k - 50)*(k - 23)", "answer_in_variable": "-7*k**2 + 111*k + 1150", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a picture frame, in square inches, is (3*s - 20)*(s - 45), where s is a border width in inches. Write this area in expanded form. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*x**2 - 155*x + 900", "id": "algebra-L2-0170807af67a96d83bb7-word", "source_id": "algebra-0170807af67a96d83bb7", "topic": "algebra", "level": 2, "kind": "algebra", "question": "The area of a picture frame, in square inches, is (3*s - 20)*(s - 45), where s is a border width in inches. Write this area in expanded form.", "answer": "3*x**2 - 155*x + 900", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-0170807af67a96d83bb7", "attack": "word_problem", "target": "algebra", "question_original": "Expand (3*x - 20)*(x - 45).", "variable": "s", "underlying_expression": "(3*s - 20)*(s - 45)", "answer_in_variable": "3*s**2 - 155*s + 900", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two tuning dials agree exactly when 10*k**2 + 50*k - 2040 = 0 for the integer setting k (settings may be negative). Find all such values of k, from smallest to largest. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-17, 12]", "id": "algebra-L2-9b4fcab9a6467a8adce3-word", "source_id": "algebra-9b4fcab9a6467a8adce3", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "Two tuning dials agree exactly when 10*k**2 + 50*k - 2040 = 0 for the integer setting k (settings may be negative). Find all such values of k, from smallest to largest.", "answer": "[-17, 12]", "expr": "10*x**2 + 50*x - 2040", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-9b4fcab9a6467a8adce3", "attack": "word_problem", "target": "algebra", "question_original": "Solve 10*x**2 + 50*x - 2040 = 0 for x. List all roots in increasing order.", "variable": "k", "underlying_expression": "10*k**2 + 50*k - 2040 = 0", "answer_in_variable": "[-17, 12]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A farmer computes the yield of a field as (9*m + 25)*(m - 11) kilograms when m extra rows are planted. Expand the expression into a polynomial in m. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*x**2 - 74*x - 275", "id": "algebra-L2-ac52a94797807482a7fc-word", "source_id": "algebra-ac52a94797807482a7fc", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A farmer computes the yield of a field as (9*m + 25)*(m - 11) kilograms when m extra rows are planted. Expand the expression into a polynomial in m.", "answer": "9*x**2 - 74*x - 275", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-ac52a94797807482a7fc", "attack": "word_problem", "target": "algebra", "question_original": "Expand (9*x + 25)*(x - 11).", "variable": "m", "underlying_expression": "(9*m + 25)*(m - 11)", "answer_in_variable": "9*m**2 - 74*m - 275", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A puzzle asks for the whole numbers n for which 10*n**2 - 140*n - 17150 = 0. Find all solutions n and list them in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [-35, 49]", "id": "algebra-L2-cb9ec1f8e78900785bb4-word", "source_id": "algebra-cb9ec1f8e78900785bb4", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A puzzle asks for the whole numbers n for which 10*n**2 - 140*n - 17150 = 0. Find all solutions n and list them in increasing order.", "answer": "[-35, 49]", "expr": "10*x**2 - 140*x - 17150", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-cb9ec1f8e78900785bb4", "attack": "word_problem", "target": "algebra", "question_original": "Solve 10*x**2 - 140*x - 17150 = 0 for x. List all roots in increasing order.", "variable": "n", "underlying_expression": "10*n**2 - 140*n - 17150 = 0", "answer_in_variable": "[-35, 49]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A tank's cross-sectional area, in square meters, is (-11*w + 24)*(w + 29), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -11*x**2 - 295*x + 696", "id": "algebra-L2-f1a7c15aa428b3d5d033-word", "source_id": "algebra-f1a7c15aa428b3d5d033", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A tank's cross-sectional area, in square meters, is (-11*w + 24)*(w + 29), where w is a width offset in meters. Rewrite the area in standard form by multiplying it out.", "answer": "-11*x**2 - 295*x + 696", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-f1a7c15aa428b3d5d033", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-11*x + 24)*(x + 29).", "variable": "w", "underlying_expression": "(-11*w + 24)*(w + 29)", "answer_in_variable": "-11*w**2 - 295*w + 696", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A company's profit at production level p is (-3*p - 20)*(p + 28) dollars. Expand the profit formula completely. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: -3*x**2 - 104*x - 560", "id": "algebra-L2-b937591b4a321fd94f5a-word", "source_id": "algebra-b937591b4a321fd94f5a", "topic": "algebra", "level": 2, "kind": "algebra", "question": "A company's profit at production level p is (-3*p - 20)*(p + 28) dollars. Expand the profit formula completely.", "answer": "-3*x**2 - 104*x - 560", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-b937591b4a321fd94f5a", "attack": "word_problem", "target": "algebra", "question_original": "Expand (-3*x - 20)*(x + 28).", "variable": "p", "underlying_expression": "(-3*p - 20)*(p + 28)", "answer_in_variable": "-3*p**2 - 104*p - 560", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A radar tracker reports that an object is at ground level when s**2 - 42*s + 272 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: [8, 34]", "id": "algebra-L2-529f704143f20480b18b-word", "source_id": "algebra-529f704143f20480b18b", "topic": "algebra", "level": 2, "kind": "quadratic", "question": "A radar tracker reports that an object is at ground level when s**2 - 42*s + 272 = 0, where s is the time in seconds relative to the radar ping (negative s is before the ping). Find all such times s in increasing order.", "answer": "[8, 34]", "expr": "x**2 - 42*x + 272", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-529f704143f20480b18b", "attack": "word_problem", "target": "algebra", "question_original": "Solve x**2 - 42*x + 272 = 0 for x. List all roots in increasing order.", "variable": "s", "underlying_expression": "s**2 - 42*s + 272 = 0", "answer_in_variable": "[8, 34]", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The area of a rectangular field, in square meters, is 8*x**2 - 592*x + 10944, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8*(x - 38)*(x - 36)", "id": "algebra-L2-5b58b2ee892eb2b88a09-word", "source_id": "algebra-5b58b2ee892eb2b88a09", "topic": "algebra", "level": 2, "kind": "factor", "question": "The area of a rectangular field, in square meters, is 8*x**2 - 592*x + 10944, where x is a length in meters. Write the area as a product of irreducible factors with integer coefficients (fully factored form), to suggest possible side lengths.", "answer": "8*(x - 38)*(x - 36)", "expr": "8*x**2 - 592*x + 10944", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L2-5b58b2ee892eb2b88a09", "attack": "word_problem", "target": "algebra", "question_original": "Factor 8*x**2 - 592*x + 10944 over the integers.", "variable": "x", "underlying_expression": "8*x**2 - 592*x + 10944", "answer_in_variable": "8*(x - 38)*(x - 36)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 5*x + 1*y = 38 and -6*x + 4*y = -30. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (7, 3)", "id": "algebra-L3-b50d21fb6641984c1e04-word", "source_id": "algebra-b50d21fb6641984c1e04", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 5*x + 1*y = 38 and -6*x + 4*y = -30. Find the corrections as an ordered pair (x, y).", "answer": "(7, 3)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-b50d21fb6641984c1e04", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 5*x + 1*y = 38, -6*x + 4*y = -30 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "5*x + 1*y = 38, -6*x + 4*y = -30", "answer_in_variable": "(7, 3)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 4*x + 6*y = 34 and -4*x - 4*y = -28. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (4, 3)", "id": "algebra-L3-ad6e7f372cb33d03006c-word", "source_id": "algebra-ad6e7f372cb33d03006c", "topic": "algebra", "level": 3, "kind": "solve", "question": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 4*x + 6*y = 34 and -4*x - 4*y = -28. Find the ordered pair (x, y).", "answer": "(4, 3)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-ad6e7f372cb33d03006c", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x + 6*y = 34, -4*x - 4*y = -28 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x + 6*y = 34, -4*x - 4*y = -28", "answer_in_variable": "(4, 3)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The average cost per crate in a shipment, in dollars, is (11*x**2 + 239*x - 322)/(x + 23), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11*x - 14", "id": "algebra-L3-259d395916b8cbcdc0bd-word", "source_id": "algebra-259d395916b8cbcdc0bd", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (11*x**2 + 239*x - 322)/(x + 23), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "11*x - 14", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-259d395916b8cbcdc0bd", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (11*x**2 + 239*x - 322)/(x - (-23)) for x != -23.", "variable": "x", "underlying_expression": "(11*x**2 + 239*x - 322)/(x + 23)", "answer_in_variable": "11*x - 14", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A machine's output rate is recorded as (5*t**2 - 81*t + 286)/(t - 11) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x - 26", "id": "algebra-L3-b59f4e5eaef5da15b1c3-word", "source_id": "algebra-b59f4e5eaef5da15b1c3", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A machine's output rate is recorded as (5*t**2 - 81*t + 286)/(t - 11) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero.", "answer": "5*x - 26", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-b59f4e5eaef5da15b1c3", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (5*x**2 - 81*x + 286)/(x - (11)) for x != 11.", "variable": "t", "underlying_expression": "(5*t**2 - 81*t + 286)/(t - 11)", "answer_in_variable": "5*t - 26", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 2*x - 3*y = -21 and -4*x + 3*y = 21. Determine the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (0, 7)", "id": "algebra-L3-23dc554843bfe72eb35c-word", "source_id": "algebra-23dc554843bfe72eb35c", "topic": "algebra", "level": 3, "kind": "solve", "question": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 2*x - 3*y = -21 and -4*x + 3*y = 21. Determine the ordered pair (x, y).", "answer": "(0, 7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-23dc554843bfe72eb35c", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 2*x - 3*y = -21, -4*x + 3*y = 21 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "2*x - 3*y = -21, -4*x + 3*y = 21", "answer_in_variable": "(0, 7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of items each worker handles is given by (5*n**2 - 24*n - 128)/(n - 8), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x + 16", "id": "algebra-L3-e1a9a1d98c4d971b43a3-word", "source_id": "algebra-e1a9a1d98c4d971b43a3", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The number of items each worker handles is given by (5*n**2 - 24*n - 128)/(n - 8), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here).", "answer": "5*x + 16", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-e1a9a1d98c4d971b43a3", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (5*x**2 - 24*x - 128)/(x - (8)) for x != 8.", "variable": "n", "underlying_expression": "(5*n**2 - 24*n - 128)/(n - 8)", "answer_in_variable": "5*n + 16", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -5*x + 1*y = -4 and 4*x - 6*y = -2. Find the positions as (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (1, 1)", "id": "algebra-L3-c414c89224379cc07cf9-word", "source_id": "algebra-c414c89224379cc07cf9", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -5*x + 1*y = -4 and 4*x - 6*y = -2. Find the positions as (x, y).", "answer": "(1, 1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-c414c89224379cc07cf9", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -5*x + 1*y = -4, 4*x - 6*y = -2 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-5*x + 1*y = -4, 4*x - 6*y = -2", "answer_in_variable": "(1, 1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -3*x - 4*y = 7 and 1*x - 4*y = 3. Find the charges as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-1, -1)", "id": "algebra-L3-a3ade6dd1f291e54d176-word", "source_id": "algebra-a3ade6dd1f291e54d176", "topic": "algebra", "level": 3, "kind": "solve", "question": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -3*x - 4*y = 7 and 1*x - 4*y = 3. Find the charges as an ordered pair (x, y).", "answer": "(-1, -1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-a3ade6dd1f291e54d176", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -3*x - 4*y = 7, 1*x - 4*y = 3 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-3*x - 4*y = 7, 1*x - 4*y = 3", "answer_in_variable": "(-1, -1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An economist's ratio of total revenue to the number of batches is (6*k**2 + 202*k - 504)/(k + 36), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 6*x - 14", "id": "algebra-L3-0c7456e73bade541dd15-word", "source_id": "algebra-0c7456e73bade541dd15", "topic": "algebra", "level": 3, "kind": "simplify", "question": "An economist's ratio of total revenue to the number of batches is (6*k**2 + 202*k - 504)/(k + 36), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined.", "answer": "6*x - 14", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-0c7456e73bade541dd15", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (6*x**2 + 202*x - 504)/(x - (-36)) for x != -36.", "variable": "k", "underlying_expression": "(6*k**2 + 202*k - 504)/(k + 36)", "answer_in_variable": "6*k - 14", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (s**2 + 75*s + 1316)/(s + 47) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: x + 28", "id": "algebra-L3-25307a65183bc3efaa29-word", "source_id": "algebra-25307a65183bc3efaa29", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (s**2 + 75*s + 1316)/(s + 47) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s.", "answer": "x + 28", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-25307a65183bc3efaa29", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (x**2 + 75*x + 1316)/(x - (-47)) for x != -47.", "variable": "s", "underlying_expression": "(s**2 + 75*s + 1316)/(s + 47)", "answer_in_variable": "s + 28", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 3*x - 3*y = 6 and -2*x + 6*y = 16. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (7, 5)", "id": "algebra-L3-f75b5c1c796400b1d63c-word", "source_id": "algebra-f75b5c1c796400b1d63c", "topic": "algebra", "level": 3, "kind": "solve", "question": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 3*x - 3*y = 6 and -2*x + 6*y = 16. Find the ordered pair (x, y).", "answer": "(7, 5)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-f75b5c1c796400b1d63c", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 3*x - 3*y = 6, -2*x + 6*y = 16 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "3*x - 3*y = 6, -2*x + 6*y = 16", "answer_in_variable": "(7, 5)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist's concentration formula is (m**2 + 12*m - 85)/(m + 17) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: x - 5", "id": "algebra-L3-d154cb366e842692af72-word", "source_id": "algebra-d154cb366e842692af72", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A chemist's concentration formula is (m**2 + 12*m - 85)/(m + 17) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero).", "answer": "x - 5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-d154cb366e842692af72", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (x**2 + 12*x - 85)/(x - (-17)) for x != -17.", "variable": "m", "underlying_expression": "(m**2 + 12*m - 85)/(m + 17)", "answer_in_variable": "m - 5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The average cost per crate in a shipment, in dollars, is (2*x**2 - 91*x + 629)/(x - 37), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 2*x - 17", "id": "algebra-L3-2a4b9e082dda60a09b0f-word", "source_id": "algebra-2a4b9e082dda60a09b0f", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (2*x**2 - 91*x + 629)/(x - 37), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "2*x - 17", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-2a4b9e082dda60a09b0f", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (2*x**2 - 91*x + 629)/(x - (37)) for x != 37.", "variable": "x", "underlying_expression": "(2*x**2 - 91*x + 629)/(x - 37)", "answer_in_variable": "2*x - 17", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A machine's output rate is recorded as (10*t**2 + 109*t + 232)/(t + 8) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*x + 29", "id": "algebra-L3-73b09ada4fa4b48fe640-word", "source_id": "algebra-73b09ada4fa4b48fe640", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A machine's output rate is recorded as (10*t**2 + 109*t + 232)/(t + 8) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero.", "answer": "10*x + 29", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-73b09ada4fa4b48fe640", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (10*x**2 + 109*x + 232)/(x - (-8)) for x != -8.", "variable": "t", "underlying_expression": "(10*t**2 + 109*t + 232)/(t + 8)", "answer_in_variable": "10*t + 29", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 4*x - 6*y = -48 and 6*x - 3*y = -48. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-6, 4)", "id": "algebra-L3-e96a211888507859fdca-word", "source_id": "algebra-e96a211888507859fdca", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 4*x - 6*y = -48 and 6*x - 3*y = -48. Find the corrections as an ordered pair (x, y).", "answer": "(-6, 4)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-e96a211888507859fdca", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x - 6*y = -48, 6*x - 3*y = -48 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x - 6*y = -48, 6*x - 3*y = -48", "answer_in_variable": "(-6, 4)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of items each worker handles is given by (11*n**2 - 292*n - 448)/(n - 28), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11*x + 16", "id": "algebra-L3-487f001cf4c33038e547-word", "source_id": "algebra-487f001cf4c33038e547", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The number of items each worker handles is given by (11*n**2 - 292*n - 448)/(n - 28), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here).", "answer": "11*x + 16", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-487f001cf4c33038e547", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (11*x**2 - 292*x - 448)/(x - (28)) for x != 28.", "variable": "n", "underlying_expression": "(11*n**2 - 292*n - 448)/(n - 28)", "answer_in_variable": "11*n + 16", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An economist's ratio of total revenue to the number of batches is (3*k**2 + 15*k + 12)/(k + 4), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 3*x + 3", "id": "algebra-L3-0e1b907ab2a4cfd6fd79-word", "source_id": "algebra-0e1b907ab2a4cfd6fd79", "topic": "algebra", "level": 3, "kind": "simplify", "question": "An economist's ratio of total revenue to the number of batches is (3*k**2 + 15*k + 12)/(k + 4), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined.", "answer": "3*x + 3", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-0e1b907ab2a4cfd6fd79", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (3*x**2 + 15*x + 12)/(x - (-4)) for x != -4.", "variable": "k", "underlying_expression": "(3*k**2 + 15*k + 12)/(k + 4)", "answer_in_variable": "3*k + 3", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (10*s**2 + 352*s + 726)/(s + 33) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*x + 22", "id": "algebra-L3-f3464e8631357f0d9d42-word", "source_id": "algebra-f3464e8631357f0d9d42", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (10*s**2 + 352*s + 726)/(s + 33) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s.", "answer": "10*x + 22", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-f3464e8631357f0d9d42", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (10*x**2 + 352*x + 726)/(x - (-33)) for x != -33.", "variable": "s", "underlying_expression": "(10*s**2 + 352*s + 726)/(s + 33)", "answer_in_variable": "10*s + 22", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 1*x - 6*y = -62 and 2*x - 6*y = -70. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-8, 9)", "id": "algebra-L3-a1238a6def42e2ec5ac9-word", "source_id": "algebra-a1238a6def42e2ec5ac9", "topic": "algebra", "level": 3, "kind": "solve", "question": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 1*x - 6*y = -62 and 2*x - 6*y = -70. Find the ordered pair (x, y).", "answer": "(-8, 9)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-a1238a6def42e2ec5ac9", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 1*x - 6*y = -62, 2*x - 6*y = -70 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "1*x - 6*y = -62, 2*x - 6*y = -70", "answer_in_variable": "(-8, 9)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give -6*x - 5*y = 6 and -6*x + 5*y = -54. Determine the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (4, -6)", "id": "algebra-L3-8ddbadf2821e45b63f5e-word", "source_id": "algebra-8ddbadf2821e45b63f5e", "topic": "algebra", "level": 3, "kind": "solve", "question": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give -6*x - 5*y = 6 and -6*x + 5*y = -54. Determine the ordered pair (x, y).", "answer": "(4, -6)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-8ddbadf2821e45b63f5e", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -6*x - 5*y = 6, -6*x + 5*y = -54 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-6*x - 5*y = 6, -6*x + 5*y = -54", "answer_in_variable": "(4, -6)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -4*x - 3*y = -13 and -2*x + 5*y = 39. Find the positions as (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-2, 7)", "id": "algebra-L3-a175fd0ca2b6c1e017cc-word", "source_id": "algebra-a175fd0ca2b6c1e017cc", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give -4*x - 3*y = -13 and -2*x + 5*y = 39. Find the positions as (x, y).", "answer": "(-2, 7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-a175fd0ca2b6c1e017cc", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -4*x - 3*y = -13, -2*x + 5*y = 39 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-4*x - 3*y = -13, -2*x + 5*y = 39", "answer_in_variable": "(-2, 7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are 6*x - 4*y = -30 and -4*x - 5*y = -3. Find the charges as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-3, 3)", "id": "algebra-L3-4f24a508be9c2a4c494d-word", "source_id": "algebra-4f24a508be9c2a4c494d", "topic": "algebra", "level": 3, "kind": "solve", "question": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are 6*x - 4*y = -30 and -4*x - 5*y = -3. Find the charges as an ordered pair (x, y).", "answer": "(-3, 3)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-4f24a508be9c2a4c494d", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 6*x - 4*y = -30, -4*x - 5*y = -3 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "6*x - 4*y = -30, -4*x - 5*y = -3", "answer_in_variable": "(-3, 3)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 4*x - 6*y = 40 and 2*x - 2*y = 14. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (1, -6)", "id": "algebra-L3-f2f379179fa3719fb122-word", "source_id": "algebra-f2f379179fa3719fb122", "topic": "algebra", "level": 3, "kind": "solve", "question": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 4*x - 6*y = 40 and 2*x - 2*y = 14. Find the ordered pair (x, y).", "answer": "(1, -6)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-f2f379179fa3719fb122", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x - 6*y = 40, 2*x - 2*y = 14 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x - 6*y = 40, 2*x - 2*y = 14", "answer_in_variable": "(1, -6)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist's concentration formula is (10*m**2 - 496*m + 294)/(m - 49) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 10*x - 6", "id": "algebra-L3-9df6e8114ebb0bd61456-word", "source_id": "algebra-9df6e8114ebb0bd61456", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A chemist's concentration formula is (10*m**2 - 496*m + 294)/(m - 49) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero).", "answer": "10*x - 6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-9df6e8114ebb0bd61456", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (10*x**2 - 496*x + 294)/(x - (49)) for x != 49.", "variable": "m", "underlying_expression": "(10*m**2 - 496*m + 294)/(m - 49)", "answer_in_variable": "10*m - 6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 2*x - 6*y = 46 and -5*x + 4*y = -38. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (2, -7)", "id": "algebra-L3-5421e22494b67a22d6bf-word", "source_id": "algebra-5421e22494b67a22d6bf", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 2*x - 6*y = 46 and -5*x + 4*y = -38. Find the corrections as an ordered pair (x, y).", "answer": "(2, -7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-5421e22494b67a22d6bf", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 2*x - 6*y = 46, -5*x + 4*y = -38 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "2*x - 6*y = 46, -5*x + 4*y = -38", "answer_in_variable": "(2, -7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The average cost per crate in a shipment, in dollars, is (5*x**2 + 191*x - 360)/(x + 40), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x - 9", "id": "algebra-L3-1647076ff8cbd67fc504-word", "source_id": "algebra-1647076ff8cbd67fc504", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (5*x**2 + 191*x - 360)/(x + 40), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "5*x - 9", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-1647076ff8cbd67fc504", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (5*x**2 + 191*x - 360)/(x - (-40)) for x != -40.", "variable": "x", "underlying_expression": "(5*x**2 + 191*x - 360)/(x + 40)", "answer_in_variable": "5*x - 9", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record -6*x + 4*y = 18 and -2*x - 6*y = 50. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-7, -6)", "id": "algebra-L3-c788c82eec61f9610daf-word", "source_id": "algebra-c788c82eec61f9610daf", "topic": "algebra", "level": 3, "kind": "solve", "question": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record -6*x + 4*y = 18 and -2*x - 6*y = 50. Find the ordered pair (x, y).", "answer": "(-7, -6)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-c788c82eec61f9610daf", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -6*x + 4*y = 18, -2*x - 6*y = 50 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-6*x + 4*y = 18, -2*x - 6*y = 50", "answer_in_variable": "(-7, -6)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 1*x - 1*y = 10 and 6*x + 3*y = -3. Determine the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (3, -7)", "id": "algebra-L3-0d9da4831687880681fe-word", "source_id": "algebra-0d9da4831687880681fe", "topic": "algebra", "level": 3, "kind": "solve", "question": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 1*x - 1*y = 10 and 6*x + 3*y = -3. Determine the ordered pair (x, y).", "answer": "(3, -7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-0d9da4831687880681fe", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 1*x - 1*y = 10, 6*x + 3*y = -3 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "1*x - 1*y = 10, 6*x + 3*y = -3", "answer_in_variable": "(3, -7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give 6*x + 6*y = -6 and 5*x - 5*y = 65. Find the positions as (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (6, -7)", "id": "algebra-L3-bb9347488ea5b9239db7-word", "source_id": "algebra-bb9347488ea5b9239db7", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give 6*x + 6*y = -6 and 5*x - 5*y = 65. Find the positions as (x, y).", "answer": "(6, -7)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-bb9347488ea5b9239db7", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 6*x + 6*y = -6, 5*x - 5*y = 65 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "6*x + 6*y = -6, 5*x - 5*y = 65", "answer_in_variable": "(6, -7)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A machine's output rate is recorded as (11*t**2 + 504*t + 880)/(t + 44) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11*x + 20", "id": "algebra-L3-c178b56ee6dd0dc7c05f-word", "source_id": "algebra-c178b56ee6dd0dc7c05f", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A machine's output rate is recorded as (11*t**2 + 504*t + 880)/(t + 44) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero.", "answer": "11*x + 20", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-c178b56ee6dd0dc7c05f", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (11*x**2 + 504*x + 880)/(x - (-44)) for x != -44.", "variable": "t", "underlying_expression": "(11*t**2 + 504*t + 880)/(t + 44)", "answer_in_variable": "11*t + 20", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of items each worker handles is given by (6*n**2 + 249*n + 360)/(n + 40), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 6*x + 9", "id": "algebra-L3-b3e9e1941ea59662892b-word", "source_id": "algebra-b3e9e1941ea59662892b", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The number of items each worker handles is given by (6*n**2 + 249*n + 360)/(n + 40), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here).", "answer": "6*x + 9", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-b3e9e1941ea59662892b", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (6*x**2 + 249*x + 360)/(x - (-40)) for x != -40.", "variable": "n", "underlying_expression": "(6*n**2 + 249*n + 360)/(n + 40)", "answer_in_variable": "6*n + 9", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are 5*x + 4*y = 77 and 6*x - 5*y = 14. Find the charges as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (9, 8)", "id": "algebra-L3-a9ece18b329028ffeeb7-word", "source_id": "algebra-a9ece18b329028ffeeb7", "topic": "algebra", "level": 3, "kind": "solve", "question": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are 5*x + 4*y = 77 and 6*x - 5*y = 14. Find the charges as an ordered pair (x, y).", "answer": "(9, 8)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-a9ece18b329028ffeeb7", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 5*x + 4*y = 77, 6*x - 5*y = 14 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "5*x + 4*y = 77, 6*x - 5*y = 14", "answer_in_variable": "(9, 8)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy -2*x - 4*y = 2 and -6*x + 4*y = -10. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (1, -1)", "id": "algebra-L3-0ec3897457e39cf5bbb3-word", "source_id": "algebra-0ec3897457e39cf5bbb3", "topic": "algebra", "level": 3, "kind": "solve", "question": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy -2*x - 4*y = 2 and -6*x + 4*y = -10. Find the ordered pair (x, y).", "answer": "(1, -1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-0ec3897457e39cf5bbb3", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -2*x - 4*y = 2, -6*x + 4*y = -10 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-2*x - 4*y = 2, -6*x + 4*y = -10", "answer_in_variable": "(1, -1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An economist's ratio of total revenue to the number of batches is (11*k**2 + 167*k - 144)/(k + 16), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 11*x - 9", "id": "algebra-L3-aa25beba513022b61d18-word", "source_id": "algebra-aa25beba513022b61d18", "topic": "algebra", "level": 3, "kind": "simplify", "question": "An economist's ratio of total revenue to the number of batches is (11*k**2 + 167*k - 144)/(k + 16), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined.", "answer": "11*x - 9", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-aa25beba513022b61d18", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (11*x**2 + 167*x - 144)/(x - (-16)) for x != -16.", "variable": "k", "underlying_expression": "(11*k**2 + 167*k - 144)/(k + 16)", "answer_in_variable": "11*k - 9", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (s**2 - 12*s - 133)/(s + 7) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: x - 19", "id": "algebra-L3-2ee4f888ffc3e698b485-word", "source_id": "algebra-2ee4f888ffc3e698b485", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (s**2 - 12*s - 133)/(s + 7) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s.", "answer": "x - 19", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-2ee4f888ffc3e698b485", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (x**2 - 12*x - 133)/(x - (-7)) for x != -7.", "variable": "s", "underlying_expression": "(s**2 - 12*s - 133)/(s + 7)", "answer_in_variable": "s - 19", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist's concentration formula is (9*m**2 + 413*m - 46)/(m + 46) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 9*x - 1", "id": "algebra-L3-99e15cb44511b34d74e1-word", "source_id": "algebra-99e15cb44511b34d74e1", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A chemist's concentration formula is (9*m**2 + 413*m - 46)/(m + 46) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero).", "answer": "9*x - 1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-99e15cb44511b34d74e1", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (9*x**2 + 413*x - 46)/(x - (-46)) for x != -46.", "variable": "m", "underlying_expression": "(9*m**2 + 413*m - 46)/(m + 46)", "answer_in_variable": "9*m - 1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give -1*x - 6*y = 4 and -2*x + 2*y = -6. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (2, -1)", "id": "algebra-L3-acd80bdc43255e50502d-word", "source_id": "algebra-acd80bdc43255e50502d", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give -1*x - 6*y = 4 and -2*x + 2*y = -6. Find the corrections as an ordered pair (x, y).", "answer": "(2, -1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-acd80bdc43255e50502d", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -1*x - 6*y = 4, -2*x + 2*y = -6 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-1*x - 6*y = 4, -2*x + 2*y = -6", "answer_in_variable": "(2, -1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The average cost per crate in a shipment, in dollars, is (8*x**2 + 235*x - 150)/(x + 30), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 8*x - 5", "id": "algebra-L3-e828a3cf26e3336eb719-word", "source_id": "algebra-e828a3cf26e3336eb719", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (8*x**2 + 235*x - 150)/(x + 30), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "8*x - 5", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-e828a3cf26e3336eb719", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (8*x**2 + 235*x - 150)/(x - (-30)) for x != -30.", "variable": "x", "underlying_expression": "(8*x**2 + 235*x - 150)/(x + 30)", "answer_in_variable": "8*x - 5", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A machine's output rate is recorded as (6*t**2 - 200*t - 136)/(t - 34) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 6*x + 4", "id": "algebra-L3-57d4746d6b55e2d6ca61-word", "source_id": "algebra-57d4746d6b55e2d6ca61", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A machine's output rate is recorded as (6*t**2 - 200*t - 136)/(t - 34) units per hour, where t is the operating temperature setting. Simplify the rate to a polynomial in t, assuming the denominator is nonzero.", "answer": "6*x + 4", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-57d4746d6b55e2d6ca61", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (6*x**2 - 200*x - 136)/(x - (34)) for x != 34.", "variable": "t", "underlying_expression": "(6*t**2 - 200*t - 136)/(t - 34)", "answer_in_variable": "6*t + 4", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The number of items each worker handles is given by (5*n**2 + 241*n + 282)/(n + 47), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x + 6", "id": "algebra-L3-90315a81aebb4ab9f8b4-word", "source_id": "algebra-90315a81aebb4ab9f8b4", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The number of items each worker handles is given by (5*n**2 + 241*n + 282)/(n + 47), where n is a staffing parameter. Write this as a simplified polynomial in n (the denominator is never zero here).", "answer": "5*x + 6", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-90315a81aebb4ab9f8b4", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (5*x**2 + 241*x + 282)/(x - (-47)) for x != -47.", "variable": "n", "underlying_expression": "(5*n**2 + 241*n + 282)/(n + 47)", "answer_in_variable": "5*n + 6", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 4*x + 1*y = -12 and -1*x - 3*y = 3. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-3, 0)", "id": "algebra-L3-ab294a28c5dad1093d11-word", "source_id": "algebra-ab294a28c5dad1093d11", "topic": "algebra", "level": 3, "kind": "solve", "question": "A robot moves x meters east and y meters north (negative values mean west or south). Its sensors record 4*x + 1*y = -12 and -1*x - 3*y = 3. Find the ordered pair (x, y).", "answer": "(-3, 0)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-ab294a28c5dad1093d11", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x + 1*y = -12, -1*x - 3*y = 3 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x + 1*y = -12, -1*x - 3*y = 3", "answer_in_variable": "(-3, 0)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "An economist's ratio of total revenue to the number of batches is (5*k**2 - 262*k + 1269)/(k - 47), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 5*x - 27", "id": "algebra-L3-63187691a963cfb64011-word", "source_id": "algebra-63187691a963cfb64011", "topic": "algebra", "level": 3, "kind": "simplify", "question": "An economist's ratio of total revenue to the number of batches is (5*k**2 - 262*k + 1269)/(k - 47), with k a pricing parameter. Simplify the ratio into a polynomial in k, valid wherever it is defined.", "answer": "5*x - 27", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-63187691a963cfb64011", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (5*x**2 - 262*x + 1269)/(x - (47)) for x != 47.", "variable": "k", "underlying_expression": "(5*k**2 - 262*k + 1269)/(k - 47)", "answer_in_variable": "5*k - 27", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 4*x - 4*y = -28 and 6*x + 1*y = 21. Determine the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (2, 9)", "id": "algebra-L3-d4c4456d11df0fffa83e-word", "source_id": "algebra-d4c4456d11df0fffa83e", "topic": "algebra", "level": 3, "kind": "solve", "question": "In a store's accounting, x and y are the daily profits (in hundreds of dollars, losses negative) of two branches. Last week's reports give 4*x - 4*y = -28 and 6*x + 1*y = 21. Determine the ordered pair (x, y).", "answer": "(2, 9)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-d4c4456d11df0fffa83e", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x - 4*y = -28, 6*x + 1*y = 21 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x - 4*y = -28, 6*x + 1*y = 21", "answer_in_variable": "(2, 9)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give 4*x - 1*y = -5 and -1*x + 1*y = 5. Find the positions as (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (0, 5)", "id": "algebra-L3-bee579680cb51f5330b1-word", "source_id": "algebra-bee579680cb51f5330b1", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two weights on a balance beam sit at positions x and y (in decimeters from the pivot, negative on the left). The equilibrium conditions give 4*x - 1*y = -5 and -1*x + 1*y = 5. Find the positions as (x, y).", "answer": "(0, 5)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-bee579680cb51f5330b1", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 4*x - 1*y = -5, -1*x + 1*y = 5 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "4*x - 1*y = -5, -1*x + 1*y = 5", "answer_in_variable": "(0, 5)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -1*x - 5*y = -8 and 2*x + 1*y = -11. Find the charges as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-7, 3)", "id": "algebra-L3-136b3cb95a42a506564b-word", "source_id": "algebra-136b3cb95a42a506564b", "topic": "algebra", "level": 3, "kind": "solve", "question": "A chemist adjusts the charges x and y of two ions in a model (charges may be negative or zero); the model's constraints are -1*x - 5*y = -8 and 2*x + 1*y = -11. Find the charges as an ordered pair (x, y).", "answer": "(-7, 3)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-136b3cb95a42a506564b", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: -1*x - 5*y = -8, 2*x + 1*y = -11 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "-1*x - 5*y = -8, 2*x + 1*y = -11", "answer_in_variable": "(-7, 3)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 1*x + 4*y = -6 and -6*x + 6*y = -24. Find the ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (2, -2)", "id": "algebra-L3-d42249a09bc31038e02f-word", "source_id": "algebra-d42249a09bc31038e02f", "topic": "algebra", "level": 3, "kind": "solve", "question": "The scores x and y awarded in two rounds of a quiz (penalties can make a score negative or zero) satisfy 1*x + 4*y = -6 and -6*x + 6*y = -24. Find the ordered pair (x, y).", "answer": "(2, -2)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-d42249a09bc31038e02f", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 1*x + 4*y = -6, -6*x + 6*y = -24 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "1*x + 4*y = -6, -6*x + 6*y = -24", "answer_in_variable": "(2, -2)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (12*s**2 - 349*s + 29)/(s - 29) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 12*x - 1", "id": "algebra-L3-5afe382bc6ad518bcced-word", "source_id": "algebra-5afe382bc6ad518bcced", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The height of a rectangular panel, in centimeters, equals its area divided by its width, which gives (12*s**2 - 349*s + 29)/(s - 29) for a size parameter s. Simplify this expression to a polynomial in s for all allowed s.", "answer": "12*x - 1", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-5afe382bc6ad518bcced", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (12*x**2 - 349*x + 29)/(x - (29)) for x != 29.", "variable": "s", "underlying_expression": "(12*s**2 - 349*s + 29)/(s - 29)", "answer_in_variable": "12*s - 1", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "A chemist's concentration formula is (4*m**2 - 10*m - 6)/(m - 3) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 4*x + 2", "id": "algebra-L3-358b52b54816cd8127cb-word", "source_id": "algebra-358b52b54816cd8127cb", "topic": "algebra", "level": 3, "kind": "simplify", "question": "A chemist's concentration formula is (4*m**2 - 10*m - 6)/(m - 3) grams per liter, where m is a mixing parameter. Simplify the formula to a polynomial in m (assume the denominator is not zero).", "answer": "4*x + 2", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-358b52b54816cd8127cb", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (4*x**2 - 10*x - 6)/(x - (3)) for x != 3.", "variable": "m", "underlying_expression": "(4*m**2 - 10*m - 6)/(m - 3)", "answer_in_variable": "4*m + 2", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "The average cost per crate in a shipment, in dollars, is (2*x**2 - 24*x + 64)/(x - 8), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined. Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: 2*x - 8", "id": "algebra-L3-e7bfedb2f1093e0fdd48-word", "source_id": "algebra-e7bfedb2f1093e0fdd48", "topic": "algebra", "level": 3, "kind": "simplify", "question": "The average cost per crate in a shipment, in dollars, is (2*x**2 - 24*x + 64)/(x - 8), where x is a design parameter. Simplify this expression to a polynomial in x, wherever it is defined.", "answer": "2*x - 8", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-e7bfedb2f1093e0fdd48", "attack": "word_problem", "target": "algebra", "question_original": "Simplify (2*x**2 - 24*x + 64)/(x - (8)) for x != 8.", "variable": "x", "underlying_expression": "(2*x**2 - 24*x + 64)/(x - 8)", "answer_in_variable": "2*x - 8", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |
| {"instruction": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 3*x - 3*y = -6 and -2*x + 4*y = 2. Find the corrections as an ordered pair (x, y). Give the final answer on the last line as 'Answer: <expression>' (no units).", "output": "Answer: (-3, -1)", "id": "algebra-L3-ac6fc83791f684c754f2-word", "source_id": "algebra-ac6fc83791f684c754f2", "topic": "algebra", "level": 3, "kind": "solve", "question": "Two thermometers are being calibrated. If x and y are the corrections (in degrees, possibly negative) for the first and second thermometer, the test readings give 3*x - 3*y = -6 and -2*x + 4*y = 2. Find the corrections as an ordered pair (x, y).", "answer": "(-3, -1)", "expr": "", "primitive": "", "lower": "", "upper": "", "split": "test", "parent_id": "algebra-L3-ac6fc83791f684c754f2", "attack": "word_problem", "target": "algebra", "question_original": "Solve the system: 3*x - 3*y = -6, -2*x + 4*y = 2 for x and y. Give the answer as an ordered pair (x, y).", "variable": "x", "underlying_expression": "3*x - 3*y = -6, -2*x + 4*y = 2", "answer_in_variable": "(-3, -1)", "generator": "claude (Claude Agent SDK background agent; exact model id not exposed to the agent)"} | |