Algebra

A benchmark to evaluate a model's ability to solve linear and quadratic equations with integer solutions. Includes single-variable linear equations (ax + b = c) and quadratic equations with one or two integer roots.

Run Benchmark
Questions

40

Total Runs

18

Best Score

100/100

Leaderboard
Rank Model Score Run Date Actions
Qwen3 VL 8B (LMStudio)
5000 MB
100
2026-02-28 18:45:12 View Details
2 GPT-5 mini
97
2026-02-26 01:20:35 View Details
3 Gemma 3 12B (LMStudio)
8100 MB
85
2026-02-28 15:55:35 View Details
4 GPT-5 nano
80
2026-02-26 00:52:26 View Details
5 Gemma 2 9B (LMStudio)
5800 MB
72
2026-02-28 15:02:15 View Details
6 Qwen3 4B (LMStudio)
2800 MB
65
2026-02-28 18:14:15 View Details
7 OLMo 3 7B (LMStudio)
4300 MB
62
2026-02-28 17:38:02 View Details
8 Qwen3 1.7B (LMStudio)
1100 MB
60
2026-02-28 18:05:48 View Details
9 Llama 3.1 8B (LMStudio)
4900 MB
55
2026-02-28 17:02:51 View Details
10 Llama 3 8B (LMStudio)
4900 MB
47
2026-02-28 16:47:24 View Details
11 Ministral 8B (LMStudio)
4900 MB
47
2026-02-28 17:24:11 View Details
12 Granite 3.2 8B (LMStudio)
4900 MB
45
2026-02-28 16:19:58 View Details
13 Gemma 2 2B (LMStudio)
1500 MB
42
2026-02-28 03:24:00 View Details
14 Llama 3.2 1B (LMStudio)
1300 MB
42
2026-02-28 17:13:30 View Details
15 SmolLM2 1.7B (LMStudio)
1100 MB
35
2026-02-28 19:19:48 View Details
16 Gemma 2B (LMStudio)
1500 MB
30
2026-02-28 15:35:36 View Details
17 Llama 2 7B (LMStudio)
4900 MB
10
2026-02-28 03:06:27 View Details
18 Phi-3.5 Mini (LMStudio)
2500 MB
2
2026-02-28 17:50:15 View Details
Questions

Question
If 4x - 20 = -36, what is x?
Question payload
{
  "question_text": "If 4x - 20 = -36, what is x?",
  "answer_type": "numeric",
  "correct_answer": -4.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 6x + 9 = 0, what is x?
Question payload
{
  "question_text": "If x² - 6x + 9 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 3.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "2, 6",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 10x + 24 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² + 10x + 24 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-6, -4",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 4x + 4 = 0, what is x?
Question payload
{
  "question_text": "If x² + 4x + 4 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -2.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 4x + 4 = 0, what is x?
Question payload
{
  "question_text": "If x² + 4x + 4 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -2.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 2x + 1 = 0, what is x?
Question payload
{
  "question_text": "If x² + 2x + 1 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -1.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 12x + 36 = 0, what is x?
Question payload
{
  "question_text": "If x² - 12x + 36 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 14x + 49 = 0, what is x?
Question payload
{
  "question_text": "If x² + 14x + 49 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -7.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 4x - 21 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 4x - 21 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-3, 7",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 9x + 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² + 9x + 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-8, -1",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² - 14x + 49 = 0, what is x?
Question payload
{
  "question_text": "If x² - 14x + 49 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 7.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 4x + 4 = 0, what is x?
Question payload
{
  "question_text": "If x² - 4x + 4 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 2.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 3x + 8 = 20, what is x?
Question payload
{
  "question_text": "If 3x + 8 = 20, what is x?",
  "answer_type": "numeric",
  "correct_answer": 4.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 16x + 64 = 0, what is x?
Question payload
{
  "question_text": "If x² + 16x + 64 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -8.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 4x - 7 = 9, what is x?
Question payload
{
  "question_text": "If 4x - 7 = 9, what is x?",
  "answer_type": "numeric",
  "correct_answer": 4.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 16x + 64 = 0, what is x?
Question payload
{
  "question_text": "If x² + 16x + 64 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -8.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 3x - 10 = 8, what is x?
Question payload
{
  "question_text": "If 3x - 10 = 8, what is x?",
  "answer_type": "numeric",
  "correct_answer": 6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 5x + 17 = 42, what is x?
Question payload
{
  "question_text": "If 5x + 17 = 42, what is x?",
  "answer_type": "numeric",
  "correct_answer": 5.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 12x + 36 = 0, what is x?
Question payload
{
  "question_text": "If x² - 12x + 36 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 2x + 1 = 0, what is x?
Question payload
{
  "question_text": "If x² + 2x + 1 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -1.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 12x + 36 = 0, what is x?
Question payload
{
  "question_text": "If x² - 12x + 36 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 2x + 13 = 7, what is x?
Question payload
{
  "question_text": "If 2x + 13 = 7, what is x?",
  "answer_type": "numeric",
  "correct_answer": -3.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-1, 8",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 14x + 49 = 0, what is x?
Question payload
{
  "question_text": "If x² + 14x + 49 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -7.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 5x + 19 = -6, what is x?
Question payload
{
  "question_text": "If 5x + 19 = -6, what is x?",
  "answer_type": "numeric",
  "correct_answer": -5.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + 16x + 64 = 0, what is x?
Question payload
{
  "question_text": "If x² + 16x + 64 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -8.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 12x + 36 = 0, what is x?
Question payload
{
  "question_text": "If x² - 12x + 36 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 13x + 42 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 13x + 42 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "6, 7",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 7x - 8 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-1, 8",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² - 14x + 48 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 14x + 48 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "6, 8",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² + 8x + 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-6, -2",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² - 11x + 30 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 11x + 30 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "5, 6",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 3x - 18 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² + 3x - 18 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-6, 3",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² - 3x - 40 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² - 3x - 40 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-5, 8",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}

Question
If x² + 12x + 36 = 0, what is x?
Question payload
{
  "question_text": "If x² + 12x + 36 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": -6.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² - 10x + 25 = 0, what is x?
Question payload
{
  "question_text": "If x² - 10x + 25 = 0, what is x?",
  "answer_type": "numeric",
  "correct_answer": 5.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "single_root"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 5x - 13 = -3, what is x?
Question payload
{
  "question_text": "If 5x - 13 = -3, what is x?",
  "answer_type": "numeric",
  "correct_answer": 2.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If 4x + 2 = 18, what is x?
Question payload
{
  "question_text": "If 4x + 2 = 18, what is x?",
  "answer_type": "numeric",
  "correct_answer": 4.0,
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "linear"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "result": {
        "type": "number",
        "description": "The value of x"
      }
    },
    "required": [
      "result"
    ]
  },
  "evaluation_criteria": {
    "exact_match": true,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.001,
    "alternatives": []
  }
}

Question
If x² + x - 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)
Question payload
{
  "question_text": "If x² + x - 12 = 0, what are the values of x? (Give both answers separated by a comma, smallest first.)",
  "answer_type": "free_text",
  "correct_answer": "-4, 3",
  "category": "algebra",
  "difficulty": "medium",
  "tags": [
    "algebra",
    "quadratic",
    "two_roots"
  ],
  "schema": {
    "type": "object",
    "properties": {
      "values": {
        "type": "string",
        "description": "Both values of x, comma-separated, smallest first (e.g. '-3, 5')"
      }
    },
    "required": [
      "values"
    ]
  },
  "evaluation_criteria": {
    "exact_match": false,
    "case_sensitive": false,
    "contains": false,
    "required_fields": [],
    "tolerance": 0.0,
    "alternatives": []
  }
}