{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0001","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-12)x+(-3)。求 f(-4) 的精確值。","answer":{"kind":"numeric","value":"45","explanation_zh":"f(-4)=45。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035001,"parameters":{"m":-12,"b":-3,"x":-4,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":-12,\"operation\":\"affine_evaluate\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0002","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-11)x+(-2)。求 f(-3) 的精確值。","answer":{"kind":"numeric","value":"31","explanation_zh":"f(-3)=31。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035002,"parameters":{"m":-11,"b":-2,"x":-3,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":-11,\"operation\":\"affine_evaluate\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0003","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-10)x+(-1)。求 f(-2) 的精確值。","answer":{"kind":"numeric","value":"19","explanation_zh":"f(-2)=19。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035003,"parameters":{"m":-10,"b":-1,"x":-2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":-10,\"operation\":\"affine_evaluate\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0004","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-9)x+(0)。求 f(-1) 的精確值。","answer":{"kind":"numeric","value":"9","explanation_zh":"f(-1)=9。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035004,"parameters":{"m":-9,"b":0,"x":-1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":-9,\"operation\":\"affine_evaluate\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0005","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-8)x+(1)。求 f(0) 的精確值。","answer":{"kind":"numeric","value":"1","explanation_zh":"f(0)=1。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035005,"parameters":{"m":-8,"b":1,"x":0,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":-8,\"operation\":\"affine_evaluate\",\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0006","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-7)x+(2)。求 f(1) 的精確值。","answer":{"kind":"numeric","value":"-5","explanation_zh":"f(1)=-5。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035006,"parameters":{"m":-7,"b":2,"x":1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"affine_evaluate\",\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0007","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-6)x+(3)。求 f(2) 的精確值。","answer":{"kind":"numeric","value":"-9","explanation_zh":"f(2)=-9。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035007,"parameters":{"m":-6,"b":3,"x":2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":-6,\"operation\":\"affine_evaluate\",\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0008","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-5)x+(-3)。求 f(3) 的精確值。","answer":{"kind":"numeric","value":"-18","explanation_zh":"f(3)=-18。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035008,"parameters":{"m":-5,"b":-3,"x":3,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":-5,\"operation\":\"affine_evaluate\",\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0009","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-4)x+(-2)。求 f(4) 的精確值。","answer":{"kind":"numeric","value":"-18","explanation_zh":"f(4)=-18。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035009,"parameters":{"m":-4,"b":-2,"x":4,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":-4,\"operation\":\"affine_evaluate\",\"x\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0010","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-3)x+(-1)。求 f(-4) 的精確值。","answer":{"kind":"numeric","value":"11","explanation_zh":"f(-4)=11。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035010,"parameters":{"m":-3,"b":-1,"x":-4,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":-3,\"operation\":\"affine_evaluate\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0011","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-2)x+(0)。求 f(-3) 的精確值。","answer":{"kind":"numeric","value":"6","explanation_zh":"f(-3)=6。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035011,"parameters":{"m":-2,"b":0,"x":-3,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":-2,\"operation\":\"affine_evaluate\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0012","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(-1)x+(1)。求 f(-2) 的精確值。","answer":{"kind":"numeric","value":"3","explanation_zh":"f(-2)=3。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035012,"parameters":{"m":-1,"b":1,"x":-2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"affine_evaluate\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0013","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(0)x+(2)。求 f(-1) 的精確值。","answer":{"kind":"numeric","value":"2","explanation_zh":"f(-1)=2。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035013,"parameters":{"m":0,"b":2,"x":-1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":0,\"operation\":\"affine_evaluate\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0014","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(1)x+(3)。求 f(0) 的精確值。","answer":{"kind":"numeric","value":"3","explanation_zh":"f(0)=3。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035014,"parameters":{"m":1,"b":3,"x":0,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":1,\"operation\":\"affine_evaluate\",\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0015","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(2)x+(-3)。求 f(1) 的精確值。","answer":{"kind":"numeric","value":"-1","explanation_zh":"f(1)=-1。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035015,"parameters":{"m":2,"b":-3,"x":1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":2,\"operation\":\"affine_evaluate\",\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0016","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(3)x+(-2)。求 f(2) 的精確值。","answer":{"kind":"numeric","value":"4","explanation_zh":"f(2)=4。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035016,"parameters":{"m":3,"b":-2,"x":2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"affine_evaluate\",\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0017","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(4)x+(-1)。求 f(3) 的精確值。","answer":{"kind":"numeric","value":"11","explanation_zh":"f(3)=11。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035017,"parameters":{"m":4,"b":-1,"x":3,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"affine_evaluate\",\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0018","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(5)x+(0)。求 f(4) 的精確值。","answer":{"kind":"numeric","value":"20","explanation_zh":"f(4)=20。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035018,"parameters":{"m":5,"b":0,"x":4,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"affine_evaluate\",\"x\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0019","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(6)x+(1)。求 f(-4) 的精確值。","answer":{"kind":"numeric","value":"-23","explanation_zh":"f(-4)=-23。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035019,"parameters":{"m":6,"b":1,"x":-4,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"affine_evaluate\",\"x\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0020","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(7)x+(2)。求 f(-3) 的精確值。","answer":{"kind":"numeric","value":"-19","explanation_zh":"f(-3)=-19。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035020,"parameters":{"m":7,"b":2,"x":-3,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"affine_evaluate\",\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0021","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(8)x+(3)。求 f(-2) 的精確值。","answer":{"kind":"numeric","value":"-13","explanation_zh":"f(-2)=-13。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035021,"parameters":{"m":8,"b":3,"x":-2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":3,\"domain\":\"reals\",\"m\":8,\"operation\":\"affine_evaluate\",\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0022","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(9)x+(-3)。求 f(-1) 的精確值。","answer":{"kind":"numeric","value":"-12","explanation_zh":"f(-1)=-12。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035022,"parameters":{"m":9,"b":-3,"x":-1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-3,\"domain\":\"reals\",\"m\":9,\"operation\":\"affine_evaluate\",\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0023","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(10)x+(-2)。求 f(0) 的精確值。","answer":{"kind":"numeric","value":"-2","explanation_zh":"f(0)=-2。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035023,"parameters":{"m":10,"b":-2,"x":0,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-2,\"domain\":\"reals\",\"m\":10,\"operation\":\"affine_evaluate\",\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0024","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(11)x+(-1)。求 f(1) 的精確值。","answer":{"kind":"numeric","value":"10","explanation_zh":"f(1)=10。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035024,"parameters":{"m":11,"b":-1,"x":1,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":-1,\"domain\":\"reals\",\"m\":11,\"operation\":\"affine_evaluate\",\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0025","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數精確求值","stem_zh":"在實數論域 R，f(x)=(12)x+(0)。求 f(2) 的精確值。","answer":{"kind":"numeric","value":"24","explanation_zh":"f(2)=24。先把輸入乘斜率，再加截距；m=0 的常數函數仍在仿射族中。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數精確求值"]},"variant":{"family_id":"qf-affine-exact-evaluation","seed":202610035025,"parameters":{"m":12,"b":0,"x":2,"domain":"reals","operation":"affine_evaluate","semantic_template":"qf-affine-exact-evaluation/{\"b\":0,\"domain\":\"reals\",\"m\":12,\"operation\":\"affine_evaluate\",\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0026","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-12, -2)、(-11, -14)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-12/1","explanation_zh":"斜率=-12/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035026,"parameters":{"x1":-12,"y1":-2,"x2":-11,"y2":-14,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-12,\"x2\":-11,\"y1\":-2,\"y2\":-14}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0027","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-11, -1)、(-13, -12)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"11/2","explanation_zh":"斜率=11/2。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035027,"parameters":{"x1":-11,"y1":-1,"x2":-13,"y2":-12,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-11,\"y1\":-12,\"y2\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0028","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-10, 0)、(-7, -10)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-10/3","explanation_zh":"斜率=-10/3。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035028,"parameters":{"x1":-10,"y1":0,"x2":-7,"y2":-10,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-10,\"x2\":-7,\"y1\":0,\"y2\":-10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0029","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-9, 1)、(-13, -8)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"9/4","explanation_zh":"斜率=9/4。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035029,"parameters":{"x1":-9,"y1":1,"x2":-13,"y2":-8,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-9,\"y1\":-8,\"y2\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0030","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-8, 2)、(-3, -6)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-8/5","explanation_zh":"斜率=-8/5。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035030,"parameters":{"x1":-8,"y1":2,"x2":-3,"y2":-6,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-8,\"x2\":-3,\"y1\":2,\"y2\":-6}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0031","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-7, -2)、(-13, -9)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"7/6","explanation_zh":"斜率=7/6。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035031,"parameters":{"x1":-7,"y1":-2,"x2":-13,"y2":-9,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-13,\"x2\":-7,\"y1\":-9,\"y2\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0032","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-6, -1)、(-5, -7)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-6/1","explanation_zh":"斜率=-6/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035032,"parameters":{"x1":-6,"y1":-1,"x2":-5,"y2":-7,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-6,\"x2\":-5,\"y1\":-1,\"y2\":-7}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0033","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-5, 0)、(-7, -5)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"5/2","explanation_zh":"斜率=5/2。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035033,"parameters":{"x1":-5,"y1":0,"x2":-7,"y2":-5,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-5,\"y1\":-5,\"y2\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0034","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-4, 1)、(-1, -3)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-4/3","explanation_zh":"斜率=-4/3。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035034,"parameters":{"x1":-4,"y1":1,"x2":-1,"y2":-3,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-4,\"x2\":-1,\"y1\":1,\"y2\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0035","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-3, 2)、(-7, -1)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"3/4","explanation_zh":"斜率=3/4。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035035,"parameters":{"x1":-3,"y1":2,"x2":-7,"y2":-1,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-3,\"y1\":-1,\"y2\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0036","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-2, -2)、(3, -4)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-2/5","explanation_zh":"斜率=-2/5。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035036,"parameters":{"x1":-2,"y1":-2,"x2":3,"y2":-4,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-2,\"x2\":3,\"y1\":-2,\"y2\":-4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0037","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (-1, -1)、(-7, -2)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"1/6","explanation_zh":"斜率=1/6。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035037,"parameters":{"x1":-1,"y1":-1,"x2":-7,"y2":-2,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-7,\"x2\":-1,\"y1\":-2,\"y2\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0038","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (0, 0)、(1, 0)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"0/1","explanation_zh":"斜率=0/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035038,"parameters":{"x1":0,"y1":0,"x2":1,"y2":0,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":0,\"x2\":1,\"y1\":0,\"y2\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0039","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (1, 1)、(-1, 2)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-1/2","explanation_zh":"斜率=-1/2。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035039,"parameters":{"x1":1,"y1":1,"x2":-1,"y2":2,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":1,\"y1\":2,\"y2\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0040","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (2, 2)、(5, 4)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"2/3","explanation_zh":"斜率=2/3。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035040,"parameters":{"x1":2,"y1":2,"x2":5,"y2":4,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":2,\"x2\":5,\"y1\":2,\"y2\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0041","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (3, -2)、(-1, 1)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-3/4","explanation_zh":"斜率=-3/4。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035041,"parameters":{"x1":3,"y1":-2,"x2":-1,"y2":1,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":3,\"y1\":1,\"y2\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0042","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (4, -1)、(9, 3)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"4/5","explanation_zh":"斜率=4/5。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035042,"parameters":{"x1":4,"y1":-1,"x2":9,"y2":3,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":4,\"x2\":9,\"y1\":-1,\"y2\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0043","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (5, 0)、(-1, 5)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-5/6","explanation_zh":"斜率=-5/6。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035043,"parameters":{"x1":5,"y1":0,"x2":-1,"y2":5,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":-1,\"x2\":5,\"y1\":5,\"y2\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0044","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (6, 1)、(7, 7)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"6/1","explanation_zh":"斜率=6/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035044,"parameters":{"x1":6,"y1":1,"x2":7,"y2":7,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":6,\"x2\":7,\"y1\":1,\"y2\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0045","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (7, 2)、(5, 9)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-7/2","explanation_zh":"斜率=-7/2。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035045,"parameters":{"x1":7,"y1":2,"x2":5,"y2":9,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":7,\"y1\":9,\"y2\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0046","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (8, -2)、(11, 6)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"8/3","explanation_zh":"斜率=8/3。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035046,"parameters":{"x1":8,"y1":-2,"x2":11,"y2":6,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":8,\"x2\":11,\"y1\":-2,\"y2\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0047","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (9, -1)、(5, 8)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-9/4","explanation_zh":"斜率=-9/4。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035047,"parameters":{"x1":9,"y1":-1,"x2":5,"y2":8,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":9,\"y1\":8,\"y2\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0048","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (10, 0)、(15, 10)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"2/1","explanation_zh":"斜率=2/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035048,"parameters":{"x1":10,"y1":0,"x2":15,"y2":10,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":10,\"x2\":15,\"y1\":0,\"y2\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0049","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (11, 1)、(5, 12)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"-11/6","explanation_zh":"斜率=-11/6。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035049,"parameters":{"x1":11,"y1":1,"x2":5,"y2":12,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":5,\"x2\":11,\"y1\":12,\"y2\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0050","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射圖形的兩點斜率","stem_zh":"在實數論域，仿射函數圖形含兩點 (12, 2)、(13, 14)，兩橫座標不同。求最簡正分母斜率。","answer":{"kind":"expression","value":"12/1","explanation_zh":"斜率=12/1。使用 (y₂−y₁)/(x₂−x₁)，分母非零；此式不適用垂直線。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射圖形的兩點斜率"]},"variant":{"family_id":"qf-affine-two-point-slope","seed":202610035050,"parameters":{"x1":12,"y1":2,"x2":13,"y2":14,"domain":"reals","operation":"slope","semantic_template":"qf-affine-two-point-slope/{\"domain\":\"reals\",\"operation\":\"slope\",\"x1\":12,\"x2\":13,\"y1\":2,\"y2\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0051","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(0)x+(0)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"R","explanation_zh":"零點集=R。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035051,"parameters":{"m":0,"b":0,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0052","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(0)x+(3)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"∅","explanation_zh":"零點集=∅。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035052,"parameters":{"m":0,"b":3,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":3,\"domain\":\"reals\",\"m\":0,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0053","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-10)x+(0)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{0/1}","explanation_zh":"零點集={0/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035053,"parameters":{"m":-10,"b":0,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":-10,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0054","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-9)x+(1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/9}","explanation_zh":"零點集={1/9}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035054,"parameters":{"m":-9,"b":1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":-9,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0055","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-8)x+(2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/4}","explanation_zh":"零點集={1/4}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035055,"parameters":{"m":-8,"b":2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":-8,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0056","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-7)x+(-2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-2/7}","explanation_zh":"零點集={-2/7}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035056,"parameters":{"m":-7,"b":-2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0057","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-6)x+(-1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/6}","explanation_zh":"零點集={-1/6}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035057,"parameters":{"m":-6,"b":-1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":-6,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0058","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-5)x+(0)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{0/1}","explanation_zh":"零點集={0/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035058,"parameters":{"m":-5,"b":0,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":-5,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0059","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-4)x+(1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/4}","explanation_zh":"零點集={1/4}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035059,"parameters":{"m":-4,"b":1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":-4,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0060","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-3)x+(2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{2/3}","explanation_zh":"零點集={2/3}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035060,"parameters":{"m":-3,"b":2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":-3,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0061","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-2)x+(-2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/1}","explanation_zh":"零點集={-1/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035061,"parameters":{"m":-2,"b":-2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0062","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(-1)x+(-1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/1}","explanation_zh":"零點集={-1/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035062,"parameters":{"m":-1,"b":-1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0063","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(1)x+(4)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-4/1}","explanation_zh":"零點集={-4/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035063,"parameters":{"m":1,"b":4,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":4,\"domain\":\"reals\",\"m\":1,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0064","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(1)x+(1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/1}","explanation_zh":"零點集={-1/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035064,"parameters":{"m":1,"b":1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0065","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(2)x+(2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/1}","explanation_zh":"零點集={-1/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035065,"parameters":{"m":2,"b":2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0066","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(3)x+(-2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{2/3}","explanation_zh":"零點集={2/3}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035066,"parameters":{"m":3,"b":-2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0067","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(4)x+(-1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/4}","explanation_zh":"零點集={1/4}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035067,"parameters":{"m":4,"b":-1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0068","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(5)x+(0)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{0/1}","explanation_zh":"零點集={0/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035068,"parameters":{"m":5,"b":0,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0069","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(6)x+(1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/6}","explanation_zh":"零點集={-1/6}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035069,"parameters":{"m":6,"b":1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0070","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(7)x+(2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-2/7}","explanation_zh":"零點集={-2/7}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035070,"parameters":{"m":7,"b":2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0071","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(8)x+(-2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/4}","explanation_zh":"零點集={1/4}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035071,"parameters":{"m":8,"b":-2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-2,\"domain\":\"reals\",\"m\":8,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0072","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(9)x+(-1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{1/9}","explanation_zh":"零點集={1/9}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035072,"parameters":{"m":9,"b":-1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":-1,\"domain\":\"reals\",\"m\":9,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0073","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(10)x+(0)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{0/1}","explanation_zh":"零點集={0/1}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035073,"parameters":{"m":10,"b":0,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":0,\"domain\":\"reals\",\"m\":10,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0074","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(11)x+(1)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/11}","explanation_zh":"零點集={-1/11}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035074,"parameters":{"m":11,"b":1,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":1,\"domain\":\"reals\",\"m\":11,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0075","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的完整零點集合","stem_zh":"在實數論域 R，f(x)=(12)x+(2)。求全部零點，以 R、∅ 或最簡有理數集合回答。","answer":{"kind":"expression","value":"{-1/6}","explanation_zh":"零點集={-1/6}。m≠0 時零點唯一；m=0 且 b=0 時全部實數皆為零點，m=0 且 b≠0 時無零點。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的完整零點集合"]},"variant":{"family_id":"qf-affine-zero-set","seed":202610035075,"parameters":{"m":12,"b":2,"domain":"reals","operation":"zero_set","semantic_template":"qf-affine-zero-set/{\"b\":2,\"domain\":\"reals\",\"m\":12,\"operation\":\"zero_set\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0076","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(1)x+(2)，g(x)=(1)x+(2)。只問 f(0) 與 g(0) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(0)=2, g(0)=2。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035076,"parameters":{"m":1,"b":2,"u":1,"v":2,"x":0,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":1,\"operation\":\"compare_at_input\",\"u\":1,\"v\":2,\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0077","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-11)x+(-1)，g(x)=(-10)x+(2)。只問 f(-2) 與 g(-2) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-2)=21, g(-2)=22。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035077,"parameters":{"m":-11,"b":-1,"u":-10,"v":2,"x":-2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-11,\"operation\":\"compare_at_input\",\"u\":-10,\"v\":2,\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0078","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-10)x+(0)，g(x)=(-9)x+(1)。只問 f(-1) 與 g(-1) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(-1)=10, g(-1)=10。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035078,"parameters":{"m":-10,"b":0,"u":-9,"v":1,"x":-1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":-10,\"operation\":\"compare_at_input\",\"u\":-9,\"v\":1,\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0079","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-9)x+(1)，g(x)=(-8)x+(2)。只問 f(0) 與 g(0) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(0)=1, g(0)=2。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035079,"parameters":{"m":-9,"b":1,"u":-8,"v":2,"x":0,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":-9,\"operation\":\"compare_at_input\",\"u\":-8,\"v\":2,\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0080","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-8)x+(2)，g(x)=(-7)x+(1)。只問 f(1) 與 g(1) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(1)=-6, g(1)=-6。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035080,"parameters":{"m":-8,"b":2,"u":-7,"v":1,"x":1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":-8,\"operation\":\"compare_at_input\",\"u\":-7,\"v\":1,\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0081","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-7)x+(-2)，g(x)=(-6)x+(-3)。只問 f(2) 與 g(2) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(2)=-16, g(2)=-15。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035081,"parameters":{"m":-7,"b":-2,"u":-6,"v":-3,"x":2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":-7,\"operation\":\"compare_at_input\",\"u\":-6,\"v\":-3,\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0082","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-6)x+(-1)，g(x)=(-5)x+(-4)。只問 f(3) 與 g(3) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(3)=-19, g(3)=-19。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035082,"parameters":{"m":-6,"b":-1,"u":-5,"v":-4,"x":3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-6,\"operation\":\"compare_at_input\",\"u\":-5,\"v\":-4,\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0083","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-5)x+(0)，g(x)=(-4)x+(4)。只問 f(-3) 與 g(-3) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-3)=15, g(-3)=16。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035083,"parameters":{"m":-5,"b":0,"u":-4,"v":4,"x":-3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":-5,\"operation\":\"compare_at_input\",\"u\":-4,\"v\":4,\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0084","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-4)x+(1)，g(x)=(-3)x+(3)。只問 f(-2) 與 g(-2) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(-2)=9, g(-2)=9。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035084,"parameters":{"m":-4,"b":1,"u":-3,"v":3,"x":-2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":-4,\"operation\":\"compare_at_input\",\"u\":-3,\"v\":3,\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0085","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-3)x+(2)，g(x)=(-2)x+(4)。只問 f(-1) 與 g(-1) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-1)=5, g(-1)=6。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035085,"parameters":{"m":-3,"b":2,"u":-2,"v":4,"x":-1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":-3,\"operation\":\"compare_at_input\",\"u\":-2,\"v\":4,\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0086","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-2)x+(-2)，g(x)=(-1)x+(-2)。只問 f(0) 與 g(0) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(0)=-2, g(0)=-2。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035086,"parameters":{"m":-2,"b":-2,"u":-1,"v":-2,"x":0,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":-2,\"operation\":\"compare_at_input\",\"u\":-1,\"v\":-2,\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0087","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(-1)x+(-1)，g(x)=(0)x+(-1)。只問 f(1) 與 g(1) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(1)=-2, g(1)=-1。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035087,"parameters":{"m":-1,"b":-1,"u":0,"v":-1,"x":1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":-1,\"operation\":\"compare_at_input\",\"u\":0,\"v\":-1,\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0088","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(0)x+(0)，g(x)=(1)x+(-2)。只問 f(2) 與 g(2) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(2)=0, g(2)=0。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035088,"parameters":{"m":0,"b":0,"u":1,"v":-2,"x":2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":0,\"operation\":\"compare_at_input\",\"u\":1,\"v\":-2,\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0089","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(1)x+(1)，g(x)=(2)x+(-1)。只問 f(3) 與 g(3) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(3)=4, g(3)=5。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035089,"parameters":{"m":1,"b":1,"u":2,"v":-1,"x":3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":1,\"operation\":\"compare_at_input\",\"u\":2,\"v\":-1,\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0090","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(2)x+(2)，g(x)=(3)x+(5)。只問 f(-3) 與 g(-3) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(-3)=-4, g(-3)=-4。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035090,"parameters":{"m":2,"b":2,"u":3,"v":5,"x":-3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":2,\"operation\":\"compare_at_input\",\"u\":3,\"v\":5,\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0091","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(3)x+(-2)，g(x)=(4)x+(1)。只問 f(-2) 與 g(-2) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-2)=-8, g(-2)=-7。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035091,"parameters":{"m":3,"b":-2,"u":4,"v":1,"x":-2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":3,\"operation\":\"compare_at_input\",\"u\":4,\"v\":1,\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0092","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(4)x+(-1)，g(x)=(5)x+(0)。只問 f(-1) 與 g(-1) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(-1)=-5, g(-1)=-5。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035092,"parameters":{"m":4,"b":-1,"u":5,"v":0,"x":-1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":4,\"operation\":\"compare_at_input\",\"u\":5,\"v\":0,\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0093","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(5)x+(0)，g(x)=(6)x+(1)。只問 f(0) 與 g(0) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(0)=0, g(0)=1。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035093,"parameters":{"m":5,"b":0,"u":6,"v":1,"x":0,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":5,\"operation\":\"compare_at_input\",\"u\":6,\"v\":1,\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0094","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(6)x+(1)，g(x)=(7)x+(0)。只問 f(1) 與 g(1) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(1)=7, g(1)=7。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035094,"parameters":{"m":6,"b":1,"u":7,"v":0,"x":1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":6,\"operation\":\"compare_at_input\",\"u\":7,\"v\":0,\"x\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0095","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(7)x+(2)，g(x)=(8)x+(1)。只問 f(2) 與 g(2) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(2)=16, g(2)=17。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035095,"parameters":{"m":7,"b":2,"u":8,"v":1,"x":2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":7,\"operation\":\"compare_at_input\",\"u\":8,\"v\":1,\"x\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0096","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(8)x+(-2)，g(x)=(9)x+(-5)。只問 f(3) 與 g(3) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(3)=22, g(3)=22。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035096,"parameters":{"m":8,"b":-2,"u":9,"v":-5,"x":3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-2,\"domain\":\"reals\",\"m\":8,\"operation\":\"compare_at_input\",\"u\":9,\"v\":-5,\"x\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0097","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(9)x+(-1)，g(x)=(10)x+(3)。只問 f(-3) 與 g(-3) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-3)=-28, g(-3)=-27。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035097,"parameters":{"m":9,"b":-1,"u":10,"v":3,"x":-3,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":-1,\"domain\":\"reals\",\"m\":9,\"operation\":\"compare_at_input\",\"u\":10,\"v\":3,\"x\":-3}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0098","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(10)x+(0)，g(x)=(11)x+(2)。只問 f(-2) 與 g(-2) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(-2)=-20, g(-2)=-20。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035098,"parameters":{"m":10,"b":0,"u":11,"v":2,"x":-2,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":0,\"domain\":\"reals\",\"m\":10,\"operation\":\"compare_at_input\",\"u\":11,\"v\":2,\"x\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0099","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(11)x+(1)，g(x)=(12)x+(3)。只問 f(-1) 與 g(-1) 是否相等？","answer":{"kind":"short_text","value":"否","explanation_zh":"f(-1)=-10, g(-1)=-9。答案是否；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035099,"parameters":{"m":11,"b":1,"u":12,"v":3,"x":-1,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":1,\"domain\":\"reals\",\"m\":11,\"operation\":\"compare_at_input\",\"u\":12,\"v\":3,\"x\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261003-r05-linear-function-0100","batch_id":"batch-20261003-r05-linear-function-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-function"],"title_zh":"仿射函數的單點比較","stem_zh":"在實數論域 R，f(x)=(12)x+(2)，g(x)=(13)x+(2)。只問 f(0) 與 g(0) 是否相等？","answer":{"kind":"short_text","value":"是","explanation_zh":"f(0)=2, g(0)=2。答案是是；單點輸出相同不代表全域相等。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["仿射函數的單點比較"]},"variant":{"family_id":"qf-affine-pointwise-comparison","seed":202610035100,"parameters":{"m":12,"b":2,"u":13,"v":2,"x":0,"domain":"reals","operation":"compare_at_input","semantic_template":"qf-affine-pointwise-comparison/{\"b\":2,\"domain\":\"reals\",\"m\":12,\"operation\":\"compare_at_input\",\"u\":13,\"v\":2,\"x\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication"],"warning_zh":"僅為獨立出題上下文的候選與自檢；主架構者仍須獨立驗收，不構成人工審定或一般形式證明。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent peer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-03","contract_version":"ocme-question-factory-v0.1"}}