{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0001","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-12x+(3)，求 f′(-2)。","answer":{"kind":"short_text","value":"-12","explanation_zh":"導數=-12。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084001,"parameters":{"m":-12,"b":3,"x":-2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-12\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0002","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-11x+(2)，求 f′(-1)。","answer":{"kind":"short_text","value":"-11","explanation_zh":"導數=-11。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084002,"parameters":{"m":-11,"b":2,"x":-1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-11\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0003","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-10x+(1)，求 f′(0)。","answer":{"kind":"short_text","value":"-10","explanation_zh":"導數=-10。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084003,"parameters":{"m":-10,"b":1,"x":0,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-10\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0004","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-9x+(0)，求 f′(1)。","answer":{"kind":"short_text","value":"-9","explanation_zh":"導數=-9。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084004,"parameters":{"m":-9,"b":0,"x":1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-9\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0005","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-8x+(-1)，求 f′(2)。","answer":{"kind":"short_text","value":"-8","explanation_zh":"導數=-8。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084005,"parameters":{"m":-8,"b":-1,"x":2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-8\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0006","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-7x+(-2)，求 f′(-2)。","answer":{"kind":"short_text","value":"-7","explanation_zh":"導數=-7。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084006,"parameters":{"m":-7,"b":-2,"x":-2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-7\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0007","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-6x+(-3)，求 f′(-1)。","answer":{"kind":"short_text","value":"-6","explanation_zh":"導數=-6。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084007,"parameters":{"m":-6,"b":-3,"x":-1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-6\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0008","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-5x+(-4)，求 f′(0)。","answer":{"kind":"short_text","value":"-5","explanation_zh":"導數=-5。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084008,"parameters":{"m":-5,"b":-4,"x":0,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-5\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0009","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-4x+(-5)，求 f′(1)。","answer":{"kind":"short_text","value":"-4","explanation_zh":"導數=-4。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084009,"parameters":{"m":-4,"b":-5,"x":1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-4\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0010","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-3x+(-6)，求 f′(2)。","answer":{"kind":"short_text","value":"-3","explanation_zh":"導數=-3。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084010,"parameters":{"m":-3,"b":-6,"x":2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-3\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0011","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-2x+(-7)，求 f′(-2)。","answer":{"kind":"short_text","value":"-2","explanation_zh":"導數=-2。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084011,"parameters":{"m":-2,"b":-7,"x":-2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-2\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0012","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-1x+(-8)，求 f′(-1)。","answer":{"kind":"short_text","value":"-1","explanation_zh":"導數=-1。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084012,"parameters":{"m":-1,"b":-8,"x":-1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"-1\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0013","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=0x+(-9)，求 f′(0)。","answer":{"kind":"short_text","value":"0","explanation_zh":"導數=0。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084013,"parameters":{"m":0,"b":-9,"x":0,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"0\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0014","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=1x+(-10)，求 f′(1)。","answer":{"kind":"short_text","value":"1","explanation_zh":"導數=1。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084014,"parameters":{"m":1,"b":-10,"x":1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"1\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0015","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=2x+(-11)，求 f′(2)。","answer":{"kind":"short_text","value":"2","explanation_zh":"導數=2。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084015,"parameters":{"m":2,"b":-11,"x":2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"2\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0016","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=3x+(-12)，求 f′(-2)。","answer":{"kind":"short_text","value":"3","explanation_zh":"導數=3。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084016,"parameters":{"m":3,"b":-12,"x":-2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"3\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0017","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=4x+(-13)，求 f′(-1)。","answer":{"kind":"short_text","value":"4","explanation_zh":"導數=4。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084017,"parameters":{"m":4,"b":-13,"x":-1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"4\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0018","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=5x+(-14)，求 f′(0)。","answer":{"kind":"short_text","value":"5","explanation_zh":"導數=5。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084018,"parameters":{"m":5,"b":-14,"x":0,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"5\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0019","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=6x+(-15)，求 f′(1)。","answer":{"kind":"short_text","value":"6","explanation_zh":"導數=6。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084019,"parameters":{"m":6,"b":-15,"x":1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"6\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0020","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=7x+(-16)，求 f′(2)。","answer":{"kind":"short_text","value":"7","explanation_zh":"導數=7。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084020,"parameters":{"m":7,"b":-16,"x":2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"7\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0021","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=8x+(-17)，求 f′(-2)。","answer":{"kind":"short_text","value":"8","explanation_zh":"導數=8。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084021,"parameters":{"m":8,"b":-17,"x":-2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"8\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0022","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=9x+(-18)，求 f′(-1)。","answer":{"kind":"short_text","value":"9","explanation_zh":"導數=9。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084022,"parameters":{"m":9,"b":-18,"x":-1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"9\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0023","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=10x+(-19)，求 f′(0)。","answer":{"kind":"short_text","value":"10","explanation_zh":"導數=10。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084023,"parameters":{"m":10,"b":-19,"x":0,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"10\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0024","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=11x+(-20)，求 f′(1)。","answer":{"kind":"short_text","value":"11","explanation_zh":"導數=11。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084024,"parameters":{"m":11,"b":-20,"x":1,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"11\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0025","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"仿射模型的導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=12x+(-21)，求 f′(2)。","answer":{"kind":"short_text","value":"12","explanation_zh":"導數=12。以 h→0 的差商極限定義解讀；偏移與求值點不改變此仿射斜率。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["仿射模型的導數"]},"variant":{"family_id":"qf-derivative-affine-slope","seed":202610084025,"parameters":{"m":12,"b":-21,"x":2,"operation":"affine_derivative","domain":"reals","semantic_template":"qf-derivative-affine-slope/{\"inputs\":[\"12\"],\"operation\":\"affine_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0026","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=0x²+(-13)x+(5)，求 f′(4)，允許 a2=0。","answer":{"kind":"short_text","value":"-13","explanation_zh":"導數=-13。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084026,"parameters":{"a2":0,"a1":-13,"a0":5,"x":4,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"-13\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0027","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-2x²+(-11)x+(2)，求 f′(-1)，允許 a2=0。","answer":{"kind":"short_text","value":"-7","explanation_zh":"導數=-7。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084027,"parameters":{"a2":-2,"a1":-11,"a0":2,"x":-1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-2\",\"-11\",\"-1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0028","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=3x²+(-10)x+(1)，求 f′(0)，允許 a2=0。","answer":{"kind":"short_text","value":"-10","explanation_zh":"導數=-10。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084028,"parameters":{"a2":3,"a1":-10,"a0":1,"x":0,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"-10\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0029","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-4x²+(-9)x+(0)，求 f′(1)，允許 a2=0。","answer":{"kind":"short_text","value":"-17","explanation_zh":"導數=-17。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084029,"parameters":{"a2":-4,"a1":-9,"a0":0,"x":1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-4\",\"-9\",\"1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0030","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=5x²+(-8)x+(-1)，求 f′(2)，允許 a2=0。","answer":{"kind":"short_text","value":"12","explanation_zh":"導數=12。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084030,"parameters":{"a2":5,"a1":-8,"a0":-1,"x":2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"5\",\"-8\",\"2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0031","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-6x²+(-7)x+(-2)，求 f′(-2)，允許 a2=0。","answer":{"kind":"short_text","value":"17","explanation_zh":"導數=17。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084031,"parameters":{"a2":-6,"a1":-7,"a0":-2,"x":-2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-6\",\"-7\",\"-2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0032","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=7x²+(-6)x+(-3)，求 f′(-1)，允許 a2=0。","answer":{"kind":"short_text","value":"-20","explanation_zh":"導數=-20。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084032,"parameters":{"a2":7,"a1":-6,"a0":-3,"x":-1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"7\",\"-6\",\"-1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0033","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-8x²+(-5)x+(-4)，求 f′(0)，允許 a2=0。","answer":{"kind":"short_text","value":"-5","explanation_zh":"導數=-5。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084033,"parameters":{"a2":-8,"a1":-5,"a0":-4,"x":0,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"-5\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0034","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=9x²+(-4)x+(-5)，求 f′(1)，允許 a2=0。","answer":{"kind":"short_text","value":"14","explanation_zh":"導數=14。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084034,"parameters":{"a2":9,"a1":-4,"a0":-5,"x":1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"9\",\"-4\",\"1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0035","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-10x²+(-3)x+(-6)，求 f′(2)，允許 a2=0。","answer":{"kind":"short_text","value":"-43","explanation_zh":"導數=-43。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084035,"parameters":{"a2":-10,"a1":-3,"a0":-6,"x":2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-10\",\"-3\",\"2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0036","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=11x²+(-2)x+(-7)，求 f′(-2)，允許 a2=0。","answer":{"kind":"short_text","value":"-46","explanation_zh":"導數=-46。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084036,"parameters":{"a2":11,"a1":-2,"a0":-7,"x":-2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"11\",\"-2\",\"-2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0037","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-12x²+(-1)x+(-8)，求 f′(-1)，允許 a2=0。","answer":{"kind":"short_text","value":"23","explanation_zh":"導數=23。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084037,"parameters":{"a2":-12,"a1":-1,"a0":-8,"x":-1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-12\",\"-1\",\"-1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0038","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=13x²+(0)x+(-9)，求 f′(0)，允許 a2=0。","answer":{"kind":"short_text","value":"0","explanation_zh":"導數=0。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084038,"parameters":{"a2":13,"a1":0,"a0":-9,"x":0,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"0\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0039","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-14x²+(1)x+(-10)，求 f′(1)，允許 a2=0。","answer":{"kind":"short_text","value":"-27","explanation_zh":"導數=-27。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084039,"parameters":{"a2":-14,"a1":1,"a0":-10,"x":1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-14\",\"1\",\"1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0040","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=15x²+(2)x+(-11)，求 f′(2)，允許 a2=0。","answer":{"kind":"short_text","value":"62","explanation_zh":"導數=62。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084040,"parameters":{"a2":15,"a1":2,"a0":-11,"x":2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"15\",\"2\",\"2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0041","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-16x²+(3)x+(-12)，求 f′(-2)，允許 a2=0。","answer":{"kind":"short_text","value":"67","explanation_zh":"導數=67。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084041,"parameters":{"a2":-16,"a1":3,"a0":-12,"x":-2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-16\",\"3\",\"-2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0042","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=17x²+(4)x+(-13)，求 f′(-1)，允許 a2=0。","answer":{"kind":"short_text","value":"-30","explanation_zh":"導數=-30。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084042,"parameters":{"a2":17,"a1":4,"a0":-13,"x":-1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"17\",\"4\",\"-1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0043","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-18x²+(5)x+(-14)，求 f′(0)，允許 a2=0。","answer":{"kind":"short_text","value":"5","explanation_zh":"導數=5。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084043,"parameters":{"a2":-18,"a1":5,"a0":-14,"x":0,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"5\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0044","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=19x²+(6)x+(-15)，求 f′(1)，允許 a2=0。","answer":{"kind":"short_text","value":"44","explanation_zh":"導數=44。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084044,"parameters":{"a2":19,"a1":6,"a0":-15,"x":1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"19\",\"6\",\"1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0045","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-20x²+(7)x+(-16)，求 f′(2)，允許 a2=0。","answer":{"kind":"short_text","value":"-73","explanation_zh":"導數=-73。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084045,"parameters":{"a2":-20,"a1":7,"a0":-16,"x":2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-20\",\"7\",\"2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0046","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=21x²+(8)x+(-17)，求 f′(-2)，允許 a2=0。","answer":{"kind":"short_text","value":"-76","explanation_zh":"導數=-76。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084046,"parameters":{"a2":21,"a1":8,"a0":-17,"x":-2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"21\",\"8\",\"-2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0047","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-22x²+(9)x+(-18)，求 f′(-1)，允許 a2=0。","answer":{"kind":"short_text","value":"53","explanation_zh":"導數=53。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084047,"parameters":{"a2":-22,"a1":9,"a0":-18,"x":-1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-22\",\"9\",\"-1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0048","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=23x²+(10)x+(-19)，求 f′(0)，允許 a2=0。","answer":{"kind":"short_text","value":"10","explanation_zh":"導數=10。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084048,"parameters":{"a2":23,"a1":10,"a0":-19,"x":0,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"slope_only\",\"10\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0049","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-24x²+(11)x+(-20)，求 f′(1)，允許 a2=0。","answer":{"kind":"short_text","value":"-37","explanation_zh":"導數=-37。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084049,"parameters":{"a2":-24,"a1":11,"a0":-20,"x":1,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"-24\",\"11\",\"1\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0050","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"至多二次式的點導數","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=25x²+(12)x+(-21)，求 f′(2)，允許 a2=0。","answer":{"kind":"short_text","value":"112","explanation_zh":"導數=112。產生端以值與導數的雙數 Horner 計算，不依有限點抽樣；常數項不改變導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["至多二次式的點導數"]},"variant":{"family_id":"qf-derivative-quadratic-point","seed":202610084050,"parameters":{"a2":25,"a1":12,"a0":-21,"x":2,"operation":"quadratic_derivative","domain":"reals","semantic_template":"qf-derivative-quadratic-point/{\"inputs\":[\"25\",\"12\",\"2\"],\"operation\":\"quadratic_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0051","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=0x²+(2)x+(3)，x=4、整數步長 h=-1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"2/1","explanation_zh":"指定步差商=2/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084051,"parameters":{"a2":0,"a1":2,"a0":3,"x":4,"h":-1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"affine_quotient\",\"2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0052","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-1x²+(-11)x+(2)，x=-1、整數步長 h=-2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-7/1","explanation_zh":"指定步差商=-7/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084052,"parameters":{"a2":-1,"a1":-11,"a0":2,"x":-1,"h":-2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-1\",\"-11\",\"-1\",\"-2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0053","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=2x²+(-10)x+(4)，x=0、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-4/1","explanation_zh":"指定步差商=-4/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084053,"parameters":{"a2":2,"a1":-10,"a0":4,"x":0,"h":3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"2\",\"-10\",\"0\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0054","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-3x²+(-9)x+(6)，x=1、整數步長 h=-1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-12/1","explanation_zh":"指定步差商=-12/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084054,"parameters":{"a2":-3,"a1":-9,"a0":6,"x":1,"h":-1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-3\",\"-9\",\"1\",\"-1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0055","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=4x²+(-8)x+(8)，x=2、整數步長 h=2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"16/1","explanation_zh":"指定步差商=16/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084055,"parameters":{"a2":4,"a1":-8,"a0":8,"x":2,"h":2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"4\",\"-8\",\"2\",\"2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0056","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-5x²+(-7)x+(10)，x=-2、整數步長 h=-3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"28/1","explanation_zh":"指定步差商=28/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084056,"parameters":{"a2":-5,"a1":-7,"a0":10,"x":-2,"h":-3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-5\",\"-7\",\"-2\",\"-3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0057","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=6x²+(-6)x+(12)，x=-1、整數步長 h=1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-12/1","explanation_zh":"指定步差商=-12/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084057,"parameters":{"a2":6,"a1":-6,"a0":12,"x":-1,"h":1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"6\",\"-6\",\"-1\",\"1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0058","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-7x²+(-5)x+(14)，x=0、整數步長 h=-2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"9/1","explanation_zh":"指定步差商=9/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084058,"parameters":{"a2":-7,"a1":-5,"a0":14,"x":0,"h":-2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-7\",\"-5\",\"0\",\"-2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0059","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=8x²+(-4)x+(16)，x=1、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"36/1","explanation_zh":"指定步差商=36/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084059,"parameters":{"a2":8,"a1":-4,"a0":16,"x":1,"h":3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"8\",\"-4\",\"1\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0060","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-9x²+(-3)x+(18)，x=2、整數步長 h=-1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-30/1","explanation_zh":"指定步差商=-30/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084060,"parameters":{"a2":-9,"a1":-3,"a0":18,"x":2,"h":-1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-9\",\"-3\",\"2\",\"-1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0061","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=10x²+(-2)x+(20)，x=-2、整數步長 h=2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-22/1","explanation_zh":"指定步差商=-22/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084061,"parameters":{"a2":10,"a1":-2,"a0":20,"x":-2,"h":2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"10\",\"-2\",\"-2\",\"2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0062","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-11x²+(-1)x+(22)，x=-1、整數步長 h=-3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"54/1","explanation_zh":"指定步差商=54/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084062,"parameters":{"a2":-11,"a1":-1,"a0":22,"x":-1,"h":-3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-11\",\"-1\",\"-1\",\"-3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0063","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=12x²+(0)x+(24)，x=0、整數步長 h=1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"12/1","explanation_zh":"指定步差商=12/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084063,"parameters":{"a2":12,"a1":0,"a0":24,"x":0,"h":1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"12\",\"0\",\"0\",\"1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0064","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-13x²+(1)x+(26)，x=1、整數步長 h=-2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"1/1","explanation_zh":"指定步差商=1/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084064,"parameters":{"a2":-13,"a1":1,"a0":26,"x":1,"h":-2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-13\",\"1\",\"1\",\"-2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0065","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=14x²+(2)x+(28)，x=2、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"100/1","explanation_zh":"指定步差商=100/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084065,"parameters":{"a2":14,"a1":2,"a0":28,"x":2,"h":3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"14\",\"2\",\"2\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0066","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-15x²+(3)x+(30)，x=-2、整數步長 h=-1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"78/1","explanation_zh":"指定步差商=78/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084066,"parameters":{"a2":-15,"a1":3,"a0":30,"x":-2,"h":-1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-15\",\"3\",\"-2\",\"-1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0067","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=16x²+(4)x+(32)，x=-1、整數步長 h=2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"4/1","explanation_zh":"指定步差商=4/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084067,"parameters":{"a2":16,"a1":4,"a0":32,"x":-1,"h":2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"16\",\"4\",\"-1\",\"2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0068","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-17x²+(5)x+(34)，x=0、整數步長 h=-3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"56/1","explanation_zh":"指定步差商=56/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084068,"parameters":{"a2":-17,"a1":5,"a0":34,"x":0,"h":-3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-17\",\"5\",\"0\",\"-3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0069","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=18x²+(6)x+(36)，x=1、整數步長 h=1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"60/1","explanation_zh":"指定步差商=60/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084069,"parameters":{"a2":18,"a1":6,"a0":36,"x":1,"h":1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"18\",\"6\",\"1\",\"1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0070","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-19x²+(7)x+(38)，x=2、整數步長 h=-2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-31/1","explanation_zh":"指定步差商=-31/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084070,"parameters":{"a2":-19,"a1":7,"a0":38,"x":2,"h":-2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-19\",\"7\",\"2\",\"-2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0071","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=20x²+(8)x+(40)，x=-2、整數步長 h=3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"-12/1","explanation_zh":"指定步差商=-12/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084071,"parameters":{"a2":20,"a1":8,"a0":40,"x":-2,"h":3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"20\",\"8\",\"-2\",\"3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0072","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-21x²+(9)x+(42)，x=-1、整數步長 h=-1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"72/1","explanation_zh":"指定步差商=72/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084072,"parameters":{"a2":-21,"a1":9,"a0":42,"x":-1,"h":-1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-21\",\"9\",\"-1\",\"-1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0073","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=22x²+(10)x+(44)，x=0、整數步長 h=2≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"54/1","explanation_zh":"指定步差商=54/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084073,"parameters":{"a2":22,"a1":10,"a0":44,"x":0,"h":2,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"22\",\"10\",\"0\",\"2\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0074","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=-23x²+(11)x+(46)，x=1、整數步長 h=-3≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"34/1","explanation_zh":"指定步差商=34/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084074,"parameters":{"a2":-23,"a1":11,"a0":46,"x":1,"h":-3,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"-23\",\"11\",\"1\",\"-3\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0075","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"指定非零步長的有限差商","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=24x²+(12)x+(48)，x=2、整數步長 h=1≠0。求 (f(x+h)−f(x))/h，採最簡正分母分數。","answer":{"kind":"expression","value":"132/1","explanation_zh":"指定步差商=132/1。這是有限差商，不是取極限的導數定義；仿射等特殊模型可有相同數值，不能反向推論一般導數存在。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["指定非零步長的有限差商"]},"variant":{"family_id":"qf-derivative-finite-quotient","seed":202610084075,"parameters":{"a2":24,"a1":12,"a0":48,"x":2,"h":1,"operation":"finite_quadratic_quotient","domain":"reals","semantic_template":"qf-derivative-finite-quotient/{\"inputs\":[\"24\",\"12\",\"2\",\"1\"],\"operation\":\"finite_quadratic_quotient\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0076","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-12)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"不存在","explanation_zh":"左導數=-1；右導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084076,"parameters":{"c":-12,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"0\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0077","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-11)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-1；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084077,"parameters":{"c":-11,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-1\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0078","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-10)|，求 f′(-8)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=2；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084078,"parameters":{"c":-10,"x":-8,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"2\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0079","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-9)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-3；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084079,"parameters":{"c":-9,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-3\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0080","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-8)|，求 f′(-4)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=4；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084080,"parameters":{"c":-8,"x":-4,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"4\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0081","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-7)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-5；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084081,"parameters":{"c":-7,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-5\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0082","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-6)|，求 f′(0)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=6；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084082,"parameters":{"c":-6,"x":0,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"6\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0083","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-5)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-7；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084083,"parameters":{"c":-5,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-7\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0084","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-4)|，求 f′(4)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=8；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084084,"parameters":{"c":-4,"x":4,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"8\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0085","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-3)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-9；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084085,"parameters":{"c":-3,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-9\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0086","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-2)|，求 f′(8)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=10；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084086,"parameters":{"c":-2,"x":8,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"10\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0087","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(-1)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-11；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084087,"parameters":{"c":-1,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-11\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0088","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(0)|，求 f′(12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=12；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084088,"parameters":{"c":0,"x":12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"12\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0089","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(1)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-13；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084089,"parameters":{"c":1,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-13\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0090","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(2)|，求 f′(16)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=14；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084090,"parameters":{"c":2,"x":16,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"14\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0091","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(3)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-15；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084091,"parameters":{"c":3,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-15\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0092","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(4)|，求 f′(20)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=16；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084092,"parameters":{"c":4,"x":20,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"16\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0093","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(5)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-17；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084093,"parameters":{"c":5,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-17\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0094","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(6)|，求 f′(24)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=18；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084094,"parameters":{"c":6,"x":24,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"18\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0095","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(7)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-19；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084095,"parameters":{"c":7,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-19\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0096","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(8)|，求 f′(28)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=20；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084096,"parameters":{"c":8,"x":28,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"20\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0097","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(9)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-21；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084097,"parameters":{"c":9,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-21\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0098","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(10)|，求 f′(32)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=22；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084098,"parameters":{"c":10,"x":32,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"22\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0099","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(11)|，求 f′(-12)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"-1","explanation_zh":"相對位置=-23；導數=-1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084099,"parameters":{"c":11,"x":-12,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"-23\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261007-advance-20261008-r04-derivative-0100","batch_id":"batch-20261007-advance-20261008-r04-derivative-foundations","language":"zh-Hant","source_mko_ids":["mko-derivative"],"title_zh":"平移絕對值的導數與角點","stem_zh":"全實數論域，以下函數／點均以明示實數模型解讀。f(x)=|x−(12)|，求 f′(36)；若不存在則回答「不存在」。","answer":{"kind":"short_text","value":"1","explanation_zh":"相對位置=24；導數=1。離角點按左右位置取斜率，在角點兩側導數不相同；不能把對稱有限差商零當導數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["平移絕對值的導數與角點"]},"variant":{"family_id":"qf-derivative-shifted-absolute","seed":202610084100,"parameters":{"c":12,"x":36,"operation":"shifted_absolute_derivative","domain":"reals","semantic_template":"qf-derivative-shifted-absolute/{\"inputs\":[\"24\"],\"operation\":\"shifted_absolute_derivative\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-07","contract_version":"ocme-question-factory-v0.1"}}