{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0001","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-3,\"b\":-12,\"xs\":[-3,-2,0]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-3, -12, [-3, -2, 0], [[-3, -3], [-2, -6], [0, -12]])","explanation_zh":"應用擴展核對=(-3, -12, [-3, -2, 0], [[-3, -3], [-2, -6], [0, -12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211001,"parameters":{"a":-3,"b":-12,"xs":[-3,-2,0],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":-12,\"xs\":[-3,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0002","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-2,\"b\":-11,\"xs\":[-2,-1,1]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-2, -11, [-2, -1, 1], [[-2, -7], [-1, -9], [1, -13]])","explanation_zh":"應用擴展核對=(-2, -11, [-2, -1, 1], [[-2, -7], [-1, -9], [1, -13]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211002,"parameters":{"a":-2,"b":-11,"xs":[-2,-1,1],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":-11,\"xs\":[-2,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0003","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-1,\"b\":-10,\"xs\":[-1,0,2]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-1, -10, [-1, 0, 2], [[-1, -9], [0, -10], [2, -12]])","explanation_zh":"應用擴展核對=(-1, -10, [-1, 0, 2], [[-1, -9], [0, -10], [2, -12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211003,"parameters":{"a":-1,"b":-10,"xs":[-1,0,2],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":-10,\"xs\":[-1,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0004","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":0,\"b\":-9,\"xs\":[0,1,3]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(0, -9, [0, 1, 3], [[0, -9], [1, -9], [3, -9]])","explanation_zh":"應用擴展核對=(0, -9, [0, 1, 3], [[0, -9], [1, -9], [3, -9]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211004,"parameters":{"a":0,"b":-9,"xs":[0,1,3],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":-9,\"xs\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0005","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":1,\"b\":-8,\"xs\":[1,2,4]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(1, -8, [1, 2, 4], [[1, -7], [2, -6], [4, -4]])","explanation_zh":"應用擴展核對=(1, -8, [1, 2, 4], [[1, -7], [2, -6], [4, -4]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211005,"parameters":{"a":1,"b":-8,"xs":[1,2,4],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":-8,\"xs\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0006","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":2,\"b\":-7,\"xs\":[2,3,5]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(2, -7, [2, 3, 5], [[2, -3], [3, -1], [5, 3]])","explanation_zh":"應用擴展核對=(2, -7, [2, 3, 5], [[2, -3], [3, -1], [5, 3]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211006,"parameters":{"a":2,"b":-7,"xs":[2,3,5],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":-7,\"xs\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0007","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":3,\"b\":-6,\"xs\":[3,4,6]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(3, -6, [3, 4, 6], [[3, 3], [4, 6], [6, 12]])","explanation_zh":"應用擴展核對=(3, -6, [3, 4, 6], [[3, 3], [4, 6], [6, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211007,"parameters":{"a":3,"b":-6,"xs":[3,4,6],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":-6,\"xs\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0008","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-3,\"b\":-5,\"xs\":[-3,-2,0]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-3, -5, [-3, -2, 0], [[-3, 4], [-2, 1], [0, -5]])","explanation_zh":"應用擴展核對=(-3, -5, [-3, -2, 0], [[-3, 4], [-2, 1], [0, -5]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211008,"parameters":{"a":-3,"b":-5,"xs":[-3,-2,0],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":-5,\"xs\":[-3,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0009","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-2,\"b\":-4,\"xs\":[-2,-1,1]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-2, -4, [-2, -1, 1], [[-2, 0], [-1, -2], [1, -6]])","explanation_zh":"應用擴展核對=(-2, -4, [-2, -1, 1], [[-2, 0], [-1, -2], [1, -6]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211009,"parameters":{"a":-2,"b":-4,"xs":[-2,-1,1],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":-4,\"xs\":[-2,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0010","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-1,\"b\":-3,\"xs\":[-1,0,2]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-1, -3, [-1, 0, 2], [[-1, -2], [0, -3], [2, -5]])","explanation_zh":"應用擴展核對=(-1, -3, [-1, 0, 2], [[-1, -2], [0, -3], [2, -5]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211010,"parameters":{"a":-1,"b":-3,"xs":[-1,0,2],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":-3,\"xs\":[-1,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0011","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":0,\"b\":-2,\"xs\":[0,1,3]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(0, -2, [0, 1, 3], [[0, -2], [1, -2], [3, -2]])","explanation_zh":"應用擴展核對=(0, -2, [0, 1, 3], [[0, -2], [1, -2], [3, -2]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211011,"parameters":{"a":0,"b":-2,"xs":[0,1,3],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":-2,\"xs\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0012","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":1,\"b\":-1,\"xs\":[1,2,4]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(1, -1, [1, 2, 4], [[1, 0], [2, 1], [4, 3]])","explanation_zh":"應用擴展核對=(1, -1, [1, 2, 4], [[1, 0], [2, 1], [4, 3]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211012,"parameters":{"a":1,"b":-1,"xs":[1,2,4],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":-1,\"xs\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0013","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":2,\"b\":0,\"xs\":[2,3,5]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(2, 0, [2, 3, 5], [[2, 4], [3, 6], [5, 10]])","explanation_zh":"應用擴展核對=(2, 0, [2, 3, 5], [[2, 4], [3, 6], [5, 10]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211013,"parameters":{"a":2,"b":0,"xs":[2,3,5],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":0,\"xs\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0014","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":3,\"b\":1,\"xs\":[3,4,6]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, [3, 4, 6], [[3, 10], [4, 13], [6, 19]])","explanation_zh":"應用擴展核對=(3, 1, [3, 4, 6], [[3, 10], [4, 13], [6, 19]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211014,"parameters":{"a":3,"b":1,"xs":[3,4,6],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":1,\"xs\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0015","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-3,\"b\":2,\"xs\":[-3,-2,0]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-3, 2, [-3, -2, 0], [[-3, 11], [-2, 8], [0, 2]])","explanation_zh":"應用擴展核對=(-3, 2, [-3, -2, 0], [[-3, 11], [-2, 8], [0, 2]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211015,"parameters":{"a":-3,"b":2,"xs":[-3,-2,0],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":2,\"xs\":[-3,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0016","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-2,\"b\":3,\"xs\":[-2,-1,1]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-2, 3, [-2, -1, 1], [[-2, 7], [-1, 5], [1, 1]])","explanation_zh":"應用擴展核對=(-2, 3, [-2, -1, 1], [[-2, 7], [-1, 5], [1, 1]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211016,"parameters":{"a":-2,"b":3,"xs":[-2,-1,1],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":3,\"xs\":[-2,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0017","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-1,\"b\":4,\"xs\":[-1,0,2]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-1, 4, [-1, 0, 2], [[-1, 5], [0, 4], [2, 2]])","explanation_zh":"應用擴展核對=(-1, 4, [-1, 0, 2], [[-1, 5], [0, 4], [2, 2]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211017,"parameters":{"a":-1,"b":4,"xs":[-1,0,2],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-1,\"b\":4,\"xs\":[-1,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0018","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":0,\"b\":5,\"xs\":[0,1,3]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(0, 5, [0, 1, 3], [[0, 5], [1, 5], [3, 5]])","explanation_zh":"應用擴展核對=(0, 5, [0, 1, 3], [[0, 5], [1, 5], [3, 5]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211018,"parameters":{"a":0,"b":5,"xs":[0,1,3],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":5,\"xs\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0019","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":1,\"b\":6,\"xs\":[1,2,4]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(1, 6, [1, 2, 4], [[1, 7], [2, 8], [4, 10]])","explanation_zh":"應用擴展核對=(1, 6, [1, 2, 4], [[1, 7], [2, 8], [4, 10]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211019,"parameters":{"a":1,"b":6,"xs":[1,2,4],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":1,\"b\":6,\"xs\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0020","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":2,\"b\":7,\"xs\":[2,3,5]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(2, 7, [2, 3, 5], [[2, 11], [3, 13], [5, 17]])","explanation_zh":"應用擴展核對=(2, 7, [2, 3, 5], [[2, 11], [3, 13], [5, 17]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211020,"parameters":{"a":2,"b":7,"xs":[2,3,5],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":2,\"b\":7,\"xs\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0021","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":3,\"b\":8,\"xs\":[3,4,6]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(3, 8, [3, 4, 6], [[3, 17], [4, 20], [6, 26]])","explanation_zh":"應用擴展核對=(3, 8, [3, 4, 6], [[3, 17], [4, 20], [6, 26]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211021,"parameters":{"a":3,"b":8,"xs":[3,4,6],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":3,\"b\":8,\"xs\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0022","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-3,\"b\":9,\"xs\":[-3,-2,0]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-3, 9, [-3, -2, 0], [[-3, 18], [-2, 15], [0, 9]])","explanation_zh":"應用擴展核對=(-3, 9, [-3, -2, 0], [[-3, 18], [-2, 15], [0, 9]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211022,"parameters":{"a":-3,"b":9,"xs":[-3,-2,0],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-3,\"b\":9,\"xs\":[-3,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0023","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":-2,\"b\":10,\"xs\":[-2,-1,1]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(-2, 10, [-2, -1, 1], [[-2, 14], [-1, 12], [1, 8]])","explanation_zh":"應用擴展核對=(-2, 10, [-2, -1, 1], [[-2, 14], [-1, 12], [1, 8]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211023,"parameters":{"a":-2,"b":10,"xs":[-2,-1,1],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":-2,\"b\":10,\"xs\":[-2,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0025","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-affine-table；資料={\"a\":0,\"b\":12,\"xs\":[0,1,3]}。請依 [a,b,xs,table] 欄序回答。","answer":{"kind":"expression","value":"(0, 12, [0, 1, 3], [[0, 12], [1, 12], [3, 12]])","explanation_zh":"應用擴展核對=(0, 12, [0, 1, 3], [[0, 12], [1, 12], [3, 12]])；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-affine-table","seed":202610211025,"parameters":{"a":0,"b":12,"xs":[0,1,3],"domain":"Finite_representation_bridge","operation":"representation-affine-table","semantic_template":"qf-app21-representation-affine-table/{\"a\":0,\"b\":12,\"xs\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0026","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-2,-6],[-1,-9]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-1, -9], [-2, -6]], -3, -12)","explanation_zh":"應用擴展核對=([[-1, -9], [-2, -6]], -3, -12)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211026,"parameters":{"points":[[-2,-6],[-1,-9]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-9],[-2,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0027","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-1,-9],[1,-13]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-1, -9], [1, -13]], -2, -11)","explanation_zh":"應用擴展核對=([[-1, -9], [1, -13]], -2, -11)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211027,"parameters":{"points":[[-1,-9],[1,-13]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,-9],[1,-13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0031","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-2,-11],[1,-5]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-2, -11], [1, -5]], 2, -7)","explanation_zh":"應用擴展核對=([[-2, -11], [1, -5]], 2, -7)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211031,"parameters":{"points":[[-2,-11],[1,-5]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-2,-11],[1,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0039","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[1,4],[3,10]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[1, 4], [3, 10]], 3, 1)","explanation_zh":"應用擴展核對=([[1, 4], [3, 10]], 3, 1)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211039,"parameters":{"points":[[1,4],[3,10]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,4],[3,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0041","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-2,7],[-1,5]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 5], [-2, 7]], -2, 3)","explanation_zh":"應用擴展核對=([[-1, 5], [-2, 7]], -2, 3)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211041,"parameters":{"points":[[-2,7],[-1,5]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,5],[-2,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0042","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-1,5],[1,3]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 5], [1, 3]], -1, 4)","explanation_zh":"應用擴展核對=([[-1, 5], [1, 3]], -1, 4)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211042,"parameters":{"points":[[-1,5],[1,3]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,5],[1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0044","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[1,7],[2,8]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[1, 7], [2, 8]], 1, 6)","explanation_zh":"應用擴展核對=([[1, 7], [2, 8]], 1, 6)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211044,"parameters":{"points":[[1,7],[2,8]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,7],[2,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0045","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[2,11],[4,15]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[2, 11], [4, 15]], 2, 7)","explanation_zh":"應用擴展核對=([[2, 11], [4, 15]], 2, 7)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211045,"parameters":{"points":[[2,11],[4,15]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[2,11],[4,15]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0046","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-2,2],[1,11]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-2, 2], [1, 11]], 3, 8)","explanation_zh":"應用擴展核對=([[-2, 2], [1, 11]], 3, 8)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211046,"parameters":{"points":[[-2,2],[1,11]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-2,2],[1,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0047","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[-1,12],[0,9]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 12], [0, 9]], -3, 9)","explanation_zh":"應用擴展核對=([[-1, 12], [0, 9]], -3, 9)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211047,"parameters":{"points":[[-1,12],[0,9]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[-1,12],[0,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0048","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[0,10],[2,6]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[0, 10], [2, 6]], -2, 10)","explanation_zh":"應用擴展核對=([[0, 10], [2, 6]], -2, 10)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211048,"parameters":{"points":[[0,10],[2,6]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[0,10],[2,6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0049","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-two-point-rule；資料={\"points\":[[1,10],[4,7]]}。請依 [points,slope,intercept] 欄序回答。","answer":{"kind":"expression","value":"([[1, 10], [4, 7]], -1, 11)","explanation_zh":"應用擴展核對=([[1, 10], [4, 7]], -1, 11)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-two-point-rule","seed":202610211049,"parameters":{"points":[[1,10],[4,7]],"domain":"Finite_representation_bridge","operation":"representation-two-point-rule","semantic_template":"qf-app21-representation-two-point-rule/{\"points\":[[1,10],[4,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0051","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-12],[1,-11],[1,-10],[2,-5]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -12], [1, -10], [1, -11], [2, -5]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, -12], [1, -10], [1, -11], [2, -5]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211051,"parameters":{"pairs":[[0,-12],[1,-11],[1,-10],[2,-5]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-12],[1,-10],[1,-11],[2,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0052","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-11],[1,-10],[1,-10],[2,-3]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -11], [1, -10], [2, -3]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -11], [1, -10], [2, -3]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211052,"parameters":{"pairs":[[0,-11],[1,-10],[1,-10],[2,-3]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-11],[1,-10],[2,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0053","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-10],[1,-9],[1,-9],[2,-1]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -10], [1, -9], [2, -1]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -10], [1, -9], [2, -1]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211053,"parameters":{"pairs":[[0,-10],[1,-9],[1,-9],[2,-1]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-10],[1,-9],[2,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0055","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-8],[1,-7],[1,-6],[2,3]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -8], [1, -6], [1, -7], [2, 3]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, -8], [1, -6], [1, -7], [2, 3]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211055,"parameters":{"pairs":[[0,-8],[1,-7],[1,-6],[2,3]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-8],[1,-6],[1,-7],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0056","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-7],[1,-6],[1,-6],[2,5]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -7], [1, -6], [2, 5]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -7], [1, -6], [2, 5]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211056,"parameters":{"pairs":[[0,-7],[1,-6],[1,-6],[2,5]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-7],[1,-6],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0058","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-5],[1,-4],[1,-4],[2,9]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -5], [1, -4], [2, 9]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -5], [1, -4], [2, 9]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211058,"parameters":{"pairs":[[0,-5],[1,-4],[1,-4],[2,9]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-5],[1,-4],[2,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0059","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-4],[1,-3],[1,-2],[2,11]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -4], [1, -2], [1, -3], [2, 11]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, -4], [1, -2], [1, -3], [2, 11]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211059,"parameters":{"pairs":[[0,-4],[1,-3],[1,-2],[2,11]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-4],[1,-2],[1,-3],[2,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0060","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-3],[1,-2],[1,-2],[2,13]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -3], [1, -2], [2, 13]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -3], [1, -2], [2, 13]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211060,"parameters":{"pairs":[[0,-3],[1,-2],[1,-2],[2,13]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-3],[1,-2],[2,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0061","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-2],[1,-1],[1,-1],[2,15]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -2], [1, -1], [2, 15]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -2], [1, -1], [2, 15]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211061,"parameters":{"pairs":[[0,-2],[1,-1],[1,-1],[2,15]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-2],[1,-1],[2,15]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0062","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,-1],[1,0],[1,0],[2,17]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, -1], [1, 0], [2, 17]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, -1], [1, 0], [2, 17]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211062,"parameters":{"pairs":[[0,-1],[1,0],[1,0],[2,17]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,-1],[1,0],[2,17]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0063","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,0],[1,1],[1,2],[2,19]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [1, 1], [1, 2], [2, 19]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, 0], [1, 1], [1, 2], [2, 19]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211063,"parameters":{"pairs":[[0,0],[1,1],[1,2],[2,19]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,0],[1,1],[1,2],[2,19]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0064","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,1],[1,2],[1,2],[2,21]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [1, 2], [2, 21]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 1], [1, 2], [2, 21]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211064,"parameters":{"pairs":[[0,1],[1,2],[1,2],[2,21]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,1],[1,2],[2,21]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0065","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,2],[1,3],[1,3],[2,23]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 2], [1, 3], [2, 23]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 2], [1, 3], [2, 23]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211065,"parameters":{"pairs":[[0,2],[1,3],[1,3],[2,23]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,2],[1,3],[2,23]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0066","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,3],[1,4],[1,4],[2,25]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 3], [1, 4], [2, 25]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 3], [1, 4], [2, 25]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211066,"parameters":{"pairs":[[0,3],[1,4],[1,4],[2,25]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,3],[1,4],[2,25]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0067","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,4],[1,5],[1,6],[2,27]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 4], [1, 5], [1, 6], [2, 27]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, 4], [1, 5], [1, 6], [2, 27]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211067,"parameters":{"pairs":[[0,4],[1,5],[1,6],[2,27]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,4],[1,5],[1,6],[2,27]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0068","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,5],[1,6],[1,6],[2,29]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 5], [1, 6], [2, 29]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 5], [1, 6], [2, 29]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211068,"parameters":{"pairs":[[0,5],[1,6],[1,6],[2,29]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,5],[1,6],[2,29]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0069","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,6],[1,7],[1,7],[2,31]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 6], [1, 7], [2, 31]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 6], [1, 7], [2, 31]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211069,"parameters":{"pairs":[[0,6],[1,7],[1,7],[2,31]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,6],[1,7],[2,31]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0070","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,7],[1,8],[1,8],[2,33]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 7], [1, 8], [2, 33]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 7], [1, 8], [2, 33]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211070,"parameters":{"pairs":[[0,7],[1,8],[1,8],[2,33]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,7],[1,8],[2,33]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0071","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,8],[1,9],[1,10],[2,35]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 8], [1, 10], [1, 9], [2, 35]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, 8], [1, 10], [1, 9], [2, 35]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211071,"parameters":{"pairs":[[0,8],[1,9],[1,10],[2,35]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,8],[1,10],[1,9],[2,35]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0072","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,9],[1,10],[1,10],[2,37]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 9], [1, 10], [2, 37]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 9], [1, 10], [2, 37]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211072,"parameters":{"pairs":[[0,9],[1,10],[1,10],[2,37]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,9],[1,10],[2,37]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0073","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,10],[1,11],[1,11],[2,39]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 10], [1, 11], [2, 39]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 10], [1, 11], [2, 39]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211073,"parameters":{"pairs":[[0,10],[1,11],[1,11],[2,39]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,10],[1,11],[2,39]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0074","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,11],[1,12],[1,12],[2,41]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 11], [1, 12], [2, 41]], [0, 1, 2], [], 是)","explanation_zh":"應用擴展核對=([[0, 11], [1, 12], [2, 41]], [0, 1, 2], [], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211074,"parameters":{"pairs":[[0,11],[1,12],[1,12],[2,41]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,11],[1,12],[2,41]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0075","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-function-audit；資料={\"pairs\":[[0,12],[1,13],[1,14],[2,43]]}。請依 [pairs,domain,conflicting_x,function_table] 欄序回答。","answer":{"kind":"expression","value":"([[0, 12], [1, 13], [1, 14], [2, 43]], [0, 1, 2], [1], 否)","explanation_zh":"應用擴展核對=([[0, 12], [1, 13], [1, 14], [2, 43]], [0, 1, 2], [1], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-function-audit","seed":202610211075,"parameters":{"pairs":[[0,12],[1,13],[1,14],[2,43]],"domain":"Finite_representation_bridge","operation":"representation-function-audit","semantic_template":"qf-app21-representation-function-audit/{\"pairs\":[[0,12],[1,13],[1,14],[2,43]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0076","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-2,\"b\":-10,\"pairs\":[[0,-10],[1,-12],[2,-13]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-2, -10, [[0, -10, -10, 是], [1, -12, -12, 是], [2, -13, -14, 否]], 否)","explanation_zh":"應用擴展核對=(-2, -10, [[0, -10, -10, 是], [1, -12, -12, 是], [2, -13, -14, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211076,"parameters":{"a":-2,"b":-10,"pairs":[[0,-10],[1,-12],[2,-13]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":-10,\"pairs\":[[0,-10],[1,-12],[2,-13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0077","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-1,\"b\":-9,\"pairs\":[[0,-9],[1,-10],[2,-11]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-1, -9, [[0, -9, -9, 是], [1, -10, -10, 是], [2, -11, -11, 是]], 是)","explanation_zh":"應用擴展核對=(-1, -9, [[0, -9, -9, 是], [1, -10, -10, 是], [2, -11, -11, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211077,"parameters":{"a":-1,"b":-9,"pairs":[[0,-9],[1,-10],[2,-11]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":-9,\"pairs\":[[0,-9],[1,-10],[2,-11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0078","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":0,\"b\":-8,\"pairs\":[[0,-8],[1,-8],[2,-8]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(0, -8, [[0, -8, -8, 是], [1, -8, -8, 是], [2, -8, -8, 是]], 是)","explanation_zh":"應用擴展核對=(0, -8, [[0, -8, -8, 是], [1, -8, -8, 是], [2, -8, -8, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211078,"parameters":{"a":0,"b":-8,"pairs":[[0,-8],[1,-8],[2,-8]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":-8,\"pairs\":[[0,-8],[1,-8],[2,-8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0079","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":1,\"b\":-7,\"pairs\":[[0,-7],[1,-6],[2,-5]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(1, -7, [[0, -7, -7, 是], [1, -6, -6, 是], [2, -5, -5, 是]], 是)","explanation_zh":"應用擴展核對=(1, -7, [[0, -7, -7, 是], [1, -6, -6, 是], [2, -5, -5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211079,"parameters":{"a":1,"b":-7,"pairs":[[0,-7],[1,-6],[2,-5]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":-7,\"pairs\":[[0,-7],[1,-6],[2,-5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0080","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":2,\"b\":-6,\"pairs\":[[0,-6],[1,-4],[2,-1]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(2, -6, [[0, -6, -6, 是], [1, -4, -4, 是], [2, -1, -2, 否]], 否)","explanation_zh":"應用擴展核對=(2, -6, [[0, -6, -6, 是], [1, -4, -4, 是], [2, -1, -2, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211080,"parameters":{"a":2,"b":-6,"pairs":[[0,-6],[1,-4],[2,-1]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":-6,\"pairs\":[[0,-6],[1,-4],[2,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0081","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-2,\"b\":-5,\"pairs\":[[0,-5],[1,-7],[2,-9]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-2, -5, [[0, -5, -5, 是], [1, -7, -7, 是], [2, -9, -9, 是]], 是)","explanation_zh":"應用擴展核對=(-2, -5, [[0, -5, -5, 是], [1, -7, -7, 是], [2, -9, -9, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211081,"parameters":{"a":-2,"b":-5,"pairs":[[0,-5],[1,-7],[2,-9]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":-5,\"pairs\":[[0,-5],[1,-7],[2,-9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0082","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-1,\"b\":-4,\"pairs\":[[0,-4],[1,-5],[2,-6]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-1, -4, [[0, -4, -4, 是], [1, -5, -5, 是], [2, -6, -6, 是]], 是)","explanation_zh":"應用擴展核對=(-1, -4, [[0, -4, -4, 是], [1, -5, -5, 是], [2, -6, -6, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211082,"parameters":{"a":-1,"b":-4,"pairs":[[0,-4],[1,-5],[2,-6]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":-4,\"pairs\":[[0,-4],[1,-5],[2,-6]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0083","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":0,\"b\":-3,\"pairs\":[[0,-3],[1,-3],[2,-3]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(0, -3, [[0, -3, -3, 是], [1, -3, -3, 是], [2, -3, -3, 是]], 是)","explanation_zh":"應用擴展核對=(0, -3, [[0, -3, -3, 是], [1, -3, -3, 是], [2, -3, -3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211083,"parameters":{"a":0,"b":-3,"pairs":[[0,-3],[1,-3],[2,-3]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":-3,\"pairs\":[[0,-3],[1,-3],[2,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0084","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":1,\"b\":-2,\"pairs\":[[0,-2],[1,-1],[2,1]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(1, -2, [[0, -2, -2, 是], [1, -1, -1, 是], [2, 1, 0, 否]], 否)","explanation_zh":"應用擴展核對=(1, -2, [[0, -2, -2, 是], [1, -1, -1, 是], [2, 1, 0, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211084,"parameters":{"a":1,"b":-2,"pairs":[[0,-2],[1,-1],[2,1]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":-2,\"pairs\":[[0,-2],[1,-1],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0085","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":2,\"b\":-1,\"pairs\":[[0,-1],[1,1],[2,3]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(2, -1, [[0, -1, -1, 是], [1, 1, 1, 是], [2, 3, 3, 是]], 是)","explanation_zh":"應用擴展核對=(2, -1, [[0, -1, -1, 是], [1, 1, 1, 是], [2, 3, 3, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211085,"parameters":{"a":2,"b":-1,"pairs":[[0,-1],[1,1],[2,3]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":-1,\"pairs\":[[0,-1],[1,1],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0086","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-2,\"b\":0,\"pairs\":[[0,0],[1,-2],[2,-4]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-2, 0, [[0, 0, 0, 是], [1, -2, -2, 是], [2, -4, -4, 是]], 是)","explanation_zh":"應用擴展核對=(-2, 0, [[0, 0, 0, 是], [1, -2, -2, 是], [2, -4, -4, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211086,"parameters":{"a":-2,"b":0,"pairs":[[0,0],[1,-2],[2,-4]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":0,\"pairs\":[[0,0],[1,-2],[2,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0087","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-1,\"b\":1,\"pairs\":[[0,1],[1,0],[2,-1]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-1, 1, [[0, 1, 1, 是], [1, 0, 0, 是], [2, -1, -1, 是]], 是)","explanation_zh":"應用擴展核對=(-1, 1, [[0, 1, 1, 是], [1, 0, 0, 是], [2, -1, -1, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211087,"parameters":{"a":-1,"b":1,"pairs":[[0,1],[1,0],[2,-1]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":1,\"pairs\":[[0,1],[1,0],[2,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0088","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":0,\"b\":2,\"pairs\":[[0,2],[1,2],[2,3]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, [[0, 2, 2, 是], [1, 2, 2, 是], [2, 3, 2, 否]], 否)","explanation_zh":"應用擴展核對=(0, 2, [[0, 2, 2, 是], [1, 2, 2, 是], [2, 3, 2, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211088,"parameters":{"a":0,"b":2,"pairs":[[0,2],[1,2],[2,3]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":2,\"pairs\":[[0,2],[1,2],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0089","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":1,\"b\":3,\"pairs\":[[0,3],[1,4],[2,5]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, [[0, 3, 3, 是], [1, 4, 4, 是], [2, 5, 5, 是]], 是)","explanation_zh":"應用擴展核對=(1, 3, [[0, 3, 3, 是], [1, 4, 4, 是], [2, 5, 5, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211089,"parameters":{"a":1,"b":3,"pairs":[[0,3],[1,4],[2,5]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":3,\"pairs\":[[0,3],[1,4],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0090","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":2,\"b\":4,\"pairs\":[[0,4],[1,6],[2,8]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, [[0, 4, 4, 是], [1, 6, 6, 是], [2, 8, 8, 是]], 是)","explanation_zh":"應用擴展核對=(2, 4, [[0, 4, 4, 是], [1, 6, 6, 是], [2, 8, 8, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211090,"parameters":{"a":2,"b":4,"pairs":[[0,4],[1,6],[2,8]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":4,\"pairs\":[[0,4],[1,6],[2,8]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0091","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-2,\"b\":5,\"pairs\":[[0,5],[1,3],[2,1]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-2, 5, [[0, 5, 5, 是], [1, 3, 3, 是], [2, 1, 1, 是]], 是)","explanation_zh":"應用擴展核對=(-2, 5, [[0, 5, 5, 是], [1, 3, 3, 是], [2, 1, 1, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211091,"parameters":{"a":-2,"b":5,"pairs":[[0,5],[1,3],[2,1]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":5,\"pairs\":[[0,5],[1,3],[2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0092","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-1,\"b\":6,\"pairs\":[[0,6],[1,5],[2,5]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-1, 6, [[0, 6, 6, 是], [1, 5, 5, 是], [2, 5, 4, 否]], 否)","explanation_zh":"應用擴展核對=(-1, 6, [[0, 6, 6, 是], [1, 5, 5, 是], [2, 5, 4, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211092,"parameters":{"a":-1,"b":6,"pairs":[[0,6],[1,5],[2,5]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":6,\"pairs\":[[0,6],[1,5],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0093","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":0,\"b\":7,\"pairs\":[[0,7],[1,7],[2,7]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(0, 7, [[0, 7, 7, 是], [1, 7, 7, 是], [2, 7, 7, 是]], 是)","explanation_zh":"應用擴展核對=(0, 7, [[0, 7, 7, 是], [1, 7, 7, 是], [2, 7, 7, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211093,"parameters":{"a":0,"b":7,"pairs":[[0,7],[1,7],[2,7]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":7,\"pairs\":[[0,7],[1,7],[2,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0094","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":1,\"b\":8,\"pairs\":[[0,8],[1,9],[2,10]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(1, 8, [[0, 8, 8, 是], [1, 9, 9, 是], [2, 10, 10, 是]], 是)","explanation_zh":"應用擴展核對=(1, 8, [[0, 8, 8, 是], [1, 9, 9, 是], [2, 10, 10, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211094,"parameters":{"a":1,"b":8,"pairs":[[0,8],[1,9],[2,10]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":8,\"pairs\":[[0,8],[1,9],[2,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0095","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":2,\"b\":9,\"pairs\":[[0,9],[1,11],[2,13]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(2, 9, [[0, 9, 9, 是], [1, 11, 11, 是], [2, 13, 13, 是]], 是)","explanation_zh":"應用擴展核對=(2, 9, [[0, 9, 9, 是], [1, 11, 11, 是], [2, 13, 13, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211095,"parameters":{"a":2,"b":9,"pairs":[[0,9],[1,11],[2,13]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":9,\"pairs\":[[0,9],[1,11],[2,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0096","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-2,\"b\":10,\"pairs\":[[0,10],[1,8],[2,7]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-2, 10, [[0, 10, 10, 是], [1, 8, 8, 是], [2, 7, 6, 否]], 否)","explanation_zh":"應用擴展核對=(-2, 10, [[0, 10, 10, 是], [1, 8, 8, 是], [2, 7, 6, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211096,"parameters":{"a":-2,"b":10,"pairs":[[0,10],[1,8],[2,7]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-2,\"b\":10,\"pairs\":[[0,10],[1,8],[2,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0097","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":-1,\"b\":11,\"pairs\":[[0,11],[1,10],[2,9]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(-1, 11, [[0, 11, 11, 是], [1, 10, 10, 是], [2, 9, 9, 是]], 是)","explanation_zh":"應用擴展核對=(-1, 11, [[0, 11, 11, 是], [1, 10, 10, 是], [2, 9, 9, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211097,"parameters":{"a":-1,"b":11,"pairs":[[0,11],[1,10],[2,9]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":-1,\"b\":11,\"pairs\":[[0,11],[1,10],[2,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0098","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":0,\"b\":12,\"pairs\":[[0,12],[1,12],[2,12]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(0, 12, [[0, 12, 12, 是], [1, 12, 12, 是], [2, 12, 12, 是]], 是)","explanation_zh":"應用擴展核對=(0, 12, [[0, 12, 12, 是], [1, 12, 12, 是], [2, 12, 12, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211098,"parameters":{"a":0,"b":12,"pairs":[[0,12],[1,12],[2,12]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":0,\"b\":12,\"pairs\":[[0,12],[1,12],[2,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0099","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":1,\"b\":13,\"pairs\":[[0,13],[1,14],[2,15]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(1, 13, [[0, 13, 13, 是], [1, 14, 14, 是], [2, 15, 15, 是]], 是)","explanation_zh":"應用擴展核對=(1, 13, [[0, 13, 13, 是], [1, 14, 14, 是], [2, 15, 15, 是]], 是)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211099,"parameters":{"a":1,"b":13,"pairs":[[0,13],[1,14],[2,15]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":1,\"b\":13,\"pairs\":[[0,13],[1,14],[2,15]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261021-r01-mathematical-representation-0100","batch_id":"batch-20261013-advance-20261021-r01-mathematical-representation-foundations","language":"zh-Hant","source_mko_ids":["mko-mathematical-representation"],"title_zh":"數學表徵語義橋","stem_zh":"明示文字規則、符號或有限表格。操作=representation-consistency-audit；資料={\"a\":2,\"b\":14,\"pairs\":[[0,14],[1,16],[2,19]]}。請依 [a,b,rows,all_match] 欄序回答。","answer":{"kind":"expression","value":"(2, 14, [[0, 14, 14, 是], [1, 16, 16, 是], [2, 19, 18, 否]], 否)","explanation_zh":"應用擴展核對=(2, 14, [[0, 14, 14, 是], [1, 16, 16, 是], [2, 19, 18, 否]], 否)；依完整明示資料重算；完整明示的有限／精確切片不是一般定理或人員判定；不由圖形外觀補值；有限表徵一致不證未列域上的等價。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["數學表徵語義橋"]},"variant":{"family_id":"qf-app21-representation-consistency-audit","seed":202610211100,"parameters":{"a":2,"b":14,"pairs":[[0,14],[1,16],[2,19]],"domain":"Finite_representation_bridge","operation":"representation-consistency-audit","semantic_template":"qf-app21-representation-consistency-audit/{\"a\":2,\"b\":14,\"pairs\":[[0,14],[1,16],[2,19]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、真實學生診斷、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}