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{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0019","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 -4x+(6)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=-4≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260946,"parameters":{"a":-4,"b":6,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":-4,\"b\":6,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0020","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 -3x+(7)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=-3≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260947,"parameters":{"a":-3,"b":7,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":-3,\"b\":7,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0021","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 0x+(8)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"a=0，因此只是退化常數等式，不得稱為一次方程。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260948,"parameters":{"a":0,"b":8,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":0,\"b\":8,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0022","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 -1x+(9)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=-1≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260949,"parameters":{"a":-1,"b":9,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":-1,\"b\":9,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0023","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 1x+(10)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=1≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260950,"parameters":{"a":1,"b":10,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":10,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0024","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 1x+(11)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=1≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260951,"parameters":{"a":1,"b":11,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":1,\"b\":11,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-form-validity-0025","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程形式有效性","stem_zh":"在有理數論域，考慮 2x+(12)=0。依本 MKO，這是否是一元一次方程？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"a=2≠0，所以是本 MKO 的一元一次方程。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["一次係數","方程形式"]},"variant":{"family_id":"qf-linear-equation-form-validity","seed":20260952,"parameters":{"a":2,"b":12,"domain":"rationals","operation":"form_validity","semantic_template":"qf-linear-equation-form-validity/{\"a\":2,\"b\":12,\"domain\":\"rationals\",\"operation\":\"form_validity\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0001","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -5x+(-15)=0；a=-5 已明示非零。","answer":{"kind":"short_text","value":"-3","explanation_zh":"x=−(-15)/-5=-3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261028,"parameters":{"a":-5,"b":-15,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":-15,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0002","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -4x+(-8)=0；a=-4 已明示非零。","answer":{"kind":"short_text","value":"-2","explanation_zh":"x=−(-8)/-4=-2；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261029,"parameters":{"a":-4,"b":-8,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":-8,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0003","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -3x+(-1)=0；a=-3 已明示非零。","answer":{"kind":"short_text","value":"-1/3","explanation_zh":"x=−(-1)/-3=-1/3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261030,"parameters":{"a":-3,"b":-1,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":-1,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0004","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -2x+(6)=0；a=-2 已明示非零。","answer":{"kind":"short_text","value":"3","explanation_zh":"x=−(6)/-2=3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261031,"parameters":{"a":-2,"b":6,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-2,\"b\":6,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0005","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -1x+(13)=0；a=-1 已明示非零。","answer":{"kind":"short_text","value":"13","explanation_zh":"x=−(13)/-1=13；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261032,"parameters":{"a":-1,"b":13,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-1,\"b\":13,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0006","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 1x+(-11)=0；a=1 已明示非零。","answer":{"kind":"short_text","value":"11","explanation_zh":"x=−(-11)/1=11；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261033,"parameters":{"a":1,"b":-11,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":-11,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0007","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 1x+(-4)=0；a=1 已明示非零。","answer":{"kind":"short_text","value":"4","explanation_zh":"x=−(-4)/1=4；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261034,"parameters":{"a":1,"b":-4,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":-4,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0008","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 2x+(3)=0；a=2 已明示非零。","answer":{"kind":"short_text","value":"-3/2","explanation_zh":"x=−(3)/2=-3/2；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261035,"parameters":{"a":2,"b":3,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":2,\"b\":3,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0009","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 3x+(10)=0；a=3 已明示非零。","answer":{"kind":"short_text","value":"-10/3","explanation_zh":"x=−(10)/3=-10/3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261036,"parameters":{"a":3,"b":10,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":3,\"b\":10,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0010","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 4x+(-14)=0；a=4 已明示非零。","answer":{"kind":"short_text","value":"7/2","explanation_zh":"x=−(-14)/4=7/2；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261037,"parameters":{"a":4,"b":-14,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":4,\"b\":-14,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0011","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 5x+(-7)=0；a=5 已明示非零。","answer":{"kind":"short_text","value":"7/5","explanation_zh":"x=−(-7)/5=7/5；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261038,"parameters":{"a":5,"b":-7,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":5,\"b\":-7,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0012","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -5x+(0)=0；a=-5 已明示非零。","answer":{"kind":"short_text","value":"0","explanation_zh":"x=−(0)/-5=0；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261039,"parameters":{"a":-5,"b":0,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":0,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0013","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -4x+(7)=0；a=-4 已明示非零。","answer":{"kind":"short_text","value":"7/4","explanation_zh":"x=−(7)/-4=7/4；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261040,"parameters":{"a":-4,"b":7,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":7,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0014","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -3x+(14)=0；a=-3 已明示非零。","answer":{"kind":"short_text","value":"14/3","explanation_zh":"x=−(14)/-3=14/3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261041,"parameters":{"a":-3,"b":14,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":14,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0015","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -2x+(-10)=0；a=-2 已明示非零。","answer":{"kind":"short_text","value":"-5","explanation_zh":"x=−(-10)/-2=-5；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261042,"parameters":{"a":-2,"b":-10,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-2,\"b\":-10,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0016","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -1x+(-3)=0；a=-1 已明示非零。","answer":{"kind":"short_text","value":"-3","explanation_zh":"x=−(-3)/-1=-3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261043,"parameters":{"a":-1,"b":-3,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-1,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0017","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 1x+(4)=0；a=1 已明示非零。","answer":{"kind":"short_text","value":"-4","explanation_zh":"x=−(4)/1=-4；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261044,"parameters":{"a":1,"b":4,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":4,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0018","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 1x+(11)=0；a=1 已明示非零。","answer":{"kind":"short_text","value":"-11","explanation_zh":"x=−(11)/1=-11；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261045,"parameters":{"a":1,"b":11,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":1,\"b\":11,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0019","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 2x+(-13)=0；a=2 已明示非零。","answer":{"kind":"short_text","value":"13/2","explanation_zh":"x=−(-13)/2=13/2；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261046,"parameters":{"a":2,"b":-13,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":2,\"b\":-13,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0020","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 3x+(-6)=0；a=3 已明示非零。","answer":{"kind":"short_text","value":"2","explanation_zh":"x=−(-6)/3=2；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261047,"parameters":{"a":3,"b":-6,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":3,\"b\":-6,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0021","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 4x+(1)=0；a=4 已明示非零。","answer":{"kind":"short_text","value":"-1/4","explanation_zh":"x=−(1)/4=-1/4；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261048,"parameters":{"a":4,"b":1,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":4,\"b\":1,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0022","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 5x+(8)=0；a=5 已明示非零。","answer":{"kind":"short_text","value":"-8/5","explanation_zh":"x=−(8)/5=-8/5；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261049,"parameters":{"a":5,"b":8,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":5,\"b\":8,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0023","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -5x+(15)=0；a=-5 已明示非零。","answer":{"kind":"short_text","value":"3","explanation_zh":"x=−(15)/-5=3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261050,"parameters":{"a":-5,"b":15,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-5,\"b\":15,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0024","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -4x+(-9)=0；a=-4 已明示非零。","answer":{"kind":"short_text","value":"-9/4","explanation_zh":"x=−(-9)/-4=-9/4；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261051,"parameters":{"a":-4,"b":-9,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-4,\"b\":-9,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-exact-solve-0025","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的精確解","stem_zh":"在有理數論域精確解 -3x+(-2)=0；a=-3 已明示非零。","answer":{"kind":"short_text","value":"-2/3","explanation_zh":"x=−(-2)/-3=-2/3；以 gcd 約成正分母 canonical rational。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數","canonical fraction"]},"variant":{"family_id":"qf-linear-equation-exact-solve","seed":20261052,"parameters":{"a":-3,"b":-2,"domain":"rationals","operation":"exact_solve","semantic_template":"qf-linear-equation-exact-solve/{\"a\":-3,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"exact_solve\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-verification-0001","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"有理解的交叉乘積驗證","stem_zh":"在有理數論域，方程 -4x+(-14)=0；候選 x=-7/2。候選值是否為解？","answer":{"kind":"choice","value":"是","choices":["是","否"],"explanation_zh":"q=2≠0；-4×-7+(-14)×2=0，所以為解。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["有理數代入","交叉乘積"]},"variant":{"family_id":"qf-linear-equation-solution-verification","seed":20261128,"parameters":{"a":-4,"b":-14,"p":-7,"q":2,"domain":"rationals","operation":"cross_multiplication_substitution","semantic_template":"qf-linear-equation-solution-verification/{\"a\":-4,\"b\":-14,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-7,\"q\":2}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-verification-0002","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"有理解的交叉乘積驗證","stem_zh":"在有理數論域，方程 -3x+(-9)=0；候選 x=-2。候選值是否為解？","answer":{"kind":"choice","value":"否","choices":["是","否"],"explanation_zh":"q=1≠0；-3×-2+(-9)×1=-3，所以不是解。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["有理數代入","交叉乘積"]},"variant":{"family_id":"qf-linear-equation-solution-verification","seed":20261129,"parameters":{"a":-3,"b":-9,"p":-2,"q":1,"domain":"rationals","operation":"cross_multiplication_substitution","semantic_template":"qf-linear-equation-solution-verification/{\"a\":-3,\"b\":-9,\"domain\":\"rationals\",\"operation\":\"cross_multiplication_substitution\",\"p\":-2,\"q\":1}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0009","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 0x+(8)=0 的解集。","answer":{"kind":"short_text","value":"無解","explanation_zh":"a=0 且 b=8≠0，等式為 8=0，所以無解。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261236,"parameters":{"a":0,"b":8,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":0,\"b\":8,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0010","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 3x+(-3)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=1","explanation_zh":"a=3≠0，所以唯一解為 −b/a=1。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261237,"parameters":{"a":3,"b":-3,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":-3,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0011","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 4x+(-2)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=1/2","explanation_zh":"a=4≠0，所以唯一解為 −b/a=1/2。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261238,"parameters":{"a":4,"b":-2,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":-2,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0015","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 1x+(2)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-2","explanation_zh":"a=1≠0，所以唯一解為 −b/a=-2。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261242,"parameters":{"a":1,"b":2,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":1,\"b\":2,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0016","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 2x+(3)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-3/2","explanation_zh":"a=2≠0，所以唯一解為 −b/a=-3/2。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261243,"parameters":{"a":2,"b":3,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":2,\"b\":3,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0017","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 3x+(4)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-4/3","explanation_zh":"a=3≠0，所以唯一解為 −b/a=-4/3。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261244,"parameters":{"a":3,"b":4,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":4,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0018","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 4x+(5)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-5/4","explanation_zh":"a=4≠0，所以唯一解為 −b/a=-5/4。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261245,"parameters":{"a":4,"b":5,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":5,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0019","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 5x+(6)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-6/5","explanation_zh":"a=5≠0，所以唯一解為 −b/a=-6/5。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261246,"parameters":{"a":5,"b":6,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":5,\"b\":6,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0020","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 6x+(7)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-7/6","explanation_zh":"a=6≠0，所以唯一解為 −b/a=-7/6。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261247,"parameters":{"a":6,"b":7,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":6,\"b\":7,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0021","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 7x+(8)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-8/7","explanation_zh":"a=7≠0，所以唯一解為 −b/a=-8/7。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261248,"parameters":{"a":7,"b":8,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":7,\"b\":8,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0022","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 1x+(9)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-9","explanation_zh":"a=1≠0，所以唯一解為 −b/a=-9。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261249,"parameters":{"a":1,"b":9,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":1,\"b\":9,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0023","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 2x+(10)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-5","explanation_zh":"a=2≠0，所以唯一解為 −b/a=-5。"},"difficulty":{"band":"lower_secondary","level":3,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261250,"parameters":{"a":2,"b":10,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":2,\"b\":10,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0024","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 3x+(11)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-11/3","explanation_zh":"a=3≠0，所以唯一解為 −b/a=-11/3。"},"difficulty":{"band":"lower_secondary","level":1,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261251,"parameters":{"a":3,"b":11,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":3,\"b\":11,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20260927-linear-equation-solution-class-0025","batch_id":"batch-20260927-linear-equation-foundations","language":"zh-Hant","source_mko_ids":["mko-linear-equation"],"title_zh":"一次方程的解分類","stem_zh":"在有理數論域，分類 4x+(12)=0 的解集。","answer":{"kind":"short_text","value":"唯一解 x=-3","explanation_zh":"a=4≠0，所以唯一解為 −b/a=-3。"},"difficulty":{"band":"lower_secondary","level":2,"skills":["解分類","退化常數等式"]},"variant":{"family_id":"qf-linear-equation-solution-class","seed":20261252,"parameters":{"a":4,"b":12,"domain":"rationals","operation":"solution_class","semantic_template":"qf-linear-equation-solution-class/{\"a\":4,\"b\":12,\"domain\":\"rationals\",\"operation\":\"solution_class\"}"}},"verification":{"status":"candidate","checks":["schema_pending","independent_recomputation_pending"],"warning_zh":"本題為 candidate；整數與有理數的有限精確重算不是形式證明或人工審查。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-09-27","contract_version":"ocme-question-factory-v0.1"}}