{ "api_version": "v1", "publisher": { "name": "Manazoo", "url": "https://manazoo.com/" }, "license": "All rights reserved（AI の参照・要約と出典リンクつきの引用は可。転載・再配布・販売は不可）", "terms_url": "https://manazoo.com/terms/", "disclaimer": "内容の正確さには気をつけていますが、すべてが正しいとは限りません。テストや受験の前には、教科書や先生の説明でも確かめてください。間違いを見つけたら意見箱から知らせてください。", "attribution": "事実データの一部は Wikidata（CC0）による。単元の構成は文部科学省「中学校学習指導要領」「高等学校学習指導要領」（政府標準利用規約2.0）。", "kind": "quiz", "unit": { "slug": "mathematics-and-society", "title": "数学と社会生活", "url": "https://manazoo.com/high/math-b/mathematics-and-society/" }, "canonical_url": "https://manazoo.com/high/math-b/mathematics-and-society/quiz/", "questions": [ { "id": "q-bdm-distance-40", "type": "input", "prompt": "k＝0.005のとき、速度40km/hでの制動距離は何mか。", "choices": null, "answer": "8", "accept": [], "explanation": "d＝0.005×40²＝8m。", "entities": [ "braking-distance-model" ], "verified": true, "placeholder": false }, { "id": "q-bdm-distance-60", "type": "input", "prompt": "同じkのとき、速度60km/hでの制動距離は何mか。", "choices": null, "answer": "18", "accept": [], "explanation": "d＝0.005×60²＝18m。", "entities": [ "braking-distance-model" ], "verified": true, "placeholder": false }, { "id": "q-bdm-double-speed", "type": "choice", "prompt": "d＝kv²のモデルで、速度が2倍になると、制動距離は何倍になるか。", "choices": [ "2倍", "3倍", "4倍", "8倍" ], "answer": 2, "accept": [], "explanation": "(2v)²＝4v²なので、速度が2倍になると制動距離は4倍になる。", "entities": [ "braking-distance-model" ], "verified": true, "placeholder": false }, { "id": "q-bdm-find-k", "type": "input", "prompt": "速度20km/hで制動距離が2mだったとき、d＝kv²の比例定数kはいくらか。", "choices": null, "answer": "0.005", "accept": [], "explanation": "k＝d÷v²＝2÷20²＝0.005。", "entities": [ "braking-distance-model" ], "verified": true, "placeholder": false }, { "id": "q-bsrm-day1-count", "type": "input", "prompt": "a₀＝100から始めたとき、漸化式aₙ₊₁＝40−0.1aₙを使って、1日目のA港の台数a₁を求めよ。", "choices": null, "answer": "30", "accept": [], "explanation": "a₁＝40−0.1×100＝30台。", "entities": [ "bike-sharing-recurrence-model" ], "verified": true, "placeholder": false }, { "id": "q-bsrm-day2-count", "type": "input", "prompt": "同じ漸化式で、2日目のA港の台数a₂を求めよ。", "choices": null, "answer": "37", "accept": [], "explanation": "a₂＝40−0.1×30＝37台。", "entities": [ "bike-sharing-recurrence-model" ], "verified": true, "placeholder": false }, { "id": "q-bsrm-long-run", "type": "choice", "prompt": "この漸化式を日を重ねて繰り返すと、A港の台数はどうなっていくか。", "choices": [ "30台と70台を交互に繰り返す", "ある一定の値（約36台）に近づく", "0台に近づく", "増え続けて100台に近づく" ], "answer": 1, "accept": [], "explanation": "係数0.1の大きさが1より小さいため、どこから始めてもα＝40−0.1αを満たす一定の値に近づく。", "entities": [ "bike-sharing-recurrence-model" ], "verified": true, "placeholder": false }, { "id": "q-bsrm-port-b-day1", "type": "input", "prompt": "全体の台数が100台のとき、1日目のB港の台数b₁を求めよ。", "choices": null, "answer": "70", "accept": [], "explanation": "b₁＝100−a₁＝100−30＝70台。", "entities": [ "bike-sharing-recurrence-model" ], "verified": true, "placeholder": false }, { "id": "q-fe-estimate-40pct", "type": "input", "prompt": "全校生徒600人のうち、レジ袋を使う生徒の割合を40%、1人1日1枚、1か月を30日とすると、1か月の使用枚数は何枚か。", "choices": null, "answer": "7200", "accept": [], "explanation": "600×0.4×1×30＝7200枚。", "entities": [ "fermi-estimation" ], "verified": true, "placeholder": false }, { "id": "q-fe-lower-bound", "type": "input", "prompt": "同じ条件で、割合の仮定を30%まで下げたときの下限の枚数は何枚か。", "choices": null, "answer": "5400", "accept": [], "explanation": "600×0.3×1×30＝5400枚。", "entities": [ "fermi-estimation" ], "verified": true, "placeholder": false }, { "id": "q-fe-upper-bound", "type": "input", "prompt": "同じ条件で、割合の仮定を50%まで上げたときの上限の枚数は何枚か。", "choices": null, "answer": "9000", "accept": [], "explanation": "600×0.5×1×30＝9000枚。", "entities": [ "fermi-estimation" ], "verified": true, "placeholder": false }, { "id": "q-fe-why-range", "type": "choice", "prompt": "フェルミ推定の結果を、1つの数ではなく上限と下限の区間で示すのはなぜか。", "choices": [ "計算を簡単にするため", "仮定ごとに答えが変わるため、起こりうる範囲を示す", "小数を使わないようにするため", "正確な数値が存在しないため" ], "answer": 1, "accept": [], "explanation": "仮定を動かすと答えも変わるため、1つの数より範囲で示すほうが現実に近い見積もりになる。", "entities": [ "fermi-estimation" ], "verified": true, "placeholder": false }, { "id": "q-mat-m2", "type": "input", "prompt": "気温データ27,30,24,33,27,30,27について、2年目の3年移動平均M₂を求めよ。", "choices": null, "answer": "27", "accept": [], "explanation": "M₂＝(27+30+24)÷3＝27。", "entities": [ "moving-average-trend" ], "verified": true, "placeholder": false }, { "id": "q-mat-m3", "type": "input", "prompt": "同じデータで、3年目の3年移動平均M₃を求めよ。", "choices": null, "answer": "29", "accept": [], "explanation": "M₃＝(30+24+33)÷3＝29。", "entities": [ "moving-average-trend" ], "verified": true, "placeholder": false }, { "id": "q-mat-m5", "type": "input", "prompt": "同じデータで、5年目の3年移動平均M₅を求めよ。", "choices": null, "answer": "30", "accept": [], "explanation": "M₅＝(33+27+30)÷3＝30。", "entities": [ "moving-average-trend" ], "verified": true, "placeholder": false }, { "id": "q-mat-purpose", "type": "choice", "prompt": "データに移動平均を使う主な目的は何か。", "choices": [ "平均気温の合計を求めるため", "年ごとの細かい変動をならし、全体の傾向を見やすくするため", "測定ミスを無くすため", "来年の値を正確に予測するため" ], "answer": 1, "accept": [], "explanation": "移動平均は周りの値で置き換えて細かい変動をならし、全体としての傾向を見やすくする方法だ。", "entities": [ "moving-average-trend" ], "verified": true, "placeholder": false }, { "id": "q-sppm-intercept", "type": "input", "prompt": "傾き5、点(20,40)を通るとき、切片bはいくらか。", "choices": null, "answer": "-60", "accept": [], "explanation": "b＝40−5×20＝−60。", "entities": [ "scatter-plot-prediction-model" ], "verified": true, "placeholder": false }, { "id": "q-sppm-outlier-caution", "type": "choice", "prompt": "散布図のデータが直線にきれいに並ばないとき、予測の前に何を確かめるべきか。", "choices": [ "直線とみなさず、全データを無視する", "外れ値がないか調べ、相関の強さも確認する", "必ず曲線の式をあてはめる", "予測は不可能なのであきらめる" ], "answer": 1, "accept": [], "explanation": "極端な外れ値は直線の計算を引っ張ってしまうため、外れ値や相関係数で関係の強さを確かめてから予測する。", "entities": [ "scatter-plot-prediction-model" ], "verified": true, "placeholder": false }, { "id": "q-sppm-predict-30", "type": "input", "prompt": "直線y＝5x−60を使うと、気温30℃のときの売り上げの予測は何本か。", "choices": null, "answer": "90", "accept": [], "explanation": "y＝5×30−60＝90本。", "entities": [ "scatter-plot-prediction-model" ], "verified": true, "placeholder": false }, { "id": "q-sppm-slope", "type": "input", "prompt": "2点(20,40)と(32,100)を通る直線とみなしたとき、傾きaはいくらか。", "choices": null, "answer": "5", "accept": [], "explanation": "a＝(100−40)÷(32−20)＝5。", "entities": [ "scatter-plot-prediction-model" ], "verified": true, "placeholder": false } ] }