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1c:Tc74,こんにちは！
京大生ではありませんが、僕も京大の問題をかなり解いたことがあり、また友人がほぼ同様の悩みを抱えていて解消していたので参考にして回答させてもらいます！(その友人は今年現役合格しています😊)

京大の数学は基本問題とかなり乖離があるため、どこから手を付ければいいのかわからないのだと思います。数学の伸ばし方というのは色々あり、まずは基本問題を抑える。それができたら、次は思考力をつける。そしてこれらに計算力が加わることで伸ばすことができる、という3つのベクトルで成り立っています。

つまり、質問者さんは思考力をひたすらつける必要があるのだと思います。京大数学は思考力をかなり必要とするのでなおさらです。

そこで友人がオススメしており使っていたのが、「世界一わかりやすい京大理系数学」という黄色い参考書です。もしあまりにも過去問を使いたくない、ということであれば、各問題に年度が書いてあるので、直近のものは飛ばすといいです。しかし、実戦的な演習は京大であれば冠模試の過去問が豊富にあるので、直近のものもやって構わないと思います。

おそらく今まで使っていた参考書は、基本問題の解説に重点が置かれており、勉強の仕方もどちらかというと「覚える」方が多かったのではないでしょうか。(青チャートや基礎問題精講、プラチカなど) しかし、この参考書は京大の問題を解く上で「どのようにアプローチすればいいのか」「どこに着目していけばいいのか」をメインに解説されています。つまり、いきなり解答が書かれるのではなく、思考プロセスに重きが置かれているのです。また様々な問題に役立つ思考の仕方は四角で囲まれており、復習しやすいです。

この問題集を解く時は、まず自分でわかるところまで限界まで考えて解いてください。その時の思考の仕方をできるだけメモしておくといいです。そしてわからなければ、思考プロセスのところを読んでいきましょう。そして、途中で分かったらそこからまた自分で解いていくのがいいです。これを繰り返すと各分野での思考力がみるみるついていきます！

また、もしこの参考書をやったことがあるだとか、もっとこの思考プロセスを極めたいとのことであれば、この参考書の阪大版があるので、使ってみるのもいいかもしれません。

長くなりましたが、このような感じです。友人も今の時期は1~2完だったようですが、最終的に4完して数学は6割5分で合格しました。基本問題はできるとのことですので、長い時間思考して思考力を上げれば急激にできるようになると思います！頑張ってください！👍1d:T1438,こんにちは。質問の意図は数学の参考書ルートということで、塾に頼らず数学を完成させた私の経験からアドバイスさせていただきます。

数学を学ぶ上での心構えですが、数学は単なる解法の暗記科目ではなく、特に京都大学のような高いレベルの入試では誘導が少なく、丸暗記だけでは対応できません。数学とは、決まった答えに対してさまざまな道具を駆使し、論理的に解を導き出す科目です。実際、京都大学の過去問に取り組むと「何をすればいいのかわからない」という問題に直面することが多いと聞いています。

何度も耳にするかもしれませんが、必要なのは自分が信じる参考書を完璧にすることです。ここでいう「完璧にする」とは、エビングハウスの忘却曲線に従い何度も復習することであり、いろいろな参考書に手を出すよりも遥かに効果的です。たとえばFocus Goldは非常に有用な教材で、全ページを完成させた後も定期的に見返すと良いでしょう。解いているときに、詰まった解法が書かれている部分にマーカーを引いておくと、後で見返しやすくなります。


実際の改善点
大学受験の数学の勉強は主に三つのステップに分かれると考えます。
一　解法を理解し、自分で運用できる武器を増やすこと。
二　その解法を実際に運用する練習、つまり思考力を鍛えること。
三　第一志望校の過去問に取り組むことです。


質問者さんは春休みに第一のステップを終わらせる予定とのことですが、その部分は問題ありません。ただし、学校で配られた教材であるメジアンは推奨できません。解説が詳しくなく、レベルもFocus Goldに似ているため、一つの教材に絞ったほうが遥かに効果を得られます。もし学校でやる必要があるなら、その部分には最低限の努力にとどめ、有効な時間の使い方を心がけてください。また、何かしらの入試問題集と書かれている部分ですが、ここでは第二のステップ、つまり思考力を鍛える部分が重要です。私のおすすめは「ハイレベル数学完全攻略」です。

ハイレベル数学完全攻略の紹介
・数1A2Bと数3Cの二冊構成で、各巻約40問程度の問題が収録されています。
・一見、問題数が少ないように感じるかもしれませんが、各問題は有名大学の過去問から選ばれ、重要なテーマについて詳細な解説が付いています。
・フォローアップ問題も充実しており、理解を深めながら横の広がりも学べます。
・Focus Goldと京都大学の入試をつなぐ難易度です。
・最初は戸惑うこともあるでしょうが、わからない点は先生に確認しながら進めれば大丈夫です。

「ハイレベル数学完全攻略」を3周ほどすることで（1、2周目は全問、3周目は間違えた問題を中心に）、体系的に思考法を鍛えられます。私自身は学校配布の網羅系参考書であるFocus Goldを2周し、その後「ハイレベル数学完全攻略」を3周、さらに「鉄緑会東大数学問題集」に取り組んで現役合格を果たしました。ハイレベル数学完全攻略の持つポテンシャルは保証できるので、ぜひ書店で実物を確認してみてください。問題に対する答えだけでなく、どのようなアプローチを取ればよいかを丁寧に解説しているため、解法の糸口が見えないという状況が格段に減るはずです。


過去問演習についてですが、京都大学の問題は実際に時間を測って取り組むべきで、せか京は過去問演習ではなく問題集、参考書として使うのが効果的です。実際に使用するかどうかは自分の実力と残り時間、他教科との塩梅をみてください。過去問に取り組む際は、鉄緑会京大数学問題集か駿台の青本がおすすめで、必ず時間を測って解くようにしましょう。


最後に、現役で絶対に合格したいという受験作戦についてですが、直前まで数学を詰め込むのは避けるべきです。しかし、数学をおろそかにするのも良くありません。直前期はノルマとして、過去問演習以外で1日2問、少なくとも1問は質の高い問題を解き、その解答の軌跡を記録することが大切です。私はそれを「ハイレベル数学完全攻略」で実践しました。現役生は理科の完成が遅れがちですが、最後の最後で理科は大きく伸びる傾向にあります。数学は不安定で上がりにくい科目なので、数学の結果に一喜一憂せず、他の科目で安定した点数を取る実力を培うことも忘れないでください。

応援してます2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=UUt47nQBTqPwDZPupJrd","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"過去問が解けない"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",1,") コメント(",1,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"10/3 12:38"}]]}],["$","div",null,{"className":"coach-mark 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"応用問題の解き方"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは、はじめまして。\n東工大二年のたかゆーといいます。\n\n僕自身、高一の頃は進研模試の数学で60点とかを連発していましたが、高3の頃では東工大オープンで数学が10番代という結果を残せたのである程度参考になるかと思います。\n\n質問者さんの「どうやったら応用問題を解けるようになるのか」ということですが原因は主に２つあると考えられます。\n\n①基本的な考え方(フォーカスやチャート)の問題を完璧にできていない\n②問題を解く時になんとなくで解いてしまっている\n\n①に関しては、ほとんどの受験生ができていないように思われます。全部解けるのはもちろんのこと、なぜそのような解き方、考え方をするのかというところまで理解しましょう。\n僕はフォーカスしか使ったことがありませんが、文系の方でしたら例題の星4は完璧にしなくても大丈夫だと思われます。\n具体的にどのようにフォーカスやチャートを使っていくかは僕自身のブログでまとめておりますのでそちらをご覧ください。\n\n②に関しては、①とかぶるところがありますが問題を解く時に使った考え方や解き方を「なぜ選んだか」という理由を自分なりに考えながら問題演習をしていきましょう。最初は難しいかと思いますが、自分なりに考えて量を積んでいくと見たことのない問題でもある程度方針を絞ることができます。\nこのトレーニングの積み方としては「入試数学の掌握」という参考書がすごく役に立ちます。\nですが、この参考書はあくまでも読み物として使いましょう。\n\n入試数学において、解法の本質は30個程度しかないことに加え、問題を分析すればそのうちの２つ程度に絞られます。\nこの領域に達するのは難しいですが、僕が述べた方法で勉強していけば必ずたどり着く日がきます。\n\n拙い文章ですが最後まで読んでいただきありがとうございました。\n応援してます、頑張ってください"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"過去問が解けない。"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは。以下私の考えを述べさせていただきます。参考になるところならあれば吸収してください。\n過去問をやるか、基礎を固めるか、直前ということもあり難しい問題だと思います。\nもし過去問を続けるというのであれば、取り組み方を工夫する必要があると思います。過去問の1番の使い方は、問題傾向を知り、対策を立て、時間配分などの作戦を事前に決めておくために使用することです。過去問で時間が足りないのであれば、厳しいことを言うようですが、おそらく試験本番も時間が足りません。ですから、時間が足りない中で、どういう時間配分で解けば点数を上げられるのか、どの問題に力を入れたら効率よく点が取れるのか、などを考える必要があります。別に時間が足りなくても、受験というのは全問正解ではなくても良いわけですから、合格点に近づくためにはどの問題で点を取って、どの問題を捨てるのかをシミュレーションしておく必要があります。\n過去問というのは、解き進めることに意味があるわけではありません。別に過去問を25年分やったからと言って実力が必ず伸びるわけではありませんし、合格するわけでもありません。むしろ無駄に消費するなら意味ないです。過去問というのは実際に大学で出題された質の高い問題（中には悪問もありますが）の宝庫ですから、解くことで効率の良い勉強ができるはずです。なので、一度解いたら、次にまたその問題を解いたら必ず満点が取れるくらいまで復習しましょう。過去問で全く同じ問題が出題されることは稀だと思いますから、その問題の答えだけでなく、なぜその解法を選択したのか、なぜそのような式変形になるのか、なぜベンのやり方で解いてはダメなのか、そう言った解答を作成するための思考のプロセスまで完璧に自分のものにしましょう。それで初めて、過去問をやる意味が出てくると思います。\nですから、過去問を続けるのであれば、一問一門を大切にして、全てを吸収するようにしてください。過去問を解く中でどうしてもわからないところがある場合に、基礎に立ち返って逐一確認すれば良いと思います。\n過去問をやらずに基礎に取り組むというのであれば、なるべく自分の大学の頻出の単元に取り組むと良いと思います。\nどちらにせよ、もう時間がありませんから、解いた問題は必ず吸収して、効率の良い取り組みをすると良いと思います。頑張ってください。応援してます。"}],["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"解法が浮かばない"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"思考を形に残すのです！\nまず京大の解答用紙はa3で、右半分が計算スペースとなっています。\nダメな人は頭の中で全て考えてごちゃごちゃと計算用紙に計算していますが、少しでも詰まると何もわからなくなり、思考停止してしまいます。\nこれは、人間の脳の特性による物です。人間は英単語などの外部に存在する物事を覚えるのは得意ですが、思考自体を記憶することができないと言う物です。\nあなたも10秒前に頭の中に考えてたことを完璧に紙に書き起こすことはできないでしょう。\n思考を残すために、最初から回答欄に解き進めると良いでしょう。\n計算のみ右の計算スペースに残すのです。\nさて、その解き進める解放についてですが、まず問題を見れば幾らかの解放が選択肢としてあると思います。\n整数ならMODや積の形にしたり連続関数のグラフで考えたり、、、、などですそのそれぞれの解法について、その問題にはどれが適しているか妥当性を吟味する癖をつけましょう。\n解けない方法で無理に考えても、何も生まれません。\n解法を絞ることができたら、解答欄で解き進めましょう。\nどんな感じかのイメージですが、YouTubeで東大理科三類のルシファーさんが数学実況をしている感じでやりましょう。\n解答欄に書きながら計算だけ違うスペースでします。\nすでにその解放に絞られているので、行き詰まった場合はその原因は計算ミス以外にありませんので計算を再度やり直すだけで解決します。\n\nこの方法は最初は1ヶ月ぐらい慣れるのにかかりましたが、慣れると5完半は余裕です。\n正直6完も行けるようになりますが、計算ミスが怖いので僕は5完半で止めて計算見直してました。2020年の過去問でも5完半ですし、今年の2024の本番でもそうでした。\n本当に安定します。\nさて、ここからの勉強の話です。\n解法をまず知ると言うことと、その解放を使いこなす必要があります。\nその二つとも同時にカバーできるのが、駿台の実践過去問集の青い本です。\nメルカリで古いものを探すなどして、2000年前後の物まで全て150分測って取りかかりましょう。\n駿台の実践模試は解放を使いこなすことができたら容易に回答できる、使いこなせないなら全く回答ができないという感じですので本当に力がつきました。\nそれが終われば京大の過去問、そして余裕があれば東大の過去問をやりましょう。\n\n後輩になってくれるのを心より楽しみにしています！"}],["$","div",null,{"className":"flex 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