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1c:Tcf2,こんにちは。東京科学大（旧東工大）工学院のプロトンです。勉強お疲れ様です。10月の今から11月中旬までの約1ヶ月の間にやるべき数学の参考書についてアドバイスしていきたいと思います。よろしくお願いします！


まず本来であれば10月に過去問演習を始めておきたいところですが、
世界一わかりやすい阪大理系数学講座（以下せかはんと略します）、これを使っていきましょう。勉強時間は、学校がある日は最低5時間、休日は10時間確保してください。

黄チャートを持っているのであれば、数3全範囲のエクササイズを解きます。分からなかったら印をつけて後で見返せるようにしてください。全力でできるだけ早く終わらせてください。

1周終わったら、2周目は、せかはんと同時並行で進めていきます。阪大理系数学の少し昔の問題を扱い、問題への向き合い方を効率よく学びます。数学にはいろいろな解法があり、どの解法を選ぶかは結構点数に関わってきます。計算が煩雑にならないようにするにはどうしたらよいか、など解法を見極める力を身につけましょう。

黄チャートの2周目は、1周目に分からなかった問題を解きます。ここまでを11月の第2週目くらいまでに終わらせられるように頑張りましょう。時間が足りない！と思ったかもしれませんが、みんなも同じです。みんなこの時期は焦っているんです。大丈夫、自信を持って勉強しましょう。

11月中旬から共通テスト対策に移るということですが、黄チャート・せかはんに触れる日を週に少なくとも3日は取りましょう。どうしても共通テスト対策に集中していると、共テ後に二次試験対策をさあ始めようとしたときになんも覚えていないという、所謂共通テストぼけが起きる方が一定数います。そうならないために少しずつでいいので、解き直しは忘れないようにしましょう。

共通テストが終わったらその次の日からが勝負の1ヶ月です。共テ後は過去問メインです。解法が分からなかったら、せかはん、チャートに戻って復習しましょう
この1ヶ月で過去問演習に集中できるように、準備をしておきます。


《阪大理系数学　傾向》
2024年：1⃣極限　2⃣複素数平面　3⃣空間図形　4⃣積分(回転体)　5⃣整数問題
2023年：1⃣極限　2⃣平面ベクトル　3⃣図形と方程式(図示)　4⃣空間ベクトル　5⃣確率と漸化式
2022年：1⃣複素数平面　2⃣三角関数　3⃣図形と方程式　4⃣総合問題(微分、極限)　5⃣積分(媒介変数)

2021年度以前は、微分積分や確率、極限が頻出分野となっています。
参考にしてください。

以上、数Ⅲの今からの進め方、参考書、共テ後の勉強についてアドバイスさせていただきました。こんなに長い文章を読んでくださりありがとうございます。
頑張ってください！1e:Te13,結論、これから進めるべき順序は以下の通りです。
①核心の星1、2(3は得意でない限り多分しんどい)
②阪大過去問2年以上(特に頻出分野は入念に)
③本番のOP・実践とその復習
④阪大過去問10年分くらいを2周

入試問題の核心の問題チョイスはかなりいいですし、一冊で数Ⅲまで網羅できるのでオススメですが、解答の思考の流れに違和感を持つことがあったので、注意してください。(解答通りの解法でなくて良い。数学センスのある人に質問できると良し)
星3はかなり難しい(正直解けなくても構わない)ので、まず星1、2あたりから始めることをオススメします。
難関編を解いたことはありませんが、正直必要ないと思います。
あくまで、全単元の復習＆初見力向上＆パターン化が目的という認識で大丈夫です。

入試問題の核心に入る時期もかなり遅めなので、実践模試の過去問は、まず必要ないと思います。
ただ、試験に使った5時間が無駄になるので、本番のOP実戦の復習はしてください。
過去問も同様ですが、復習する際は、どういう力が足りないのか、過去に学んだ知識がどう使われているのかをきちんと分析してください。


普段の勉強の復習法は、
①自力で解く
②解答チラ見
③もう少し自力で解く
④解答を見て、初見の段階でどう考えていれば正解できていたのか考える
⑤④の内容を抽象化してメモする
⑥解き方とそれを思い付いた理由を空で言えるようにする
⑦頻繁に自分のメモを見返す
⑧期間をおいて⑥をする

こんな流れです。
メモするのは面倒ですが、復習する際 結果的に時短になるのでオススメです。(僕の場合、計算ミスを減らすためその原因と対策もメモして、何度も見返していました)


僕の分析では、阪大は以下の問題が頻出です。
①体積の問題
②複素数平面＋α(特に回転)
③微分・積分を絡めた不等式＋極限
④確率・漸化式＋極限
⑤気持ち悪い整数問題(対策困難で捨て問になることが多い)or任意の単元から一題

特に複素数は広い概念を持ち、色々な分野との複合問題が作りやすいので、ほぼ100%出ると思っていいです。
あと、体積問題の本質は軌跡と領域で、特に一文字固定法と相性が良いので、よく勉強しておいてください。
不等式は大-小して微分したり、グラフ的に考えたりすれば、どうにかなります。(類似問題をたくさん解くべき)

阪大は出る単元がほぼ決まっていますし、細かい知識はあまり問われないので、きちんと対策すれば半分以上は取れます。
受験生は、マニアックな知識が必要だと考えがちですが、大学が求める人材や公平性を考慮すると、それを問うことにメリットがありません。(これを理解した上で解くと、思考にノイズが入りにくいです)

「その問題のみで使える知識」に意味はありませんから、「本番でも使える知識」だけを抽出して学び取るよう意識してください。(そのための抽象化です)
残り時間は少ないですが、正しい受験理論をお持ちだと思うので、自信を持って頑張ってください。1f:Tecd,4月から高校3年生になるということだと思いますが、今すぐ数Ⅲに入るべきです。その理由はただ1つです。それは数Ⅲは他の科目と比べてもはるかに習得するためにかかる負担が大きいことです。理系に進む生徒の中には夏以降の学習の過半数は数Ⅲの勉強だったというものも少なくありません。理系大学進学の難易度を著しく引き上げている原因や理系が文系に比べると難しいと言われる原因は数Ⅲにあるとも考えられています。

数Ⅲは関数（分数関数や無理関数、逆関数や合成関数）、極限、微分法の基本・応用、積分法の基本・応用の6分野で構成されています。6分野の中で比較的難易度の低い関数や極限ですら、数ⅡBCの1つの分野以上の難しさです。しかも極限は数Ⅱ範囲の対数関数や数B範囲のΣ計算の基本ができていなければ習得することはできません。微分法や積分法に関しては名前からもわかる通り数Ⅱの微分法と積分法の発展です。そのうえこれはあくまでも基本の話です。応用に関してはさらに難易度が高く、問題作成するにあたり比較的応用問題・発展問題を作りやすい分野でもあります。ただでさえ難しい分野ですからその応用問題や発展問題の難易度の高さはかなりのものになります。

かなり厳しいことを言うようですが、千葉大学レベルの国公立大学を志望している高校生は高校2年生の終わりまでに数Ⅲの範囲を1周は終えていることがほとんどです。今更言われても…と思われるかと思いますが、受験数学はなるべく早く1通りの学習範囲を終えることが鉄則です。確かに、数Ⅲに関しては数ⅡBCがある程度完成されていないと習得することが困難な科目ではあります。しかし、共通テストでの完成度を高めることよりも先に数Ⅲを1通り学習することの方が優先度が高いと言えます。

ただ質問者さんはかなり数ⅡBCの完成度が高いと見受けられます。今後夏までの３か月半程度で数Ⅲを確実に完成させてください。そのためには今後の数学学習の大半を数Ⅲにあてることになります。その間も最低限これまでの数学学習で得た技能を低下させないように週に1,2度復習し、1か月で全範囲を軽く1周するのが理想です。

また、数Ⅲの学習方法についてですが、入門問題精巧も青チャートもというととてもやりきれないと思います。基礎から応用までやることのできる問題集を何か1冊に絞って学習することをおすすめします。なお学校で配布されている教科書傍用問題集があればそれをある程度完璧にすることが望ましいです。ちなみにここでいう完璧とは7,8割の完成を3周かけて目指すことです。

しかも質問者さんの得意科目が数学で苦手科目が漢文となるとかなり大変だと思います。質問者さんの英語や化学、物理のレベルがわからないので何とも言えないですが、高校3年生の1年間は平日には1日５時間、休日は1日15時間程度の学習が必要になると思いますし、しかもその学習もかなり効率の良いものでなければなりません。大変なことも多いと思いますが、学習方法や悩み事についてご相談があればいつでもお伺いいたします。いえさんの受験勉強を心から応援しています。20:Te68,日々の勉強お疲れ様です。数3の疑問、と言うことですが一般的には京大は他の理系大学と比べて数3の難問が出ることは低い傾向にあります。実際、数3であれば阪大というイメージが私の受験生時代にもありました。ただ、これはあくまでも傾向で、実際に難問、奇問（いわゆる捨て問）が出ている年もありすます。そのため、出にくいから対策しなくてよい、ということは一切ありません。模試の判定から判断するに、夏まで、もしくは夏が終わるまでに数学の基礎を総ざらいする、ということをお勧めいたします。この理由は、結局受かる受験生というのは、基礎的な問題が解ける受験生であるからです。（基礎的な問題とは赤本のA、B問題、各種予備校の出す標準〜やや難あたりを想定しています。）また、京大は数3が絡む問題といえど、途中は1A、2Bでの議論を進めて、結論だけ極限をもちいる、といったこともしばしば見受けられます。そのため、繰り返しとはなりますが一度ご自身の持っている参考書をやりきる、という視点を持ってみてはいかがでしょうか。手前味噌ながら私が受験期の夏休み前、夏休みに勉強した数学を申し上げますと、今までの模試や定期テストで間違えた問題をピックアップ、解き直しを2週間のうちに3、4回ほど、そして赤チャート、優しい理系数学（通称やさり）の練習問題？をとく。できなかった問題をピックアップ、解き直しを2週間のうちに3、4回、加えてニガテだと感じた範囲はとことん補充問題（ページの下の方に書いてあったりするやつ）を解く。ということです。この際注意していただきたい点があります。それは、その問題だけの復習にしない、ということです。数学を含め、勉強というものはどこかつながっています。ですからその問題に対応するための復習ではなくて、その”ような”問題が出てきた時に対応できるような復習をぜひ重ねてください。例えば、記述の言い回しだったり、式変形の手順、途中式の形など細かいところまで模範解答を真似してみてください。きっと問題の見え方が変わってくることと思います。つまり、数学3の中のどこを重点的に勉強すれば良いのか、という視点ではなく、どこも満遍なく勉強することをこの時期はおすすめします。また夏には河合のオープンや駿台実践があると思います。私としては、どちらか一方を受ければ十分であると思います。（現に私がそうでした。）これは、さまざま意見があると思いますが、模試を受けるとなるとそのために1日潰れる上、準備に最低1週間かかります。夏であれば、まだ基礎固めをする方が私としては最適だと思いますので、冠模試はどちらか一方を受けることをおすすめいたします。（私は実践をうけました。）模試の前には1.2年で十分だと思いますが過去問を解いてみてくださいね。
P.S 駿台全国は京大と型が違うので、あんまり気にしなくてだいじょーぶです！和訳とかその辺だけは復習しときましょう。
京大は素晴らしい大学です。ぜひ夏を乗り越えてください。応援しています。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=M9fJJqf884m0uTDqXhlY","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"阪大理学部志望 数三の勉強法について"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",8,") コメント(",2,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"6/26 14:53"}]]}],["$","div",null,{"className":"coach-mark mb-4","children":"UniLink利用者の80%以上は、難関大学を志望する受験生です。これまでのデータから、偏差値の高いユーザーほど毎日UniLinkアプリを起動することが分かっています。"}],["$","div",null,{"className":"mb-4","children":["$","$L13",null,{"clientImageUrl":null,"clientUserName":"おけ","infoString":"高3 東京都 大阪大学理学部(61)志望","adviceId":"M9fJJqf884m0uTDqXhlY"}]}],["$","div",null,{"className":"mb-8","children":[["$","div",null,{"className":"leading-loose whitespace-pre-wrap","children":[["$","div","consultation-part-0",{"children":[null,"高３阪大理学部志望です。\n数三の勉強方法が分かりません。\n学校では2週目に入っているのに基礎から出来ていなくて授業にすらついていけていません。\n青チャートの例題を中心にやっていますが身についている感じがしなくて勉強方法が間違っているんじゃないかと不安になっています。\n何かアドバイスがあれば欲しいです。"]}]]}],["$","div",null,{"className":"pt-4","children":["$","$L14",null,{}]}],null]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"回答"}],["$","div",null,{"className":"mb-4","children":["$","$L15",null,{"adviserImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_J2cPn95jsVgBegSruzNx1wIbnik2.jpg?alt=media&token=0dbf3a0c-5801-4d6b-8e15-ce6e9291e1e5","adviserName":"スカル","adviserDepartment":"東京工業大学工学院","adviceId":"M9fJJqf884m0uTDqXhlY"}]}],["$","div",null,{"className":"coach-mark mb-4","children":"すべての回答者は、学生証などを使用してUniLinkによって審査された東大・京大・慶應・早稲田・一橋・東工大・旧帝大のいずれかに所属する現役難関大生です。加えて、実際の回答をUniLinkが確認して一定の水準をクリアした合格者だけが登録できる仕組みとなっています。"}],["$","div",null,{"className":"mb-8","children":[["$","div",null,{"className":"leading-loose whitespace-pre-wrap mb-4","children":[["$","div","advice-part-0",{"children":[null,"こんにちはー😃\n数三は高校数学の最高峰であるうえに受験で必ず出題されるのでついていけなくなると不安になりますよねー数三の分野別にアドバイスしていきますね\n\n①関数\n分数関数や無理関数、逆関数なんかを扱う単元ですけどぶっちゃけあんまり出題されないです。強いて言うなら逆関数の微分積分なんかはできるようになった方がいいですけど今はまだやるべきじゃないと思います。過去問や問題演習で出てくると思うのでそのときにやり方を覚えるくらいでいいと思います。\n\n②極限\n極限は阪大とかでは基本的にははさみうちの原理が一番出題されますかねーはさみうちは誘導の有無にもよるんですが基本的には自分で不等式を立てなくてはいけないのでこれも慣れが必要なんですよね。だからこれも演習のときで良いと思います。今はチャートの例題にある自然対数の底eの公式を使ったやつだったり微分の定義から導くやつだったりに慣れるのが大事ですね。コンパス3までの例題をやれば基本的な極限計算は身に付くと思うのでまずはそこを目指しましょう。はさみうち以外の極限の問題で落とすのが一番もったいないですからね。\n\n③微分\n数三の本題はここからですよねーまずは基本的な微分の公式を一瞬で頭に浮かぶようにする、合成関数や積、商の微分をミス無く素早くできるようになることが重要です。ミス一つで大問丸々落とすなんてこともありますからねーここは問題演習を積むことで鍛えるしかないです。あとは増減表なんかを用いてグラフも絶対に書けなくちゃいけないです。微分の問題はグラフを使って解くことが多く、チャートや問題演習をやってくとまた微分かーってなるようになります。特にチャートは例題を一通りやれば9割の解法は必ず身に付くので、まずはコンパス3までの例題を二周することをおすすめします。正直阪大はチャートを完璧にしたらもう過去問に入ってもいいくらいだと思ってます。なのでコンパス3が終わったら4,5と順に難しくしていくのがいいと思います。特にコンパス5は阪大レベルのもあると思うので難しいと思いますが頑張ってください。"]}],["$","div","advice-part-1",{"children":[["$","div",null,{"className":"my-4","children":["$","$L16",null,{"id":"adsbygoogle-init-on-advice-M9fJJqf884m0uTDqXhlY-1"}]}],"④積分\nまあこれが一番難しいですよね。多分阪大で出題されなかった年はそうそう無いと思います。でも数三の積分は慣れてしまえば簡単ってパターンも多いです。そのようになるためにはまずは基本的な積分のパターンを覚えましょう。積分を見たら微分系の接触なのか、置換が必要なのか、必要なら何を何に置換すれば良いか、はたまた部分積分なのか。最初は素早く正確にするのは難しいと思います。でもこれもチャートを完璧にこなせばできるようになります。そこで問題演習も重ねれば怖いものなしです。なのでこれもまずはコンパス3までを完璧にし、その後4,5と進めていくのをおすすめします。積分の置換パターンはめちゃくちゃ数があると思うのでとにかく問題を解きまくることが大事です。僕はヨビノリの積分を百個全部見ました。そこまでやる必要はないかもしれませんが、隙間時間に何個かサムネイルでわからないやつを見てみるのはすごくおすすめです。積分計算は夏休み終わりまでには完璧にしておけるとその後がぐぐっと楽になります。頑張ってください。\n\n全体を通して言えることは、チャートを続けるで良いと思います。質問者さんは学校の授業についていけないとのことなので、まずはコンパス3までを微積中心に完璧にする。これをしておけば置いていかれることは無いと思います。とにかく夏休み終わりまでに基礎を完璧にし、過去問に素早く入れるように勉強頑張ってください！"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L17",null,{"adviserImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_J2cPn95jsVgBegSruzNx1wIbnik2.jpg?alt=media&token=0dbf3a0c-5801-4d6b-8e15-ce6e9291e1e5","adviserName":"スカル","adviserDepartment":"東京工業大学工学院","adviceId":"M9fJJqf884m0uTDqXhlY","numberOfFan":4,"clipsAvg":3,"adviceRateAvg":5,"profile":""}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink 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mb-1","children":"僕からは青チャートの具体的な進め方をお伝えします。\n\n1;解放暗記として例題だけをやってしまって、全て一通り解けるようにする。目標は、問題文を見た瞬間、初手から完答までの流れが頭で再現できるようになることです。\nイメージは、例えば三次関数の解の個数問題で、問題文見た途端、あー、この問題はまず定数分離して、微分して増減表書いて、グラフ書いて、定数動かせば終了だな！って感じ。\n\nこの時に、最初の一周目というのは一分くらい考えて答えが分からないなら、すぐ下の解説を見ながら解いてオッケーです。ただ、解説を暗記しちゃダメで、あくまでも解放を暗記してください。\n例えば、二次関数の解の配置問題なら頂軸端に注目！みたいな、、、\n\n二周目は一周目で解けなかった問題を自力で解いてみてください。\n\n自力と言っても、覚えたことを思い出せるかのチェックですけど。\n\n三周目は、二周目でも解けなかった問題(多分一分野で３題くらいかな)\n\n\n\n　\nこのやり方だと、一周目に一問30分くらい、二周目三周目は一問10分くらいの感覚で解いていった気がします。\n\n\n2.最後の章末問題を解きます。ここでは、解放暗記が役に立つのかのチェックと、思考力を鍛えてください。\nだから、わかるまで時間をかけて粘るべきです。\n1週間くらい考えるのもありだと思いますよ。\n\n\n\nちなみに、例題の下の練習は、面倒だったので僕はやりませんでしたが、時間があるならやっても良いんじゃないでしょうか。ただそれよりもチャートは分厚いので、サクサク進めていった方がいいと思います。\n\n\n\n\n正直、地方国立大だったら、解放暗記で十分だと思うので、2️⃣の必要はあんまりないかもしれませんが、旧帝大クラスになると思考力は必須です。\n\n自分の志望大に合わせて、時間配分して頑張ってください。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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\n（適当に手を動かすのは練習になりません。「この積分は、どの解法で解くのかな…？」「これだ！これならいける！」ってなるまでは手を動かしてはいけません。）\n\n呼吸をするように積分しましょう！\n（そのために微分の練習が不可欠です。）\n\n\n複素平面について\n実は受験で出たら確実に解けるランキング第1位なんじゃないか？って思っています。複素数の解き方には数パターンしかないんです。出題のされ方もパターン化され切っています。「あ〜こういう系ね。」と分かるくらいまで練習していれば、確実に大問1個分正解できてしまうんです。\n\n「青チャートが一対一になっていて演習量に不満がある」ということでしたが、複素平面に関しては安心してください。青チャートに載っていない解法の問題はおそらく出ません。青チャートの複素平面の問題を全て完璧に解けるように何周も練習することもオススメします！\n\n\n受験勉強って結構モチベ保つのしんどいですよね。好きなお菓子食べたりするといいですよ。それと、数学に飽きたらほかの勉強しちゃっていいですよ。ほかの勉強が飽きた後に数学に帰ってくればいいんです。\n数学の問題集にもいずれ飽きが来ると思います。そうなったら1度過去問に手をつけてみましょう。（〇進の過去問データベースおすすめ！）\n過去問演習が1番数学の中で楽しいですよ！"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 0h24v24H0V0z","children":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"阪大工学部志望 数学の参考書ルートを教えて"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"初めまして。\n\nチャートは問題数も多く、一周するのに時間がかなりかかってしまいます。網羅性が高いですが、何周もできるような努力が必要だと考えており、他の教科も対策する必要がある中では大変なタスクだと思います。\nそのため、一対一対応や標準問題精講などの薄いですが要点が絞られている問題集をまずは一冊丁寧に仕上げることをお勧めします。\n\n夏までに何か上記のレベル帯の参考書を仕上げてみてはいかがでしょうか。チャートは、苦手な分野の補強として使うことがおすすめです。\n\n夏は苦手分野の補強や、終わっていない科目(3年生で習う分野など)を対策しつつ(数学以外も含めて)、阪大の二次試験の傾向を分析し、その傾向に対する対策をしてみてはいかがでしょうか。\n\n秋は模試がたくさんあると思うので、より一層二次試験の対策(阪大数学25ヵ年など)をやってみてください。難易度A,Bを確実に解けるように、難易度Cは方針を知ることができるように、してみることがおすすめです。(難易度Dは必要ないです。)無理に25ヵ年全てを解こうとするよりも、上記のようなことを心がけることが大切だと思います。\n冬は共通テストの勉強量が増えると思うので、なるべく秋までの目標を立ててみてはいかがでしょうか。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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