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1b:Tbee,確かに正面問題は難しいですよね。でも、大方ジャンルごとに区分できます。
まず、演繹法と帰納法で考えましょう。演繹法は、もともと与えられている情報から、公式や条件を利用して式を変形、立式して解く方法です。帰納法は、ある変数indexについていつでも成り立つことを考える方法です。これを意識することから始めましょう。だいたい所感としては、前者の演繹法での証明問題が多い気がします。また証明問題は普通に大学入試で出ます。出し方としては、小問で問題内容のある部分を示させたのち、その特性を利用した求値問題へと導く出題形式が王道です。だから、最初がわからないと手の出しようがなく雪崩のように点を落としてしまう可能性がぬぐえません。そのため、証明問題に強くなることは必須です。
ここからは、証明問題の対策の仕方について記述します。
整数問題の証明について：帰納法を警戒してください。だいたいindexをnとする数学的帰納法に持ち込んで解くケースは非常に多く、シンプルながら忘れやすいためこの発想はいつでも持つようにしてください。それがダメなら、ようやく演繹法です。法則性や条件から、立式、変形していくことで求める式や結果にたどり着きます。ただしこの方法に一貫した解法の仕方はないのでその問題ごとに情報を分析して考える必要があります。ちなみにこの問題が数学でかなり難しい部類に入りやすいのでそこまで気にしなくても受かります。だからまずは、帰納法を検討してください。
図形について：主に考えらるのは、図形的に処理する方法、関数的に導く方法です。どちらも演繹法です。ここにもしindexNが出てきた場合は帰納法を検討して下さい。図形的に処理するのか、関数的に処理するのかは問題よって異なるため一概には言えません。しかし、大体の場合は関数的に解くほうが必ず解ける場合が多いと感じます。しかし、計算が煩雑になることもあるので注意が必要です。逆に一般的な図形に対しての議論をする場合は、ベクトルや図形的に処理するほうが楽にできることが多いです。普遍的な性質を議論する場合、図形の性質、定義を使った定理を出題者側が求めていることが多いからです。
まとめると、まず帰納法を考える。次に演繹法を考えて、一般的な図形ならばベクトルや図形的性質から考える。複雑なある条件下でしかできないような図形ならば、関数からの導入（二次元平面までがおすすめ）で解く方法もありです。
応援してます頑張ってください。
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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"証明や導出がすごい気になってしまう"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"三味線さん、はじめまして。\n\nお気持ちはすごく分かります。\nたしかに解答の細かいところに疑問を持ったり、その都度公式を導出していると参考書の進むペースは遅くなってしまいますが、その分、質は高くなると思うので全然良いことだと思いますし、むしろそうするべきだと思います。\n\nよく言われる「数学は理解」という言葉は、なぜその公式を使ったのか、なぜその解法で解くのか、なぜその変換を行うのか、もっと細かいことで言うと、なぜその順に解答を記述するのかといったことを理解することです。\n\n「数学は暗記」という言葉もたまに聞きますが、これは単純に英単語みたいに暗記すると言うことではなくて、どうしてこの解法を使うのかを理解した上でどうゆう問題が出たらどの解法を使うのかを暗記すると言うことです。\n仮に理解の過程を飛ばして暗記だけすると、少し問題の形が変わっただけで解法が思い浮かばないということになってしまいます。\n\nそして理解を深めるためには、三味線さんのように細かいところにも疑問を持って問題を解くのが一番の近道です。公式は導出ができる方が理解度ははるかに上がりますし、たまにある公式の導出に基づいた問題なんかも出題されることもあります。\nまた質問文中のことで触れると、なぜ置換積分はこうゆう形でするのか、一次独立とは何か、解答に使われている言葉の意図、こういったことに疑問をもって考えるのはとても良いことだと思います。確認しても忘れてしまうのは人間なので仕方ないことで、確認してその時に理解したことをノートなんかに纏めておきましょう。次に同じような疑問が出た時にノートを見返すことで少しずつ定着して力になっていくはずです。\n私の場合だと2.3回では定着せず、5回とか10回その都度見返すことで定着し始めた感じだったので、忘れているから力になっていないと焦らずに、自分のペースで頑張ってください！\n\n応援しています☺️\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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