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1c:Tc25,まずはどの科目にも言えることですが、基礎をしっかり理解し、解けるようにしてください。

基本問題を解き、わからないところは教科書や参考書に立ち返り復習する癖をつけましょう。
そして解法パターンを身につければ、応用問題も怖くありません。

数学はとにかく問題を解けばいい、と思っていませんか？
実はわたしもそう思っていました。
なので理論もわからず、とにかく問題集（私は青チャートを使っていました）を解き、間違える日々。

しかしこの勉強法は間違っている、と浪人してからやっと気付きました。

数学には定型パターンがあります。
高校数学を難しく感じるのは、そのパターンが非常に多いためです。
なので、まずはお決まりのパターンをしっかり覚えるようにしてください。

こういう問題がきたら、この公式だな、ってすぐに思いつくレベルまでもっていくのです。

以下、具体的な方法です。

私は青チャートを使っていたので、青チャートをイメージしてお答えしますが、ご自身の使っている問題集に置き換えて参考にしてみてください。

1.まずは一通り例題を解き、公式の使いどころを覚える。（基本問題）
→数学には解法パターンがあります。こういう問題が来たら、こういう方法で解く、というのが反射的にわかる、身につく、というところまでもっていきます。
この時、公式がわからない、理解できないときは教科書を開いて理解するようにしましょう。

2.例題の下にある問題を解く（標準問題）
→わからなくてもすぐに答えなどみずに、10分は考えるようにしましょう。この時色々な公式や解法が頭に浮かべば、知識は身についている証拠です。
逆に標準問題で手も足も出ないなら、教科書に立ち返りましょう。
ここまでできれば、定期テストや模試である程度の得点は見込めます。（青チャートなら国立大やマーチレベル）

3.章末問題を解く（応用、発展問題）
→数学を得点源にしたい人、難関国立大や早慶を狙う人は最終的に解けるようにしましょう。
このレベルだとさまざまな公式を合わせて使う、複合タイプの問題になります。
この問題をやるときは、「自分がどこまでわかっていて、どこからがわからないのか」をしっかり把握するようにしてください。復習するときはできないところの例題などを見返し、できるようにしましょう。
これが解ければ模試の大問もほぼ完投できます。


このように、大事なことはとにかく、
理論を理解する
ことです。
闇雲にやって量をこなすのではなく、丁寧に時間をかけて勉強してください。
1d:T10ae,こんにちは。今回は青チャート云々というより数学の勉強について答えていきます。

まず前提として数学は暗記科目ではありません。定義や定理、公式は覚えて身につける必要がありますが、それを覚えたからといって直接点数には結びつかない場合が多いです。だからこそ難しいのですが、、、


ではどうしたら良いか。ということでまず、、、


センター試験レベルの問題は定義や定理や公式を暗記し、一般的な解法を何度も反復することで満点は取れるようになります。センターは教科書レベルのものの理解度を試すものであるからです。ということは、まず当面の目標としてセンターで時間をかけてもいいから満点を安定して取れるレベルを目指しましょう。
青チャートの7割の例題の解法を覚えているなら容易いと思います。


次に、、、

この次の段階に行くにはどうしたら良いかを説明します。例題の中で暗記しやすいものはいわゆる典型問題というもので何かしらの公式や定理を当てはめるだけで答えが出ます。そして覚えにくい問題というのは公式の単純な当てはめでは解けないもの、いくつかの定理を組み合わせなければいけないものです。
これらは典型問題のような解法暗記では解けるようになりません。問題によって考え方を変え、応用しなければならないからです。

応用問題、複合問題では解法の暗記が重要なのではなく、解答のプロセスと問題のテーマが重要です。ですので、１つひとつなぜこの公式を使うのか、解答を得るために何が必要なのかを意識するようにします。「なぜ」という疑問を常にもち、必ず納得して勉強をしましょう。
そしてそのあと、ほったらかしにせず、翌日や翌週などに問題見て頭の中で解答のプロセスを順序だてて辿ります。これは書いても良いですがサラサラとメモっぽくで十分です。とにかく論理だてて、理由をつけて考えるようにします。
そうすることでどのような場合にどのような考えを使えばいいのかがわかるようになってきます。

また、考え方を予め決めておくのもおススメです。

例えば、
図形の問題が出てきたら、
1-三角関数、2-ベクトル、3-初等幾何、4-座標に置き換え、5-複素数平面
の順に考える。などです。そうすることで詰まってもどんどんほかの解法でチャレンジ出来、初見の問題でも解けるようになります。

解法の選び方、論理立てて考える方法、公式や定義や定理の応用の仕方などが書いてある参考書があります。それは「世界一わかりやすい京大の数学」という本です。これは数学の根本に基づく解き方、プロセスが事細かに書かれているため非常に参考になるのでおススメです。京大の問題は思考力を要する問題であるため、数学のレベルアップにはうってつけです。数学1A2Bを一通り学んだものであれば問題なく使用できるので、京大だからと物怖じせずにやることをかなり強くオススメします。僕はこれでかなり偏差値が上がりました。


最後に、、、

数学は簡単に伸びる科目ではありません。できるようになるには長い時間がかかります。我慢して我慢して解法を論理立て考え深い理解をすることで、徐々に解けるようになってきます。
簡単に身につくものは簡単に忘れてしまいます。じっくりと根気よく数学に真摯に取り組むことが遠回りに見えて最短の道のりです。諦めることなく続けていきましょう。

大変ではあると思いますが、必ずできるようになるので最後まで頑張ってください。第一志望の大学に合格出来ることを心より祈っています。
1e:Tfd4,ほさかさんの質問に答える前に、少し遠回りをさせてください！！

私は数学の実力をつけるために
①解法暗記
②複数の解法を組み合わせる、複数の解法から一つに絞る力をつける(数学的思考力をつける)
ことが大切だと考えています。
①では「すぐ答えを見ること」は正しいですが、②では逆に長考することが推奨されます。
手も足も出ない問題とは方針がまるっきり立たない問題だと推測します。
方針が立たない場合、そもそも解法を知らないパターンと、どの解法が使えるのかわからないパターンがあります。前者は①に、後者は②に対応します。
①
解法暗記をすべき問題は青チャートの例題が特にそうですし、京大でもそうカテゴライズされるべき問題はあります。(京大理系2022大問3のユークリッドの互除法など)
例えば青チャートを終えたとしても、発展問題の演習の中で出てきた新しい解法を知識として蓄えることは重要なんです。
それと一応説明すると、解法暗記とはある問題のパターンに対してどのような解法が合致するのか覚えるということです。数学の性質を根拠に基づいて解法を覚えるべきことです。(部分的には高度な内容もあるで、初学〜中級者の方はパスしても構わない場合もあると思います)
②
目新しい条件が設定されていたりして、どんな解法が使えるかすらわからない時や、一見典型問題に見えていつも通りな解法が通じない時があります。そのような問題に対処するためにはとにかく時間をかけていろいろ試す他ありません。値を代入したり、より簡単な条件で考えてみるなどの実験から着想を得て既知の解法に帰着することや、別の分野から問題を考えてみる(たとえば、微積の問題だけど、ベクトル、三角関数、図形の性質の分野の解法を使う)ことなど色々試すパターンがあります。どんなパターンがあるかを多くの問題を解く中で経験していくことが重要です。
(=数学的思考力をつける、という意味で私は使います)

ここからほさかさんの質問に答えます！
①解法暗記②数学的思考力をつける、の両方の面で多くの問題を解くことが一番大切になります。知識を網羅してさらに定着させるためです。
青チャートなどの網羅系参考書では回転率を上げてまさしく解法を網羅するのが良いと思います。多くの問題を解くことが一番の目標です(理解が二の次でいいということではありません)。この段階では、解法を知らないのだから、わからない問題は答えをすぐにみるべきです。
プラチカなどの演習問題の載っている参考書でも、多くの問題を解くことが目標となります。演習問題を解く理由は二つあり、一つは解法暗記の知識を定着させること、わからない問題に対し試すことのパターンを知ること、またそれを定着させることです。手も足も出ない問題に対処するパターンを知らない段階では手も足も出ない問題の答えはすぐ見るべきです。演習を繰り返すうちにいずれ手と足が出るようになります。そのときからいろいろ試すと解ける可能性が出てくるため、時間をかけて演習する価値が出ます。

⒈網羅系参考書では答えをすぐに見て良い。
⒉演習不足の段階では手も足も出ない問題の答えはすぐに見て良い。
⒊演習して手と足が出てきたら難しい問題も時間をかけると良い。

受験を通して思った個人的な思想なので参考までにしてください！2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=FuVb_mcBTqPwDZPufnjb","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"チャート式の使い方について"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",24,") コメント(",1,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"12/30 18:04"}]]}],["$","div",null,{"className":"coach-mark 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mb-2","children":"回答"}],["$","div",null,{"className":"mb-4","children":["$","$L15",null,{"adviserImageUrl":null,"adviserName":"pome","adviserDepartment":"京都大学総合人間学部","adviceId":"FuVb_mcBTqPwDZPufnjb"}]}],["$","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":[["$","div","advice-part-0",{"children":[null,"私が受験期にやっていて、成績が伸びたチャートの独自のやり方を紹介させていただきます。合わないと思ったら真似しなくて大丈夫です！\n 1周目\n①例題の問題文をじっくり読みます。\n(何も求めないといけないかを意識)\n②解かずに解答を見ます。求めるものを意識して、それまでの【流れ】を頭の中に染み込ませてください。具体的な数字は必要ないです。\n③次の日に例題の問題を読んで、解答の【流れ】をイメージできればOKです。\n④また1日あけて、次は演習問題を【流れ】を意識しながら、解いてください。\n\n全てクリアした後の復習(2周目以降)は、時間短縮のため、【流れ】が分かるかだけを確かめていました。\n\n数学の問題では、問題文を読んだ後、すぐに解き始めるのではなく、必ずこの【流れ】を考えるようにしてください。\n\n1日あけるのは記憶定着のためです。\n\n手を動かすのが演習問題だけなので、普通にやるより時間と手間を短縮できます。"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":null,"adviserName":"pome","adviserDepartment":"京都大学総合人間学部","adviceId":"FuVb_mcBTqPwDZPufnjb","numberOfFan":8,"clipsAvg":13.714285714285714,"adviceRateAvg":4.5,"profile":"現役時理系。\n文系の学部に興味があり、浪人して文転。\n志望校を上げ、京大に合格。"}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink 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mb-1","children":"個人的にそこまでしなくて良いと思います。チャートは解法の流れを抑えるのに使いましょう。赤チャートをⅠ.Ⅱ.Ⅲと総合演習以外全部解きましたが、各章ごとに毎回⭐️1.2.3を最初に全部解き、ミスも直した後に⭐️4.5を解き、そこのミスも治してから章末問題を解く、という流れで使いました。東大、京大の入試問題も基本的な問題、もしくは基本的な問題で使う解法の流れを幾つか合わせた様なものです。　　\n\n　なので解答を一言一句覚えるというよりかは寧ろ、解答の流れ、どこに着目したらそう解けるのか(対称性の利用、直角があるから座標設定、ベクトル利用)、必要十分性に気を配りながら読む、教科書には書いていない事が書いてあるコラムを読んで使える様にしてみる、と言ったことの方が大事です。特に京大を受けるなら必要十分性には気を配りましょう。\n　\n　自分も去年京大を受けました。本番では2問完答して3問半分くらい解いて出しましたが結局点数から見るに必要十分性の議論で誤りがあった問題はほとんど点数が来ていません。また、完答の京大で有名な様に京大は途中で出した解答、途中間違えがある解答はどれだけ解答の流れが合っていても点数をくれません。完答主義は特に求値問題で顕著でそういう意味でも≠0の議論などに気を配らないといけないので解答を覚えている時間はあまりないと思います。\n　\n　いくら日本語が拙くてもそこは受験生の解答ということで論理が合ってさえいれば点はくれるので上に挙げた数学的な内容に気を配りながらチャートを使うことをおすすめします。"}],["$","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 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mb-1","children":"青チャートのやり方について\n\nまず、一つずつやるのか同時にやるのかということは、自分のやりやすい方で良いと思います。\n\n具体的な進め方\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。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。\n"}],["$","div",null,{"className":"flex 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mb-1","children":"僕は青チャート信者なので！！\n青チャートの進め方をお伝えさせてください。\n\n具体的な進め方\n1;解放暗記として例題だけをやってしまって、全て一通り解けるようにする。目標は、問題文を見た瞬間、初手から完答までの流れが頭で再現できるようになることです。\nイメージは、例えば三次関数の解の個数問題で、問題文見た途端、あー、この問題はまず定数分離して、微分して増減表書いて、グラフ書いて、定数動かせば終了だな！って感じ。\n\nこの時に、最初の一周目というのは一分くらい考えて答えが分からないなら、すぐ下の解説を見ながら解いてオッケーです。ただ、解説を暗記しちゃダメで、あくまでも解放を暗記してください。\n例えば、二次関数の解の配置問題なら頂軸端に注目！みたいな、、、\n\n二周目は一周目で解けなかった問題を自力で解いてみてください。\n自力と言っても、覚えたことを思い出せるかのチェックですけど。\n\n三周目は、二周目でも解けなかった問題(多分一分野で３題くらいかな)\n\n\n\n　\nこのやり方だと、一周目に一問30分くらい、二周目三周目は一問10分くらいの感覚で解いていった気がします。\n\n\n2.最後の章末問題を解きます。ここでは、解放暗記が役に立つのかのチェックと、思考力を鍛えてください。\nだから、わかるまで時間をかけて粘るべきです。\n1週間くらい考えるのもありだと思いますよ。\n\n\n\nちなみに、例題の下の練習は、面倒だったので僕はやりませんでしたが、時間があるならやっても良いんじゃないでしょうか。ただそれよりもチャートは分厚いので、サクサク進めていった方がいいと思います。\n\n\n\n\n正直、地方国立大だったら、解放暗記で十分だと思うので、2️⃣の必要はあんまりないかもしれませんが、旧帝大クラスになると思考力は必須です。\n\n自分の志望大に合わせて、時間配分して頑張ってください。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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