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1c:Teb3,こんにちは！

数学の勉強について、2点お話しします。

①文系最高峰と言われる一橋数学のレベルでも、典型的な解法の充実が最も大切です。一橋大学の数学は一見すると解法が全く思いつかないような問題でも、図式化したり具体的な値を代入して考えてみたりすることで基本的な問題に帰着することがよくあります。基本的な問題に帰着というのは基本レベルの網羅系参考書に載っているような考え方で最後答えに辿り着けることがあるということです。そのためには基本的、典型的な解法にすぐ反応できるようにしておく必要があります。（具体的に典型解法とは青チャートのコンパス3個分ぐらいのイメージです。）このレベルの解法は網羅系参考書で何度も何度も繰り返すべきだと思います。覚えるというと暗記してるだけのように思われがちですが、仕組みや原理を理解した上で典型的な解法については考えるよりも先に体が動くぐらいまでやり込むべきだと思います。質問の答えとしてはまずは確実な理解を心がけた後は忘れることをあまり気にせず、繰り返すことが大切だということです。忘れてしまうのは確かに根本的な理解が不足している場合も考えられますが、基本レベルの問題は何より繰り返しましょう。

②夏に到達したいレベルについては、もちろん理想は偏差値も高ければ高いほどいいと思いますが、社会学部志望であれば夏前あるいは夏休み中に青チャートのコンパス3個分までが確実に備わっていればそこからの過去問演習や2次試験レベルの演習で伸ばすことが可能だと思います。何より重要なのは基礎をおろそかにしないことです。実力の足りなさや問題の難しさに動揺したり焦りを感じたりして難易度の高い演習にすぐに移ろうとはせず自分の進行度と向き合って基礎を固くすることが大切だと思います。

+α 
典型解法の充実の重要性について書きましたが、一橋大学の数学は過去問演習が大きな意味を持ちます。過去と似た問題や似た考え方が出ることが今までかなりあったからです。もちろん網羅系参考書などで全ての範囲をおさえることを目指すとともに、早めの過去問演習で傾向を掴み、社会学部であれば特に出る単元にある程度集中して対策することも現実的なプランだと思います。一橋数学では、整数、確率、平面図形、空間図形、数列、微積などが頻出です。

また、質問とは直接関係ありませんが演習を解いていく上で１つのノートを作る勉強が個人的に効果的でした。そのノートには演習をやる中で間違えた部分をまとめておくものですが、間違えた問題とその解法などを書くのではありません。数学で難しいのは解法の一手目が思いつかない時全く歯が立たないことだと思います。そのため、問題を解いてて解法が思いつかず解答などをみた時にどうしたらこの一手目を思いつくかまでしっかり考えてそれをノートに書いておくのです。一手目を思いつくヒントになる問題文の文章や設定とセットで、一手目の考え方をメモしておくことで少しずつ「一手目の考え方」を蓄積していくことができ、後で見返すのにも便利です。1d: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。
1e:T1103,まず、この時点でチャートの例題が解けるようになっているのは素晴らしいと思います👍
基礎力は着実についてきていると思うので全く悲観しなくて良いです。

どういう所で点を落としているのかわからないですが、どの分野も青チャートの例題はほぼ解ける状態だとすると、その先の訓練が少し足りていないのかなと思います。

具体的には「少しひねってあるが、青チャートレベルの基礎知識を上手く使えば解き切れる標準問題を見抜いて・解ききる力」をつけることです。

(ここでいう基礎知識というのは、青チャートの例題1つ1つが扱っているポイントのことです。)


入試問題は

🔆「青チャート例題レベルの基礎問題」

🔆「少しひねってあるが、青チャート例題レベルの基礎知識を組み合わせたり、発展させたりすれば解き切れる標準問題」

🔆「基礎知識だけでは解きにくく、最後に回すべき難問」

の３つに大別されます。

入試本番は全5問がどの種類なのかを見極め、解く順番を決めた上で、上記の基礎問題と標準問題を解けるところまで解き切る必要があります。

基礎問題はほとんどの受験者が解ききれ、標準問題はそれ以前の勉強によって差がつき、難問は極めて少数の人間しか試験時間内に解けないため、標準問題をどれだけ解けるかが勝負となります。


では先述の、「少しひねってあるが、青チャートレベルの基礎知識を上手く使えば解き切れる標準問題を見抜いて・解ききる力」をつけるには何をすれば良いのか？

その答えが過去問演習になります。

普通の参考書ではダメなのかと思うかもしれませんが、一般的に難しいとされている参考書は、ここでいう標準問題だけを集めたものが多いです。
なので、こういった参考書だけでは実際に入試で出る基礎問題や難問の手触りが学べません。

また、過去問と同じ問題は出ないと思われるかもしませんが、ポイントとなる部分が同じ、つまり傾向に沿った「似た」問題はよく出るので、過去問演習はとても効果的な志望校対策といえます。

早めに過去問演習を始めた方が、より早く自分の弱点に気づくことになり、余裕を持って対策を立てられるので、今から取り組み出して良いかと思います。


具体的な進め方ですが、はじめのうちは、得意な分野からでも、近い年度からセットで解いていっても、好きなように進めればいいと思います。（直前期の演習用に、最近の2、3年度分は残しておくことをお勧めします。）
時間制限も秋ごろまではかけなくていいと思います。

とにかく、

🔆その問題がどの種類の問題なのかを考える
（多くの過去問集には難易度指標がついているのでそれを参考にしてください。鉄緑のものが詳しくて良いと思います。）

🔆標準問題を通して基礎知識の応用方法を吸収していく
（重要なポイントをまとめているのはとてもいいと思います！自分も大事だと思ったところをルーズリーフに書き溜めていき、試験前にはファイリングしたものに目を通していました。）

🔆基礎問題や標準問題が解けなかった場合、どうして解けなかったのかを考え、次に同じようなところで詰まらないようにするにはどうすればいいか考える

🔆基礎知識の抜けに気付いた場合は、適宜チャートを見返したりして復習する

といったことを意識して進めてください。

注意点としては難問の復習に時間をかけすぎないことです。必要最低限の知識だけ吸収してとばしましょう。

色々と書きましたが、この辺りのことは「受験の叡智」という本に、より詳しく、説得力のある形で書かれているのでぜひ読んでみてください！2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=tBLa2moBTqPwDZPuR5Ud","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"図形の性質を勉強するとき"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",15,") コメント(",3,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"5/21 23:44"}]]}],["$","div",null,{"className":"coach-mark 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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":[["$","div","advice-part-0",{"children":[null,"この単元は、二次試験では単独で出ることはあまりありませんが、センターでは必出ですよね。図形の性質で大事なのは\n1.三角形の五心の性質を区別し、理解する\n2.方べきの定理を「覚えて」「使える」ようにする。\n3.オイラーの多面体定理など空間図形に慣れる。\nことだと思います。1.に関しては図形の性質だけでなく、ベクトルや図形と式などの分野とも絡んできますので必ずできるようにした方が良いでしょう。2.はセンターで頻出の問題ですから、チャートやセンター型の問題集でたくさん演習しましょう。3.は、センターでもあまり出題されてないような気がしますが、範囲内である以上来年出されても文句は言えないので、\n教科書やチャートで基本事項を確認して、演習もしておくと良いでしょう。まず大事なのは、1.2.を完璧にすることだと思います。"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":null,"adviserName":"AO","adviserDepartment":"北海道大学法学部","adviceId":"tBLa2moBTqPwDZPuR5Ud","numberOfFan":25,"clipsAvg":7.954954954954955,"adviceRateAvg":4.454545454545454,"profile":"お願い:質問する際は、文系/理系を明示した上で、質問したいことをできるだけ具体的にお示しください。抽象的すぎる質問は回答のしようがありません。\nお願いします。"}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink 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8:22"}]]}],["$","div",null,{"className":"text-xs whitespace-pre-wrap","children":"ありがとうございます！\nセンターしか使わないのですが、証明等もやっといた方がいいですか？"}]]}]]}],["$","div",null,{"className":"flex py-4","children":[["$","div",null,{"className":"mr-2","children":["$","$L19",null,{"avatarUrl":null,"contributorName":"AO","adviceId":"tBLa2moBTqPwDZPuR5Ud"}]}],["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"flex justify-between","children":[["$","div",null,{"className":"mb-2","children":["$","$L1a",null,{"contributorName":"AO","adviceId":"tBLa2moBTqPwDZPuR5Ud"}]}],["$","div",null,{"className":"text-xs text-caption","children":"5/22 16:37"}]]}],["$","div",null,{"className":"text-xs whitespace-pre-wrap","children":"センターでも証明問題が穴埋め形式で出題されることがありますので、やっておいた方がいいですね。"}]]}]]}],["$","div",null,{"className":"flex py-4","children":[["$","div",null,{"className":"mr-2","children":["$","$L19",null,{"avatarUrl":null,"contributorName":"アキピー","adviceId":"tBLa2moBTqPwDZPuR5Ud"}]}],["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"flex justify-between","children":[["$","div",null,{"className":"mb-2","children":["$","$L1a",null,{"contributorName":"アキピー","adviceId":"tBLa2moBTqPwDZPuR5Ud"}]}],["$","div",null,{"className":"text-xs text-caption","children":"5/22 21:25"}]]}],["$","div",null,{"className":"text-xs whitespace-pre-wrap","children":"わかりました！ありがとうございます！"}]]}]]}]]}]}],["$","h1",null,{"className":"text-xl font-semibold","children":"よく一緒に読まれている人気の回答"}],["$","div",null,{"className":"mb-8","children":["$","div",null,{"className":"divide-y","children":[["$","div",null,{"children":["$","$L7",null,{"href":"/advice/pVFw2H0BTqPwDZPuGI3u","children":["$","div",null,{"className":"flex items-center 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mb-1","children":"個人的な意見ですが、整数と場合の数が比較的できるということは数学自体が苦手だとは思えません。これを踏まえて、時間配分、勉強法のアドバイスをさせていただきます。\n\nまず、時間配分についてですが、取れるところから取ることが基本だと思います。もちろん大問1から始めて間に合うならばいいのですが、間に合わない場合は自分のできるところから取り組んだほうがいいです。\nぐみさんの場合、1Aは整数と確率を初めにやったほうがいいと思います。まずはどんな問題が来ても各12分前後で解き切ることを目標にしましょう。\n2Bは得意単元がないようなので、時間配分については何とも言えません。\n\n次に勉強法です。\n整数と場合の数が得意なのなら、おそらく数列は理解できると思います。だからまずは教科書で数列の基本的なパターン(nの式で表された漸化式、等差、等比の一般項、その和の求め方など)を覚えたほうがいいと思います。\n苦手な単元についてですが、三角関数、指数関数は共通テストでもおそらく狙われるため早急に行ったほうがいいです。まずは教科書の問題を用いて、グラフを用いた解き方をするといいと思います。現にセンター試験ではグラフを用いて解くように誘導することがよくあり、数式を見える形にする訓練は必要です。\n\nあと、三角関数、指数関数が苦手だというよりもしかしたら二次関数が苦手なのかもしれません。三角関数、指数関数、対数関数などの関数系は結局二次関数や不等式の問題に帰着することが多々あります。\n文字が入った二次関数の最大最小を求める際に、なぜ軸で場合分けするのか、f(0)が正であることを用いるのか、その意味が分かりますか？グラフで考えると当たり前ですが、式だけでは伝わらないことがあります。\n\n参考書を一周するのはもちろん素晴らしいことで、継続する力は本当に尊敬しますが、それよりも教科書をもう一度見直したほうが良いです。教科書の章末問題は一瞬で解法が浮かぶくらいがちょうど良いです。そこから少しずつ応用問題にチャレンジしてどの解法が基礎になっているのかを考えることが大切です。\n\n\nとても大きな質問だったので、具体的には回答できなかったかと思います。また何かあったら何でも聞いてください"}],["$","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":"物理の学習法"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"重要問題集と名門の森に取り組めば十分だと思います。\n後は過去問と模試の復習で弱点をつかみつつ、本番の試験の感覚を掴むといった具合でしょう。\n\n物理は\n①正しく図示して\n②正しく立式して\n③正しく計算する\nこれで上手くいきます。\n\n\n－－－－－－－－－\n\n【①について】\n\n多くの人が疎かにする部分です。\n物理の力はここにかかっていると過言ではありません。\n必ずどんなに簡単な問題でも最初は意識的に図示を丁寧にすることです。\n図示をすっ飛ばして解答する人がめちゃくちゃ多いですが、とんでもないです。\n\n\n－－－－－－－－－\n\n【②について】\n\n速度、変位の式\n運動方程式\nエネルギー保存則\n運動力保存則\netc...\n\n基本法則に従って、正負に気をつけて、スカラー量なのかベクトル量なのかに気をつけて、立式することです。\n\nこれも物理の力が試されていますが、前提として①が出来てなければ正確な立式など不可能です。\n\n\n【③について】\n\n③は数学の計算力と共通ですが、違うところが二つあると思っています。\n\n＊単位(ディメンション)が正しいかどうかを追いかける力\n→化学でも求められますね。\n\n＊省略可能な計算パターンを省略する力\n→覚えていたら思考段階を飛ばせるパターンが存在します。\n\n前者はとにかく意識して追いかけること。\n後者は数をこなすと身についてきますし、物理の先生はこういうの教えるのが好きな人が一定数います。\n\n\n－－－－－－－－－\n\n【まとめ】\n\n問題集は質問者様のやろうとしている2冊で十分。\n後は模試の復習、過去問。\nただし、①をキチンと意識的に取り組むこと。\n②と③は①と比べると、問題集を進めていく中で自然と身につくと思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"素早く、確実に要点を理解する勉強法"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"しっかり復習をしていたなら、復習の仕方を考え直した方がいいかもしれませんね。ただ、1Aと２Ｂを比較した時、２Ｂの方が覚えて解くというのが強い気がします。なので２Ｂは1度習得さえすればあまり落とすことはなくなると思うので、これから頑張れば問題ないと思います！\n本題ですが、基礎問題精講はやり直すにはけっこういい教材だと思うので、それと重要問題集を使うなら参考書に関しては問題ないでしょう。勉強の仕方ですが、分からない問題に直面した時、解説を流し読みするのではなく、1行1行しっかり読んでみてください。そうすると場合分けであったり、ちょっとした記述で分からない文があるはずです。そこを先生に質問してください。ここの文までは理解出来て、この式(文)で混乱orわからなくなりました。そう伝えれば先生も、この子は何がよく分からないのかというのが分かるので、しっかりピンポイントで教えてくれるはずです。それを繰り返していれば、だんだんと成績が上がってくると思います。また、間違えたところをノートに書くのもオススメです。メモ程度です。例えば、三角形の重心と内心の性質を逆に考えてしまっていたら\n・重心は1:2   と自分でノートに記して、それを繰り返していくといつもミスしてる点は嫌でも頭に残りミスが減ります。見返すわけではないので殴り書きでもかまいません、時間を取られない程度にどんなミスでも書いておくと、記憶に残ります。\n \nつまり、ポイントは2つで\n・解説はどこの文まで理解出来ているのかを明確に\n・間違えたところは些細なことでも、専用ノートにメモする\n\nです。\n参考になると嬉しいです。"}],["$","div",null,{"className":"flex 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