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14:Tef4,今年の東大模試の文系数学で全体6位を取り、現在は仮面浪人をしている者です。
質問に答えさせていただきます。
京大文系数学は20年程度解きました。

以下、「標準的」「解きやすい」といった表現はは京大文系数学の本試験の問題を基準に考えるものとします。

京大文系数学ですが、2021年以降は易化傾向にあることはご存知だと思います。具体的には、問題の難易度は標準的なものが多いぶん、計算力や論理性（必要条件・十分条件の使い分け）が重要になったということです。これは、数学が苦手でも愚直な努力（※1）をすることで合格点がとりやすくなったことを意味しています。

※1　過去問や問題集を反復し、計算を含めて早く正確に解けるようにする・不安な箇所は添削を受ける、といったいわゆる”普通”の勉強を指します。

数学が苦手ということなので、恐らく4割〜6割が目安になると思います。座標・微積分の問題は過去問の何十年を通して頻出であり、解きやすい問題が多いため、座標・微積分（+その他の比較的簡単な問題）で完答を狙うことが最適かと思われます。
今年の場合、座標・図形（第3問・第5問）+比較的簡単な問題（第2問）の3問のうち2問以上を解き切る、といった感じです。

これまでのことを踏まえると、以下のような勉強の進め方がお勧めです。（具体的に今どのような勉強をされているか分かりかねるので、質問者様の状況に応じて不要な部分は省いて考えてください！）

①入試標準レベルの問題集（文系プラチカやスタ演など）の問題を20分以内に解けるまで何度も反復する。

学校や塾などで質問できる環境がある少しでもある場合はスタ演がお勧めです。易〜標準レベルの問題・計算力が必要な問題が多く載っているからです。
「京大の問題では定石が上手く使えない」とのことですが、そういった場合はスタ演レベル（≒京大入試で易しめの問題）の問題を解いて定石を使う経験を地道に積むのが最適だと思います。
間違えた問題は解き直すだけでなく、その問題を解くために必要だった考え方（例:平面図形で90°が出てきたら三角比の利用を考える）を解答解説のページや専用のノートなどに残しておくと幅広い問題に対応しやすくなります。


②別の問題集や他大学の過去問で座標・微積分の問題のみをやる

座標・微積分はどの大学でも出題頻度が高いので、かなり対策しやすいと思います。東大文系・一橋・旧帝文系の過去問から座標・微積のみを選んでやるのがお勧めです。これらの分野は具体的な問題を通して計算力を鍛えることが最も重要です。自分の場合、計算処理がスムーズにできるまで同じ問題を何度も解き直すことで計算力を付けました。
座標・微積は、その場での思いつき（※2）が必要とされないぶん、愚直に計算力を付ければ、安定して得点ができる分野です。

※2 整数問題で実験をして規則性を見出す、場合の数で数え上げを工夫するなど


成績を拝見させていただきましたが、京大に現役合格する力は持っておられると思いますし、数学が人並みにできるようになれば合格がさらに確実なものになると思います！

是非頑張ってください！！15:T1821,こんにちは

僕自身は高1〜2のうちはなんとなく感覚で数学を解いており、範囲の狭い定期テストや基礎中心の間はなんとかなったのですが、高3になって演習や応用を始めてから、数学が周りよりできなくなってしまいました。

ですので、数学ができる人ではなくできない人からのアドバイスだと思ってください。

もちろん周りの数学のできる友人を見ていて気付いたこともお伝えしますが、数学できる人のアドバイスを求めていた場合はお役に立てないかもしれません。

申し訳ありません。


まず、数学のインプットの仕方ですが、これは質の高い例題を解いてその解説を読んだり受けたりして、さらにそれを復習して自分のものにするというのが良い形かなと思います。

質の高い例題というのは、参考書でも学校の授業でも塾などなんでも良いですが、各分野の典型的な問題をさしています。

これをまずは自力で解くのが大切です。

難しい問題は手も足も出ないかもしれませんが、自分の思考回路を知ることでインプットしやすくなると思います。

自分に何が足りないのか、逆にどこまでは理解しているのかをまずは知りましょう。

次に解説ですが、これに関しても参考書を読んでも他の人や先生にお願いしても良いですが、問題の解答ではなく、どういう思考でその解答に至ったかを特に見てください。

数学は暗記科目ではないと言われますが、ある程度定石があってそれを問題に当てはめ応用していくものなのかなと個人的には思っています。

その定石を解説を通じて自分でおさえてください。

僕は数学が苦手だったので定石を覚えてしまって、これは◯◯の問題だから◯通りの解法があって、今回はこれかな？というふうに解いていました。

もちろん、本来は例題の類題や同じ分野の問題をこなすことで定石を身につけると良いと思います。

高2のうちは特にいわゆる問題集をやったほうが良いです。

僕が数学が苦手だったのは高2までで全然問題集をやらず例題だけやっていたからでした。

例題と似た典型問題は解けるので、定期テストや簡単な模試は解けるのですが、高3になり実際の入試問題やちょっと捻った問題を解くとダメという感じでした。

そのため、高2のうちになるべく多く問題に触れておくと良いと思います。

高3になると余計に他の教科に力を入れなくてはいけなくなると思います。

そのためにもなるべく高2のうちに英数は完成させておきたいところです。

もちろん数学が苦手でしたら高3でもある程度力をいれる必要がありますが、たくさん問題を解けるのは高2までかなと思います。

少し話がそれましたが、問題集などの問題を解くときについて書きます。

問題を多くやる理由は見たことある問題を増やすという意味と定石をどう運用するかを身につけるという意味があります。

見たことある問題が増えれば、初見の問題に対してあの時の解法を試してみよう！と思える機会が増えるでしょう。

また、問題演習をこなす中でインプットした定石を自分のものにできると良いと思います。

次に、苦手意識に関して。

これについては成功体験を積むのが一番かなと思います。

といってもなかなか難しいですよね。

僕が問題演習をサボっていたのはどうせ解けないだろという気持ちがあったからでした。

でも今思えば、数学が苦手なのだから一周目でできるなんて思ったのがだめでした。

結局入試で解ければ良いのだから一周目で解けなくても、二周三周してでも自力で解き切れば良かったとお思います。

そうすれば自分の力にもなるし、何より解ける問題が多くなれば数学への苦手意識も改善したと思います。

中々すぐには数学への気持ちは変わらないと思いますが、好きこそものの上手なれ、ということでやっぱり数学を好きになるのが成績upの近道だと思います。

理科社会のように暗記した知識ベースではなく、定石という武器をどう使うのかという思考力が試される数学は、難しいですがそこが面白みなのではないでしょうか。(数学苦手だった僕がいうのも変ですが)

中々短期で成績upは難しいかもしれません。。

でもやっていけば必ず伸びる科目ではあります。

ぜひ腐らずに続けていってもらえたらと思います。

緊張で他の教科に影響してしまうことに関しては、もう少し自分に(というか数学に)甘くても良いかなと思います。

数学は苦手なんだからと割り切って、他の科目よりは緩いペースで実力をげていけば良いのではないでしょうか。

高3になってもそうだと思いますが、自分のたてた計画というのは中々完璧には遂行されないものです。

特に苦手科目は後回しにしたり、他教科よりも計画と違ったりすると思います。

もちろん自分を律するのも大切ですが、それで思い詰めてしまうのは他教科にとっても悪影響です。

数学に関してはある程度ゆるい計画を立て、むしろ息抜き的に他教科をやっても良いかもしれません。



めちゃくちゃ長文になってしまいましたが、参考になったら嬉しいです。

また分からないことや疑問点あれば気軽にコメント・質問してください。

では。

16:Tf72,数学の応用問題を解くには二種類の力が必要です。
㊀定石 公式等の理解
㊁定石 公式等を使ってどう問題を解くか考える力

もし㊀ができていないと感じているならば チャートやその他の問題集を使って 分野別に勉強しましょう。

㊀はできているならば 融合問題を解くことで 考える力を養いましょう。
もし融合問題が見つからないというならば
Googleで 電数と調べてみてください。
各大学の過去問などが載っている 数学のサイトがあります。活用してみてください。

しかし”考える力”とはなんなのか 次の問題を解く際の僕の思考回路をお伝えしながら解いていこうと思います。

問題 Tan1°は有理数かどうか(2006年 京大)

僕の頭の中
㊀「三角関数かー 確信はないけどおそらく無理数やろうなあ、、 背理法かなんかで証明すればええんかな、、？」
ここまでは誰でも閃きそうですね。

㊁「有理数と無理数の話やから 分数うまく使って背理法やろうなぁ」
この発想は rute2の無理数証明での定石から思いつきます。

㊂「tan=a/bでおいてもどうしようもないなあ。 cos=b/rute a2 b2になるだけやしなあ。」
この発想から逃れるのは少し難しいかもしれませんが、何度か試すと これじゃダメだと気づくはずです。

㊃「ならどうやって分数の話に持ち込もうかな、、 あっ！ tanの加法定理って分数じゃなかったっけ！」
これは日常的にしっかりとtanの加法定理を意識できているかどうかですね。

㊄「じゃあどーせ背理法やし tan1°を有理数として 加法定理使ってみよかな。
 tan(1-0)=tan1-tan0/1-tan1tan0=tan1
あれ 元に戻ってもた。」
ここでのポイントはtan1を有理数として背理法を使うことですが、これは㊁から明らかですよね。rute2=a/bっておいて背理法するでしょ？

㊅「次tan2はどうやろか
tan2=tan(1 1)=tan1 tan1/1-tan1tan1
あれっ？ tan1が有理数なら tan2も有理数になってもたぞ！？」
ここが最大のポイント！
整数の問題全般に言えることですが、方針がたちづらい時は 数を増やしたりして実験しましょう。
∴例えば nが関わる問題なら n=1やn=2を代入してみるのです。

㊆「tan3=tan(1 2)=...  tan6=tan(3 3)
これ続けてったらtan@全部有理数になんね？   ってことはtan60も有理数なってまうやん！」
決定的な一打です。
㊇「ならtan1が有理数ならtan60も有理数なるってこと示して終了やな！」


僕の思考回路を砕いて説明しました。
この問題は入試において有名な難問ですが、 所詮はこの程度です。
思考回路に特別なセンスが感じられるところありましたか？ ないでしょう？
多くの定石を身につけていれば必然的にこのように解くことができるはずです。


自習で融合問題を解く際、わかってもわからなくても 自分で思考のフローチャートを書きながら解いてみてください。 
もし問題が解けたなら 解答をみて 自分のフローチャートと見比べてみましょう。 
問題が解けていないならば どこの発想が足りなかったのかしっかり分析しましょう。

長くなりましたが最後にまとめるならば
 「この問題解けない！ 解答みよ！ 」だけはやめましょう。 
「この問題 ここまではフローチャートかけたけど どうしてもここから進まない、、 
解答みて どの思考が足りなかったか確認しよう、」  こうしましょう。
まだまだ時間はあるので 頑張ってください！17:T19f9,こんにちは、僕も高1の頃は定期テストで0点を取るほど数学がダメダメだったので、数学への苦手意識はとても共感できます🥲
しかし以下のような勉強をすることで最終的に数学を武器に合格できたので、お伝えしようと思います！
苦手意識がある高校1年生ということで、過去問とかをやる段階ではないと思うので、割と基礎的なほうの段階についてお伝えしようと思います。

大前提を先に言います。
①「どんな問題も、解く過程を全て紙に書いて、記述する」
二次関数の頂点を求めよといっためちゃくちゃ基本的なものでも面倒ですが絶対に途中過程を書いてほしいです。
②「正解した問題は別解を考え、間違えた問題はできるようになるまで繰り返し続ける」
解く引き出しを増やし、解けない問題を無くしましょう。
模試でも同じで、復習の際には、解けなかった問題は絶対に解けるように、合ってた問題は別解がないか考える(楽しみながら！)ことを大切にしてほしいです。
③「計算ミスは実力だ！！」
計算ミスだから、といって放置しないことです。計算ミスをしたら、どこでミスしたのか探して、最初から解き直しましょう。仮に共テや二次で計算ミスしたら命取りです。本当に数十点飛びます(経験あり)。
④「解説見てもわからなかったら人に聞く」
学校の先生でも、数学できる友達でも、塾の先生でも、だれでもいいので、わからなかった問題は質問しましょう。放置しないことです。ただし、聞く前に自分で考え抜きましょう！！それでもわからなかったら聞きましょう👍

(1)やった参考書について
(2)意識すること
(3)これで到達するレベルはどれくらいか

(1)
まず基礎問題精講をやってみましょう。こんな簡単なのやる意味ある？って思っても、意外と解けない問題ってあります。そういう問題を解けるようにしましょう。基礎問題精講に関しては解けない問題は一個もない！全問すぐに解答を書き上げられる！っていう状態にしましょう。

次に青チャート、FocusGoldといった網羅系の参考書です。これもとても重要で、この先難問に当たったとき、「考える」ための「引き出し・手段」として、必ず身につけなければならないものばかりです。絶対に完璧にしましょう。仮に数学が偏差値60くらいあるとしても今一度やり直してほしいです。意外と解けない問題、あります。
ここは何周もしてほしいです。(ぼくは高2のときに青チャート1A2Bを全問3周しました、このおかげで数学偏差値49→73になりました) 面倒ですよね、、、けど受験勉強は気合いが大事です。やるしかないのでやりましょう。例題と練習問題がありますが、全部やりましょう。
青チャートは、高2,3になっても、模試で苦手分野がはっきりしててー、っていう場合にその分野を全問解く、などしましょうね！！基礎は本当に大事です。

次に1対1です(僕は挫折してしまいました)。
結構難しいです。1A2Bのうち、AとBはいらないかなーと思いました。正直ここは全部やりきれなかった、、でもいいと思います。しかしやれば得られるものはとても大きいです。たとえば、引き出しがとても増えるし、計算が重いので計算力がつきます。ぜひやり抜きましょう。例題と演習題がありますが、他の科目とのバランスがとれるようなら演習題もやりましょう。

(2)
①「本質」「定石」のようなものを意識してみましょう。
たとえば、「二次関数のグラフとx軸の交点は、二次方程式の解」「確率はすべてのものを区別する」「図を描いて考えてみる」「二次関数に帰着する」「〇〇=tと置いたら変域を考える」などです。これは、基礎的な段階でも意識してほしいし、その先の段階(旧帝の入試問題など)でもずっと意識すべきことです。こういう基本的なところで大きく差がついてしまいます。

②上に挙げたもの“だけ”をやってると、飽きます。そしてつまらなくなります。そんなときは、入試問題や模試の過去問を解いてみましょう。オススメなのはセンター数学です！(共テじゃなくてセンター！)
センター数学は基礎力を測るにはとてもいいものです。たまーにやってみましょう。時間も計りましょう。ここで注意点ですが、選択問題もありますが、時間測るときは選んでいいですが、その後選ばなかった問題も解きましょう！大きく意味があるものになります。

③目的意識を持って勉強しましょう。「受かるため！」というものではなく、たとえばこの勉強であれば、
「苦手分野をつぶす」
「応用問題を考えるための引き出しを増やす」
「基礎を固める」
といったものです。

④「引き出しを得る」ためのものですが、基礎的な問題、特に二次関数以降の分野においては、常に「考え」て解きましょう。①を意識するような感じです。

⑤細かいことを意識しましょう。たとえば、
「分母に文字や式が出たら、分母が0にならないか確認する」
「〇〇=tとおいたとき、変域を書く」
「判別式は二次方程式にしか使えない(2次の係数が文字のとき、(文字)=0のときを確認しているか)」
などです。今の段階から意識しましょう。こういう細かな点が、入試や模試の採点の大事な要素となっていますし、数学を「考える」大事な要素です。

(3)
ここまでやれば、進研模試でいえば偏差値70〜75まではいきます。旧帝大のやや易〜標準レベルの問題を、時間はかかるけど解けるようになります。一橋志望ということでもっと高いレベルを目指してほしいですが、焦らず、まずは基礎を固めることです。地に足つけて、ぜひ頑張ってください。18:T16e1,⑴　数学を学ぶことの目的は何か
　およそ勉強をするにあたって、今自らが学びつつある学問が目的としているものが一体何であるのかを明確にすることは、いかなる内容の学習の際にも必要となる基本中の基本事項です。というのも、それがわからなければ、教えられることや教科書に書いてあることを暗記するよりほかに学習のしようがなく、結局いつまでたってもその学問について理解できる段階には至らないのは当然だからです（この勉強における目的意識の重要性については、末弘厳太郎先生の著書を読んだときに大いに感銘をうけた部分であり、私の勉強観の根幹を成しています）。
　ことに高校数学に至っては、その目的は「数学的に思考する力の涵養」であると言えましょう。微分や積分、指数対数、三角関数など、日常生活でこれらの知識が生きることはまず少ないでしょうし、ともすると、それらをはじめ数学的な知識の習得が目的としてあるとは考えにくい。にもかかわらず、数学において数学的な知識を習得させられるという実態を考慮すると、数学的な知識を習得することは目的ではなく手段であり、真なる目的は、与えられた問題をそれを使っていかに解決していくかという段階にあり、すなわち、数学的に物事を考えて問題の解決に取り組むその能力を養うことにあると考えられます。模試などの記述問題でも、解答部分よりもそれを導き出すまでの過程を重視して採点されることと思いますが、それもこのことを証左しているのではないでしょうか。
　では、数学的に物事を考えるとはどういうことをいうのかと問えば、（私は専門家ではないので適切な答えであるかどうかは定かではありませんが）それは恐らく、その場に適切な規則、原理（いわゆる定理や公式）をうまく活用して問題の解決を図ることだ、と考えられるでしょう。この点で数学は、事実を基にその場その場に適当な法理を見出し、それを使って問題の解決を図る法律学と似通っている部分があると思います。ただ、両者を決定的に異なるものたらしめる点は何かというと、裁判官による法理の解釈によって結論に一定の幅が出る法律学に対し、数学の規則は常に客観的に不変であるということ。これが、かえって数学における問題解決を簡単にする場合があるということです。

⑵高校数学の学習態度
　脱線が過ぎました。このように考えてみると、公式や定理を理解し、頭に入れることは単なる手段であり、実際にこれを活用できなければ意味がないということがわかるはずです。したがって、数学学習で最初に努めるべきは、公式・定理の理解です。数学Ⅱ、数学Ａ、数学Ｂをこれから先取りで学習しようと考えていらっしゃるようですが、これらに限らず、現在学んでいる数学Ⅰについても基本は一緒です。まずは教科書に出てくる公式や定理を理解することを心がけるとよいと思います。教科書にはそれらの証明、すなわちなぜその定理・公式が成り立つのかについても書かれていると思いますので、自分で証明でき、また人にそれを説明できるほどになれば立派なものです。
　単純に暗記するだけでは危険です。受験勉強ではとかく効率が求められがちですが、そうやって小さな部分を見落としても、本番でそれが問われて見事に足をすくわれるなんてことはざらにあります。いつしかの東大ではsinθとcosθの定義と加法定理の証明が、いつしかの阪大では点と直線の距離を求める公式の証明が出題されています。定理や公式を真に理解していれば、いずれも貴重な得点源となってライバルたちを出し抜くことも成し遂げえただろう問題です。こういった問題は、いつどこで出題されるか分かりません。

⑶問題演習の取り組み方
　さて、公式・定理を頭に入れるためには、同時にそれを正しく使える力も養う必要があります。上述したように、高校数学の目的は「数学的な思考能力の涵養」であり、いくら公式や定理を頭に入れてもそれを正しく使えなければ問題解決は難しくなります。なので、同時に問題演習にも取り組みましょう。最初は教科書に載っている基本例題から、だんだんと練習問題、章末問題、そして問題集の応用問題へと段階を踏んでいきます。問題演習を通じて、どういったところでどんな規則がどのように使えるのか、またなぜそのように使えるのかということを自分自身で見極めることを心がければ、複雑な問題にも対応できるだけの発展的な思考はおのずと身についていきます。

⑷問題集
　チャートについては、使ったことがないので色と難易度の関係などよくわかりませんが、高校1年生の初期から使うくらいですから、Focus GoldやNew Action（名前はうろ覚え）などと同じようなものだとしておきます。私の高校では、日々の課題は教科書や学校の問題集（4STEP）、長期休暇の課題として2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-6","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/xmlqqjx3","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":["「","数学の定石","」の検索結果"]}],["$","div",null,{"className":"border-b-2 mb-2"}],["$","div",null,{"className":"mb-4","children":["$","div",null,{"className":"divide-y","children":[["$","div",null,{"children":["$","$L7",null,{"href":"/advice/lkcOCpZAhz7BLjQezcH3","children":["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"計算練習した方がいい分野"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは。勉強お疲れ様です。\n「計算練習」をひたすらにやれ！という分野であれば、間違いなく微分積分です。ですが、私が次に推したいのは実は「複素平面」の練習なのです…。\n\n微分積分について\n理系の受験数学で、出ないことはない！と言い張れるくらいにはめっちゃ出ます。ほんとうに。\n必ず出る分野ならば、そこは「早く解く」ことができて、さらに「確実に正解する」ことができることが大事ですよね。「早く解く」、「確実に正解する」ともなれば、それに必要なのは計算練習です。微分、積分の練習については以下に記す通りにやるのがオススメです。\n\n微分の練習\n①時間制限を設けて、スラスラ微分する。\n（現時点の自分の全速力でかかった時間×0.8で設定してみてください。間に合うまで頑張りましょう。）\n②微分後（導関数）の形を覚えてしまう。\n（積分でめっちゃ役に立つんです。「微分形の接触（f(g)g'の形）」の際に、「これ、gの微分形じゃん！」ってすぐに見抜けるようになるのです。）\n\n積分の練習\n☆手を動かす前に頭で考える。 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"京大文系数学の勉強法は？"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"僕は受験が終わってからパズルのようなものだったなと考えてます。いわゆる定石をいかに組み合わせるかが解く上でポイントとなるからです。\nつまり対策としてはまずは武器となる定石を完璧にすること。青チャートとかですかね。その際それぞれの定石がなぜその時かなをするのかまで考えてください。\n基礎ができたらそれを使った応用の演習。過去問やプラチカとかですかね。\nここで大事なのが演習を繰り返す中でそれぞれの問題でできなかったらなぜできなかったかを徹底的に突き詰めてください。この定石を使う発想がなかった、ならなぜ浮かばなかったか、なぜそれを使うのかといった感じです。この辺りノートにまとめて行くといいと思います。これを繰り返せば確実に力がつき安定してきます。\n頑張ってください"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$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 5.79 8 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