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1c:T10ea,受験数学にひらめきは全く必要ありません。

実際、数学者と数学の得意な高校生が、受験数学で勝負すると高校生が圧勝します（実話です）。一体何が、高校生を勝たせるのだと思いますか？

受験数学には、確かに、「ひらめきのようなもの」を要求する場面があります。特に整数問題などで顕著ですが。しかし、ほとんどの問題は、今まで身につけてきた解法で対応できてしまうんですね。

例えばですが、多変数関数 f(x,y)の最大値、最小値を求めよという問題が出たとします。（f(x,y)の中身は、例えば、x^2 3xy y^2などですね。ここではそれは本質ではないのでスルーします。）その時、方針が何通りかあるんですが、それを列挙できますか？
あるいは、図形問題に対して、どのようなアプローチを考えるべきか説明できますか？
（答えはどちらも回答の最後に載せますね）

もし1つも分からない場合や、何個かしか挙げられない時は、少し補充的な勉強をする必要があります。
問題ごとに、それを解くための最適な方針がありますね。それをメモ程度で十分なので、どんどんまとめていってください。すると、多種多様に見える問題も、スタートは必ず同じことをしていたり、何個かのパターンの方針しか使っていなかったりします。本当はこういうことを分かっていくのは、問題演習を通してだんだん培っていくべきものなんでしょうが、99％の人は出来ないでしょう。僕も全然出来ませんでしたし。

なんにせよ、こういう「解法の整理」をしていくと、全く手が付かない問題はほとんどなくなってきます。途中までは行けるようになるんですね。そして、「ひらめき」は大抵こういう場面で使うものですね。例えば最後の最後に有名不等式を使ったりなどでしょうか。しかし、これすらも、方針としてカテゴライズすることが可能です。いわゆる純粋なひらめきは、受験数学においてはあり得ないといって良いでしょう。大抵、「閃かない」時は、解法が浮かばない時です。かなり具体的な問題に帰着できましたね。
僕は、ノートの見開き1ページに、この問題が来たら、この方針がよく登場する！というフローチャートのようなものを作っていましたね。頭の中が整理されていく感じがして楽しいですよ。

ちなみに、基礎ができていないということは、多少あるにせよ直接的な原因ではなく、いくら固めたところで、成果が微々たるものしか出ないので、気をつけましょう。青チャート、フォーカスゴールド、どちらも持っている時点でフル装備なので、多少の復習はもちろん必要といえども、頑張る必要はありません。

さて、先ほどの問題、わからずじまいは良くないですから簡単に
多変数関数の最大最小問題：
・等式があればxかyに代入してそれを消去する（いわゆる文字消去）
・xかyのどちらかを定数とみなし、ただの１変数関数とみなして考える（いわゆる文字固定）
・有名不等式の利用（相加相乗平均の関係、コーシーシュワルツの不等式、三角不等式など）
・逆像法
・線型計画法
・グラフを書いて考える
Etc.

図形問題のアプローチ
・まずは初等幾何で解けないか考える。
・次に、位置ベクトルを導入することで、内積などを利用して解けないか考える。
・もし対称性の高い図形だったら、座標平面を設定するのも考える。

僕がこの解法整理についての対策を編み出し、始めたのは12月の半ばです。今なら相当早いタイミングから対策できますから、ぜひ過去問での得点をぐんぐん挙げて、自信をつけていってほしいと思います。

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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"今からでも間に合いますか？"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"全然間に合います。\n\n偏差値53とのことですが、もちろん受けた模試にもよりますが、基礎の部分がまだ全然完成していないんだと思います。\n\n英語に関しては単語力が全然足りていなかったり、文法の理解がガタガタだったり、全然問題慣れしていなかったり…改善点はたくさんあると思います。\n\n数学も同様で、いわゆる基本問題さえも解けなかったりするレベルなんじゃないでしょうか。\nまずは教科書を読んで、基礎を理解していきましょう。\n例えば、「y=x^2を微分したものにx=1を代入して求まる値はy=x^2のx=1における傾きなんだ」みたいに、微分を勉強するなら、微分する意味まで理解してほしいと思います。\nそれが応用問題への第一歩です。\n他の分野も同様です。\n\n社会も、例えば歴史であれば、細かい単語どころか、歴史の流れもまだ覚えられていないんじゃないでしょうか。\nまずは、教科書を読むなりして、話の流れを掴みましょう。\n\n「間に合うのかどうか」というのは受験生なら一度は経験する悩みです。\nでも、間に合わないって言われて、諦められますか？\n間に合わせるしかないですよね。\nこんなことで、とまでは言いませんが、悩んでも何も変わらないので、とにかく目の前のやるべきことをきっちりやりましょう。\n時間はたっぷりあります。"}],["$","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 mr-3","children":[["$","div",null,{"className":"mb-1","children":"E判定です。"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"可能性はいくらでもあります。僕は最後のセンタープレでMARCHすらE判定でした。それでも今こうして早稲田にいます。それは最後の最後まで決して諦めなかったからです。シンプルな理由です。\n\n今結果が出ないからといって志望校を下げるのは非常にもったいないです。志望校を下げてしまったらその時点で慶應にいける可能性は0%になってしまいます。でも諦めなかったら可能性は少なくとも1%以上はあるんです。可能性が0か1%以上か。どちらを選択しますか？当然可能性がある方に決まっていますよね。よし！これであなたがやることはきまった！！ひたすら慶應に合格するために諦めずに勉強しまくるだけれがんばって😊"}],["$","div",null,{"className":"flex mb-1","children":[["$","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":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 5.79 8 8s1.79 4 4 4 4-1.79 4-4-1.79-4-4-4zm0 10c-2.67 0-8 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"良問の風はセンター対策につながるか"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"初めまして\n\n物理をセンターで使うということで理系選択者ということで話を進めますね\n\n結論としては、使い方を間違えなければ対応できます\n\n物理という学問は最初の一手、概念理解の重要度がとてつもなく高いものです\nつまり、問題を解きまくって、解答に慣れて、類題を解けるようになって、、という勉強法では少し状況が変わった時に(その少しの程度は本人の理解に依ますが)非常に高い確率で何をしたらいいのかわからなくなります\n\nなんで、なんでその解法を取ったかの理解が重要ですが、理解すればわかりますがほとんどが定義通り、ルーティンどおりであることがわかります\n\n例えば力学で言えば、①注目する物体を【1つ】決める②その物体とそれにかかる力を図示する かかる力は遠隔作用(重力、電気力、磁気力のみ)か、近接作用(物体に【直接触れている部分からかかる力】)のみ ③その力をx成分、y成分(必要ならばz成分)に分け、各方向で運動方程式を立てる(つりあいの式は運方のa=0バージョン)\n④そこから加速度aをだす ⑤aが出ればv,xも求まる ⑥他の保存則の式を立てる\nというようにするルーティンどおりにやればどの問題も解けるようになっています 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"受験を乗り越えられる気がしない"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"この春受験を終えたものです。私も受験期は相当悩みましたが今になって振り返ってみると、受験生というのはみんな頭がおかしくなるものなのだなー、と笑って言えます。ぜひこの辛い時期を乗り越えて欲しいので、少しだけお話しします。\n\n伝えたいポイントを２つに絞ってお伝えすると、\n1、周りの言うことは気づかないうちに影響する\n2、伸びるのは最後\nです。\n\n一つ目、周りの言うことは気づかないうちに影響するというのは、受かるよ！と言われ続けた人は実際に合格し、無理そうじゃない？と言われ続けた人は不合格になってしまう人が多いというものです。実際このような研究がされており、結果もでています。ここで言いたいのは、この事実を知っておくだけで合格も同然ということです。あなたは受かる見込みないから出願するのやめなさい、と言われても、あなたがそう言うから落ちる可能性が上がるけど、私はそうはいかないぞ、と思えばいいのです。そうすれば無意識に周囲の言葉に紛らわされることもありませんし、合格する確率が下がるということもありません。\n\n二つ目、伸びるのは最後というのは、これもそのままで、受験生は12月から本番にかけてかなり伸びます。私は、12月の共通テスト模試から、本番まで100点ほど伸びました。諦めずに最後まで勉強していると、必ず報われます。とりあえずはy=x^2のグラフをイメージしながら、私は最後に急上昇するんだ！と信じて頑張るしかないでしょう。\n\n最後に、私は頑張らない時期というのがあっても良いと思います。おそらく、その時期は合格にとって必要な休養期間なのです。ぜひ自分を責めることなく、勉強したい！と思える時までぐっと耐えて下さい。応援しております。"}],["$","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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