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UniLink"}],["$","meta","3",{"name":"description","content":"東工大を目指している高2です。数学の公式を証明することはできるのですが、定理の証明が難しいです。定理は理解さえしていれば良いのでしょうか。例えば平均値の定理やロルの定理自体は理解しているのですが証明まではできません。東工大を目指す上で全ての公式や定理の証明はできた方が良いでしょうか?"}],["$","link","4",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","5",{"rel":"icon","href":"/icon.png?2c0dc65a59843333","type":"image/png","sizes":"180x180"}],["$","link","6",{"rel":"apple-touch-icon","href":"/apple-icon.png?2c0dc65a59843333","type":"image/png","sizes":"180x180"}],["$","meta","7",{"name":"next-size-adjust"}]] 1:null 13:I[3903,["51","static/chunks/795d4814-03346c8d233b4adb.js","212","static/chunks/212-70508e17017a12c2.js","231","static/chunks/231-5dc9f3acdba63b0c.js","54","static/chunks/54-f848f8ba1c362ca7.js","23","static/chunks/app/advice/%5Bid%5D/page-53a773e0095d4429.js"],"ClientInfo"] 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1a:I[6549,["51","static/chunks/795d4814-03346c8d233b4adb.js","212","static/chunks/212-70508e17017a12c2.js","231","static/chunks/231-5dc9f3acdba63b0c.js","54","static/chunks/54-f848f8ba1c362ca7.js","23","static/chunks/app/advice/%5Bid%5D/page-53a773e0095d4429.js"],"CommentItemName"] 1b:I[3866,["51","static/chunks/795d4814-03346c8d233b4adb.js","212","static/chunks/212-70508e17017a12c2.js","231","static/chunks/231-5dc9f3acdba63b0c.js","54","static/chunks/54-f848f8ba1c362ca7.js","23","static/chunks/app/advice/%5Bid%5D/page-53a773e0095d4429.js"],"AdOnAdviceList1"] 1c:T11a4,現代文難しいですよね.自分もあまり高校時代は点が上がらず諦めていました. ただ大学生になって改めて現代文を読んでみるとかなり読めるようになっています. 試しに2020の現代文を解いたら確信を持ってすべて正解できました.少なくとも高校のときにここまで確信を持って解けたことはあまりありませんでした. これは大学の数学等のおかげだと感じています. 大学の数学は,定義と定理を深く理解しないと全く前に進めません. 例えば,微分積分(大学で言う解析学)の授業では所謂微積がなぜ成り立つのかというようなことを永遠教えられますが, これを理解するためには本当に多くの定義・定理を覚え理解する必要があります.(定理というのは定義や定理から導き出される新たな論理です) Aの定義は~,Bの定義は~,AとBがそういう定義だから定理Cが成り立つよね(定理C),Aの定義がこれで定理Cが成り立つから定理Dが成り立つよねというようなことが本当に何回も繰り返されて微積などの証明がなされます. このように本当に一つ一つの事実を正確に頭で理解し,脳内にとどめておかないと一向に理解がすすみません. ただ逆に言えばすべての定理は既出の定義と定理を理解すれば自ずと導き出される事実でもあります. 現代文の話に戻りますが,現代文も結局大学数学とたいして変わらないと思っています. つまり現代文も一文一文を正確に理解し,各文の論理関係を追っていけばかならず理解できるようにできています. (もちろん論理関係の破綻している文章は入試には出ないので) つまり言いたいのはさらーと読まずにちゃんと一文一文,頭で理解することを心がけるということです. ここで言っている「文を理解する」というのは,まずその文の種類の判別ができる必要がありますね. その文が物事の定義なのか,それとも定理のように既出の事実から導かれた主張なのか.... そして後者であればなぜその主張ができるのかの理由(論理関係)までをちゃんと答えられて「理解する」ということだと思います. 大学数学はこの理解のプロセスが必ず必要になるため,自分はそれが習慣づけられ,現代文を読むときにも正確に一文一文理解するようになったのだと思います. これにより高校時代より現代文の文章の全体の理解度が向上しそれが問題を解く上での手助けになったのだと思います. 現代文が数学と違う点は,数式が出ずひたすら日本語でかかれているので,一文一文をちゃんと理解していなくてもなんとなく文章全体の趣旨を理解できてしまうところです. ただ国語が苦手な人は,その全体の趣旨はなんとなく理解できているけど,その主張を導くための論理関係の理解がかなりおろそかになり,あまり点が出ないのだと思います. 国語力はいかに文章の定義を把握し,そこから導き出される論理をしっかりと咀嚼できるかということだと思います. 所詮日本語で書いてあることが理解できないわけはないというスタンスで,一文一文「は?なんでこういえるの?」と地道に理解することを心がけるのがいいかなと思います. 最初はとても時間がかかる作業だと思いますが,慣れれば本当に国語力だけでなく大学の学問でも通じる論理・思考能力がつくと思います. ちなみに現代文って数学の下位互換だしいらなくね?と言っている友達も結構います. 試しに大学の解析学の教科書読んでみるのもいいかもですね. 特に解析学の基礎は(上で述べたようにちゃんと定義・定理の理解を地道にできれば)高校数学の知識レベルで十分理解できる内容です. 上から目線みたいになってしまいごめんなさい. 何言ってるかわからないかもですが,すこしでもお役に立てれたら光栄です. 頑張ってください!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=JD1wSG8BTqPwDZPuAL9p","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"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"定理の証明"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",4,") コメント(",1,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"12/28 2:38"}]]}],["$","div",null,{"className":"coach-mark mb-4","children":"UniLink利用者の80%以上は、難関大学を志望する受験生です。これまでのデータから、偏差値の高いユーザーほど毎日UniLinkアプリを起動することが分かっています。"}],["$","div",null,{"className":"mb-4","children":["$","$L13",null,{"clientImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_093197FCC2DE4DB2A9B84CFD849B21E6.jpg?alt=media&token=b48fa5f3-4b86-4b36-bb48-281512c53938","clientUserName":"もん","infoString":"高2 埼玉県 東京工業大学志望","adviceId":"JD1wSG8BTqPwDZPuAL9p"}]}],["$","div",null,{"className":"mb-8","children":[["$","div",null,{"className":"leading-loose whitespace-pre-wrap","children":[["$","div","consultation-part-0",{"children":[null,"東工大を目指している高2です。数学の公式を証明することはできるのですが、定理の証明が難しいです。定理は理解さえしていれば良いのでしょうか。例えば平均値の定理やロルの定理自体は理解しているのですが証明まではできません。東工大を目指す上で全ての公式や定理の証明はできた方が良いでしょうか?"]}]]}],["$","div",null,{"className":"pt-4","children":["$","$L14",null,{}]}],null]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"回答"}],["$","div",null,{"className":"mb-4","children":["$","$L15",null,{"adviserImageUrl":null,"adviserName":"鴨医","adviserDepartment":"京都大学医学部","adviceId":"JD1wSG8BTqPwDZPuAL9p"}]}],["$","div",null,{"className":"coach-mark mb-4","children":"すべての回答者は、学生証などを使用してUniLinkによって審査された東大・京大・慶應・早稲田・一橋・東工大・旧帝大のいずれかに所属する現役難関大生です。加えて、実際の回答をUniLinkが確認して一定の水準をクリアした合格者だけが登録できる仕組みとなっています。"}],["$","div",null,{"className":"mb-8","children":[["$","div",null,{"className":"leading-loose whitespace-pre-wrap mb-4","children":[["$","div","advice-part-0",{"children":[null,"定理を理解しているだけでも問題ない場合がほとんどだと思いますが、稀に入試問題に定理の証明が問われることがあります。またなぜ成り立つのかを考え定理の証明を理解することで数学のことをより深く理解できるようになります。"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":null,"adviserName":"鴨医","adviserDepartment":"京都大学医学部","adviceId":"JD1wSG8BTqPwDZPuAL9p","numberOfFan":182,"clipsAvg":4.963636363636364,"adviceRateAvg":4.4267100977198695,"profile":"京都大学医学部医学科に100点差以上で合格しました。\n京大模試全国1位を取ったことがあります。\n家庭教師募集しています"}]}],["$","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 パンフレットバナー画像","className":"mt-4 rounded"}]}]}],["$","div",null,{"className":"pt-4","children":["$","$L17",null,{"id":"adsbygoogle-init-under-advice"}]}]]}],["$","div",null,{"className":"flex justify-between","children":[["$","h1",null,{"className":"text-xl font-semibold","children":["コメント(",1,")"]}],["$","$L18",null,{"adviceId":"JD1wSG8BTqPwDZPuAL9p"}]]}],["$","div",null,{"className":"mb-8","children":["$","div",null,{"className":"divide-y","children":[["$","div",null,{"className":"flex py-4","children":[["$","div",null,{"className":"mr-2","children":["$","$L19",null,{"avatarUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_093197FCC2DE4DB2A9B84CFD849B21E6.jpg?alt=media&token=b48fa5f3-4b86-4b36-bb48-281512c53938","contributorName":"もん","adviceId":"JD1wSG8BTqPwDZPuAL9p"}]}],["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"flex 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mb-1","children":"こんにちは!東北大学文学部のkitaです!\nお答えさせて頂きます!\n\n理想としては、教科書で習った公式は証明できないといけません。\n大学の先生に、参考書にあったよね?と言われても知らん!と言えますが、教科書でやったよね?、と言われたら何も言えません😅\n\nただ、全てを意味もなく丸暗記するのはナンセンスです。\nそこで、僕が実際に行っていたのは、何度も出る公式(使用頻度が多い)や、今までに他の大学も含め問われたことのある公式、は必ずやりました!\n例としては、正弦余弦、加法定理、点と直線の距離公式、積分の面積公式あたりが王道でしょうか。\n\n他には、僕は数学が好きだったので、ちょっと勉強に疲れた時に、息抜きとして公式の証明を調べて、エレガントな証明方法があると感動してました(笑)\n\n数学の定理や公式の証明は、1つの証明にさまざまな知識を必要とします。それなので、基礎がないと自力で行うのが難しいですし、逆に出来るようになるとかなりの数学がついた、と言ってもいいでしょう。\n\n質問の的確な答えになっているか分かりませんが、入試に出るかも大事ですが、その定理や公式の根本を知ると、間違いなく入試に役立ちます!\n\n最後に、たくとさんの目標が達成されることをお祈りしています。頑張ってください!!"}],["$","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 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"東工大志望校高二です。"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"めっちゃわかるわ〜!!!!その気持ち。\n定期考査の時は問題覚えてるからスラスラ出てくるんだけど、数ヶ月後の模試になると出て来なくなっちゃうんよな…\n\n公式っていっても覚えたほうがいいのと覚えなくてもいいのがあるよね。それについて少し下に書こうかな。\n\n三角関数の定理とか公式とか結構色々あるよね。和積の公式とか積和の公式って覚えさせられるかと思うけどあんなの覚える必要はないからね。加法定理さえ覚えてれば全部導けるから。\n\n定期テストで完璧に覚えるべきなのは「定理」ね。\nこれは「Apple」って言われたら頭の中で「りんご」が浮かぶくらいに当たり前にすることが大事。「加法定理」って言われたらこんな形だな〜って頭の中で浮かんでくるようにすること。\n\n逆に「公式」は定理さえ覚えてれば問題用紙の端っこに書いて出せるからおぼえなくていい!導き方だけ3.4回練習しとこ?\n\n人間だから全部の公式を完璧に覚えるのってすごく大変だと思う。ただでさえ君は国立を目指して科目数も多いから他にも暗記することが沢山だと思う。一回試してみて自分に合うやり方を見つけて見てね!"}],["$","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",[["$","path","0",{"fill":"none","d":"M0 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"公式の証明について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは!回答させていただきます。\n\n公式の証明を覚えているとどう役に立つかということですが、正直、受験に合格するという観点では公式の証明問題が解ける以上のメリットはあまりないです!\n公式の証明では、受験数学のセオリーからみれば特殊な考え方を使うものが多く、考え方が他の問題に役立つ事も少ないのです。\n数学という学問を修める意味では、公式の証明を理解していることは重要だと思いますが。\n\nしかし、本番で公式の証明問題が解けるという一点だけで、覚える理由としては十分ではないでしょうか?\n実際の入試でそういった問題が出ているわけですし。4完を狙うなら公式の証明問題は落とせませんしね!\n\n余談ですが、三角関数の和積の公式とか、ベクトルの内積を使った三角形の面積の公式とかを、もし暗記せずにテスト中に導こうと思ってるなら、それはダメですよ!時間がもったいないですから。これはマジです!\n\n長文失礼しました。頑張ってくださいね!\n\n\n\n\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","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":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"数学公式"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"\n文系ですが答えさせてもらいます。(数学は使ってました)\n\n今でもそうなんですが、公式の仕組みが納得できないと個人的には気持ち悪くてしょうがないんですよね。\nどうしてこの公式になるかを納得する\n→公式を暗記\n→実際に公式を使って、使用方法と公式を頭に定着させる\n\nこんな感じですかね。\n理由としては、1番はそうじゃないと気持ち悪いっていうのがあるんですが、、、笑笑\nでも、実際問題、公式の導出を問われたりする問題ありますし、また、公式の仕組みが分かってないと解けないような問題も一定数あります。\n特に、三角関数・微積分・シグマ計算あたりの公式は導出過程を理解できてると、数学的な思考力の幅が広がるイメージあります。\nもちろん、導出過程を知らなくていいのもあります。でも、一回は導出にチャレンジしてみるといいです。それで、「あー、これは公式だけ覚えておけばいい感じかな?」みたいなやつもたくさんあります。導出過程がめんどくさかったりするから、わざわざ公式にされているんで、それを覚えてしまうこと自体悪いことではないです。\n\n公式の結果だけを覚えておくパターンのやつは、とくに物理・化学に多い印象ですね。「実験の結果、こうなった」とか、「この公式を定義とする」みたいのは、理科系では多いです。そういうのは、あまりこだわらず、一回くらい説明書き読む程度でいいと思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"図形の性質はやらなくていい?"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"今年一橋大商学部に合格したものです。確かに図形の性質に関する証明問題が出ることはほぼないですが、その性質を利用する問題は普通にでます。定理や性質を説明することはできるが、証明はできないということは、おそらく理解はしているが自分からそれを発見することができないという状態だと思います。その状態では二次試験はもちろん、共テでも手詰まりになってしまうことが起こるかもしれません。\n\nわざわざ証明文を書く必要はありませんが、頭の中で証明の流れを作り出せるようにする必要はあると思います。おすすめは自分で授業をするように証明問題を解いていくことです。そうすれば自然と図形への苦手意識も減っていくと思います。\n\nまたセンターの過去問を解くのもいいですが、結構単純で簡単な問題が多いので、それだけでなく共テ形式の問題を解くこともお勧めします。\n\n一橋なら整数や確率、微積に優先して取り組むべきではありますが、図形も軽視せずにチャートレベルは解けるようにしといた方がいいです。\n\n来年キャンパスで会えることを楽しみにしています。応援してます!"}],["$","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",[["$","path","0",{"fill":"none","d":"M0 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"公式の証明"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"はじめまして!\n\n公式の証明は度々入試に登場します。ただ1度やっておけばいざ出れば手が動くかも、ぐらいの期待値ですね。\n入試は今まで見たことない問題も山ほど出ます。そんな中でもしかしたら出るかもをやっておく分には損はないかと思います。ヤマカンまで張る必要は絶対ないですが。もし出た時に「あの時やっておけば!!!」と後悔しないための安心材料ぐらいの感じです。\n\nもちろん他の勉強とかの兼ね合いもあるので実力試しにやってみるぐらいでいいと思います。もれなくやらないと!って焦るほどでは無いです(その分野を展開するための始点なのでやったからといってもその分野の応用が身につく訳ではないですからね)。\n\n以上、あくまで個人的意見なのであまりあてにしすぎないでください笑。\nただ公式を証明してしっかりと理解を深めるのも無駄なことでは無いと思います。\n上手い時間の使い方ができることを願っています。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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 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