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目盛の間隔を正確に図示する必要はなく、それぞれの端の大小と、黒丸白丸があっているかが重要です。(黒丸の場合はその点を含む、白丸の時はその点を含まないことを表します。不等号に=が入っているかどうかの違いとも言えます。) 例えば、 p: x>1 q:x≦2 のように与えられていた時、右向きの数直線上に左から1と2の点を書きます。 pについては、x>1(つまり「xは1より大きい」)であることから、先ほど書いた1の点に白丸を書き、そこから右上がりに少し直線を書き、そこから右向きに直線を伸ばします。新幹線のような形になります。この形は、1の点を含まないことを表すもので、白丸と同じ意味ですが、ぱっと見で分かるように両方使います。また、この線がpであることをどこかに書いておいてください。 qについては、x≦2(つまり｢xは2以下｣)であるので、2の点に黒丸を書き、そこから真下に少し直線を書き、左向きの直線を伸ばします。こちらは、電車のような形になります。この形は、2を含むことを表すもので、黒丸と同じ意味です。こちらの線にも、qであることを書いておいてください。 このように、範囲を一つ一つ図示していくと、次のようになります。 _______________ p / 2 ---------○-----●------->x 1 | q --------------- これを見れば、「pかつq」や、「pまたはq」「p⇒q は真か偽か」はすぐに分かるはずです。たとえば｢pかつq｣なら、pとqが重なっているところなので、10 軸>0 判別式≧0 で必要十分ですよね。これは大丈夫でしょうか？ これの少しひねった問題が例えば二次方程式の解が00 f(1)>0 0<軸<1 判別式≧0 で必要十分です。これと先ほどの上の条件と比較すると同じような感じですよね？つまり端点のみに具体的な数字の条件があるときにこのような条件で進めていくのがセオリーです。 上の解法を知識ゼロから解けと言われたら厳しいものがあるかと思いますが、一通り通っていることなら問題を見たときに「あっ、この問題はこの解法かな？」と瞬時に判断できるはずです。その感覚が大事です。「あー、これどうすればいいんだっけ…？」みたいな感じになっているのは良くないです。 これは勉強する時は問題を解き始める前に一瞬立ち止まって考えください。これを意識するしないとでは雲泥の差です。これは私自身、現役の時には気づかなかったことですが、浪人してからはこのことを意識するだけで、解ける問題のレパートリーが増えました。 闇雲にただ問題をこなすだけなら、むしろその場しのぎになってしまいます。それなら、数学の問題とかは時間がないのなら問題をみてこのような解法でいけばいいかなと思えるなら解かなくていいです。 要は、解き方に“意識“して問題演習を行ってください。時間のかける方はこっちの方です。 模試の前とかは、全国模試であれば定期テストなどでできなかった問題の教科書レベルの類題を確認する感じでいいと思います。高校生は部活等で時間がないと思われますので。1c:Tbce,私は現代文なら接続詞、英語ならディスコースマーカーには必ず印をつけるようにしています。 例えば現代文だったら「たしかに〜。しかし〜。」という譲歩の構造を見つけたら、「しかし」の後に書いてあることが重要度が高いことなので、「たしかに」に丸○、「しかし」に逆三角形▽をつけてわかりやすくしています。 英語もこれと同じで、of courceで譲歩した後に、howeverで筆者の意見を述べるという構造があります。それを見つけたら、上の現代文の例と同じようにマークをつけてわかりやすくすると、その文章全体の要旨が掴みやすくなると思います。 また、()については、無闇につける必要はないと思います。私は()をつけるのは2種類あって、 ①一文が長い時、文構造をはっきりさせるために使う ②本文に関係ない挿入や例を()でくくる という使い方をしていました。 詳しくお話しすると、例えば How people will react when robots reject commands is another open-ended subject for research. In the years to come, will humans take robots that question their practical or moral judgments seriously? という文章があった時、ぱっと見では文構造が取りにくいかもしれません。そこで()を活用してみると How people will react (when robots reject commands) is another open-ended subject for research. (In the years to come,) will humans take robots 〈that question their practical or moral judgments seriously〉? これだけで随分読みやすくなったと思いませんか？私は副詞節は()、関係代名詞節は〈〉というように少し形を変えて使うようにしていました。 ここの回答では上手く表現しにくいのですが、上の文章にさらに下線を引いてSVOCを振ってみると、完全に文構造が取れると思います。 このような英文解釈は全文やる必要はなく（そんなことをしていたら時間が足りません）、ぱっと見だとちょっと読みにくいな〜という文に出会った時だけやるといいと思います。 共通テストの問題でしたら、あまり複雑な文構造のものはないと思うので、英文解釈はそんなに気にしなくて大丈夫です。でも、共通テストは文章量が多いので、設問に対応する答えを文章中から素早く見つけることが大事になってきます。そこで役に立つのが下線です。 長い文章があると、どこに何の情報があるのか分かりづらくなりがちです。答えを素早く見つけるためには、設問で何を聞かれているのかを掴んで、それについて触れられている箇所に下線を引くといいと思います。大抵は2文程度に絞れると思うので、そこから答えを探せば一瞬です✨2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=F1M3jIUBTqPwDZPunisQ","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"『∴』『∵』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(",3,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"1/7 21:32"}]]}],["$","div",null,{"className":"coach-mark 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mb-4","children":[["$","div","advice-part-0",{"children":[null,"用法が間違っていなければ大丈夫です。\nそれらは学術記号と言い、厳密に意味が定義されている記号です。\n\nすこし状況は違いますが、「□」(墓石記号などと呼ばれる)「Q.E.D.」なども証明完了の代用として用いて構いません。ここらへんはノリで論文とかでもよく使われるからです。\n\nもし不安なら、記述模試で何度か使ってみて減点がないことを確認すれば安心できると思います。\n\n最低限用法を調べて、変な使い方をしないように気をつけてください。∴などはあまり連続で使いすぎると不自然だったりします。"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_odm7iUfHgAawef27vsCB0fqAOzq1.jpg?alt=media&token=c442f50d-b666-44b9-b48c-e307b8580b4f","adviserName":"さしみポン酢","adviserDepartment":"東京大学理科一類","adviceId":"F1M3jIUBTqPwDZPunisQ","numberOfFan":6,"clipsAvg":6.923076923076923,"adviceRateAvg":4.916666666666667,"profile":"2021年4月東京大学入学\n現役合格です\n2021年共通テストは823点、二次は250点くらいだったと思います"}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink 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text-caption line-clamp-2 mb-1","children":"はじめまして。\n正直｢使い方次第｣というのが本音です笑。よく｢問題で提示されている条件を満たす｣という身で｢題意を満たす｣という表現を用いますが、そういう理解でしょうか？そういう理解という前提で話します。\n減点はされるかどうかは分かりませんが、問題に条件が多いと、どれを示しているのか曖昧になります。そうなると、今どこの条件を使ったのか出題者が分からないということが起こり得て、せっかく合っていてももったいないことになります。\n解答で必要なのはわかりやすいかどうかです。多少めちゃくちゃでも出題者は大学教授だから何となくわかってくれるという人がいますが、確かに白紙よりはマシですが、別に大学教授はその問題を解く手伝いをして欲しくて出すと言うより、その問題を通して求めているものを論理的にわかりやすく説明して欲しくて出していると私は思います。条件を漏らしていないか、必要性・十分性を担保しているか。ただ解いて欲しいだけだったらそれらはそこまで厳しい採点基準にはならないはず。でも実際はなっている(大学にもよるとは思いますが)。\n何が言いたいかと言うと、少しでもわかりにくいと思ったらやめた方がいいと思う、ということです。試験は実は相対評価です。絶対評価的な部分はありますが、受験生全体の出来次第で採点基準を変更しています。なので、わかりやすい文章を書く受験生と何を指しているのかわかりにくい受験生が居たらどっちを取るか、と考えた時に、わかりやすく曖昧な記述は避けた方がいいだろう、というのが私の考えです。\nまぁほとんど私の憶測なので参考程度に流し読んでいただければと思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary mr-1","children":["$undefined",[["$","path","0",{"fill":"none","d":"M0 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mb-1","children":"三味線さん、はじめまして。\n\nお気持ちはすごく分かります。\nたしかに解答の細かいところに疑問を持ったり、その都度公式を導出していると参考書の進むペースは遅くなってしまいますが、その分、質は高くなると思うので全然良いことだと思いますし、むしろそうするべきだと思います。\n\nよく言われる「数学は理解」という言葉は、なぜその公式を使ったのか、なぜその解法で解くのか、なぜその変換を行うのか、もっと細かいことで言うと、なぜその順に解答を記述するのかといったことを理解することです。\n\n「数学は暗記」という言葉もたまに聞きますが、これは単純に英単語みたいに暗記すると言うことではなくて、どうしてこの解法を使うのかを理解した上でどうゆう問題が出たらどの解法を使うのかを暗記すると言うことです。\n仮に理解の過程を飛ばして暗記だけすると、少し問題の形が変わっただけで解法が思い浮かばないということになってしまいます。\n\nそして理解を深めるためには、三味線さんのように細かいところにも疑問を持って問題を解くのが一番の近道です。公式は導出ができる方が理解度ははるかに上がりますし、たまにある公式の導出に基づいた問題なんかも出題されることもあります。\nまた質問文中のことで触れると、なぜ置換積分はこうゆう形でするのか、一次独立とは何か、解答に使われている言葉の意図、こういったことに疑問をもって考えるのはとても良いことだと思います。確認しても忘れてしまうのは人間なので仕方ないことで、確認してその時に理解したことをノートなんかに纏めておきましょう。次に同じような疑問が出た時にノートを見返すことで少しずつ定着して力になっていくはずです。\n私の場合だと2.3回では定着せず、5回とか10回その都度見返すことで定着し始めた感じだったので、忘れているから力になっていないと焦らずに、自分のペースで頑張ってください！\n\n応援しています☺️\n"}],["$","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":[["$","div",null,{"className":"mb-1","children":"公式の証明"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 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 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"理系科目の記述について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"思考の流れが追える程度で大丈夫です。\n細かい式変形などはスキップしてよく、\n例えば「こんな図が描けて、釣り合いからこの式が立つので、答えは◯」という粒度です。\n\n教授の独り言なので定かではないですが、\n採点のときに見るのは「正しく思考しているか」らしいです。\nつまり、計算過程などどうでもよく、\nどの情報・理論を使い、どのような式を立てたか。\nもちろん正答しているかも重要ですが、\n正しい理論に基づいて思考しているか、を見ているとのことです。\n(何度も言いますが、教授の独り言です。ホントのところは分かりません。)\n\nしたがって、他の人が質問者さんの解答を見て、\nどう考えて解答に至ったのかが判ればよいということです。\n式変形も文字の定義も細かく書く必要はありません。\n　この関係を使うとこの式が立つので、\n　これを解いて答えはAです。\nこの程度で十分伝わります。\n\nまた、解答のまとめ方ですが、\n多くの人がやっているように、\n私は試験前に真ん中に縦線を引いていました。\n東大の解答用紙は普通に使うには横に広すぎるので、\n2行に分けることで見やすく、書きやすくなります。\n(これは理科に限らず数学でも使えるのでご活用ください。)\n\n解答の記述に慣れるには、\n普段から自分の思考を書き出す癖をつけてください。\n私のオススメは、計算用紙と解答用紙を分けることです。\n計算用紙は裏紙でもなんでも良いです。\n解答用紙は罫線の入ったノートが良いと思います。\n\n問題演習の際は、解答用紙の真ん中に線を引き、\n1週間後に見直しても自分がどう考えていたのか分かるよう記述してください。\nもちろん知識問題は思考も何もないので答えだけで良いですが、\nその他の問題はすべて、思考の過程を文字化してください。\n文字にすることで、論理的思考も鍛えられるので一石二鳥です。\n\n最後になりますが、解答すべき問題に気をつけてください。\n東大の理科では、小問一つで2つ解答を求められることが多々あります。\n(〇〇はなにか。また、□□を考慮して〇〇を求めよ。みたいに。)\n私は本番、これで1つ解答を飛ばしてしまいました。\n取れる点数を落とさないためにも、\n解答すべき文言が出てきたら下線を引くでも丸をつけるでも、\nパッと見て何が問われているのかが分かる印をつけると良いと思います。\n\n以上、参考になれば幸いです。"}],["$","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":"数学の勉強法について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"　数弱で浪人した者です。私は、質問者様が現在の勉強法を継続される事を断固支持します。確かに時間が余計に掛かる道ですが、それで問題を解くのが少しでも楽になる事を体感されているのは素晴らしいことですし、それが正しい勉強法です。\n\n　さて、この勉強法で間に合うかどうかですが、定理公式が出てきた度に取り組めば受験に間にあわないなんてことにはならないでしょう。むしろ焦って暗記に走る方が何倍も危険です。受験直前になってもなおうわべだけで分かったつもりになっているというレベルの知識は、入試本番では使い物になりません。そんな知識だけで受験に挑むのは落ちに行ってるようなものです。数学はそんなに甘くありません。数学は身につけるもの、そして、身につけるには自分の手を動かして理解していく事を繰り返すしかありません。証明を忘れてしまったら何度でも復習して下さい。私もこれを幾度となく繰り返しました。また、有名な定理公式の導出方法＝証明を知っているとあっさり解ける、なんて問題も整数分野などではよくあります。\n\n　一つお勧めは、問題の解答を見てとっぴな解法だなあと感じることがあれば、それは問題の基礎的な部分が分かってない証拠だと疑ってみることです。例えば数学が全くできない人に問題を解説してあげるとき、自分では当たり前に感じている箇所で、\"なんでそうやんの？\"と聞かれたことはないですか？普段の問題の解説集も同じで、解法が自分にとってとっぴに見えてしまったら、その問題の要求するレベルに達してないと判断して間違いないです。質問者様の質問には直接関係ないですが、私が受験経験から学んだことですのでお伝えしておきます。\n\n　学問では回り道に見えることが結局は王道です。私は予備校でそれを痛感させられました。めんどくさそうで遠ざけていた定理公式の証明を自分の手で行なって初めて習得できた実感をえました。質問者様の強みは今すでにこの遠回りの威力を知っておられるということです。どうか自分を信じこの努力を続けて下さい。健闘を祈ります。"}],["$","div",null,{"className":"flex 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