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1a:Tf28,ある程度の数学の基礎は身についていると思うのでその先の勉強方法について話したいと思います。
数学の難しい問題というのは解き方の展望が見えてこないものが多くあります。なので、正確に文章を読んで、文章の中からヒントを拾ったり、式の形をみて、使えそうな公式や、定石となる解き方を考えてみることが必要になります。おそらくランボさんはこのようにして、いくつか選択肢に上がった解法の中に正解となる解法があったのにそれが使えなかった、ということだと思います。しかし解き方を思いついてから最終的な解答方針まで見えてくることはほとんどないと思います。難しい問題はイメージとしては壁が2〜3段階あるという感じです。最初の足がかりとなる解き方をして出てきた式が解けない。そして再び考える。それに対して解き方を考えまたやる。問題を解く時はこれの繰り返しになってきます。
難しめの問題のイメージを話したので、次は勉強方法について書いていきたいと思います。数学は多くの問題集に手を出すより、一冊完璧に、とよく言いますが、その通りだと思います。なぜなら、結局一冊の中に大方必要になってくる解法は全て入っているからです。そして例えばプラチカであればその単元ごとにまとめて学習していくことをお勧めします。その時に確率であれば、P型、C型、漸化式型、円や数珠順列、条件付き確率、じゃんけんや、勝敗を決めるパターン、etcがあると思うので、そのパターンを「漏れなく、だぶりなく」身に付けるとともに、どのパターンの問題はどうゆうような問題文になっているのかを自分なりに考察することが大切です。例えば、簡単な例ですが、組み合わせの時に同じようなものを区別するかしないかで解き方が変わると思います。このように問題文や式を観察して、どのときにどのパターンを使うことが多いか分類すると良いでしょう。このとき、「漏れ」がないことで、どれかのパターンに帰着し、「だぶり」がないことで、実は同じ解法なのに出題形式が違うから両方覚えてしまって、どっち使うか迷うような手間が省けます。そこを意識して勉強するのがいいと思います。
最後に過去問についてですが、過去問はあくまで出題形式、傾向や、時間などを確認して実践するものだと思っています。なので直近6年のものは残しておくべきでしょう。またマスターって言葉の定義は曖昧です。マスターが過去問の解き方を覚えるだけであるなら無駄だと思います。問題を見て、なんでこの解法をしたのか考え、そして始めてその問題を見たと仮定したとき、その問題文からどんなキーワードを拾ったら、自分がその解法にたどり着くかというところまで考え、身に付けることができて、始めてマスターしたと言えます。それなら過去問のマスターはかなり有用だと思います。数学は初見で考え、解いて、解答をみて、終わる人が多く、初見で考えることが重要だと思われがちですが、それを可能にするには解答をみた後の上記の考察がもっとも重要になると思います。
試験本番までまだあと4ヶ月あります。十分に身に付けるだけの時間はあると思うので最後まで頑張ってください。応援しています。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=1TOQzqZsWD7cirtX","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"単元別ではなくランダムと問題になった時どうすれば良いか"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",0,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"9/29 23:41"}]]}],["$","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":[["$","div","advice-part-0",{"children":[null,"普段の勉強時はどの単元かがあらかじめわかってるため問題へのアプローチがしやすいため解きやすくなってます。\n\nしかし、テストではアプローチの部分を自分で考えないといけません！！\n\nそこが1番重要でかつ難しいところです( ^ω^ )\n\nそのため、問題集で分野ごとに分かれてないものや、簡単な大学の過去問などでアプローチの仕方を勉強してみてください！！\n\n応援してます📣"]}]]}],["$","div",null,{"className":"mb-4","children":["$","$L16",null,{"adviserImageUrl":null,"adviserName":"tatsuya1013","adviserDepartment":"早稲田大学創造理工学部","adviceId":"1TOQzqZsWD7cirtX","numberOfFan":186,"clipsAvg":12.575,"adviceRateAvg":4.613793103448276,"profile":"早稲田大学創造理工学部総合機械学科に所属する3年生です(^^)\n自分が受験生だった頃部活が3年の6月まであったため勉強との両立に苦労しました……\n少しでも受験生の力になれるように皆さんの質問に答えて行きたいと思っています( ^ω^ )\nps:ファンやいいねが増えるとよりたくさんの質問に答えたくなるので気軽にファン登録やいいねをお願いします笑"}]}],["$","div",null,{"children":["$","$L7",null,{"href":"https://ck.jp.ap.valuecommerce.com/servlet/referral?sid=3364577&pid=884970531&vc_url=http%3A%2F%2Fshingakunet.com%2F%3Fvos%3Dnrmnvccp0000100","rel":"nofollow","target":"_blank","children":["$","$L8",null,{"src":"/images/document_request_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink パンフレットバナー画像","className":"mt-4 rounded"}]}]}],["$","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(",0,")"]}],["$","$L18",null,{"adviceId":"1TOQzqZsWD7cirtX"}]]}],["$","div",null,{"className":"mb-8","children":["$","div",null,{"className":"text-xs p-4","children":"コメントで回答者に感謝を伝えましょう！相談者以外も投稿できます。"}]}],["$","h1",null,{"className":"text-xl font-semibold","children":"よく一緒に読まれている人気の回答"}],["$","div",null,{"className":"mb-8","children":["$","div",null,{"className":"divide-y","children":[["$","div",null,{"children":["$","$L7",null,{"href":"/advice/yMA0xGUBTqPwDZPuI1Ok","children":["$","div",null,{"className":"flex items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"見たことのない問題が解けない"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"入試で問題を解く上で1番有利なのは｢この問題見たことある！｣という状況です。\nその状況を生み出すためにも、日頃から沢山問題を解いて、見たことのない問題をできる限り減らすのが正直1番いいです。\n\nしかし、頑張って勉強しても初めて見る問題は必ず出てきます。\n\n私はいつもそんな時にただ闇雲に計算するのではなく、\n｢この問題はどの分野を使わせようとしているのか？｣\nということを意識して問題を解くようにしています。\n\nつまり、\n問題みる\n↓\n学習した分野の中から使えそうな分野をピックアップする(問題文の隅に書くとよい)\n↓\nその分野の中から使えそうな公式をピックアップ\n\n……というようにすると難しく書かれている問題や、新しい問題も案外わかったりします！\n\n参考になれば嬉しいです。頑張って下さい！\n\n"}],["$","div",null,{"className":"flex 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mb-1","children":"その感じよくわかります。\n\n私の経験からお伝えするならば、あなたがお考えのようにたくさん問題を解くことと、さらに付け足すならば、制限時間を決めて難問と向き合うことが打開のカギになります。\n\n\n1つ目のたくさん問題を解くことには大きく3つの目的があります。\n\n①典型問題の典型的な解法を身につけること。\n②問題の捉え方の視野を広げること。\n③計算ミスや勘違いを防ぐ注意力を高めること。\n\n①においては、いわゆる標準レベルの問題に相当しまして、問題集などでは例題として取り上げられていることが多いです。この手の問題は考え方を理解した上で動きをパターン化させてしまうのもアリだと思います。\n\n②については発想力です。よく問題を解いていて「こういう風に考えれば良かったのか」とか「着目する場所が違った」と思った経験はございませんか？いわゆるこの発想力を高めるには演習の経験値を積んで、問題の見方や捉え方を知っていくしかないと思います。\n\n③はおそらく最後まで悩むものです。このようなミスで本番減点されないためにも演習量は確保しなければなりません。\n\n無意識的にこの目的が達成されますので、ひたすら問題を解く効果は実感しにくいですが、大変重要なものです。\n\n2つ目のきちんと難問と向き合うことについては、上述した②に近いものがあります。つまり、難問は一見問題文を読んだだけでは解法が見えてきません。\n\nそれを打破するには、とにかく問題文から分かることを書き出してみる、その書き出されたものから他に分かること、ヒントはないかと悩み、少しずつ紡いでいくことで解法が見えてくることが多いです。\n\n長い時間粘っていても効率が悪いですので、きちんと時間を決めて、その間はひたすらあれこれ考えて解法の糸口を見つける経験を日頃から積んでいると、自力で解ける問題が増えてくると思います！\n\n\nおそらく入試本番でも悩むような難問は出てきます。\nそこで自力で解法を見出せるかどうかは、やはりたくさん問題を解く経験値と日頃から難問と向き合ってきたかの2つがキーになると思います！\n\n"}],["$","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":"すぐに解法が思いつくには"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"間違っていたらすみませんが、おそらく考えている途中「手が止まっている」のではないでしょうか？\n国公立レベルの問題なら数学が得意な人でも、必死に手を動かし色んな道をトライ＆エラーを繰り返しながら、正解っぽい道筋を見つけます。\n\n過去問を初めて解く時って、自転車のコマを外された感覚に似ていると思います。バランスが取れず、どうしていいか分からない。\nでも「何も書くことがない」というのはありえませんから、コケてもいいので一生懸命漕ぐことから始めましょう。\n\n\n僕が意識していた考え方を紹介します。\n①どの単元の組み合わせで構成されているのか考える。\n数学が苦手な人にとって、初見の問題は無限の道筋があるように感じてしまい、脳が閉じてしまいます。単元を意識すると思考がスッキリして、その単元の知識を有効に使えるようになります。その上で、単元内のどの問題と似ているのか、どの公式が使えそうかなどを意識してください。\n\n②過去に似ている問題がなかったか？(①と重複するようですが)\n少し式の一部が似ているでも、直感的な雰囲気が似ているでも構いません。その問題のやり方と似た方法を試すと、うまくいくことが多いです。このアプリ内でもよく言われている、「抽象化してメモする」習慣はここで力を発揮します。普段からどういう問題のときどうするのかをパターン化しておけば、初見の問題でもほぼ困らないです。\n\n③行き詰まったら、落ち着いて情報を整理する\n自分がどの条件を使ったのか整理しましょう。\nこの式はどの条件とどの条件が含まれたものなのか。この点はどの条件とどの条件を満たすものなのか。他に満たすべき条件は？など。(文章だけだと伝わりづらいですが)\n\n\n\n上記は試験本番で意識することですが、普段の勉強から深く考える癖をつけてください。\n「数学は暗記だ」と高を括って、上っ面の勉強をしているだけでは、その問題しか解けるようになりません。\nなぜそう解くのか、どういうときにこの公式を使うのかを、根本からきちんと理解しているかどうかを、試験では問われています。\n(数学は暗記と豪語している人達は無意識にこのへんのことが出来ているんだと思います)"}],["$","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":"分からなかった問題について"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"Stayさん、初めまして！\n\nあくまでも私の意見なので参考までにしていただけたらと思いますが、この時期だったら解説をよく読んで次に行っても良いと思います。\n\n基礎ができる前だとやはり解答の流れなどを覚えると言う意味でもしっかりと書くほうがいいですが、ある程度基礎は固まっている場合にはわざわざ書く必要はないかなと思います。\n\n書いて覚えるよりかは、分からない問題でなぜその解法になっているのかを意識しながら解説を読むことの方が大事です。\n\n私が受験前の時期にやっていたのは、参考書などを解くときは最初の冒頭（方針作り）だけ書いて残りの計算などは飛ばしていました。その後に解答を見て方針が合っていれば次の問題に行くという感じでした。\nもちろんそれだけだと計算力が落ちてしまうので、過去問はしっかりと最後まで解いていました。\n\n\n参考になれば幸いです。\n応援しています。頑張ってください！"}],["$","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 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mb-1","children":"こんにちは。\n\nおそらく理系科目寄りの質問だと思うので、主に理系について書いていこうと思います。数学や化学などを勉強しているときに解法を丸暗記しようとしていませんか？もちろん覚えておくことが悪い訳では無いのですが、覚えるための勉強は理系科目だと効果があまりえられないものが多いです。(もちろん暗記が必要なとこもありますが)\n\nではどういった勉強をすればいいのかですが、1度計算の意味について考えながら解いてみるのはどうでしょうか。例えばモル計算ですが、まず問題で何が聞かれているかしっかり把握し、その数値を得るには何が必要で、どんな値の関係性が必要なのかを自分で理解することで暗記にあまり頼らずに解くことができます。\n\nそして問題で詰まってしまったり解法を読んでみて、どうしてそうなるのかわからないとき、とことん考えてみてください。自力で理論がわかった時が1番解き方を覚えられるし、それが勉強の楽しさでもあります。(割と時間が経っても手も足も出なければ誰かに聞きましょう。)\n\n質問者さんはまだ高一ということなので、もしかするとまだ高校の問題形式や、内容に慣れていないかもしれません。(これは質問者さんが悪い訳ではなくほとんどの人がそうだと思います)この慣れは問題をたくさん解いていくことによって身につくので、焦らずとことん問題に向き合うようにしていきましょう。\n\nまた模試になると解けなくなる原因についてもう1つ可能性があるのは、模試やテストで緊張してしまっているからというのもあり得ます。\nもし、完璧に解法を知っている問題でも解けないことがあるのであれば1度冷静に何が聞かれていてそのためにどれが必要なのかを見分けれればきっと解けるはずです。\n解答をみて知らない解き方、忘れてしまった解き方があれば素直に復習して覚えましょう。(丸暗記ではないです。プロセスを確認しましょう。)\n\nこの分野は完璧で友達にだって説明できる、というくらいまで勉強すればその自信が、模試でも解ける力をくれると思うので、時間がある今のうちにとことん問題と向き合いましょう。応援してます！"}],["$","div",null,{"className":"flex 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