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19:Tfd1,こんにちは！阪大工学部の者です。

僕も受験生の時に同じような悩みをもっていましたが、あることを意識するようになってから、初見の問題に対応する力がついたのでそれをお伝えできればと思います。

それはズバリ、
「簡単な場合について考えること」
です！

初見で手がつかない問題というのは、入試問題のような難しいだと思います。ではその難しさはどこからきているのかと考えると、
「問題文で扱っている内容が一般的なものである」
というケースが多いと思います。

例えば確率の問題で「○○がnのときの確率Pnはいくらか」、整数の問題で「○○となる素数p,qの組をすべて求めよ」、関数の問題で「任意の実数xに対する関数f(x)がf(x)=○○と表されるとき」などです。

このような問題で手も足もでないとき、
「n=1だったら？」「p=3、q=5だったら？」「f(0)については？」と考えるのです。それでも糸口が見えてこなければ、「n=2だったら？」「p=5、q=7だったら？」「f(1)については？」と考えていくのです。

ここで重要なのは、必ず手を動かして問題用紙の余白に整理して書いていくことです！n=1やp=3,q=5やf(0)といった簡単な場合を考えることは、ユウマさんのように基礎がしっかり身についている人なら頭の中でできてしまうと思います。しかしこの簡単な場合について考える作戦のミソは、
「簡単な場合に限って考えやすくすることで問題の仕組みを理解し、問われている一般化された事象へと応用すること」
にあります。頭の中だけで「まあn=0とかn=1のときは当然こうなるな、ふんふん」とやっているだけでは、一般化された事象へ応用できる重要な仕組みに気付きにくくなってしまいます。「n=0のときはこう、n=1のときはこう、」と表にしたりして整理して書いていくことで「n=2のときは......あ！もしかしてこの問題ってこういうことなんじゃない！？」と、解決の糸口が見つかるのです。

少し余談ですが、数学に限らず科学法則が発見される時を考えてみると、実験室で試験体を用意して、「まずは電圧を1Vにしてみたら？」「葉に当てる光の強さをこれくらいにしてみたら？」「加える液体の量をこれくらいにしてみたら？」と実験を繰り返し、その結果「最も効率がいいのは○Vのときだ！」「光が○のときに1番よく植物が成長する！」「この反応を起こすには○mL必要だ！」と発見されます。

そうです、この「簡単な場合について考えて、一般化していく」というプロセスは、実はテストの得点を稼ぐウラワザでも何でもなく、科学分野の研究における姿勢と本質的に同じだと僕は思っています！

そして大学入試の問題は、このように解決していけるように作られていることが多いです。なぜなら大学側も「この発想を思いついた人の勝ち」なんて運ゲーで生徒を振り分けたいわけではなく、一見手も足も出ないような問題だけど、すぐに諦めずに分かるところから考えて全体を理解しようとする人を取りたいはずだからです。

最後に忘れてはいけないのは、もちろん演習量を積むことは大切です。経験値がなければいくら実験しても、その実験に隠れている重要なヒントを気付けずに終わってしまいます。志望校に限らず同レベルの他の大学の入試問題を「思いつき方を学ぶ」という意識で解くとよいでしょう。

応援しています、頑張ってください！🌸1b:T1034,こんにちは！確率は苦手な人が多い単元ですよね🥲

まず、定石は覚えるべきです。ただ、難しい確率の問題を解く時には、青チャート的な定石ではなく、その一個上のレベルでの定石を知っておく必要があります！確率が苦手な人はだいたいここで詰まっていることが多いイメージです⭐️

加えて、当然経験値もかなり重要なファクターです。計算が重くなったり、場合分けが多くなったりしがちな範囲なので！最初に解き方の見通しが立たないと解きづらい問題も多いですし、「量をこなす」と「パターン化する」の両方を普段から意識する必要があります。

そこでおすすめなのが、YouTubeにあるMathematics Monster というチャンネルの動画です。僕はこれで確率の難しい定石を学びました！ネット上で問題の一覧もPDFで掲載されているので、印刷したりダウンロードしたりして取り組むことをお勧めします💪🏻

一見海外のチャンネルと思いがちですがちゃんと日本人で日本語なので安心してください！

Mathematics Monster上に確率の問題は32題あり、その全てに解説動画があります。網羅性も非常に高く、解くためのポイントもしっかり喋ったりメモしてくれているので、量とパターン化の両方を同時にこなすことが可能です！

一方で注意点を挙げるとすると、問題の難易度はかなり高いです。青チャートなどを終えていないと、初見で解ける問題は少ないかもしれません。ただ、何度も解いたり解説を聞いたりすることで、確率は絶対得意になります！僕自身がそうだったのでこれは確信を持って言えます！
あとは少し問題が古いです。(過去問演習と被りづらいともいえます)

次に確率だけを扱った参考書についてお答えします！
あくまで個人の意見なので、気になるものは実際に書店で確かめてみてください⚠️⚠️

①合格る確率
これはMathematics Monster と併用するのも有りです。確率は計算がしんどくなりがちな分野なので、合格る確率をこなしておくことで計算ミスを減らしたり、計算にかかる時間を短縮できるメリットがあります。
確率には問題を解くための定石だけでなく、ある程度は計算のパターンも存在します。それをこれで学ぶことができます💪🏻(ただ、計算はMathematics Monsterでも十分過ぎるほど学べます)

②ハッと目覚める確率
これも受験生時代にやっていたことがありますが、ネット上での評価は過大評価だと感じました。(⚠️あくまで個人の意見です)
もちろん解けば力になりますが、Mathematics Monster で十分なように感じます。ただ、ハッと目覚める確率の方が易しい問題が多いのが特徴です！

③標準問題精巧 場合の数・確率
分野別で売っている水色のやつです。網羅性も高く難易度も幅広く、難しめの定石を学ぶのには良いと思います。ただ、問題数が多いので時間がかかることが難点です。

④解法の探究・確率
大学への数学シリーズの参考書です。いわゆる大数の解き方やフォント(初めてだと少し戸惑うかもしれません)が使われています。それに抵抗がなければ非常に良い参考書です。
ただ、問題数がめちゃくちゃ多いので、覚悟を持って取り組んでください！

偉そうにレビューを色々と書かせていただきましたが、個人的には青チャートなどの網羅系→Mathematics Monster が時間的にも量的にも1番のおすすめです。

確率が得意になると数学への不安感がかなり解消されます！
ぜひご参考になさってください⭐️応援しています📣1c:Tc1f,　こういった問題独自の定義は、だいたい文字を含んでいることが多いです。例えば、
・「nを正の整数とし、3^nを10で割った余りをanとする。」（東京大2016文系）
・「正の整数nの各位の数の和をS(n)で表す。」（一橋大2018）
・「nを2以上の整数とする。金貨と銀貨を含むn枚の硬貨を同時に投げ、裏が出た金貨は取り去り、取り去った金貨と同じ枚数の銀貨を加えるという試行の繰り返しを考える。初めはn枚すべてが金貨であり、n枚すべてが銀貨になった後も試行を繰り返す。k回目の試行の直後に、n枚の硬貨の中に金貨がj枚だけ残る確率をPk(j)（0≦j≦n）で表す。」（東北大2019文系）
のように。あなたが挙げて下さった例でもそうですね。
　ご存知のように、数学で文字が使われるのはそこに入る値が不特定であるときなので、逆にいえば、自分で具体的な値を代入して実験してみれば良いわけです。k-連続和でいえば、m=1、k=2とすると、3＝1+2という等式になり、3は2-連続和であることになります（相談文のk+1はおそらくkー1の間違いですね。でなければ、nはk+2個の連続する自然数の和になってしまうので）。ちゃんと、n(3)がk(2)個の連続する自然数(1→2)の和であるという定義に則ってますね。2019年文系の確率も、例えばk＝1を代入してみると、P1(j)は「n枚の金貨を同時に投げ、そのうちj枚が表で他が裏になる確率」のことを言っているのだとわかります（ちなみにこれは小問⑴）。反復試行の確率を考えればすぐ解けますね。すると、次はk＝2、その次はk＝3、と実験数をどんどん増やしていけば、Pk(j)の内容もいずれわかるはずです。試行の手順上、残るj枚は必ず全ての試行において表でなければならず、他方それ以外の金貨はすべて、k回のうちのどこかで裏が出ればいい（全て表で残る場合の余事象）わけですから、「n枚の金貨のうち、k回の試行の直後に残るべきj枚はk回とも全て表が出て、それ以外のn−j枚はk回の試行で少なくとも一回裏が出る確率」とわかります。ここまで日本語として簡略化できれば、Pk(j)（特に、k≧2）の値もそこまで苦戦せずに出せそうですね（ちなみにこれは小問⑵）。
　このように、なるべく簡単な値から代入して実験を繰り返すことで、独自の定義が何を言っているのかは帰納的に理解できることが多いです。文字が多かったり、分かりにくい表現だったりして、複雑で難しく感じる定義が出てきたら、まずは実験してみることを心がけると良いと思います。文系の問題ですが、もしまだ解いてない場合はネタバレになってしまい申し訳ございません。1d: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":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=pu1CgWgBTqPwDZPuRjP5","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"確率 n回など"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",4,") コメント(",0,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"1/25 4:07"}]]}],["$","div",null,{"className":"coach-mark 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