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1a:Tb60,一言でいえば「経験」です。
必要条件の利用は青チャートなどのいわゆる網羅系参考書などでは得られない少し発展的な技術ですが、数学がある程度得意な人は過去にやったことがあったり、習ったことがあったりとそれを利用した経験があるのです。
なので質問者さんももう少し経験を積めば普通に利用できるようになると思います。

ここで必要条件の利用に至るまでの思考回路の簡単な例を紹介しておきます。
問題
「k を正の整数とする. 5n^2 − 2kn + 1 < 0 ー①を満たす整数 n が，ちょうど 1 個であるような k をすべて求めよ.」
これは2008年の一橋の問題です。下にプロセスを書いてますが良問であり考えがいがあるので一回自力で考えてみてください。


まず大前提として数学における問題と解は全て必要十分性を保っている必要があります、従ってこの問題を解く際必要十分を保ちながら解く(同値変形)のと必要、十分を分けて解く2通りに分かれます。この問題では実数でなく整数の2次方程式であり同値変形で解くのはややこしい(できることはできます)と判断しまず必要条件から絞ろうと考えます。
この問題を考える際式①が成り立つとき5x^2-2kx+1=0(xは実数)が二つの異なる実数解を持つー②「必要」がある(つまり②は①の必要条件である)ことを利用します、そうすることによってkの条件が分かります。そのもとで①を満たす整数nがちょうど1個である条件は5x^2-2kx+1=0の二つの解(α、βとおく)の差が2未満ー③であればいいということがわかります。②と③から得られるkの範囲が5=<k^2=<30かつkは正の整数よりk=3,4,5であることがあることが必要。ということがわかります。これらを実際に①に代入し十分性を確認することで必要十分性が保たれるわけです。(解はk=4,5です)今は難しいかもしれませんが必要条件を使う問題にたくさん触れることでスッと理解できるようになると思います。また僕が思いつく限りでもあと2つ別解があるので3年生になってからでも良いので試してください。

また全てnについて(n,a,xについての式)がなり立つためのaの条件を求めよなどの問題でも全てのnってことはn=1,2でも成り立つ「必要」があるな、と思い試したりすることもよくあるので覚えといてください。

質問者さんはまだ高1ということで完全に理解することはむずかもしれませんが受験期になればきっと理解できると思うのでそれまで勉強に励んでください。1e:Tf51,　私は、同志社大学での仮面浪人を経て慶應にいます。今直感的に何が大事だったかを考えると、「本当に仮面浪人をしてまでその大学を再受験したいのかという意志」あるいは「それほどに再受験に意義を感じているか」という精神面のところです。個人的な感覚ですが。受かるか分からないうえ、本当に行きたいのかいまいちだと、何をやっているのか分かりません。仮面浪人となると、普通の大学生活とはことなるかなり特殊な態度が普段の生活に求められます。ですから、前提としてこういった気持ちの面を整理しましょう。
　ところで、三科目受験と仮面浪人はとても相性が良いと思います。科目数が少ないので、休学したり予備校に通うには時間がありすぎてかえって時間の使い方が分からなくなることもあるでしょう。受験勉強の仕方として、英語は大学の授業を利用しました（その代わり大学の英語の成績はめちゃくちゃ良かったです笑）。自分の志望する大学の英語入試問題のレベルを鑑みて、それにおおよそ応じて英語の科目を選択します。単語の暗記や文章読解の予習等を、大学入試対策だと思って取り組みます。大学での成績を担保しつつ受験勉強を両立させる最高のやり方です。あるいは、例えば
受験科目に日本史があったら、一般教養科目で日本史を受講して、大学入試対策にからめるという
方法もあります。ちなみに慶應は小論があったのですが、同志社で受講した一般教養科目のテーマに
触れつつ書き上げて結果的に合格しました。とにかく大学の講義を「利用」する意識が大切です。
　ちなみに、春学期は単位も人並みにきっちりとって大学の講義にわりに集中していいと思います
（もちろん質問者さんの今のレベルにもよりますが）。私なんかは、夏休みに暗記科目の日本史を
中心に本格的に受験勉強を始めました（もちろん大学の英語は対策としてきちんと受けていましたが）。よって、秋学期からは単位を「最低限」必要なものにとどめるつもりで受講して、大学
入試対策に集中するのが良いと思います。過去問も解き始めます。
　もう一点、大学生は空きコマや土日などががっつり空くことが多いですね。そんなときは、私は
次のようにやっていました。まず、一日を三分割します。午前、午後、夜といった具合です（三科目対策だとピッタリですね。そして、その一つ一つのブロックに２から３個やるべきことを当てはめていくのです。午前は時間が少ないから２つ。午後は時間があるから３つみたいな感じです。そして、
これらのブロックのうち、２ブロック集中できたらＯＫという意識でいましょう。仮面浪人生には、
こうした心のゆとりが大切です。追い込めばよいものでもありません。適度に忙しく、大学生活も
楽しみつつ、大学受験も楽しむくらいの感覚でいてほしいです。
　以上、少しわかりにくい文章になってしまいましたが、思うところを語りました。ぜひ参考までに。仮面浪人は、確実に私の人生を変えたかけがえのない経験です。もし仮面浪人を行うのであれば、意志を確実なものに、そして最後まで目的を見失わず「楽しみつつ」目標成し遂げてください。
心より応援しております。
Nothing seems to be possible befor it's been done.1f:T109e,まず前提として日本史が一番得意というのは早稲田を受ける上で圧倒的に不利です。
日本史を武器にする作戦には限界があります。配点を考えたら当たり前ですが英語が一番得意になるまでは日本史はあまり力を入れない方が合格可能性は高まります。
日本史は今使ってる参考書のみに留め、多少日本史の偏差値が落ちても構わないので模試で英語の偏差値が1番になるまでは日本史の勉強時間を抑えてください。
勉強時間が足りてて早慶に落ちる人のパターンの１つに社会に時間かけすぎパターンがあります。
Rさんもこのままだと上記のパターンに陥りそうなので先に言っておきます。
次いで英語が一番得意になった後にやって欲しいことを述べます。
まずメインのインプット素材は詳説日本史研究で間違い無いと思います。
アウトプットしてあれ？って思う度に詳説日本史研究の該当箇所とその周辺を読むのが理想的です。
もう一冊用意して欲しいのが山川日本史用語集です。この語句の定義曖昧かもって思う度に都度確認して欲しいです。
史料問題については東進史料一問一答を用意して欲しいです。頭から史料を読み、問題を解く事で初見史料対策をしつつ必読史料もインプットできる優れものです。過去問で史料問題が出てきた時に一問一答の該当史料を読み、関連問題に目を通す作業もやって欲しいです。
インプット素材の最後に学校配布の図版もお勧めしておきます。年表、系図、文化作品など参照したい時にいつでも使える様に常に手元に置いて日本史の勉強をして欲しいです。
次にアウトプット用の参考書です。
最もやって欲しいのが東進一問一答です。網羅率はダントツでNo. 1です。星1までは全て記述できる様に反復するのが理想です。星0は覚えなくても合格できますが高みを目指すのであれば選択肢のある問題に対応できる程度に覚えるのが望ましいです。
日本史重要語句チェックリストは標準的な語彙に関しては網羅できますが早慶には届かないのでメインに据えるのはお勧めできません。一度全問題覚えた状態を作れたら後は東進一問一答に切り替えることをお勧めします。日本史重要語句チェックリストに載ってる問題は全て東進一問一答に載っておりかつ東進一問一答の方が実践的です。東進一問一答で早慶レベルの語句を覚えながら重要語句チェックリストの復習をするのが良いと思います。
標問は網羅率は高くないですがアウトプット用の参考書としては比較的優秀です。特別詳しくはないが解き方に拘った解説が魅力的です。早稲田は暗記だけでは対応出来ない問題が多いのでそういった問題へのアプローチの仕方を学べるので過去問演習を本格的に始める前に全問題解ける様にしておくと過去問演習がスムーズになるかと思います。
一問一答、史料一問一答でアウトプットメインの暗記はゴールがないのである程度目処をつけ早稲田過去問をどんどん解いていってください。
過去問で各学部の出題形式に慣れながら一問一答、史料一問一答で知識のメンテナンスをし、必要に応じてインプット素材に立ち返り理解を補う。この流れが王道かと私は考えます。
もちろん英語優先なので本番までに全てを理解して覚えるのは不可能です。日本史は完璧を求めず、上記の参考書を、目の前の一問一問を確実に理解して覚えることを意識して取り組んでください。
志望学部が論述を課す場合は別途論述対策が必要になってきます。志望学部を明記した上でメッセージコメントを頂けたら対策を回答します。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=9cOnEx4keDeHtVM7FYx8","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"夏休みの課題プリント解説"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",1,") コメント(",3,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"8/23 17:11"}]]}],["$","div",null,{"className":"coach-mark 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whitespace-pre-wrap","children":"分かりやすい説明ありがとうございます！"}]]}]]}],["$","div",null,{"className":"flex py-4","children":[["$","div",null,{"className":"mr-2","children":["$","$L18",null,{"avatarUrl":null,"contributorName":"ダンゴムシ","adviceId":"9cOnEx4keDeHtVM7FYx8"}]}],["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"flex justify-between","children":[["$","div",null,{"className":"mb-2","children":["$","$L19",null,{"contributorName":"ダンゴムシ","adviceId":"9cOnEx4keDeHtVM7FYx8"}]}],["$","div",null,{"className":"text-xs text-caption","children":"8/23 19:50"}]]}],["$","div",null,{"className":"text-xs whitespace-pre-wrap","children":"8X+5の8と4は、どこから来ましたか？"}]]}]]}],["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"記述における必要十分とは。"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"常に必要十分な議論をしている場合は、必要十分条件は満たされたと必ずしも書く必要性はないです。\nしかし、先に必要条件だけを示し、その後十分条件を示すような証明の形をとっている場合には、十分条件を示した後に、必要十分条件は満たされたと書くことで明確な文章とすることができるため、書くことが望ましいと思われます。\n\n\n必要条件、十分条件、必要十分条件についてですが、必要十分条件は同じ。つまりイコールを指します。\n\n\n必要条件と十分条件は、\n\n「20歳以上は成人である」\n\nという命題について、「20歳以上は成人であるという条件を\"十分に満たす\"」といえます。したがって、十分条件を満たしています。\n一方で、18歳以上から成人であることから、「20歳以上であることは成人であるために\"必要\"である」とは言えません。したがって必要条件は満たしていません。\nしたがってこの命題は、十分条件は満たすが、必要条件を満たさない命題といえます。\n\n「18歳以上は成人である」というのが必要十分条件を満たした命題です。\n\nこのように文にして当てはめるとわかりやすいと思います。\nまた、「」で括った必要条件、十分条件の書き方はそのまま数学の記述において必要・十分条件の議論をする際にも使えます。\n\n頑張ってください\n\n"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 24 24","className":"text-subPrimary 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items-center py-4","children":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"選択肢 2個まで絞って間違える"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"現代文の選択肢の選び方\n\n①文章を一通り読んで、話の流れを頭に入れる\n\n②問題文を読み、加線部とそれに関係するところをもう一度読む。\n\n③その問題に対する解答を自分で頭の中でつくる\n(大体で良い。どういう要素が必要かを考えておく)\n\n④選択肢から明らかに違うものは消す。(①の話の流れに沿わないものや③で考えた必要な要素がないものなど)\n良いと思うものには○を、間違いではないと思うが微妙と思うものには△をつける。\nこの時、どういうところが○でどういうところが△なのか明記しておくこと。\n\n⑤○と△をつけたものに関して、④でチェックをつけたところを本文と照らし合わせてもう一度精査。\n大事なのは「本文中から」解答の根拠を見つけること。\nより根拠が明確、あるいは本文中と論理的に明確なつながりがあるものを選ぶ。\n\n\n※これをやっても答えが定まらない時は、④で消したものももう一度見直してみること。\n\n以上です。\n質問者さんはおそらくほぼ出来ていると思うので、特に④、⑤を気をつけるといいと思います。\n全体的に合ってるものというのは、とても曖昧なものなので、きっちり根拠を見つけましょう。\n\n参考になれば幸いです。\n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":[["$","div",null,{"className":"flex-1 mr-3","children":[["$","div",null,{"className":"mb-1","children":"学校とは別にノートって作る必要ありますか？"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"質問を読んでいる感じ私の中学時代の勉強法に似ています。中学時代の私はノートをテスト前に作りました。主要科目のみならず実技教科まで。英語もひたすらノート1ページ英単語を書いたりしました。でも、高校生になると要領も良くなってきます。そんなことしなくても英単語は覚えられるようになりますし、実技教科の筆記もそこまで負担ではなくなります。長くなりましたが結論を言うと高校3年間授業ノートとは別に自分でノートを作り続けていたわけではありません。古典の文法などはルーズリーフにまとめて文法の参考書に挟んだりはしましたが、、、。というのも、あまり効率が良くないからです。高校の国数英は中学以上に演習が大切になります。ノートを作る余裕はありません。しかし例外はあります。数学でも先生からいただいた過去問などのコピーをノートに貼って解いたりしていました。日本史などは3年生になってから復讐を兼ねて毎日少しずつノートにやっていましたし、倫理政治経済も苦手分野はノートに書いていました。理科も要点や問題演習で間違えた問題などをまとめたりするためにノートを1冊作りました。\n\n自分でノートを作ることは必要だと思います。ポイントは細かくまとめすぎないことです。社会などは細かくやりだすとキリがなくなります。"}],["$","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":[["$","div",null,{"className":"mb-1","children":"おすすめの個別塾はありますか？"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"お勧めの個別塾などありません。あんまり個別とか集団で区別しない方がいいと思います。\n\n質問者様におすすめなのは増田塾かと思います。ガッチガチに管理してくれるのであってると思います。\n\n積み上げ式と逆算式の話は正直よくわかりませんが、そもそも逆算式でないと受験の殆どは失敗すると思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","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 0h24v24H0V0z","children":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 5.79 8 8s1.79 4 4 4 4-1.79 4-4-1.79-4-4-4zm0 10c-2.67 0-8 1.34-8 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overflow-hidden","children":["$","div",null,{"className":"w-full h-full 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mb-1","children":"かきふらいさん初めまして。\n文系ですが、回答させていただきます。\n\n本回答の構成は以下です。\n①数え落とした5通りはなにか\n②再考察が合っているか\n③数え上げる際のポイント\n\n以上3点です。\n\n①数え落とした5通りはなにか\n結論としては、端が白玉になる場合が想定されていないかなと思います。\n\nex.●◯●●◯●●◯●●◯●◯●◯\n\n上記のような場合です。\n\n②再考察が合っているか\n結論、誤りです。\n本問の場合、同色の玉に区別は存在しません。\n\n区別する場合は玉に番号が振ってあったりする場合でしょう。本問のように、玉を「色」でしか判別していない場合、区別する必要がないのです。\n\n③数え上げる際のポイント\n質問が若干抽象的なので、回答者様の解法に近いもので解く場合、私なら以下のように解きます。\n\nまずは、解答のための必要条件を具体的に導きます。\n必要条件は、\n「白玉同士は隣接しない」\n「赤玉は白玉に隣接する」\n以上の2つです。\n\nしたがって、初期配置は以下のようになります。\n\n◯●◯●◯●◯●◯●◯\n\n上記のように、赤5個、白6個を配置できます。残る赤4個をどこに配置するかですが、以下のようになります。\n\n1◯●2◯●3◯●4◯●5◯●6◯7\n\nつまり7箇所、赤を置く場所があります。なお、１つの場所につき置けるのは1つまでです。一見、「◯●」の間に置く場合も考えた方が良さそうな気がしますが、これは考慮する必要がありません。なぜなら、先ほど述べた通り、同色の玉はそれを区別する必要がないからです。\n例えば、\n「1◯●2」の2に赤を置けば、「1◯●●」となります。\n次に、\n「1◯●2」の◯●の間に●を置く場合を想定しても「1◯●●」となります。\nこのように、結果が同じになる事が分かるかと思います。\n\nしたがって、7箇所のスペースに4つの赤を置くケースを想定するので、\n\n7C4＝35\n\nよって、35通りとなります。"}],["$","div",null,{"className":"flex 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