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12:[["$","meta","0",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","1",{"charSet":"utf-8"}],["$","title","2",{"children":"新課程2025令和7年度入試での東工大の整数 | UniLink"}],["$","meta","3",{"name":"description","content":"令和7年度入試から新課程入試が始まるのですが、この新課程で共通テストは数学Aでは整数が要らなくなり、図形の性質と場合の数と確率の選択で受験出来るようになります。ここで疑問なのが2次試験です。大学が提示している資料を見れば数学A（図形の性質、場合の数と確率）という書き方になっています。本当にこれを信じて整数は全く勉強しないという事は出来るのでしょうか。自分は東工大志望なんですけど、特に東工大は整数は頻出分野であるのでやっぱり出るのではないか？という疑問です。自分的には整数は苦手なので勉強したくないし、整数に当てる時間が浮いたら別の分野の勉強も出来るので整数の勉強はしたくないです。誰かわ"}],["$","link","4",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","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"}]]
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1b:Tf48,初めまして！慶應大学経済学部A方式に合格したものです。(商学部も受かりました。)
僕は元々東京大学をめざしていたこともあり、数学は比較的得意だったので、アドバイスが出来たら嬉しいです。
慶應大学経済学部の場合、マーク部分(すなわち、第1段階選抜の点数に含まれる)に確率があります。僕自身、確率が非常に苦手で、これといった対策から逃げていましたが、共通テスト、慶應大学本番ではどちらも確率で満点をとることが出来ました。そこで僕が行っていたことについて書いていきたいと思います。(整数は後半で)
まず、けんたろうさんが挙げてらっしゃる参考書をやったことがないので、二者択一は僕にはできません(申し訳ないです) しかし、慶應経済の場合確率はカラクリに気付けば一瞬で解けてしまうが、そのカラクリに気付くのが難しいという問題が多いです。そのため、まずは基礎を徹底することが近道だと思います。僕自身先に述べたように確率が非常に苦手応用問題の対策から逃げてしまって東大の本番の確率は解き切る事が出来ませんでした。しかし、基礎だけは見直しておいたおかげで、他の分野に通づるような発想力でカラクリを見抜き、慶應経済の確率は満点を取れたので、基礎固めを行ってください。確率は、自分が何が分からないのかが分からない分野の最たる例だと思っています。そのため、何が自分を出来なくさせているのかをしっかり分析しましょう。アバウトな解答になってしまい、申し訳ないですが、これが一番の近道だと思います。
そして次に整数についてです。受験数学の整数はかなりパターン化されています。つまり、定石をどれだけ知っているかが鍵になっていると思います。東大や一橋の整数は一筋縄には行かない問題が多いですが、それでも次の三つを使いこなせばできるものが多いです。
①因数分解 ②余りに着目(modを使いこなす) ③範囲を絞る
の3つです。
①の因数分解は、例えばa^2-b^2が素数である、というものでしたら(a-b)(a+b)が素数になるのでa－bかa+bのどちらかが1になるとすぐに分かります。
②の余りに着目は、例えばN^2であれば3で割ったらあまりは0か1にしかなりません。(試して見てください)これが案外使えます。こんな感じで余りに注目します。
③の範囲を絞るは、問題の条件から文字式についてどこまでの数を取れるのか、逆にどこまでしかこの文字は動かないのかを精査することで解答を絞れます。
と言った感じで整数はパターンです。これを意識してみてください。
最後に、僕自身、けんたろうさんが言っていたような東大志望の者でした。そして、周りの結果を見てみると、一橋に受かった友達は全員慶應経済に補欠、または不合格でした。それくらい経済学部Aは難易度が高く、クラスの友達にも28人中5~6人ほど理系がいます。そのため、数学は相当力をつけておくべきです。参考書で言えば、文系数学の良問プラチカ位まで必要だと思います。(僕は東大において数学で圧倒するためにその上の上級問題精講まで手を出したました。)ただ、慶應経済の数学の特徴として時間が超絶足りない、終わるわけない、ことが挙げられるので、難易度と同じくらいに解くスピードを意識すると良いと思います。1d:Tc61,東工大情報理工学院1年です。

結論としては、今から新しい問題集をやるのは得策ではありません。今から新しい問題集をやって、それが東工大の数学に太刀打ちできる程度の理解度まで身につくとはとても思えないからです。

例外として、もしも貴方が東工大の物理化学英語全てで120点(8割)を安定して取れているのならば話は別です。数学しか伸びしろがないからです。新たな参考書を始めても良いでしょう。

しかし、そうでは無いならば、数学は今までやってきた参考書の理解度をあげる程度に留め、物化英も手を抜かずに取り組むべきです。

ここから新たな参考書をやる場合、おすすめはやはり上級問題精講でしょうか。

ここから、少し厳しめの話し方になります。東工大、しかも情理志望ということで、数学の基礎は身についているでしょう。今は、恐らくその基礎知識をどのように使えば良いか分からないという状態だと思います。

受験が近づき、焦りもあるとは思いますが、絶対に焦っては行けません。一問一問に、自分の中にある手札を使い尽くし、正解に近づいてください。目安としては、15分手が止まったら回答を見て、頭の中に解法が浮かぶ限りは戦い続けるのが良いでしょう。

この時期、上級問題精講の全ての問題をやる時間はありません。今年の問題の予想としては、昨年度、ベクトルと整数が出ていないので、さすがにそのどちらかは出題されると思います。ですので、ベクトルと整数と、あと貴方の苦手分野だけやるなど、分野を絞って取り組むべきです。

余談ですが、東工大数学はクソゲーです。正攻法で解いても、計算量が半端ないからです。さらに、その計算をミスるだけで20点ほど平気で飛んでいくためです。

東工大の問題は難しそうに見えて、毎年、100点から150点分くらいは、青チャート+‪α‬レベルの難易度の問題です。ただし計算量はアホみたいに多いですが。そこで計算ミスしないことが東工大数学攻略の最大のコツです。これからは、数学の問題を解く時は、ゆっくりでもいいので絶対に計算ミスしないように心がけてみてほしいです。それだけで点数は上がるはずです。

さらに余談ですが、数学が下振れて100点を切っても、情理にはギリ受かります。

450点取れば情理安全圏ですが、物理英語で120点、化学で満点を取り、数学で下振れに下振れて70点を取った人を知っています。

つまり、物化英が高ければ数学が低くても耐えます。

本当に本当に頑張ってください。

受験前日まで、人は成長し続けます。

来年度、貴方が大岡山の桜の下で笑っていることを心から祈っております。1e:Te64,受験勉強お疲れ様です。
結論から述べると、目的と段階によりますが、基礎問題精講と1対1シリーズの2冊で、基礎から標準レベルの、数学Ⅲの一通りの解法パターンは習得できる(※ただ基礎問題精講だけでは解法パターンは網羅できていないかな)と思いますし、一旦まず数Ⅲを一通り学習するというのであればそれで十分ですが、東工大を目指す上では別の観点から、多少馬力不足な気がします。また数Ⅲを学習する際は、数Ⅲの性格をよく知った上でやるのが効率も良いですし、得策かと思われます。僕の受験体験から数Ⅲに関して2点特徴を挙げます。
1点目、入試問題の数Ⅲは、おおよそ、傍用問題集に乗るような基礎的標準的な問題から、誰も完答できないような難問奇問まで多岐に渡ります。数1A2Bの場合には難問奇問はあまり出ません。ですが、最難関大を狙う学生たちはやはりレベルが高いため、難度の高い問題(過去問で言うレベルCやD)でも部分点ぐらいは狙ってきます。ですので、標準問題を反復するだけでは足りません(もちろん標準問題の反復は大事ですが)。もしAkiさんが一通り数Ⅲの標準問題を解けるようになったのなら、少し難度の高い問題や思考が必要な問題にも触れる必要があります。
2点目、数Ⅲは1A2Bに比べて計算量が著しく多いです。特に東工大は工業大学であるがゆえ、数Ⅲの出題では極限と微積が大部分を占めており、計算量も日本のどの大学に比べても類を見ないほどです。その一方で、基礎問題精講や1対1、チャートなどは解法パターンを習得することに主眼を置いているため本物の入試数学(特に東工大の数学)とは少々趣が異なります。つまり計算は軽めです。
以上2点からアドバイスを述べますと、基礎問題精講と1対1で解法パターンの習得は十分です。チャート式などに手を出す必要はあまりないと思われます。それよりかは、東工大レベルの息の長い計算力と思考力を少しでも鍛えるためにも、上記2冊で解法パターンの習得が済んだのならば少し上のレベルの問題を解く方が良いです。おすすめとしては、それこそ東工大の過去問に触れてみるのが一番手っ取り早いです。もちろん受験生の身としては過去問は残しておきたいのも分かりますが、結局は過去問は直近の5〜10年ぐらいをやれば十分ですので、直近10年だけ残しておいてそれより前の過去問を問題集のように解くのが得策です。他には上級問題精講・やさしい理系数学(←簡単ではない)、理系プラチカ数Ⅲなども東工大等の最難関大受験生にはおすすめです。これらの少し上のレベルの問題を解くことで負担の大きい計算力と息の長い思考力を鍛えましょう。
ちなみに1A2Bは難度の高い問題ばかりを解くよりは標準的な問題をこなす方が良いです。
長ったらしく拙い文章で申し訳ありませんが、僕のアドバイスが少しでもためになれば幸いです。
東工大の数学はやはり難しいです。ですが、そのレベルの高さにめげずに、むしろ数学極めてやるぐらいの勢いで、晴れて合格を掴み取って欲しいです。頑張ってください！1f:Te74,こんにちは！
現在一橋大学社会学部１年の者です！

私は社会学部なので必ずしも商学部と同じ勉強方針ではないかもしれませんが、何か参考になる部分があればと思い答えさせていただきます🙇‍♀️
ちなみに当日の数学の得点率は55%くらいでした。

共テと２次試験の対策（特に数学）の勉強の比率についてですが、共テは慣れの部分があると思うので直前に解きまくれば結構即効性があります。現役の時は冬休みくらいから本格的に共テ演習に移行し、浪人の時は年明けから移行して、それぞれ82%、86%くらいでした。（本格的に移行というのは完全に勉強時間の全てを共テに費やすということです。それまでは共テの対策では、共テのみの科目の復習や授業で解く演習問題、共テ模試だけだったのであまり自分で共テ演習のための時間をとっていませんでした。）
ベストの比率は質問者様の状況によりますが、意外と共テは直前でもなんとかなるので、心配なら２次試験の数学をやるので計画的には全然問題ないと思います。共テ演習に移行したら２次試験の対策に戻らずそのまま共テの形式に慣れて本番がいいのかなと思います。（共テと２次試験の対策を並行してやるのは私はやってないのでなんとも言えませんが、中途半端になりそうな気もします）ただ、２次試験で使わない古文漢文や共テ科目の社会、理科基礎の暗記や総復習は、これまでどれほどやってきているかにもよりますが、12月すぎから始めておきましょう。

また、２次試験数学の整数分野について、私は一橋の整数は慣れだと思っています。慣れというのはただ解けば得点が伸びていくのではなく、はじめの発想や途中からの考え方の似たような問題が出やすいからそれらの解法を覚えていくのが良いということです。
私も最終的に３完を目標にしており、整数は取りたい大問の１つでした。前提として、整数問題の基礎ができている必要があります。もしまだ理解が不十分な部分があれば、チャートなどの基本的なレベルの問題を解きましょう。基礎は分かるけど過去問になると解き方が分からないという場合は、過去問を整数に絞って解いて解法を覚えましょう。最初は普通に解いて詰まったら解答を確認して、覚えててもいいのでもう一度解く。数日後にも復習として解き直さなくてもいいので確認する。ひたすら解き慣れていきましょう。

共テ数学も、基礎と慣れが重要だと思っています。こちらはより基礎が重要だと考えています。なぜなら、共テ数学の演習量が多かった現役の時よりも、少なかった浪人の時の方が得点が安定して高かったからです。浪人時は基礎を一からやり直せていたので、数学の基礎的理解が深まっていました。その差が点数の差につながりました。あまり基礎が固まっていないうちに過去問や予想問題演習をしても得点の伸びに限界があると感じるので、焦らず基礎を復習した後、共テの形式に慣れるのが良いと思います。

あくまで私の一意見に過ぎませんが何かお役に立てれば嬉しいです！
勉強頑張ってください📣2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=qXSAVxl79erRRylHUxvY","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"新課程2025令和7年度入試での東工大の整数"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",2,") コメント(",1,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"5/11 16:05"}]]}],["$","div",null,{"className":"coach-mark 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mb-1","children":"【分野別対策に関して】\n\n標準問題精講を完璧にして、別の参考書に行くというのは無理だと思います。\nひと通り終えているのなら、弱点補強を目的として別の問題集に取り組むのは全然ありです。\n\n「基本を完璧にしてから応用」\nという考え方はもっともらしいのですが、実際は応用に取り組みつつ何度も基本に戻って考えるというスタイルがいいでしょう。\n別の問題集で間違えたところを標準問題精講と照らし合わせてやると良いです。\n\n－－－－－－－－－－－－\n\n【分野別対策の時期に関して】\n\n分野別にはこの対策！というのは、個人的にはありませんでした。\nセンター試験に特化した対策を年明けからやっていた、くらいでしょうか。\n\nそれまでは、難度の高い問題集や模試の復習と、高校3年間で使ってきた青チャートと4STEPを行き来しながら、弱点補強と論理構築練習を繰り返しました。\n\n\n－－－－－－－－－－－－\n\n【その他思ったこと】\n\n確率や整数が苦手な方は、ベン図をはじめとした集合の考え方がうまく使えない印象です。\n図や表を用いて確率や整数の解法を友人に説明できるかどうかを試してみましょう。\n模試の復習を通じてやると良いです。"}],["$","div",null,{"className":"flex mb-1","children":[["$","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":[]}],["$","path","1",{"d":"M12 6c1.1 0 2 .9 2 2s-.9 2-2 2-2-.9-2-2 .9-2 2-2m0 10c2.7 0 5.8 1.29 6 2H6c.23-.72 3.31-2 6-2m0-12C9.79 4 8 5.79 8 8s1.79 4 4 4 4-1.79 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mb-1","children":"こんにちは！\n\n少し難しくなると解けない、というのはよくわかります。私もそうでした。私も簡単な問題は得意だったのですが、難易度が上がると全然解けなくなりました。なのでお気持ちはよくわかります。\n\n私の場合は、難しい問題を解いて慣れようと思い、新演習を買ってやりました。新演習の難しい問題は東工大レベルの問題になります。ですが、簡単な問題も含まれており、半分ほどは標準レベルの問題になります。なので、質問者様のレベルだと全く解けないということはないと思います。\nですので、新演習のような難しめの問題集をやってみては如何でしょうか。ただ、新演習は解説が割とあっさりしています。詳しめの解答・解説が欲しいならばやさしい理系数学などのような問題集の方が良いかと思います。私の場合は、解説が詳しいと読むのが面倒だったので、新演習が合っていました。新演習は一対一と同じ出版社なので、一対一と解答のテイストは似ています。\nまた、これも東京出版ですが、大学への数学もオススメです。大学への数学は月刊の雑誌の形式となっており、月によって扱う分野が変わります。例えば2021年の7月号は座標平面を主に扱っています。8月号は数列を取り扱ってます。このように、月によって扱う分野が変わるので、苦手な分野の号を買ってみても良いかもしれません。例えば、確率が苦手なら、確率が扱われている月のものを買います。苦手な分野の強化にはうってつけの参考書・問題集だと個人的には思います。\n\n私は難しい問題に慣れようとして、難しい問題を解いていったわけですが、この方法で数学の偏差値は10以上上がりました。勿論、色んなやり方があると思いますので、私の方法はあくまでそのうちの一つの方法です。この方法を試してみて、違うなと思ったらやめていただいて良いです。また、参考書・問題集の好き・嫌いもあると思うので、書店で色々見てから購入した方が良いと思います。\n\n東工大の数学は難しいですが、配点が高いため最も重要な教科と言えます。頑張って下さい！！"}],["$","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":"場合の数・確率がどうしてもできません"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"苦手分野だからといって、捨てることはあまりオススメしません。\n\n残り時間が少ないから、限られた勉強時間でとれる得点を上げるために…と考えたくなるのはよくわかります。選択問題では苦手分野を回避できますが、2次試験では全員に同じ問題が課されます。たとえば、基礎レベルの確率分野の問題でるかもしれません。難易度が高くないなら正答率は高くなるでしょう。ですが、苦手分野だからといって捨てれば、周りとかなり差をつけられてしまいます。ですので、苦手分野であれど、苦手なりに対策しておくことが大切になってくると思います。\n\nたとえばセンターの選択問題で、時間を測るときは図形を選ぶが、あとで確率分野も解いてみる。青チャート等の問題を全て解くのは厳しいけど、このレベルまでは解けるようにしておく。など、苦手なりではあるけれど、対策をしてほしいと思います。少しでもやっときゃよかった…と後悔してるときには遅いので…\n\n残りの期間、頑張ってください。"}],["$","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 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