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1b:T13f3,こんにちは！RIZと申します。
問題集の問題は解けるけれど初見の問題では解けなくなるということですね。
まずとても当たり前の話をしますが、数学は問題文から解答を考えなければなりません。現在の、問題集の問題は解けるけれども初見の問題では手が止まってしまうというのは、単に問題集の答えを覚えているだけに他なりません。そこで、今回は初見の問題でも解けるようにするためにはどのようにすれば良いかについてお話しします。
前提として、数学の公式や定義はしっかり学習しているとします。もし質問文に書かれている数学用語というのがこうした公式や定義であるなら、定義はまずしっかり覚えてください。そして公式についてはできれば丸暗記するより、導出できるようにしたほうが良いです。ただもう時間があまりないので最悪丸暗記でもいいですが、導出できるようにすることで、なぜその公式が成り立つのか理解できるので覚えやすくもなりますし、もし忘れてしまっても対応できるようになるのでおすすめです。例えば三角関数の2倍角とか3倍角なんかは加法定理とか、数3ですがド・モアブルの定理などから簡単に導出できますよね。加法定理を毎回導出するのは流石に面倒ですが、2倍角や3倍角を加法定理から導出するのは少しの時間でできますよね。このようにあまり覚えていなくても簡単に導出できる公式はなるべく導出できるようにした方が良いです。
さて、話を戻しますが、以上のように公式や定義が頭に入っていることを前提として、初見の問題でどのように対処するべきかについてお話しします。まず冒頭でもお話ししたように、数学は問題文だけから解答を考えなければなりません。そこでまず、問題文の条件に着目します。条件というのはいろいろあります。例えばnを自然数とするとか、x、yが円の方程式を満たしているとか、垂直に交わるとか、さまざまです。他にも、直接的には書かれていないけれども重要な条件もあります。例えば与えられた式が対称式であるとかです。こうした条件から、解答を考えていきます。例えば上の例で言えば、nを自然数として、かつnに関する命題が与えられて証明しなさいといった問題であれば、自然数かつ証明問題であることから数学的帰納法が浮かびますし、x、yが円の方程式を満たしていて、かつx、yの2変数からなる関数の最大最小を考えたい時、xとyが円の方程式を満たすという条件から、θを媒介変数としてx、yをcosθとsinθで置くとかが考えられます。他にも、垂直に交わるという条件があれば、例えばその垂直に交わる直線の傾き同士の積は−1とか、内積0とか、あるいは図形的に三平方の定理を利用することも可能かもしれません。以上のように、条件を見たときにいろいろなことが考えられるようになることで、初見の問題で同じような条件が出てきたときに対応できます。もちろん入試問題というのは問題集には載っていない初見の問題である場合がほとんどです。なので普段解いている問題と全く同じでないのは当たり前ですが、条件に関して言えば部分的に共通していますよね。なのでこうしたことが想起できるようになれば、初見の問題でも対応できるようになるわけです。しかしこのように、条件を見てそこから解法を想起するというのは初見では無理ですよね。それを問題集から学ぶわけです。つまり、ただ問題を解いて、解けなかったら答えを見て覚えて終わりではなく、解法を見たとき、それが「なぜ」そうなるのかを考えます。そして、もし自分が初見でその問題を解くとしたら、まず問題文のどの条件に着目するのかを考えます。このようにすることで、解法のストックを増やしていくわけです。とにかく、解答を見たものでも初見だったらどうするのか、そして「なぜ」そうするのかまで説明できるようになることで、初見の問題でも、それまでストックした解法の引き出しから解法を想起でき、対応できるようになるわけです。なのでまずは今までやった問題集で、問題文のどの条件に着目して、「なぜ」その解答になるのか考えながら学習するようにしてみてください。以上になります。ご質問などありましたらコメント欄の方でお願いします！1d:Tf23,　こんにちは。志望校は違えど、科目などの境遇が似ているので回答させて頂きました。
　随分と焦っているようですが、焦っても何も始まりません。落ち着きましょう。今焦っている熱量は来週までは続きませんから。
　まず、英語90点との事ですが、これは素晴らしい。受験に必要な知識の大半を会得していますね。熟語や文法・語法に足下を掬われないよう注意しつつも、胸を張って受験に臨むことができるでしょう。
　さて、数学ができないと言うお悩みでしたね。
網羅系参考書はやったが、解説がわからないとの事でしたね。辛いことを言うようですが、解説が理解できずに終わってしまう学習は基本的に後の成績に一切の影響を与えません。それをやった後に何かが新しく出来る様になっているわけではないのですから。
　解説は、どんな手を使ってでも理解するようにしてください。解説の前に30分張り付くのでも、先生に聞きに行くのでも、友達に聞くのでも、ネットで聞くのでも良いです。参考書の単元ごとの最初の方についてる単元に関する公式などの解説をみるのも良いでしょう。とにかくここだけはやってください。
　解説を理解したら、もう一度解説を隠して解き直してください。解けなかったらもう一回解説をみるだけです。理解したのではなく覚えただけでは？と思うかもしれませんが、頭で納得する程理解した上での暗記なら何の問題もありません。それは応用に活きる暗記です。
　結論を言うと、あなたの問題点はありきたりな言い方をすればわからないものを解らないままにしていることです。
　解決方法はどこまで深く掘り下げようと、どこまで遡ろうともわからない問題を納得するまで理解することです。「解説がわからない」と言うのが、実は式変形に気づいていないだけなんてこともあります。これなら楽ですが、下手したら中学範囲からやり直すかもしれません。逃げないでください。逃げられません。
　時期が時期ですから、今は網羅系よりも、「決める！共通テスト」などの最低限の知識をおさらい系の方がいいかもしれません。
　また、言い方的に模試はマーク系だと思うのですが、数学が50点は実は割と悪くありません。基礎はそれなりに固まっているようにも思えます。ですから、受験も近づいて来ましたし、基礎のおさらいと並行で過去問と共通テスト対策もやってください。もちろん、双方共に納得するまで解説と睨めっこしてください。
　嬉しいことを言うと、過去問にもコツがあることがあります。お決まりのパターンで解けることがあります。過去問演習の中でその数パターンを見つけてください。
　　最後に、解説でも、新しい勉強法でも、あなたが当然のように知っている知識が出てくることがあると思います。絶対に飛ばさないでください。そこに書いてある一文を飛ばすことが致命的な影響を与えることが多々あります。熟読してください。
　とにかく、わからないものは、勉強なのですから、何分、何時間、何日かかっても理解してください。(この時間を短縮するために先生や塾講師はいます。)
僕から言えるのはこの一点に限ります。長々と失礼しました。受験がんばってね。
1e:T11a6,こんにちは！RIZと申します。
今回は夏休みに一番時間をかけた数学で点数が取れなくて悔しいとは思いますが、間違えた問題についてはしっかり復習して、もし本番で出題された時に間違わないきっかけになったと前向きに捉えましょう！あくまで模試は練習ですからね。
さて、数学の学習方法についてですが、まず数学は3つ大事な要素があります。1つ目が計算能力です。これは言わずもがなですね。2つ目が解法パターンを覚えていることです。典型的な問題の解き方を知っているということですね。最後3つ目が思考法です。これはある問題に対する解法を考えるときの過程ですね。「なぜ」その解法で解くのかということです。
以上を踏まえて、今回の模試では何が不足していたから出来なかったのか考えましょう。例えば時間が足りなかったとすれば、計算が遅かったのか、解法を思いつくまでに時間がかかったのかなどが挙げられますし、単純に解き方がわからなかったとしたら、その時答えを見て理解できた場合は3つ目の思考法が足りなかったと考えられますし、もし答えを見ても理解できない場合は2つ目の解法パターンの把握がそもそもできていないことが考えられます。ここで不足点を洗い出して今後の学習の糧にしましょう。
以下では、上記の3つの要素のうち、特に意識しないと習得できないであろう3つ目の思考法にフォーカスしてお話しさせて頂きます。夏休みの学習で多くの時間を割いたということは、恐らく2つ目の基本的な問題の解法は頭に入っている状態だったけれども、模試などの初見の問題になると解けなくなるという状態ではないでしょうか。(もし違ったら申し訳ないですが、今回はその状態を前提にします。違う場合はコメント欄で教えてください。)この時今までの学習で見直してほしいのは、ある問題に対して、「なぜ」その解法で解くのかしっかり理解していたかということです。例えば「自然数に関してある命題を示せ」といった問題があった時にその問題が解けなかったとします。そこで解答を見ると、数学的帰納法で解いていたとします。こうなった時に、単純に解答で数学的帰納法が用いられていたから、こういう問題は数学的帰納法で解けばいいのかと理解するだけではいけません。なぜ数学的帰納法で解くのかを考える必要があります。それは今回の場合、自然数という条件かつ証明問題であることから、ひとまず数学的帰納法を疑ってみるという思考法が存在するからです。他にも図形問題が出てきたら、①幾何的(図形の性質)に解くのか、②座標に置いて解くのか、③ベクトルで解くのか、などを考えたり、といった思考法も存在します。これらの例はとても単純ですが、意外とこの「なぜ」といったところまで考えていない人が多いです。この場合、単純に解法を暗記しているだけなので、すでに解いた問題は解けるものの、類題になると手も足も出ないという状態にも陥りかねません。数学はこのように、ある具体的な事例から、抽象的な「思考法」を考えることがとても重要です。この思考法は一般的に使えるので、初見の問題でも条件から適切な解法を選択することができるようになります。なのでもし今回の模試が出来なかった理由が、この「思考法」という要素が欠けていたからであれば、今まで使っていたテキストなどを見直して、「なぜ」その解法で解いているのか説明できるようにしてみると良いと思います。
最後になりますが、阪大の文系数学は基礎的なレベルの問題が多いです。今からでも十分間に合います。まずは焦らずに自分が間違えた理由を分析して、特に「なぜ」を考えて勉強してみてください。ご質問等ありましたらコメント欄でお願いします！1f:Tc93,数学と化学に関しては私も現役の時は心当たりがあります。特に数学はセンス的な要素が強いと思っていたので、解ける解けないの差が激しかったです。

さて、少しひねった問題が来ると解けないのが悩みということですが、まず、最低限の勉強ができていることが大事です。おそらくそこらへんはテスト期間で補っているので大丈夫かと思います。

その中で同じような問題で少しひねっている問題というのはどうすればいいかわからないと思うかもしれませんが、解き方としてはひねる前の解き方と同じようなのに気づくことはできているでしょうか？そのような問題の模範解答をじっくり吟味しているでしょうか？その時解けなかった問題はしょうがないですが、そのあとのフィードバックが大事です。そして、この解法やったことがあるなと感じることが大切です。

具体的に述べるのは難しいですが、例えば二次方程式の2解が正の値をとるための条件は
f(0)>0
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0<x<1の範囲で持つ条件はどうでしょうか？
これは場合分けが必要ですが、そのうち2解がともに0<x<1の範囲の時はどのような条件かというと
f(0)>0
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。2:["$","main",null,{"className":"px-4 pt-4 pb-4","children":["$","div",null,{"className":"max-w-3xl mx-auto w-full","children":[["$","div",null,{"className":"mb-8","children":["$","$L7",null,{"href":"https://unilink-app.onelink.me/isbO/h6xeh63x?advice=F83vs2YBTqPwDZPu8R5C","target":"_blank","children":["$","$L8",null,{"src":"/images/web_to_app_banner.jpg","width":3660,"height":1500,"sizes":"100vw","style":{"width":"100%","height":"auto"},"alt":"UniLink WebToAppバナー画像","className":"mb-4 rounded"}]}]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"証明問題が出来るようになるには"}],["$","div",null,{"className":"flex justify-between mb-4","children":[["$","div",null,{"className":"text-left text-xs text-caption","children":["クリップ(",1,") コメント(",1,")"]}],["$","div",null,{"className":"text-right text-xs text-caption","children":"10/27 14:12"}]]}],["$","div",null,{"className":"coach-mark mb-4","children":"UniLink利用者の80%以上は、難関大学を志望する受験生です。これまでのデータから、偏差値の高いユーザーほど毎日UniLinkアプリを起動することが分かっています。"}],["$","div",null,{"className":"mb-4","children":["$","$L13",null,{"clientImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_23679BE7C4F34D2E83F11E69595A9412.jpg?alt=media&token=b6b0ec8d-fea8-44e0-b880-cc9378f4f411","clientUserName":"Judy","infoString":"高3 群馬県 横浜国立大学志望","adviceId":"F83vs2YBTqPwDZPu8R5C"}]}],["$","div",null,{"className":"mb-8","children":[["$","div",null,{"className":"leading-loose whitespace-pre-wrap","children":[["$","div","consultation-part-0",{"children":[null,"私は国立の二次で数学を使用するのですが、数学の証明問題が全く解けません。\n現在はベネッセの大学受験講座で数学をやっているのですが、整数の証明などでは考えても全くわからず、答えを写してるという状況です。\n2次や私立の勉強などは12月前にある程度やっておいた方がいいと言われるのですが、あまりにも出来なさすぎて焦っています。\n筆記で数学を使った先輩方は証明問題をどのように勉強をしたのか教えて欲しいです！"]}]]}],["$","div",null,{"className":"pt-4","children":["$","$L14",null,{}]}],null]}],["$","h1",null,{"className":"text-xl font-semibold mb-2","children":"回答"}],["$","div",null,{"className":"mb-4","children":["$","$L15",null,{"adviserImageUrl":"https://firebasestorage.googleapis.com/v0/b/unilink-48e75.appspot.com/o/images%2Fs_6D165661F106456D991E1CB0BF4C5B4C.jpg?alt=media&token=bfeb4ed9-4629-4f10-9141-d78cf69b5295","adviserName":"mimimimistudy","adviserDepartment":"名古屋大学理学部","adviceId":"F83vs2YBTqPwDZPu8R5C"}]}],["$","div",null,{"className":"coach-mark 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 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