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1b:T122f,こんにちは～

ベクトル難しいですよね。自分も受験時にかなり苦労しながら習得していったので自分なりの考えをお伝えできればと思います！少々長くなるかもですが助けになれば幸いです！


まずベクトルをものにするうえでは大きな壁が3つほどあると思います。

1．概念そのもの
ベクトルは今まで扱ってきた数だけのスカラーに加えて方向を考える必要があるのでそれだけで十分考えるうえでの障害になります。

2．計算
ABベクトル＋BCベクトル＝ACベクトルみたいな図じゃないと理解できないものも多い＆分解、内積、位置ベクトルやベクトル方程式など全部が全く違う話に思える単元がたくさんあります。
また、未知数が大量に出てきて3つくらいの数式を連立しないと解けない場合も多いです。

3．幾何との融合
多くの場合ベクトルは図形と融合してくるので数IAで扱ったような内容がわからないと解けないこともすくなくないです。


まず1の場合は正直言って慣れるしかないかと思います。スカラーは生まれた時から20年弱親しんでいるのに対してベクトルは2年程度しか触れてないので最初は難しいとは思いますが、たくさん問題に触れてみたら意外とどうにかなったりします！（ここだけ精神論ですいません笑）


次に2の場合ですが、こちらは何が足りてないのかがわかりやすいので自己分析がかなりしやすいと思います。
もっとも大事なのは公式を覚えること。ベクトルはたくさんあるように見えて実は状況ごとに使える公式の数がとても少ないのが特徴です。（簡単なところでいえば直角が出てきた→内積＝0を使える、内分or外分点が出てきた→位置ベクトルの公式適用など）

公式を覚えきってから問題を見ていくと公式が適用できる条件を明確に認識できるようになります。

逆に立式できてるのに解けない場合はただの計算ミスだと思うので焦らずじっくりやればいいだけですしね。文系数学で出るようなベクトル問題の多くは公式を適用さえできれば慎重に解いていくだけで時間はかかっても答えは出せます。5分余計に時間かかっても完答できることのほうがよっぽど大事です！


3の場合も特に恐れる必要はありません。幾何に苦手意識があっても、前述したようにベクトルは使える公式が決まっていて雑に言えば問題がワンパターンになりやすいです。複雑に見える問題でも結局求めなければいけないのは基礎問題とおんなじということが多々あります。初見の問題を解くのは確かに難しいですが、類題を解くだけと考えれば難しくはないはずです。


たくさん書きましたが対策を一つにまとめると
公式を覚える→計算に慣れ、計算力をつける→いくつか問題を解いて解法パターンを身に着ける。
この３つだけです。
とにかく基礎を確実にしてから応用問題に取り組んでいただきたいのと、最初のうちはたくさん文字が出て混乱してしまうかもしれませんが、解法パターンさえみにつければ必要な情報を取捨選択できるようになるので安心してください！

問題演習や解法パターンの習得におすすめな参考書を書いておきます。よかったら使ってみてください！大変だとは思いますが頑張ってください！



教科書ネクスト　ベクトルの集中講義
名の通り教科書と他の教材の中間くらいのレベルです。難易度はかなり易しめですが苦手意識が強い場合はこれから取り組むことをお勧めします。

10日で極めるベクトル
解法パターンの習得におすすめです。最初はそうでもないですが、内容がどんどんむずかしくなっていくので最初の7，8日分だけ取り組むのがよいかと思います。また、ほとんどが実際の入試問題からの出題なのでそれなりに歯ごたえがありつつ実践の練習にも役に立ちます。青チャート、フォーカスゴールドなどの例題☆3，4レベルがある程度理解できるなーくらいになってから使うと効果的です。1d:T103c,①｢この問題にはこの解法だといった定石がおさえられていない｣のが原因か？
→おそらくそうです。
②どのようなことをすればいいか？学校で配られた共通テスト対策用の問題集でいいか？
→いいとおもいますが、やり方が肝心です。
③数学Bの選択分野を確率分布にするのはどうか？
→今数列とベクトルに関する知識が全くないというわけではないなら、変えない方が賢明だと思います。

   ①について。大学入試共通テストの試行調査の問題を見たところ、おおかたセンター試験と変わらないなという印象を受けました。2つの試験に共通する必要な能力は、高校数学の基本〜標準的な問題に素早く正確に答える能力です。
   それをするには、やはり典型問題の解法の記憶が不可欠といえるでしょう。たとえば、教科書にも載っているような公式や定理を正確に覚え(導出の説明ごと覚えたいが、難しいなら最悪丸暗記もやむなし)、どういう場面で使うかも知っておきましょう。公式や定理では無い場合でも、典型問題の解法はまず初めに何をするか記憶してください。このように、問題を読んだらすぐ考えて手が動くように｢定石｣を抑えることが、共通テストの数学には必要です。
   共通入試特有の｢思考力を試す問題｣も、結局は知っている知識を使いこなせるかを問うてるに過ぎず、指導要領を超えることは当然ないですから、｢定石｣をしっかり押えた上で、よく読んで典型の問題とどこが同じなのか、どう言い換えられているのかを考えるようにしましょう。やはり全ては、パターン解法の記憶からスタートだと思います。
   ②について。では、どのようにすればそれが効果的に得られるかですが、やはりたくさんの問題を解いて覚えるのが一番の近道であると考えられます。問題集は一定の難易度があればなんでもいいです。学校の問題集に加えて、共通テストの試行問題と模試、予想問題、センター試験の過去問なんかも練習材料になるでしょう。
   しかし、それらを闇雲に何も考えずに解いて丸つけして、では、先程述べたような｢定石｣に記憶は難しいです。ですから、問題ができなかったときは、何をどのように知っていたら解けたのかを考える癖をつけましょう。｢○○を求める問題では△△が必要だから、初動で□□する｣といったように日本語で整理しておくのもいいでしょう。
   そして、時間に余裕があるなら、それを覚えた上でもう一回解答などを見ずに解いてみましょう。そういったことを繰り返して確実に定着させてください。また、それによって計算力が上がることも見込まれます。
   ③について。数列やベクトルを、基本のところから全く知らないならまだしも、今から確率分布にするのは得策とは思えません。
   ①でも述べたように、共通テスト数学は前提となる知識を知っているのがスタートラインです。典型解法などがそれです。受験する分野を変えるということは、それを一から覚え直すということになってしまいます。いくらできないとしても、さらに知らないものに手を出して、出来るようになることは稀です。
   以上のように、知らなければならない事項をしっかり覚え、それを意識しながら十分な量練習すれば、点数は上がるはずです。他の科目の進捗にもよりますが、数学はしっかりやれば安定すると思われますので、まずは志望大学のボーダーを目指してください。参考になれば幸いです。頑張って！1e: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！2:["$","main",null,{"className":"px-4 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"「共通テストで数学8割5分取るには」"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"こんにちは！たまちゃんです。\n苦手なところは黄、得意なところは青で問題ないと思います。問題を解くのは問題を解けるようにするためにする行為です。当たり前だ、と思われるかもしれませんが、何も考えず、作業みたいに問題を解くのはやめて下さい。時間の無駄です。わからなかった問題も理解しようとして解説を見て下さい。そして解けなかった問題は翌日も解きましょう。そして、その日も解けなかったらその翌日もまた解きましょう。そうやって苦手を潰していきましょう。\n\nまた、たまには解法を整理してみるのも面白いです。例えば、図形の問題ならば、初等幾何(チェバ・メネラウスの定理も含む)、ベクトル、座標、複素数(数Ⅲ)の4つの解法を使う問題がほとんどです。辺の比がわかっていたら、ベクトルを使うことが多いとか、角度がわかっていたら複素数の回転使うかもしれないなとか整理出来ていると、問題を解く際に解法が思い付きやすいかと思います。まぁですが、これは結構難易度高めなので、2次試験の数学で高得点を取りたいならしても良いと思います。数学を共通テストでしか使わないならこんなことはしなくて良いです。\n\n数学は成績もなかなか上がりにくい科目です。ですが、解けなくてもあまり気にせず、軽い気持ちで解きましょう。質問者様はベクトルが好きということですが、基本的に皆苦手とする分野です。そこが好きと言うのはとても良いことです。その調子で頑張っていきましょう！！\n応援しています📣"}],["$","div",null,{"className":"flex 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items-center py-4","children":[["$","div",null,{"className":"flex-1","children":[["$","div",null,{"className":"mb-1","children":"センター数学"}],["$","div",null,{"className":"text-xs text-caption line-clamp-2 mb-1","children":"一問目から解けないという場合は、基礎がしっかりできていないのだと思います。もう一度、教科書を読み直してみたりするといいと思います。\n\n図形問題に関しては、いくつか分野があるので、公式や解き方を一度整理してみましょう。\n例えば、円が出てきたら、接弦定理を使うのか内接外接を使うのか、それとも内心や外心の性質が使えるのか… \n一つずつ公式に当てはめて解いてみることで、解けるようになります。\n\n指数関数や対数関数は、苦手な方が多いですよね…\nまずは、問題に慣れることから始めましょう。\n底の変換に常用対数、グラフや真数条件、やることがたくさんあって混乱してしまいそうですが、問題集等で一つずつを丁寧にやっていくと、自然とセンターで解けるようになります。\n\n数列も年によっては難しすぎる問題も出てきます。怯える必要はないと思いますが、解けるようになっておくと安心です。\n問題が、等差数列なのか等比数列なのか階差数列なのか、法則性は何なのか、何を数列として考えているのか。たくさんのことを聞いてきますが、一つずつ整理して、考えすぎないように解くのが大切です。\n\n\nそれぞれの分野について、簡単に説明しましたが、どの分野にも共通して言えるのは、基本的な公式は使えるようにしておこう。です。自分の知ってる公式の中に解くのに必要なものが無ければその問題は解けません。しっかりと使えるようにしましょう。\n\n\n是非参考になればと思います。"}],["$","div",null,{"className":"flex mb-1","children":[["$","svg",null,{"stroke":"currentColor","fill":"currentColor","strokeWidth":"0","viewBox":"0 0 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