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r, 大阪府公立高校入試2017数学C問題1-8 | 熊野塾

熊野塾

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大阪府公立高校入試2017数学C問題1-8

2018年6月9日 塾長からの挑戦状

 

史上最高の難易度(当社比)ともいわれる2017年のC問題より。今年の問題と比べても明らかに難しいと思います。ただ,整数問題自体が難しいので,そういう意味では標準的と言えるかもしれません。入試直前に赤本で過去問を見て,「こんなん無理!」と早々にあきらめてしまう人も多いですが,これをすてるなんてとんでもない!コツをつかめば意外とあっさり解けるので,特に理系の諸君には是非ともクリアしていただきたい問題です。

基本の手順としては,nを自然数kの関数として表し,「kが何かの倍数になっていないか」「kの最小値・最大値は何か」という視点で候補をしぼっていく・・・という感じです。「ルート〇〇が整数になるような・・・」も基本的には同じ考えですね。

それでは解答です。