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og, g, pbm, 15, ym, cp, 0, be, 9, 大阪府公立高校入試2020年数学C問題1-7 | 熊野塾

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大阪府公立高校入試2020年数学C問題1-7

2020年3月13日 塾長からの挑戦状

今年も出ました。整数問題です。C問題では毎年必ず出題されるんですが,一度見たような,どっかで解いたことのあるような問題は絶対に出題されません。毎年本当に良く吟味されていると思います。それだけに整数の性質について本当に理解できているかが問われる良問がそろっています。

今年の問題は条件に「素数である」が入りました。これがなかなか厄介なんです。まずは式で表せる「93の倍数」という条件でnを表し,n-780がどうなるかやってみるところまではできた人も多いかと思いますが,そのあとが問題でしたね。素数は式で表すことができませんから,この条件をどうさばくかで悩んだ受験生も多かったでしょう。素数は素因数分解できませんから,2数の積で表すなら「1×素数」にしかならないというところがポイントでした。

それでは解説です。

 

 

途中で1240が出てきたとき,とりあえず素因数分解してみると31でくくれるということに気づきます。あとは「1×素数」に気づけば,正解にたどり着けたでしょう。もちろん,k=13のあとは,n=31+780でもOKです。

整数問題は,その問題のポイントさえ気づけば計算自体は難しくありません。C問題受験生には是非得点源としてほしいところです。