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大阪府公立高校入試2007数学前期B「整数問題」

2019年5月23日 塾長からの挑戦状

大阪の公立高校入試,2007年の問題です。このときは入試が前期と後期の2回ありまして,前期のB問題とは文理科・理数科用の問題です。今のC問題相当と言えるでしょう。

昔から大阪では難易度の高い整数問題が出題されます。苦手とする人が多く,毎年無答率(空欄で提出する率)が高くなる問題です。反対に得意な人は「まず解ける」ので,ボーナス問題と化していることも少なくありません。

得意な人とそうでない人,何が違うのでしょうか。それはズバリ練習量です。私は普段,「解法の丸暗記はダメだ!」と言っていますが,整数問題に関してはある程度解法のパターンを知らないと「手も足も出ない」ということになりがちです。

この問題も慣れている人は確実に解けるでしょう。「数のペアを探すときは,2数の積の形で考えると候補を一気に絞ることができる」ということを知っているからです。こういった「数学マメ知識」を蓄積していくことが大事なのです。

それでは解説です。

整数問題は大学入試でもよく出題されます。得意になっておくと非常に心強いですよ。