Module 4
Words That Become Inequality Signs.
不等号になる言葉 （Futōgō ni Naru Kotoba）
帰国子女・インターナショナルスクール生のための、デジタルSAT 数学の無料教材。独学で進められます。
| English | Symbol | 日本語 |
|---|---|---|
| at least / no fewer than / no less than / minimum | ≥ | 以上 |
| at most / no more than / no greater than / maximum | ≤ | 以下 |
| more than / greater than / exceeds | > | より大きい（超） |
| less than / fewer than / below | < | 未満 |
The "no" flips your instinct, not the sign. "No more than 10" feels like a restriction and students reach for <. It means ≤ 10 — ten is allowed. Read "no more than X" as "X is the ceiling, and X is fine."
日本人がハマる理由
この区別は日本語のほうが正確です。以上 / 以下 は境界を含み、超 / 未満 は境界を含みません。境界を含むかどうかで迷うことがありません。英語は no fewer than、no less than、no more than、no greater than のように似た形の句で言い分けるので、見分けにくいです。しかも日常会話の at least は、数学の at least よりも意味がゆるいです。対応そのものは例外なく決まっていて、覚えきれる量です — 以上 = at least、未満 = less than — ただし表として覚えてください。英語の会話で身についた感覚からは出てこないからです。
練習問題
難易度は出題者による目安です。College Board の判定ではありません。
A student needs at least 240 points to pass a course. She currently has 180 points, and each remaining assignment is worth 15 points. What is the minimum number of additional assignments she must complete?
Correct Answer: B
Explanation: 180 + 15n ≥ 240 → 15n ≥ 60 → n ≥ 4. The minimum is 4.
- (A) 3:
180 + 45 = 225, which is below 240. Off by one — always substitute your answer back. - (C) 5: Correct if the requirement were "more than 240". Because "at least" includes 240 exactly, 4 is enough.
- (D) 16: From
240 ÷ 15— the 180 points she already has were ignored.
Difficulty Justification
Rated Medium. Choice C exists solely to punish reading "at least" as "more than"; both A and C are one step from correct.
A delivery van can carry no more than 1,200 kilograms. It is already loaded with 450 kilograms of equipment. If each box weighs 25 kilograms, what is the greatest number of boxes that can be added?
Correct Answer: B
Explanation: 450 + 25b ≤ 1200 → 25b ≤ 750 → b ≤ 30. The greatest number is 30.
- (A) 18: From
450 ÷ 25— the number of boxes equivalent to the existing load, not the space remaining. - (C) 48: From
1200 ÷ 25— the capacity of an empty van. The words "already loaded" were skipped. - (D) 66: From
(1200 + 450) ÷ 25— the existing load was added to the limit instead of subtracted from it.
Difficulty Justification
Rated Medium. Every distractor is a clean division of two numbers that appear in the problem, which is what makes them attractive when time is short.
A club must have no fewer than 12 members in order to compete. It currently has 7 members. What is the least number of new members who must join for the club to compete?
Correct Answer: B
Explanation: "No fewer than 12" means ≥ 12. 7 + m ≥ 12 → m ≥ 5.
- (A) 4: Leaves the club at 11 members, below the requirement.
- (C) 6: Correct only if 12 itself were not enough — that is, if the rule said "more than 12". "No fewer than" includes 12.
- (D) 19: From
7 + 12— added the two numbers given instead of finding the gap between them.
Difficulty Justification
Rated Easy. Included because "no fewer than" contains two negative-sounding words and still means 以上.