Module 9
“In Terms Of”.
〜を使って表す （~o Tsukatte Arawasu）
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。
"Solve for x in terms of y" means: rearrange until x is alone on one side, and everything left on the other side is allowed to contain y. You are not finding a number. There is no number to find.
The phrase names your target. "x in terms of y" → the answer starts x = …. Scan the choices first: any choice that begins with the wrong variable can be eliminated without any algebra at all.
日本人がハマる理由
「in terms of」を短く言い換えられる決まった日本語はありません。一番近いのは 「yを使ってxを表す」 で、単語ではなく文の形をしています。この言い方を明示的に教わっていない生徒は、「in terms of」を「regarding」や「about」と同じ「〜に関して」くらいの漠然とした前置きだと思って読み飛ばし、楽に解けるほうの文字について解いてしまいます。この語句は飾りではありません。これが指示そのものです。
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。
If 3x + 2y = 12, what is x in terms of y?
Correct Answer: C
Explanation: 3x = 12 − 2y → x = (12 − 2y)/3.
- (B) x = 12 − 2y: The division by 3 was skipped.
- (A) y = (12 − 3x)/2: Algebraically correct — but it solves for y in terms of x, the exact reverse of the instruction. This is the trap the module exists for.
- (D) x = (2y − 12)/3: A sign error; this is the negative of the correct expression.
Difficulty Justification
Rated Medium. Choice A is fully valid algebra and will look right to anyone checking their work rather than the question. Read the instruction, then the choices, then work.
The perimeter of a rectangle is given by P = 2l + 2w. What is w in terms of P and l?
Correct Answer: D
Explanation: 2w = P − 2l → w = (P − 2l)/2. Check with P = 20, l = 3: w = 14/2 = 7, and 2(3) + 2(7) = 20. ✓
- (B) w = P − 2l: Division by 2 omitted.
- (C) w = (P − l)/2: The coefficient on l was dropped — it is
2l, notl, that is subtracted. - (A) w = 2(P − l): Multiplied by 2 instead of divided.
Difficulty Justification
Rated Medium. Substituting easy numbers at the end catches every distractor here in about fifteen seconds.
If y = 3x − 4, what is x in terms of y?
Correct Answer: A
Explanation: y + 4 = 3x → x = (y + 4)/3. Check with y = 11: x = 15/3 = 5, and 3(5) − 4 = 11. ✓
- (B) x = (y − 4)/3: Subtracted 4 instead of adding it. To undo "−4" you add 4.
- (C) x = 3y + 4: The 4 was moved correctly, but y alone was multiplied by 3, instead of the whole of
y + 4being divided by 3. - (D) x = 3(y + 4): Correct on the addition, inverted on the division.
Difficulty Justification
Rated Easy. Every operation must be undone in reverse order and with the opposite sign; substituting a number verifies it instantly.