Module 8
The Answer-Form Trap.
解答形式の罠 （Kaitō Keishiki no Wana）
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。
The SAT routinely asks for something one step past the variable you solved for: not x but 4x, not a but a + 3, not the length but the area. Your correct value for x is sitting there among the choices, waiting.
The habit that fixes this permanently. Before you start, underline the final few words of the question — "what is the value of 4x". When you reach an answer, read those words again before you select. This costs about three seconds and is the highest-return habit in SAT Math.
日本人がハマる理由
これは日本語の文法のせいではありません。原因は読む速度です。第二言語で解いているあいだは、注意の大半が問題設定の読み取りに取られます。そして計算が終わるころには、最後の what is the value of … の正確な言い回しが記憶から薄れています。必要なのは語学力ではなく手順です。解き始める前に、問われている量に線を引いておきます。そうすれば、あとで読み直すのに手間はかかりません。
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 2x − 5 = 11, what is the value of 4x?
Correct Answer: C
Explanation: 2x = 16 → x = 8 → 4x = 32.
- (A) 8: The value of x. Correct arithmetic, wrong quantity — and it is the answer a student who stops one step early will always land on.
- (B) 16: The value of
2x— stopping one step earlier still. - (D) 64: The value of
8x, from doubling once too often.
Difficulty Justification
Rated Easy as algebra. Every distractor is a genuine intermediate value from the correct solution path, which is exactly why this format is so effective against fast workers.
If x + y = 7, what is the value of 3x + 3y?
Correct Answer: D
Explanation: 3x + 3y = 3(x + y) = 3 × 7 = 21. You never need x and y individually.
- (A) 7: The value of
x + y, copied without applying the factor of 3. - (B) 10: From
7 + 3— the 3 was added rather than multiplied. - (C) "Cannot be determined": The real trap. It is true that x and y cannot be found separately, and a student who believes they must find them first will conclude the problem is unsolvable. When a question asks for an expression rather than a variable, look for the expression hiding inside it.
Difficulty Justification
Rated Hard. Choice C is supported by a correct observation that leads to the wrong conclusion — the most dangerous kind of distractor.
If 5a = 20, what is the value of a + 3?
Correct Answer: B
Explanation: a = 4, so a + 3 = 7.
- (A) 4: The value of a — one step short.
- (C) 20: A number from the problem.
- (D) 23: From
20 + 3— the 3 was added before dividing by 5.
Difficulty Justification
Rated Easy, included to make the pattern unmistakable: on the SAT, "what is the value of…" is very often not the variable in the equation.