Module 10
Captions, Axes, and Units.
見出し・軸・単位 （Midashi, Jiku, Tan'i）
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。
On a data question, the numbers in the table are rarely the whole story. The constraint that changes your answer is usually written in small text above or beside it: in thousands, per capita, in millions of dollars, ages 18–24 only.
Read the caption and both axis labels before you look at a single number. Five seconds spent there protects every calculation that follows.
日本人がハマる理由
日本語の表は、単位を見出しの中に短くはっきり書きます。「単位：千円」のように枠で囲まれていることが多く、見落としようがありません。英語はそれを見出しの中にまとめず、小文字のイタリック体の一句 "in thousands of dollars" として外に置きます。指示ではなく caption（説明書き）に見えます。時間に追われて数字だけを目で追っている受験生は、これが目に入りません。そのあとの答えは、すべて 1,000 倍ずれます。
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 table titled "Company Revenue (in thousands of dollars)" lists the company's revenue as 45 in 2022 and 52 in 2023. By how many dollars did the company's revenue increase from 2022 to 2023?
Correct Answer: C
Explanation: 52 − 45 = 7, and the units are thousands of dollars, so the difference is 7 × 1,000 = $7,000.
- (A) $7: The subtraction is right; the caption was never read. This is the answer the question is built to catch.
- (B) $700: Scaled by 100 rather than 1,000.
- (D) $70,000: Scaled by 10,000.
Difficulty Justification
Rated Medium. The arithmetic is a single subtraction a child could do; the entire difficulty is the four words "in thousands of dollars" in the table's title.
A graph shows distance travelled, in kilometres, on the vertical axis and time, in hours, on the horizontal axis. The line passes through the points (2, 90) and (4, 180). What does the slope of the line represent?
Correct Answer: A
Explanation: Slope is vertical over horizontal, so its units are kilometres ÷ hours — kilometres per hour, which is speed. Numerically (180 − 90)/(4 − 2) = 45 km/h.
- (B) Total distance: That is a value read off the vertical axis, not a rate of change.
- (C) Total time: A value on the horizontal axis.
- (D) Hours per kilometre: The inverted slope — horizontal over vertical. Compare Module 6.
Difficulty Justification
Rated Medium. You can answer it from the axis labels alone, without computing anything: the units of the slope are the units of the answer.
A table lists the mass of several samples in grams. One sample is listed as 2,500. What is the mass of this sample in kilograms?
Correct Answer: B
Explanation: 1,000 grams = 1 kilogram, so 2,500 ÷ 1,000 = 2.5 kg.
- (A) 0.25: Divided by 10,000.
- (C) 25: Divided by 100.
- (D) 2,500,000: Multiplied by 1,000 instead of divided. A kilogram is larger than a gram, so the number must get smaller.
Difficulty Justification
Rated Easy. The direction check — bigger unit, smaller number — eliminates D instantly and is worth applying to every conversion.