公式、圖表同應用題:將數學變成清晰嘅英文

有個學生喺堂上做緊一個研究摘要簡報。塊投影片顯示一條整齊嘅公式:A = πr²。佢指住佢講:「A equals pi r two。」成個房靜咗一靜。佢嘅教授微笑住輕輕糾正:「A equals pi r squared。」呢個係一個音節嘅分別,但佢就係聽落流利同聽落似個讀緊屏幕符號嘅學生之間嘅分別。公式、圖表同應用題全部住喺同一區 —— 佢哋睇落似數學,但喺口語英文入面,佢哋需要字。識咗嗰啲字,就將一塊投影片變成一個故事。

點解呢樣嘢重要

量化英文出現喺講課、商務會議、實驗報告、新聞快訊,同埋幾乎每個量度口語同寫作嘅考試入面。學術整合題目、數據描述寫作題目,同好多企業面試都要求你用淺白嘅散文描述圖表。工程、財經同科學堂假設你可以好似讀一句句子噉大聲讀出一條方程式。如果你淨係識啲符號,你解到個問題但解釋唔到佢。如果你連啲字都識埋,你就可以教、簡報同說服 —— 而呢個就係量化領域入面真正流利嘅樣。

如果你仲未睇過 Percent、Percentage 同 Percentage Points:細細個字,大大個錯,留到睇完呢篇先睇 —— 圖表描述嘅成敗就喺嗰個 percent / percentage points 嘅區別。

規律

大聲讀公式。 數學符號全部都有英文名,而好多都好短易學。

• = 係 equals 或者 is。(A equals pi r squared. A is pi r squared.)
• + 係 plus 或者 and。(Two plus three. Two and three.)
• − 係 minus 或者 subtract。(Ten minus four.)
• × 係 times 或者 multiplied by。(Three times five. Three multiplied by five.)
• ÷ 係 divided by 或者 over。(Twelve divided by four. Twelve over four.)
• r² 係 r squared。r³ 係 r cubed。r⁴ 係 r to the fourth 或者 r to the power of four。
• √ 係 the square root of。∛ 係 the cube root of。
• π 係 pi,讀法似個甜品(pie)。
• ∞ 係 infinity。
• ( ) 係 parentheses(美)或者 brackets(英)。需要嗰陣大聲開合佢哋:「open parenthesis ... close parenthesis」。
• x / y 喺公式入面可以讀做 x over y 或者 x divided by y。
• |x| 係 the absolute value of x。

描述圖表。 一小撮動詞做晒大部分工夫。

• 嘢向 上:rise、climb、grow、increase、go up、jump、surge、soar。
• 嘢向 下:fall、drop、decline、decrease、go down、plunge、sink。
• 嘢保持平穩:remain stable、plateau、hold steady、stay the same、level off。
• 嘢搖擺:fluctuate、bounce around、go up and down。
• 嘢去到頂峰:reach a peak、hit a high of、top out at。
• 嘢跌到底:hit a low of、bottom out at。

然後加埋幅度同速度:sharp、steep、gradual、slight、modest、steady、rapid、dramatic。「Sales rose sharply。」「Profits declined gradually。」

拆解應用題。 應用題係匿埋咗方程式嘅故事。訣竅係去翻譯。

• of 好多時解 multiply:「twenty percent of fifty」= 0.20 × 50。
• per 解 divide 或者 for every:「miles per gallon」= miles ÷ gallons。
• total 解 add。
• difference 解 subtract。
• ratio of A to B 解 A divided by B(或者 A : B,睇語境)。
• out of 指向一個分母:「eighteen out of thirty」= 18/30。
• more than 同 less than 喺故事入面好多時解加同減,但佢哋可以好棘手。「Six more than twice a number」係 2x + 6,唔係 6 + 2x 倒轉。

錯誤 / 自然 / 點解

常見情境

喺堂上讀一條公式。 老師喺塊板寫 E = mc² 並講:「E equals m c squared — energy equals mass times the speed of light squared。」留意公式點樣一個符號一個符號噉讀,然後個意思用淺白嘅字重述一次。好嘅講者兩樣都做,因為淨係讀符號嘅版本聽落似機械人,而淨係講意思嘅版本就跳過咗數學。

描述一個折線圖。「The graph shows revenue from twenty twenty to twenty twenty-four. Revenue rose steadily from about two million to four million, peaking in twenty twenty-three at just over four point two. Then it dipped slightly to four million by the end of the period。」留意啲動詞(rose、peaking、dipped)同精確字眼(steadily、just over、slightly)。佢哋砌出幅圖畫而唔使確切數字。

比較兩個圖表。「While sales grew sharply in the first half, marketing spend stayed flat, which meant the profit margin widened. By contrast, in the second half, marketing climbed but sales leveled off。」比較字眼例如 while、by contrast、meanwhile 同 on the other hand 幫聽嘅人同時追蹤兩個趨勢。

帶過一條應用題。 一個導師解釋:「A train leaves a station at sixty miles per hour and another train leaves the same station two hours later at eighty. Let's call the time the second train travels t. We know the first train has a head start of two hours, so its distance is sixty times t plus two. The second train's distance is eighty t. For them to meet, those distances are equal。」呢個係將 大聲講解一個計算 嘅技巧套用喺代數上面。

讀一個圓餅圖。「Roughly half of the budget goes to salaries, about a quarter to rent, and the remaining quarter is split between marketing and supplies。」圓餅圖幾乎一定會將分數同百分比一齊用。溝埋 點樣講小數、分數同比例而唔會卡住,令呢種描述聽落自然。

描述一個有類別嘅條形圖。「Among the four product lines, A had the highest sales at just under ten million, followed by B at about seven, then C at five, and finally D at just over two。」例如 followed by、then、finally 同 the lowest 嘅字眼,將一個條形圖變成一個排名清單。

常犯嘅錯誤

• 將上標當作普通數字噉讀:讀 r two 而唔係 r²。標準讀法係 r squared / r cubed / r to the fourth。
• 喺圖表描述入面用 of 嚟講變化:rose of ten percent。正確介詞係 by。
• 將 sales、data 同 statistics 當作單數。喺商務同學術英文入面,sales 係複數(「sales are up」),而 data 越嚟越被接受為單數或者複數,但喺正式寫作通常係複數(「the data show」)。
• 喺動作動詞之後唔記得副詞。講咗 sales rose sharp 而唔係 sales rose sharply。
• 喺美式語境將 parentheses 叫做 brackets(或者相反)。兩個詞都存在,但喺唔同地區之間唔可以互換。
• 將 π 讀做 pie 而唔係 pi。佢哋喺英文讀音一樣,但寫法分開。淨係講「pi」。
• 喺應用題入面混淆 more than。「Six more than twice a number」係 2x + 6;「twice as many as six」係 2 × 6。
• 講咗 the chart says 而唔係 the chart shows。圖表 show、display、illustrate 或者 indicate —— 佢哋唔 say。
• 喺答案入面跳過單位。「The result is 30」空蕩蕩;「the result is 30 percent」或者「30 dollars」或者「30 square meters」先完整。

迷你練習

讀出每一項,命名晒所有符號,並好似一句句子噉讀啲數學。

1. A = πr² (the area of a circle).
2. The line graph rose ___ 20% in Q1 and then dropped ___ 10% in Q2. (Fill in the prepositions.)
3. Twenty percent ___ fifty ___ ten. (Fill in of and the equals word.)
4. (3 + 4)² = 49 (read it aloud).
5. Describe in one sentence: a bar chart where Product A sold 80 units, B sold 60, C sold 40, and D sold 20.

總結

數學英文有三層:符號(大聲讀做完整嘅字例如 squared、over、pi)、圖表動詞(rose、fell、plateaued,加埋副詞例如 sharply 或者 gradually),同埋 應用題翻譯(of 解乘、per 解除、out of 解一個分數)。當你流暢噉喺符號、圖表同故事之間穿梭,量化英文就唔再係一隻外語入面嘅一隻外語。每日練習讀一條公式同大聲描述一個圖表,幾個星期之內,你嘅數據簡報就會聽落似英文,而唔係數學嘅翻譯。

想喺真實嘅試題句子入面練習數字、量詞同單位?喺 ExamRift 開始練習。