📚 Vocabulary and Terminology Quick-Memory Guide for Year 10 CIE Further Mathematics | CIE 10年级进阶数学词汇术语速记指南
In Year 10 CIE Further Mathematics (often IGCSE Additional Mathematics 0606), mastering the terminology is just as important as solving equations. This quick-memory guide provides clever mnemonics, visual analogies, and concise English–Chinese explanations for essential vocabulary across all major topics. Let's boost your maths dictionary with fun and speed!
在CIE 10年级进阶数学（常对应IGCSE附加数学0606）中，掌握术语和解题同等重要。这份速记指南为各核心章节的关键词汇打造了巧妙的记忆法、直观类比和精炼的英中解释，帮助你快速扩张数学词库！
1. Functions: Core Concepts | 函数核心概念
A function is a rule that assigns every input exactly one output. To fix the idea, imagine a passport photo machine: you insert a coin (input) and always get a specific photo strip (output); you cannot get two different photos from the same action. Memory clue: "One input, one output – identity not in doubt!"
函数是一种映射规则，每个输入只有一个输出。记忆法：想象自动拍照机，塞入硬币（输入）只出来特定一版照片（输出），不会变出两样。口诀：“一入准一出，绝不迷糊。”
The domain an is the complete set of possible x-values that you can plug into a function without breaking maths rules (e.g., no division by zero). Think of "domain" as the king's domain – only allowed territories. Quick trick: Domain = x-zone, the land where the formula lives.
定义域是允许代入函数的全体x值集合，要避开分母为零等禁区。关联记忆：“域”就是领地，定义域就是x能合法活动的范围。口诀：“定义域，x的领地图。”
The range is all the y-values (outputs) that actually come out of the function. Visualise a rocket's range – the height it reaches. Memory tip: Range = y-values that "arrange" themselves along the y-axis. To find range, ask "what y-values appear on the graph?"
值域是函数实际吐出的所有y值（输出）。想象火箭的射程——能够到达的高度。记忆法：“值域”是纵轴上的y值分布。找值域时问自己：“图上能看到哪些y？”
A composite function fg(x) means f(g(x)) – you apply g first, then f. Use the cake analogy: g is baking the cake, f is adding icing. Order matters! Mnemonic: "Rightmost function works first; read from the inside out." Or think "g before f – ghost then fog."
复合函数 fg(x) 意即 f(g(x))——先执行 g，再执行 f。类比做蛋糕：g 是烤蛋糕底，f 是抹奶油。顺序不可颠倒！助记：“最右的函数最先做，从里向外
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