IGCSE CCEA Further Mathematics: Key Terminology Memory Guide | IGCSE CCEA 进阶数学：词汇术语速记指南

📚 IGCSE CCEA Further Mathematics: Key Terminology Memory Guide | IGCSE CCEA 进阶数学：词汇术语速记指南

In CCEA IGCSE Further Mathematics, precise terminology is not just useful for communication – it is frequently tested directly in wording and definitions. Building a quick-recognition vocabulary allows you to interpret questions faster and avoid losing marks through avoidable confusion.

在 CCEA IGCSE 进阶数学中，准确术语不仅有助于表达，还经常直接出现在题干与定义考查中。建立快速识别的词汇库，可以让你更快读懂题目，避免因概念混淆而失分。

1. Algebraic Expressions and Manipulation | 代数表达式与运算

In algebra, a term is a single number, variable, or product of both. Like terms can be combined because they have identical variable parts. The coefficient is the numerical factor in a term.

在代数中，项是单个数字、变量或两者的乘积。同类项因为变量部分完全相同，可以合并。系数是项中的数字因子。

Key commands include expand (remove brackets by multiplication) and factorise (put brackets back by finding common factors or using patterns). The factor theorem states that (x − a) is a factor of polynomial f(x) if f(a) = 0.

关键指令包括展开（通过乘法去括号）和因式分解（通过提取公因式或使用公式重新添加括号）。因式定理指出，若 f(a) = 0，则 (x − a) 是多项式 f(x) 的因式。

The discriminant of ax² + bx + c is b² − 4ac. It tells you the nature of roots: positive gives two real roots, zero gives one repeated root, negative gives no real roots.

二次式 ax² + bx + c 的判别式是 b² − 4ac。它判断根的性质：正数有两个实根，零有一个重根，负数没有实根。

Memory aid: think of a coefficient as the number ‘riding in front’ of a variable; like terms wear the same variable ‘outfit’.

记忆技巧：把系数看作变量前面 ‘骑乘’ 的数字；同类项穿同样的变量 ‘外衣’。

2. Functions and Graphs | 函数与图像

A function maps each input from the domain to exactly one output in the range. The notation f(x) means the output of function f for input x.

函数将定义域中的每个输入对应到值域中的唯一输出。记号 f(x) 表示函数 f 对输入 x 的输出。

Composite functions apply one function after another: fg(x) means f(g(x)). The inverse function f⁻¹(x) reverses the effect of f(x); swap x and y and solve for y.

复合函数是指连续应用两个函数：fg(x) 即 f(g(x))。反函数 f⁻¹(x) 将 f(x) 的效果逆转：交换 x 与 y

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