📚 SAT2 Math: Categorized Vocabulary & Knowledge Connection | SAT2 数学：分类词汇与知识串联
Mastering SAT2 Math requires not only problem-solving skills but also a solid grasp of subject-specific terminology. This article categorizes essential vocabulary by topic and demonstrates how these terms connect core concepts, aiding both comprehension and exam performance. Each term is paired with its Chinese equivalent and contextual explanation to build a bilingual mathematical mindset.
掌握SAT2数学不仅需要解题技巧，还需要扎实掌握学科专用术语。本文按主题分类必要词汇，并展示这些术语如何串联核心概念，有助于理解和考试表现。每个术语都配有中文对应和背景解释，以构建双语数学思维。
1. Arithmetic & Number Theory | 算术与数论
Arithmetic and number theory form the foundation of all quantitative reasoning. Key terms such as integer, prime, rational, and absolute value are interdependent — prime factorization leads to GCD and LCM, and the real number system unifies rational and irrational numbers.
算术与数论是所有定量推理的基础。整数、质数、有理数、绝对值等关键术语相互依存——质因数分解引出最大公因数和最小公倍数，而实数系将有理数和无理数统一起来。
Integer: A whole number from the set {…, –2, –1, 0, 1, 2, …}. Integers are the building blocks of counting and support additive inverses.
整数：属于集合{…, –2, –1, 0, 1, 2, …}的整数。整数是计数的基本单元，并支持加法逆元。
Prime number: A positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself. Recognizing primes is essential for simplifying fractions and finding the greatest common divisor.
质数：大于1且恰好有两个不同正因数的正整数：1和自身。识别质数对于化简分数和求最大公因数至关重要。
Composite number: A positive integer with more than two positive divisors. Every composite can be factored into a unique product of primes, illustrating the Fundamental Theorem of Arithmetic.
合数：拥有多于两个正因数的正整数。每个合数都可以唯一分解为质数的乘积，这体现了算术基本定理。
Rational number: Any number that can be written as a fraction p/q where p and q are integers and q ≠ 0. Terminating and repeating decimals are rational, linking decimal notation to fractions.
有理数：任何可表示为分数p/q的数，其中p和q为整数且q≠0。有限小数和循环小数都是有理数，这建立了小数表示与分数之间的联系。
Irrational number: A real number that cannot be expressed as a ratio of two integers; its decimal expansion is non‑terminating and non‑repeating. Examples include √2 and π, which fill the gaps between rationals on the number line.
无理数：不能表示为两整数之比的实数；其小数展开无限不循环。例如√2和π，它们填补了数轴上有理数之间的空隙。
Absolute value: The distance of a number from zero on the real number line, denoted |x|. It is used to express magnitude without regard to sign, crucial in distance and error analysis.
绝对值：一个数在实数轴上到零的距离，记作|x|。它用于表示不考虑符号的量值，在距离和误差分析中至关重要。
2. Algebraic Foundations | 代数基础
Algebra introduces variables and symbols to generalize arithmetic. Mastering vocabulary such as variable, expression, equation, and the quadratic formula allows students to model and solve a wide range of problems.
代数引入变量和符号来推广算术。掌握变量、表达式、方程以及二次公式等词汇，使学生能够建模并解决各类问题。
Variable: A symbol, usually a letter, that represents an unknown or changeable quantity. Variables are central to forming expressions and equations.
变量：通常为字母的符号，代表未知或可变的量。变量是构建表达式和方程的核心。
Coefficient: A numerical factor multiplying a variable. In the term 5x², 5 is the coefficient. Coefficients determine the shape and scale of algebraic expressions.
系数：乘以变量的数值因子。在项5x²中，5是系数。系数决定了代数表达式的形状和比例。
Expression: A combination of numbers, variables, and operations without an equality sign. Algebraic expressions can be simplified, factored, or expanded.
表达式：由数字、变量和运算符号组成的式子，不含等号。代数表达式可以进行化简、因式分解或展开。
Equation: A mathematical statement that two expressions are equal, linked by “=”. Solving an equation involves finding the values of the variable that make the statement true.
方程：声明两个表达式相等的数学语句，用“=”连接。解方程就是找出使命题成立的变量值。
The quadratic formula provides the roots of any quadratic equation ax² + bx + c = 0.
二次公式给出任意二次方程 ax² + bx + c = 0 的根。
x = [–b ± √(b² – 4ac)] / (2a)
3. Functions and Graphs | 函数与图像
Functions describe relationships between quantities. Key vocabulary — domain, range, inverse, and the vertical line test — connects algebraic representation with graphical behavior.
函数描述量之间的关系。定义域、值域、反函数和垂直线检验等关键词汇将代数表示与图像行为联系起来。
Function: A rule that assigns each input exactly one output. Often denoted f(x), functions can be represented as equations, tables, or graphs.
函数：一种规则，为每个输入恰好指定一个输出。常记为f(x)，函数可以用方程、表格或图像表示。
Domain: The set of all possible input values (x) for which a function is defined. Identifying the domain prevents undefined operations like division by zero or negative radicands.
定义域：函数有定义的所有可能输入值（x）的集合。确定定义域可避免除以零或负根号等无意义操作。
Range: The set of all possible output values (f(x)) that result from using the domain. Understanding range helps predict the function’s values.
值域：由定义域得出的所有可能输出值（f(x)）的集合。理解值域有助于预测函数的取值。
Inverse function: A function that reverses the effect of the original function. If f and g are inverses, then f(g(x)) = x. Graphically, they are reflections across the line y = x.
反函数：逆转原函数作用的函数。若f与g互为反函数，则f(g(x)) = x。图像上，它们关于直线y = x对称。
Vertical line test: A graphical method to determine if a curve represents a function. If any vertical line intersects the graph more than once, the relation is not a function.
垂直线检验：判断曲线是否表示函数的图像方法。若任意垂直线与图像相交多于一次，则该关系不是函数。
4. Polynomials and Rational Functions | 多项式与有理函数
Polynomials are algebraic expressions with non‑negative integer exponents. The vocabulary of degree, root, factor theorem, and asymptote reveals the structure and behavior of polynomial and rational functions.
多项式是指数为非负整数的代数表达式。次数、根、因式定理和渐近线等词汇揭示了多项式与有理函数的结构和行为。
Polynomial: An expression of the form aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₀, where n is a non‑negative integer. Classified by degree, polynomials model curves of various shapes.
多项式：形如 aₙxⁿ + aₙ₋₁xⁿ⁻¹ + … + a₀ 的表达式，其中n为非负整数。按次数分类，多项式可模拟各种形状的曲线。
Degree: The highest exponent of the variable. A polynomial of degree 2 is quadratic, degree 3 is cubic. The degree determines the number of roots and overall graph shape.
次数：变量的最高指数。次数为2的是二次多项式，次数为3的是三次多项式。次数决定了根的个数和图像的整体形状。
Root (or zero): A value of x for which f(x) = 0. Roots correspond to x‑intercepts of the graph and are solutions to the equation f(x) = 0.
根（或零点）：使得f(x) = 0的x值。根对应图像的x轴截距，是方程f(x) = 0的解。
Factor theorem: x – a is a factor of a polynomial f(x) if and only if f(a) = 0. This theorem directly links roots to factorization.
因式定理：x – a 是多项式 f(x) 的因式当且仅当 f(a) =
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