📚 ACT Math Essential English Vocabulary Summary | ACT 数学必考英文词汇总结
Mastering the English vocabulary used in ACT Math questions is critical for achieving a high score. Ambiguous terms such as “product”, “integer”, or “hypotenuse” can easily derail your calculations if you misunderstand them. This comprehensive guide organizes the must-know ACT Math terms into clear categories, providing bilingual English-Chinese explanations to help you quickly decipher every problem on test day.
掌握 ACT 数学题目中使用的英语词汇是取得高分的关键。像 “product”（乘积）、”integer”（整数）或 “hypotenuse”（斜边）这类模糊术语，一旦误解就可能让你的计算全部白费。本指南将必考的 ACT 数学术语整理成清晰的类别，并提供中英双语解释，帮助你在考试当天迅速破译每道题目。
1. Basic Number Types and Properties | 基本数的类型和性质
Integer: A whole number that can be positive, negative, or zero, containing no fractional or decimal part. For example, -5, 0, 12 are integers, but 3.14 and 2/3 are not.
整数：一个可以是正数、负数或零的完整数字，不含分数或小数部分。例如，-5、0、12 是整数，但 3.14 和 2/3 不是。
Even / Odd: An even number is any integer divisible by 2 (e.g., 4, 16, -2), while an odd number is an integer not divisible by 2 (e.g., 7, 13, -5).
偶数 / 奇数：偶数是任何能被 2 整除的整数（如 4、16、-2），而奇数是不能被 2 整除的整数（如 7、13、-5）。
Prime Number: A positive integer greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, 11. Note that 1 is not prime.
质数（素数）：一个大于 1 的正整数，除了 1 和它自身外没有其他正约数。例如 2、3、5、7、11。注意 1 不是质数。
Rational / Irrational: A rational number can be expressed as a fraction p/q where p and q are integers and q ≠ 0 (e.g., 3/4, 0.5, -2). An irrational number cannot be written as a simple fraction (e.g., √2, π).
有理数 / 无理数：有理数可以表示为分数 p/q，其中 p 和 q 是整数且 q ≠ 0（如 3/4、0.5、-2）。无理数不能写成简单分数（如 √2、π）。
Factor / Multiple: A factor of a number divides it evenly without a remainder. A multiple is the product of that number and an integer. For instance, 3 is a factor of 12, and 12 is a multiple of 3.
因数 / 倍数：一个数的因数是能整除该数且没有余数的数。倍数则是该数与整数的乘积。例如，3 是 12 的因数，12 是 3 的倍数。
2. Arithmetic Operations and Relations | 算术运算和关系
Sum, Difference, Product, Quotient: The sum is the result of addition; difference is the result of subtraction; product is the result of multiplication; quotient is the result of division.
和、差、积、商：和是加法的结果；差是减法的结果；积是乘法的结果；商是除法的结果。
Remainder: The amount left over after dividing one integer by another. When 17 is divided by 5, the quotient is 3 and the remainder is 2 (since 17 = 5 x 3 + 2).
余数：一个整数除以另一个整数后剩下的部分。17 除以 5，商为 3，余数为 2（因为 17 = 5 x 3 + 2）。
Divisible: An integer a is divisible by b if the quotient a/b is an integer and the remainder is 0. For example, 24 is divisible by 6, but 24 is not divisible by 5.
整除：若整数 a 除以 b 的商是整数且余数为 0，则 a 能被 b 整除。例如，24 能被 6 整除，但 24 不能被 5 整除。
Square Root / Cube Root: The square root of a number x is a value r such that r² = x, denoted √x. The cube root satisfies r³ = x, written ³√x. For instance, √25 = 5, ³√8 = 2.
平方根 / 立方根：数 x 的平方根是满足 r² = x 的值 r，记作 √x。立方根满足 r³ = x，写作 ³√x。例如 √25 = 5，³√8 = 2。
Absolute Value: The distance of a number from zero on the number line, always nonnegative. Denoted by vertical bars: |−7| = 7, |5| = 5.
绝对值：一个数在数轴上到零的距离，总是非负值。用竖线表示：|−7| = 7，|5| = 5。
Inequality Symbols: “>” means greater than, “<" means less than, "≥" means greater than or equal to, "≤" means less than or equal to. For example, x ≥ 3 means x is at least 3.
不等式符号：”>” 表示大于，”<" 表示小于，"≥" 表示大于或等于，"≤" 表示小于或等于。例如，x ≥ 3 表示 x 至少为 3。
3. Fractions, Decimals, and Percentages | 分数、小数和百分比
Fraction, Numerator, Denominator: A fraction represents a part of a whole. The numerator (top) indicates how many parts are taken; the denominator (bottom) indicates the total number of equal parts. In 3/8, 3 is the numerator, 8 is the denominator.
分数、分子、分母：分数表示整体的一部分。分子（上方）表示取了多少份；分母（下方）表示整体被分成的等份数。在 3/8 中，3 是分子，8 是分母。
Improper Fraction / Mixed Number: An improper fraction has a numerator larger than or equal to its denominator (e.g., 7/4). A mixed number combines a whole number and a proper fraction (e.g., 1 3/4). They represent the same quantity.
假分数 / 带分数：假分数的分子大于或等于分母（如 7/4）。带分数由整数和真分数组成（如 1 3/4）。两者表示相同的量。
Percent Increase / Decrease: The percent change relative to the original amount. Percent increase = (New – Original) / Original x 100%; percent decrease = (Original – New) / Original x 100%.
百分比增长 / 减少：相对于原始数量的百分比变化。增长百分比 = (新值 – 原值) / 原值 x 100%；减少百分比 = (原值 – 新值) / 原值 x 100%。
Ratio / Proportion: A ratio compares two quantities (e.g., 3:4). A proportion is an equation stating that two ratios are equal (e.g., a/b = c/d). Cross-multiplication is often used to solve proportions.
比率 / 比例：比率比较两个数量（如 3:4）。比例是表明两个比率相等的等式（如 a/b = c/d）。常用交叉相乘来求解比例问题。
4. Algebra and Equations | 代数和方程
Variable, Constant, Coefficient: A variable is a symbol (often x or y) that represents an unknown value. A constant is a fixed number. A coefficient is a number multiplying a variable. In 5x + 3, 5 is the coefficient, x is the variable, and 3 is the constant.
变量、常量、系数：变量是表示未知值的符号（通常为 x 或 y）。常量是固定的数字。系数是乘以变量的数字。在 5x + 3 中，5 是系数，x 是变量，3 是常量。
Expression vs. Equation: An expression is a combination of numbers, variables, and operations (e.g., 2x + 5). An equation states that two expressions are equal using an equals sign (e.g., 2x + 5 = 11).
表达式与方程：表达式是数字、变量和运算的组合（如 2x + 5）。方程通过等号表明两个表达式相等（如 2x + 5 = 11）。
Quadratic Equation: An equation of the form ax² + bx + c = 0, where a ≠ 0. Solutions are often found by factoring, completing the square, or using the quadratic formula.
二次方程：形式为 ax² + bx + c = 0 的方程，其中 a ≠ 0。通常通过因式分解、配方法或二次公式求解。
Slope and y-intercept: The slope of a line measures its steepness, often represented as m in y = mx + b. The y-intercept is the point where the line crosses the y-axis (0, b).
斜率和 y 截距：直线的斜率衡量其倾斜程度，常在 y = mx + b 中用 m 表示。y 截距是直线与 y 轴相交的点 (0, b)。
y = mx + b
System of Equations: A set of two or more equations with the same variables. The solution satisfies all equations simultaneously. Methods to solve include substitution and elimination.
方程组：一组含有相同变量的两个或更多方程。其解同时满足所有方程。解法包括代入法和消元法。
5. Geometry Vocabulary | 几何词汇
Point, Line, Line Segment, Ray: A point is an exact location. A line extends infinitely in both directions. A line segment is part of a line between two endpoints. A ray has one endpoint and extends infinitely in one direction.
点、直线、线段、射线：点是精确的位置。直线向两端无限延伸。线段是直线上两点之间的部分，有两个端点。射线有一个端点，并向一个方向无限延伸。
Angle Types: Acute, Right, Obtuse: An acute angle measures less than 90°. A right angle is exactly 90°. An obtuse angle measures more than 90° but less than 180°.
角度类型：锐角、直角、钝角：锐角小于 90°。直角恰好等于 90°。钝角大于 90° 但小于 180°。
Parallel / Perpendicular: Parallel lines never intersect and have the same slope. Perpendicular lines intersect at a right angle (90°) and their slopes are negative reciprocals.
平行 / 垂直：平行线永不相交，斜率相等。垂直线相交成直角（90°），它们的斜率为负倒数。
Triangle Types: Equilateral (all sides equal, all angles 60°), isosceles (at least two sides equal), scalene (no sides equal). Right triangle has one 90° angle.
三角形类型：等边三角形（所有边相等，所有角为 60°），等腰三角形（至少两边相等），不等边三角形（没有边相等）。直角三角形有一个 90° 角。
Quadrilaterals: Square (four equal sides, four right angles), rectangle (opposite sides equal, four right angles), parallelogram (opposite sides parallel), trapezoid (at least one pair of parallel sides).
四边形：正方形（四条边相等，四个直角），矩形（对边相等，四个直角），平行四边形（对边平行），梯形（至少有一对平行边）。
Circle: radius (distance from center to circle), diameter (twice the radius, through center), circumference (distance around, 2πr), area (πr²).
圆：半径（圆心到圆周的距离），直径（通过圆心的两倍半径），周长（圆的一圈，2πr），面积（πr²）。
Circumference = 2πr, Area = πr²
Perimeter, Area, Volume: Perimeter is the distance around a 2D shape. Area is the amount of surface it covers. Volume is the space inside a 3D object.
周长、面积、体积：周长是二维图形边界的总长度。面积是其覆盖的表面大小。体积是三维物体内部的空间。
Hypotenuse and Legs: In a right triangle, the hypotenuse is the side opposite the right angle (the longest side). The legs are the other two sides.
斜边和直角边：在直角三角形中，斜边是直角对边（最长的边）。直角边是另外两条边。
c² = a² + b²
6. Coordinate Geometry | 坐标几何
Coordinate Plane, x-axis, y-axis, Origin: The coordinate plane consists of a horizontal x-axis and a vertical y-axis intersecting at the origin (0, 0). Points are located by ordered pairs.
坐标平面、x 轴、y 轴、原点：坐标平面由水平的 x 轴和垂直的 y 轴组成，它们在原点 (0, 0) 处相交。点用有序对定位。
Ordered Pair: A pair (x, y) that gives the coordinates of a point. x is the horizontal position, y is the vertical position.
有序对：给出点的坐标的对 (x, y)。x 是水平位置，y 是垂直位置。
Slope Formula: The slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is (y₂ – y₁) / (x₂ – x₁).
斜率公式：通过点 (x₁, y₁) 和 (x₂, y₂) 的直线的斜率 m 为 (y₂ – y₁) / (x₂ – x₁)。
Distance Formula: Distance between two points = √[(x₂ – x₁)² + (y₂ – y₁)²].
距离公式：两点间距离 = √[(x₂ – x₁)² + (y₂ – y₁)²]。
Midpoint: The midpoint of a segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).
中点：端点为 (x₁, y₁) 和 (x₂, y₂) 的线段的中点为 ((x₁ + x₂)/2, (y₁ + y₂)/2)。
7. Statistics and Probability | 统计和概率
Mean, Median, Mode, Range: Mean is the average (sum / count). Median is the middle value when data are ordered. Mode is the most frequent value. Range is the difference between maximum and minimum.
平均数、中位数、众数、极差：平均数是总和除以个数。中位数是数据排序后的中间值。众数是最频繁出现的值。极差是最大值与最小值的差。
Standard Deviation: A measure of how spread out numbers are from the mean. A low standard deviation means data points are close to the mean; high means they are spread out.
标准差：衡量数据偏离平均数程度的指标。标准差低表示数据点接近平均数；高则表示分散。
Probability: The likelihood of an event occurring, calculated as (number of favorable outcomes) / (total number of possible outcomes). Expressed as a fraction, decimal, or percentage between 0 and 1.
概率：事件发生的可能性，计算公式为（有利结果数）/（所有可能结果的总数）。用 0 到 1 之间的分数、小数或百分比表示。
Independent / Dependent Events: Independent events do not affect each other’s probability (e.g., rolling a die twice). Dependent events change the probability of the next event (e.g., drawing cards without replacement).
独立事件 / 相关事件：独立事件不影响彼此的概率（如掷两次骰子）。相关事件会改变后续事件的概率（如不放回地抽牌）。
Combination / Permutation: Combination counts selections where order does not matter (e.g., choosing a committee). Permutation counts arrangements where order matters (e.g., ranking winners).
组合 / 排列：组合计算顺序无关的选择方式数（如选委员会）。排列计算顺序重要的安排方式数（如排名获奖者）。
8. Trigonometry | 三角学
Sine, Cosine, Tangent: Fundamental trigonometric ratios in a right triangle. sin(θ) = opposite / hypotenuse, cos(θ) = adjacent / hypotenuse, tan(θ) = opposite / adjacent.
正弦、余弦、正切：直角三角形中的基本三角比。sin(θ) = 对边 / 斜边，cos(θ) = 邻边 / 斜边，tan(θ) = 对边 / 邻边。
Opposite, Adjacent, Hypotenuse: For a given acute angle, the opposite side is across from the angle, the adjacent side is next to the angle (not the hypotenuse), and the hypotenuse is always the longest side.
对边、邻边、斜边：对于一个给定的锐角，对边是角对面的边，邻边是紧靠角的边（不是斜边），斜边始终是最长的边。
SOH CAH TOA: A mnemonic to remember the trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
SOH CAH TOA
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