📚 ACT Math: Core Vocabulary Handbook | ACT 数学：核心词汇手册
Mastering ACT Math isn’t just about solving problems—it’s about understanding the language used in the questions. A strong command of key mathematical terms in English can dramatically improve your speed and accuracy. This handbook covers essential vocabulary that frequently appears on the ACT, organized by topic, with clear definitions and examples to help you succeed on test day.
攻克 ACT 数学不仅仅在于解题技巧，更在于理解题目中使用的语言。熟练掌握关键的英文数学术语可以显著提高你的解题速度和准确率。本手册涵盖了 ACT 考试中频繁出现的核心词汇，按主题分类，附带清晰的定义和示例，助你在考试中取得佳绩。
1. Number and Operations | 数与运算
Integer: A whole number that can be positive, negative, or zero. Examples: -3, 0, 7. Integers do not include fractions or decimals.
整数：可以是正数、负数或零的整数。例如：-3, 0, 7。整数不包括分数或小数。
Rational number: Any number that can be expressed as a fraction a/b where a and b are integers and b ≠ 0. This includes repeating and terminating decimals.
有理数：可以表示为分数 a/b 的任何数，其中 a 和 b 是整数且 b ≠ 0。包括循环小数和有限小数。
Factor: A number that divides another number exactly without leaving a remainder. For instance, 3 is a factor of 12.
因数：能整除另一个数而不留余数的数。例如，3 是 12 的因数。
Multiple: The result of multiplying a number by an integer. For example, multiples of 5 are 5, 10, 15, 20…
倍数：一个数乘以整数得到的结果。例如，5 的倍数有 5, 10, 15, 20……
Prime number: A positive integer greater than 1 that has exactly two distinct positive factors: 1 and itself. Examples include 2, 3, 5, 7, 11.
质数：大于 1 的正整数，恰好有两个不同的正因数：1 和它本身。例如 2, 3, 5, 7, 11。
Absolute value: The distance of a number from zero on the number line, always nonnegative. Written as |x|. | -4 | = 4.
绝对值：数在数轴上到零的距离，始终为非负值。记作 |x|。| -4 | = 4。
2. Algebra Essentials | 代数基础
Variable: A symbol, usually a letter, used to represent an unknown or changing quantity. In the expression 2x + 5, x is the variable.
变量：一个符号，通常是字母，用来表示未知或变化的量。在表达式 2x + 5 中，x 是变量。
Coefficient: The numerical factor multiplied by a variable in an algebraic term. In 7y, 7 is the coefficient.
系数：代数项中乘以变量的数字因子。在 7y 中，7 是系数。
Constant: A fixed value that does not change. In the polynomial x² – 3x + 8, 8 is a constant term.
常数：一个固定不变的值。在多项式 x² – 3x + 8 中，8 是常数项。
Expression: A combination of numbers, variables, and operations that represents a value. 2a + 5b is an expression; it does not contain an equals sign.
表达式：由数字、变量和运算组成的，表示一个值的式子。2a + 5b 是一个表达式；它不含等号。
Like terms: Terms that have exactly the same variable parts raised to the same powers. 3x and -7x are like terms and can be combined.
同类项：具有完全相同变量部分且指数相同的项。3x 和 -7x 是同类项，可以合并。
Polynomial: An algebraic expression consisting of one or more terms, each with nonnegative integer exponents. Examples: 5x³ – 2x + 1.
多项式：由一个或多个项组成的代数表达式，每项的指数均为非负整数。例如：5x³ – 2x + 1。
3. Equations and Inequalities | 方程与不等式
Equation: A mathematical statement that two expressions are equal, using the = sign. 2x + 3 = 11 is an equation.
方程：一个表明两个表达式相等的数学陈述，使用等号。2x + 3 = 11 是一个方程。
Solution: A value that makes an equation or inequality true. For x + 5 = 9, the solution is x = 4.
解：使方程或不等式成立的值。对于 x + 5 = 9，解为 x = 4。
Inequality: A relation comparing two expressions using signs like <, >, ≤, ≥, or ≠. x > 7 means x is greater than 7.
不等式：使用 <, >, ≤, ≥ 或 ≠ 等符号比较两个表达式的关系。x > 7 表示 x 大于 7。
System of equations: A set of two or more equations with the same variables, solved simultaneously. Example: y = 2x and y = -x + 6.
方程组：包含两个或更多具有相同变量的方程，需要同时求解。例如：y = 2x 和 y = -x + 6。
Root: Another name for the solution of an equation, especially when an expression is set equal to zero. The roots of x² – 4 = 0 are x = ±2.
根：方程解的另一种叫法，特别是当表达式设为零时。x² – 4 = 0 的根是 x = ±2。
4. Functions and Graphs | 函数与图像
Function: A relation where each input (x) has exactly one output (y). Often written as f(x). f(x) = x + 2 is a function.
函数：每个输入 (x) 恰好对应一个输出 (y) 的关系。常写作 f(x)。f(x) = x + 2 是一个函数。
Domain: The set of all possible input values (x-values) for which a function is defined.
定义域：函数有定义的所有可能输入值（x 值）的集合。
Range: The set of all possible output values (y-values) that a function can produce.
值域：函数能产生的所有可能输出值（y 值）的集合。
Slope: The measure of steepness of a line, calculated as rise over run (change in y / change in x). In y = mx + b, m is the slope.
斜率：直线陡峭程度的度量，计算公式为纵向变化/横向变化（y 的变化/x 的变化）。在 y = mx + b 中，m 是斜率。
Intercept: The point where a graph crosses an axis. The y-intercept of y = 2x – 3 is -3.
截距：图形与坐标轴相交的点。y = 2x – 3 的 y 截距是 -3。
Vertex: The highest or lowest point on a parabola. For f(x) = (x – 1)² + 2, the vertex is (1, 2).
顶点：抛物线上的最高点或最低点。对于 f(x) = (x – 1)² + 2，顶点为 (1, 2)。
5. Geometry Fundamentals | 几何基础
Perimeter: The total distance around the outside of a shape. The perimeter of a square with side s is 4s.
周长：围绕形状外部的总距离。边长为 s 的正方形的周长是 4s。
Area: The amount of space inside a two‑dimensional figure. Area of a rectangle = length × width.
面积：二维图形内部的空间大小。矩形的面积 = 长 × 宽。
Circumference: The distance around a circle, equal to 2πr or πd, where r is radius and d is diameter.
圆周长：围绕圆的距离，等于 2πr 或 πd，其中 r 是半径，d 是直径。
Hypotenuse: The longest side of a right triangle, opposite the right angle. In a 3-4-5 triangle, the hypotenuse is 5.
斜边：直角三角形中最长的边，与直角相对。在 3-4-5 三角形中，斜边为 5。
Congruent: Having the same size and shape. Two triangles are congruent if all corresponding sides and angles are equal.
全等：大小和形状相同。如果两个三角形的所有对应边和对应角都相等，则它们全等。
Parallel lines: Lines in a plane that never intersect and are always the same distance apart. Indicated by the symbol ∥.
平行线：平面内永不相交且距离始终相等的直线。用符号 ∥ 表示。
6. Coordinate Geometry | 坐标几何
Quadrant: One of the four regions of the coordinate plane divided by the x‑axis and y‑axis. Quadrant I has positive x and positive y.
象限：坐标平面被 x 轴和 y 轴分成的四个区域之一。第一象限中 x 和 y 均为正。
Midpoint: The point exactly halfway between two endpoints. The midpoint of (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
中点：两个端点正中间的点。(x₁, y₁) 和 (x₂, y₂) 的中点是 ((x₁+x₂)/2, (y₁+y₂)/2)。
Distance formula: Based on the Pythagorean theorem, the distance between two points is √[(x₂ – x₁)² + (y₂ – y₁)²].
距离公式：基于勾股定理，两点间的距离为 √[(x₂ – x₁)² + (y₂ – y₁)²]。
Reflection: A transformation that flips a figure over a line, creating a mirror image. Reflecting (3, 4) over the x-axis gives (3, -4).
反射：将图形沿一条直线翻转，产生镜像。将 (3, 4) 关于 x 轴反射得到 (3, -4)。
Translation: Sliding a figure without rotating or resizing it. Adding (2, -1) to each point shifts the figure right 2 and down 1.
平移：在不旋转或不改变大小的情况下滑动图形。将每个点加上 (2, -1) 使图形向右移 2、向下移 1。
7. Trigonometry | 三角学
Sine(sin): In a right triangle, the ratio of the length of the side opposite an angle to the hypotenuse. sin(θ) = opposite/hypotenuse.
正弦 (sin)：直角三角形中，一个角的对边长度与斜边长度的比值。sin(θ) = 对边/斜边。
Cosine(cos): Ratio of the adjacent side to the hypotenuse. cos(θ) = adjacent/hypotenuse.
余弦 (cos)：邻边与斜边的比值。cos(θ) = 邻边/斜边。
Tangent(tan): Ratio of the opposite side to the adjacent side. tan(θ) = opposite/adjacent. Also equals sin(θ)/cos(θ).
正切 (tan)：对边与邻边的比值。tan(θ) = 对边/邻边，也等于 sin(θ)/cos(θ)。
Radian: An alternative unit for measuring angles. One full circle = 2π radians, so 180° = π rad.
弧度：一种度量角的替代单位。一整圆 = 2π 弧度，因此 180° = π 弧度。
Unit circle: A circle with radius 1 centered at the origin, used to define trigonometric functions for all real numbers.
单位圆：以原点为圆心、半径为 1 的圆，用于定义所有实数的三角函数。
8. Statistics and Probability | 统计与概率
Mean: The average of a set of numbers, calculated by summing all values and dividing by the count.
平均数：一组数字的平均值，通过将所有值相加再除以个数来计算。
Median: The middle value when data is ordered from smallest to largest. If there is an even number of terms, the median is the average of the two middle numbers.
中位数：将数据从小到大排序后位于中间的值。若项数为偶数，则中位数是中间两个数的平均值。
Mode: The value that appears most frequently in a data set. A set may have one mode, more than one mode, or no mode.
众数：数据集中出现频率最高的值。一个数据集可能有一个众数、多个众数或没有众数。
Probability: A number between 0 and 1 that indicates how likely an event is to occur. Probability = (favorable outcomes) / (total outcomes).
概率：一个介于 0 和 1 之间的数，表示事件发生的可能性大小。概率 = (有利结果数) / (总结果数)。
Independent events: Two events where the occurrence of one does not affect the probability of the other. Rolling a die twice involves independent events.
独立事件：一个事件的发生不影响另一个事件概率的两个事件。掷两次骰子是独立事件。
9. Word Problems and Applications | 应用题与应用
Rate: A ratio comparing two related quantities measured in different units, often involving time. Example: miles per hour (mph).
率：比较两个以不同单位计量的相关量的比率，常涉及时间。例如：英里每小时 (mph)。
Proportion: An equation stating that two ratios are equal. If a/b = c/d, then ad = bc (cross multiplication).
比例式：表示两个比相等的方程。若 a/b = c/d，则 ad = bc（交叉相乘）。
Percent increase/decrease: The percentage change relative to the original amount. Percent change = (amount of change/original) × 100%.
百分比增加/减少：相对于原始数量的百分比变化。变化百分比 = (变化量/原始量) × 100%。
Interest: Money paid for the use of borrowed money. Simple interest: I = P × r × t, where P is principal, r is rate, t is time.
利息：因使用借入资金而支付的金钱。单利：I = P × r × t，其中 P 为本金，r 为利率，t 为时间。
Ratio: A comparison of two quantities by division. The ratio of a to b can be written as a:b or a/b.
比：通过除法对两个量进行比较。a 与 b 的比可写作 a:b 或 a/b。
10. Miscellaneous Key Terms | 其他关键术语
Exponent: A small number written as a superscript indicating how many times a base is multiplied by itself. In 2³, 3 is the exponent, meaning 2×2×2.
指数：写在右上角的数字，表示基数自乘的次数。在 2³ 中，3 是指数，意味着 2×2×2。
Square root: A value that, when multiplied by itself, gives the original number. √25 = 5 because 5×5 = 25.
平方根：一个值，当它乘以自身时得到原数。√25 = 5，因为 5×5 = 25。
Sequence: An ordered list of numbers, often following a pattern. Arithmetic sequences have a common difference; geometric sequences have a common ratio.
数列：按特定顺序排列的数，常遵循某种模式。等差数列有公差；等比数列有公比。
Matrix: A rectangular array of numbers arranged in rows and columns. Used on the ACT for addition, subtraction, and sometimes multiplication.
矩阵：按行和列排列的数字矩形阵列。ACT 考试中用于加法、减法，有时也用于乘法。
Complex number: A number of the form a + bi, where i = √(-1). ACT problems may require adding or multiplying complex numbers.
复数：形如 a + bi 的数，其中 i = √(-1)。ACT 题目可能要求对复数进行加减或乘法运算。
Published by TutorHao | ACT Math Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply