AP/SAT2/ACT Math Essential English-Chinese Vocabulary | AP/SAT2/ACT 数学：必考英文词汇汇总

📚 AP/SAT2/ACT Math Essential English-Chinese Vocabulary | AP/SAT2/ACT 数学：必考英文词汇汇总

Mastering mathematical terminology in English is crucial for success in AP, SAT Subject Test Math Level 1 & 2, and ACT Math. A strong command of these terms helps you parse word problems accurately and avoid costly misunderstandings under time pressure. This guide organizes the must‑know vocabulary by topic and provides clear English definitions immediately followed by their Chinese equivalents. Whether you are a non‑native English speaker or simply need a quick review, this compilation will sharpen your exam readiness.

掌握英文数学术语对在AP、SAT2数学（一级和二级）和ACT数学考试中取得成功至关重要。牢固掌握这些词汇有助于准确解析应用题，避免在时间压力下产生代价高昂的误解。本指南按主题分类整理了必考词汇，每个术语先给出清晰的英文定义，紧接着提供对应的中文解释。无论你是非英语母语者还是需要快速复习，这份汇总都能提升你的备考状态。

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1. Algebra Basics & Expressions | 代数基础与表达式

Variable: A symbol, usually a letter, that represents an unknown numerical value which can change.

变量：一个符号，通常为字母，代表一个可变动的未知数值。

Constant: A fixed numerical value that does not change, such as 5 or −2.

常数：一个固定的数值，如5或−2，不会发生变化。

Coefficient: The numerical factor multiplying a variable in a term, e.g., 3 in 3x.

系数：项中与变量相乘的数字因子，例如3x中的3。

Expression: A combination of numbers, variables, and operation symbols without an equality or inequality sign, e.g., 2x + 5.

表达式：由数字、变量和运算符号组成的式子，不含等号或不等号，如 2x + 5。

Equation: A mathematical statement that asserts the equality of two expressions, usually containing an equals sign (=).

方程：断言两个表达式相等的数学陈述，通常包含等号 (=)。

Inequality: A statement that compares two expressions using <, >, ≤, or ≥ to indicate relative size.

不等式：使用 <、>、≤ 或 ≥ 比较两个表达式大小关系的陈述。

Term: A single number, variable, or product of numbers and variables separated by addition or subtraction, e.g., 4xy is a term.

项：通过加法或减法分隔的单个数字、变量或数字与变量的乘积，如 4xy 是一项。

Like terms: Terms that have identical variable parts raised to the same powers; only coefficients differ. 3x and −7x are like terms.

同类项：变量部分及其指数完全相同的项，仅系数不同。3x 和 −7x 是同类项。

Factor: A number or expression that divides another number or expression evenly. Also, to rewrite an expression as a product.

因数 / 因式分解：能被另一数或式子整除的数或式子。也可指将表达式写成乘积形式的过程。

Exponent: A superscript number that indicates how many times a base is multiplied by itself, e.g., in 2³, 3 is the exponent.

指数：上标数字，表示底数自乘的次数，如在 2³ 中，3 是指数。

Base: The number or expression that is raised to a power. In 5², 5 is the base.

底数：被乘方的数或表达式。在 5² 中，5 是底数。

Power: The result of raising a base to an exponent; also used to refer to the exponent itself (e.g., “to the power of 3”).

幂：底数被乘方后得到的结果；有时也指指数本身（如“3次幂”）。

Polynomial: An algebraic expression consisting of one or more terms with non‑negative integer exponents, e.g., 2x³ − x + 7.

多项式：由一项或多项组成、且指数为非负整数的代数表达式，如 2x³ − x + 7。

Binomial: A polynomial with exactly two terms, such as x + 4.

二项式：恰好有两项的多项式，如 x + 4。

Trinomial: A polynomial with exactly three terms, such as x² − 3x + 1.

三项式：恰好有三项的多项式，如 x² − 3x + 1。

Simplify: To rewrite an expression in its most compact or standard form by combining like terms, canceling, or reducing.

化简：通过合并同类项、约分或约简，将表达式改写为最紧凑或标准的形式。

Expand: To multiply out brackets and write an expression as a sum of terms, e.g., (x+2)(x−3) → x² − x − 6.

展开：将括号乘开并把表达式写成各项之和，如 (x+2)(x−3) → x² − x − 6。

Factorize: To break an expression down into a product of simpler factors, e.g., x² − 9 = (x−3)(x+3).

因式分解：将表达式分解为若干较简单因式的乘积，如 x² − 9 = (x−3)(x+3)。

Linear: Describes an equation or expression where the variable is raised only to the first power, producing a straight‑line graph.

线性：描述变量只出现一次幂的方程或表达式，其图像是一条直线。

Quadratic: Involving a variable squared; a quadratic expression has degree 2, e.g., 3x² + 2x − 1.

二次：涉及变量的平方；二次表达式的次数为2，如 3x² + 2x − 1。

Cubic: Involving a variable cubed; a cubic expression has degree 3.

三次：涉及变量的立方；三次表达式的次数为3。

Root / Solution: A value that, when substituted into an equation, makes the equation true. Also called a zero of a function.

根 / 解：代入方程后使等式成立的数值，也称作函数的零点。

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2. Geometry | 几何

Angle: The figure formed by two rays sharing a common endpoint; measured in degrees or radians.

角：由两条共端点的射线构成的图形，以度数或弧度度量。

Acute angle: An angle whose measure is less than 90°.

锐角：小于90°的角。

Right angle: An angle of exactly 90°, often indicated by a small square in diagrams.

直角：恰好90°的角，图中常用小正方形标识。

Obtuse angle: An angle greater than 90° but less than 180°.

钝角：大于90°但小于180°的角。

Straight angle: An angle of exactly 180°, forming a straight line.

平角：恰好180°的角，形成一条直线。

Complementary angles: Two angles whose measures sum to 90°.

余角：两个角的度数之和为90°。

Supplementary angles: Two angles whose measures sum to 180°.

补角：两个角的度数之和为180°。

Vertical angles: Opposite angles formed by two intersecting lines; they are always congruent.

对顶角：两条直线相交形成的对角；对顶角总是相等。

Adjacent angles: Two angles that share a common side and a common vertex, but do not overlap.

邻角：共享一条公共边和一个公共顶点且不重叠的两个角。

Parallel lines: Lines in a plane that never intersect; they have the same slope.

平行线：平面内永不相交的直线；它们具有相同的斜率。

Perpendicular lines: Lines that intersect at a right angle (90°).

垂直线：相交成直角（90°）的直线。

Polygon: A closed plane figure bounded by straight line segments. Triangles, quadrilaterals, and pentagons are polygons.

多边形：由线段围成的封闭平面图形。三角形、四边形和五边形都是多边形。

Triangle: A polygon with three sides. Types include equilateral, isosceles, scalene, right, acute, and obtuse triangles.

三角形：有三条边的多边形。类型包括等边三角形、等腰三角形、不等边三角形、直角三角形、锐角三角形和钝角三角形。

Quadrilateral: A polygon with four sides, such as square, rectangle, rhombus, parallelogram, trapezoid.

四边形：有四条边的多边形，如正方形、矩形、菱形、平行四边形和梯形。

Circle: The set of all points in a plane at a fixed distance (radius) from a given point (center).

圆：平面内到一定点（圆心）的距离等于定长（半径）的所有点的集合。

Radius: The distance from the center of a circle to any point on the circle; half the diameter.

半径：从圆心到圆周上任意一点的距离；直径的一半。

Diameter: A chord passing through the center of a circle; twice the radius.

直径：经过圆心的弦；半径的两倍。

Circumference: The distance around a circle; given by C = 2πr or πd.

圆周：圆的周长；公式为 C = 2πr 或 πd。

Chord: A line segment whose endpoints lie on the circle.

弦：端点均在圆周上的线段。

Tangent: A line that touches a circle at exactly one point, called the point of tangency.

切线：与圆恰好在一个点（切点）接触的直线。

Secant: A line that intersects a circle at two points.

割线：与圆相交于两点的直线。

Arc: A part of the circumference of a circle. A major arc is greater than 180°; a minor arc is less than 180°.

圆弧：圆周的一部分。优弧大于180°，劣弧小于180°。

Sector: A region bounded by two radii and their intercepted arc; resembles a “pizza slice”.

扇形：由两条半径及其所夹弧围成的区域，形似“披萨切片”。

Area: The measure of the amount of surface inside a closed 2‑D figure.

面积：二维封闭图形内部表面大小的度量。

Perimeter: The total distance around the outside of a 2‑D figure.

周长：二维图形外部边界的总长度。

Volume: The amount of space occupied by a 3‑D object, measured in cubic units.

体积：三维物体所占据空间的大小，以立方单位度量。

Surface area: The total area of all faces and surfaces of a 3‑D solid.

表面积：三维立体所有面的总面积。

Prism: A 3‑D solid with two parallel congruent polygonal bases and rectangular lateral faces.

棱柱：具有两个平行且全等多边形底面和矩形侧面的三维立体。

Cylinder: A 3‑D solid with two parallel congruent circular bases and a curved lateral surface.

圆柱：具有两个平行且全等的圆形底面和一个弯曲侧面的三维立体。

Pyramid: A polyhedron with a polygonal base and triangular lateral faces that meet at a common vertex.

棱锥：具有多边形底面、且各侧面为三角形并交于同一顶点的多面体。

Cone: A 3‑D solid with a circular base and a curved surface that tapers to a point (apex).

圆锥：具有圆形底面和一个逐渐收缩至一点（顶点）的曲面的三维立体。

Sphere: The set of all points in space at a fixed distance (radius) from a center point.

球体：空间内到一定点（球心）距离等于半径的所有点的集合。

Congruent: Figures that have exactly the same shape and size; denoted by ≅.

全等：形状和大小完全相同的图形，用 ≅ 表示。

Similar: Figures that have the same shape but not necessarily the same size; corresponding angles are equal and sides are proportional.

相似：形状相同但大小不一定相同的图形；对应角相等，对应边成比例。

Pythagorean theorem: In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².

勾股定理：直角三角形中，斜边的平方等于两直角边的平方和：a² + b² = c²。

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3. Trigonometry | 三角函数

Sine (sin): In a right triangle, the ratio of the length of the opposite side to the hypotenuse.

正弦 (sin)：直角三角形中对边与斜边的长度之比。

Cosine (cos): The ratio of the adjacent side to the hypotenuse.

余弦 (cos)：直角三角形中邻边与斜边之比。

Tangent (tan): The ratio of the opposite side to the adjacent side; also equal to sin/cos.

正切 (tan)：对边与邻边之比；也等于 sin/cos。

Cosecant (csc): The reciprocal of sine: 1/sin.

余割 (csc)：正弦的倒数：1/sin。

Secant (sec): The reciprocal of cosine: 1/cos.

正割 (sec)：余弦的倒数：1/cos。

Cotangent (cot): The reciprocal of tangent: 1/tan, or cos/sin.

余切 (cot)：正切的倒数：1/tan，或 cos/sin。

Hypotenuse: The longest side of a right triangle, opposite the right angle.

斜边：直角三角形中最长的边，直角所对的边。

Opposite side: The side across from a given angle in a right triangle.

对边：直角三角形中与给定角相对的边。

Adjacent side: The side next to a given angle that is not the hypotenuse.

邻边：直角三角形中与给定角相邻且非斜边的边。

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。

Radian: A unit of angle measure; 1 radian ≈ 57.3°. 180° = π radians.

弧度：角度度量单位；1 弧度 ≈ 57.3°。180° = π 弧度。

Degree: A unit of angle measure where a full circle is 360°.

度：角度度量单位，一整个圆周为360°。

Period: The length of the smallest interval over which a trigonometric function repeats its values.

周期：三角函数的输出值重复出现的最小自变量的区间长度。

Amplitude: Half the distance between the maximum and minimum values of a sine or cosine wave.

振幅：正弦或余弦波形的最大值与最小值之差的一半。

Phase shift: A horizontal translation of a trigonometric graph; e.g., sin(x − c) shifts right by c.

相位移：三角函数图像的水平平移；例如 sin(x − c) 向右平移 c 个单位。

Identity: An equation involving trigonometric ratios that is true for all permissible values of the variable, e.g., sin²θ + cos²θ = 1.

恒等式：包含三角比且对所有允许的变量值都成立的等式，如 sin²θ + cos²θ = 1。

Law of sines: a/sin A = b/sin B = c/sin C for any triangle.

正弦定理：对于任意三角形，有 a/sin A = b/sin B = c/sin C。

Law of cosines: c² = a² + b² − 2ab cos C; generalizes the Pythagorean theorem.

余弦定理：c² = a² + b² − 2ab cos C；是勾股定理的推广。

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4. Functions & Graphs | 函数与图像

Function: A rule that assigns each input exactly one output; often written f(x).

函数：为每一个输入指定唯一输出的规则；常写作 f(x)。

Domain: The set of all possible input values (x‑values) for which the 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) produced by the function.

值域：函数产生的所有可能输出值（y 值）的集合。

One‑to‑one function: A function where each y‑value is paired with exactly one x‑value; passes the horizontal line test.

一一对应函数：每个 y 值都恰好对应一个 x 值的函数；通过水平线检验。

Inverse function: A function that “undoes” the original function, swapping input and output; denoted f⁻¹(x).

反函数：对原函数进行“逆转”操作、将输入和输出互换的函数；记为 f⁻¹(x)。

Composition: Applying one function to the result of another, written (f ∘ g)(x) = f(g(x)).

复合函数：将一个函数作用于另一个函数的结果，写作 (f ∘ g)(x) = f(g(x))。

Even function: A function symmetric about the y‑axis; f(−x) = f(x).

偶函数：图像关于 y 轴对称的函数；满足 f(−x) = f(x)。

Odd function: A function symmetric about the origin; f(−x) = −f(x).

奇函数：图像关于原点对称的函数；满足 f(−x) = −f(x)。

Polynomial function: A function of the form f(x) = aₙxⁿ + … + a₁x + a₀.

多项式函数：形如 f(x) = aₙxⁿ + … + a₁x + a₀ 的函数。

Rational function: A function expressed as a ratio of two polynomials, e.g., f(x) = (x+1)/(x−2).

有理函数：表示为两个多项式之比的函数，如 f(x) = (x+1)/(x−2)。

Exponential function: A function of the form f(x) = a·bˣ, where b > 0, b ≠ 1.

指数函数：形如 f(x) = a·bˣ 的函数，其中 b > 0, b ≠ 1。

Logarithmic function: The inverse of an exponential function; f(x) = logₐ(x).

对数函数：指数函数的反函数；f(x) = logₐ(x)。

Absolute value function: f(x) = |x|, which returns the non‑negative magnitude of x.

绝对值函数：f(x) = |x|，返回 x 的非负大小。

Piecewise function: A function defined by different formulas over different parts of its domain.

分段函数：在其定义域的不同部分由不同公式定义的函数。

Asymptote: A line that a graph approaches but never touches. Vertical, horizontal, or oblique.

渐近线：图像无限逼近但永不触及的直线，可分为垂直渐近线、水平渐近线和斜渐近线。

Intercept: The point where a graph crosses an axis. The x‑intercept occurs when y=0; the y‑intercept occurs when x=0.

截距：图像与坐标轴的交点。x 截距在 y=0 时出现，y 截距在 x=0 时出现。

Zero / Root: An x‑value that makes a function equal to zero; same as x‑intercept.

零点 / 根：使函数值为零的 x 值，等同于 x 截距。

Increasing function: A function whose y‑values get larger as x increases.

递增函数：随着 x 增加，y 值也随之增大的函数。

Decreasing function: A function whose y‑values get smaller as x increases.

递减函数：随着 x 增加，y 值反而减小的函数。

Maximum / Minimum: The highest or lowest point on a graph over a specified interval or the entire domain. Local (relative) vs. global (absolute).

最大值 / 最小值：图像在给定区间或整个定义域上的最高点或最低点，分为局部（相对）与全局（绝对）两种。

Inflection point: A point where the curve changes concavity (from concave up to concave down, or vice versa).

拐点 / 反曲点：曲线凹凸性发生改变的点（由上凹变下凹，或反之）。

Translation: Sliding a graph horizontally, vertically, or both without changing its shape.

平移：将图像沿水平、竖直或两个方向滑动而不改变其形状。

Reflection: Flipping a graph across a line (e.g., x‑axis, y‑axis, or y = x).

反射 / 翻折：将图像关于一条直线（如 x 轴、y 轴或 y = x）进行翻转。

Stretch / Shrink: Multiplying all y‑values (vertical stretch/shrink) or x‑values (horizontal stretch/shrink) by a constant factor.

拉伸 / 压缩：将所有的 y 值（竖直拉伸/压缩）或 x 值（水平拉伸/压缩）乘以一个常数因子。

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5. Coordinate Geometry | 坐标几何

Cartesian coordinate system: A plane formed by two perpendicular number lines (x‑axis and y‑axis) intersecting at the origin.

笛卡尔坐标系：由两条互相垂直的数轴（x 轴和 y 轴）在原点相交构成的平面。

Origin: The point (0,0) where the axes intersect.

原点：坐标轴相交的点 (0,0)。

Ordered pair (x, y): A pair of numbers that locates a point in the coordinate plane; x is the horizontal coordinate, y is the vertical coordinate.

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