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数学和逻辑SAT - Mathematics

在这里,你将学习一些与数学相关的英语单词,如“变量”、“直方图”、“域”等,这些单词是你通过SAT考试所需要的。

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SAT Vocabulary for Math and Logic
intercept
intercept
[名词]

the point where a line, curve, or surface crosses an axis on a graph

截距, 交点

截距, 交点

Ex: The graph clearly shows the intercepts where the function crosses the axes .图表清楚地显示了函数穿过轴线的**截距**。
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plane
plane
[名词]

a flat, two-dimensional surface that extends infinitely in all directions

平面, 平坦的表面

平面, 平坦的表面

Ex: Understanding planes is fundamental to the study of three-dimensional shapes and spaces .理解**平面**对于研究三维形状和空间至关重要。
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function
function
[名词]

(mathematics) a quantity whose value changes according to another quantity's varying value

函数

函数

Ex: Statisticians analyze data using functions such as mean , median , and standard deviation to understand distributions and trends .统计学家使用**函数**(如均值、中位数和标准差)分析数据以理解分布和趋势。
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to model
to model
[动词]

to make a representation of something, especially one based on mathematics

建模, 代表

建模, 代表

Ex: By modeling the financial system , they were able to predict the economic impact of the policy changes .通过**建模**金融系统,他们能够预测政策变化的经济影响。
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constant
constant
[名词]

a quantity or value that remains the same and does not change in a specific mathematical context

常数

常数

Ex: In a mathematical formula , a constant does not change , unlike a variable .在数学公式中,**常数**不像变量那样变化。
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expression
expression
[名词]

a combination of numbers, variables, operations, and grouping symbols that collectively represent a numerical value or relationship

表达式, 公式

表达式, 公式

Ex: Euler ’s formula , ( e^{ipi } + 1 = 0 ) , is often cited as a beautiful mathematical expression due to its simplicity and depth .欧拉公式,( e^{ipi} + 1 = 0 ),由于其简洁和深刻,常被引用为美丽的数学**表达式**。
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equivalent
equivalent
[形容词]

(of mathematical expressions or quantities) having the same value or function, even if they appear in different forms

等价的

等价的

Ex: The decimal 0.75 and the fraction 3/4 are equivalent because they represent the same quantity .小数0.75和分数3/4是**等价的**,因为它们表示相同的数量。
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to intersect
to intersect
[动词]

to meet or cross another path, line, etc. at a particular point

相交, 交叉

相交, 交叉

Ex: The paths of the two hikers intersected in the dense forest .两位徒步旅行者的路径在茂密的森林中**相交**。
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scatter plot
scatter plot
[名词]

a type of graph used in statistics and data analysis to display and compare two sets of numerical data

散点图, 点图

散点图, 点图

Ex: The scatter plot helped the scientists visualize the spread of the experimental results .**散点图**帮助科学家们可视化了实验结果的分布。
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line of best fit

a straight line drawn through the center of a group of data points on a scatter plot representing the best approximation of the relationship between the variables being studied

最佳拟合线, 回归线

最佳拟合线, 回归线

Ex: The software automatically calculates and displays the line of best fit on the graph .软件自动计算并在图表上显示**最佳拟合线**。
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variable
variable
[名词]

(mathematics) a quantity that is capable of assuming different values in a calculation

变量

变量

Ex: In statistical analysis , variables can be classified as independent or dependent , depending on their role in the study .在统计分析中,**变量**可以根据其在研究中的作用分为独立变量或依赖变量。
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scale
scale
[名词]

a system of numerical values used to quantify and compare levels, degrees, or values

尺度, 等级

尺度, 等级

Ex: The Likert scale is commonly used in surveys to gauge responses .李克特**量表**通常用于调查中以衡量回应。
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figure
figure
[名词]

a diagram or illustration that is used to show or explain something, such as a chart, graph, or drawing

图, 图表

图, 图表

Ex: The figure in the article provided a visual representation of the survey results .文章中的**图**提供了调查结果的可视化表示。
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domain
domain
[名词]

the set of all possible input values for which a given function is defined

定义域, 域

定义域, 域

Ex: The teacher asked the students to identify the domain of each function on their homework .老师要求学生在他们的作业中识别每个函数的**定义域**。
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graph
graph
[名词]

(mathematics) a set of points whose coordinates are in agreement with one another

图, 图表

图, 图表

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histogram
histogram
[名词]

a diagram consisting of bars with different heights that represent the amount of a variable

直方图, 条形图

直方图, 条形图

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interval
interval
[名词]

a set of real numbers that includes all the numbers between any two specified numbers within the set

间隔, 区间

间隔, 区间

Ex: An interval like [ 2 , 2 ] includes only the number 2 , as both endpoints are the same .像[2, 2]这样的**区间**只包括数字2,因为两个端点相同。
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linear function

a mathematical function that creates a straight line when graphed

线性函数, 线性映射

线性函数, 线性映射

Ex: The relationship between distance and time in uniform motion can be described by a linear function.匀速运动中距离和时间的关系可以用**线性函数**来描述。
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rational function

a function that can be expressed as the ratio of two polynomials, where the denominator is not zero

有理函数, 有理分式

有理函数, 有理分式

Ex: When graphing a rational function, it 's important to identify any asymptotes and intercepts to understand its behavior .绘制**有理函数**图形时,识别任何渐近线和截距以理解其行为非常重要。
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coordinate
coordinate
[名词]

any set of numbers that represents an exact position on a map or graph

坐标, 地理坐标

坐标, 地理坐标

Ex: The drone was programmed to fly to specific coordinates.无人机被编程飞向特定的**坐标**。
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integer constant

a fixed numerical value that is a whole number, either positive, negative, or zero

整数常量, 整型常数

整数常量, 整型常数

Ex: The formula calculates the area of a square by multiplying the length of its side by itself , without needing an integer constant.该公式通过将正方形的边长乘以自身来计算其面积,而不需要**整数常数**。
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linear equation

an equation that makes a straight line when graphed

线性方程, 直线方程

线性方程, 直线方程

Ex: The teacher explained how to convert a standard form linear equation to slope-intercept form .老师解释了如何将标准形式的**线性方程**转换为斜截式。
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to correspond

to have a direct relationship or alignment with something else, such as paired values or elements

对应, 与...有直接关系

对应, 与...有直接关系

Ex: In the table of values , each row corresponds to a different solution of the linear equation .在数值表中,每一行**对应**线性方程的不同解。
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term
term
[名词]

a single number, variable, or the product of numbers and variables in an expression or equation, separated by addition or subtraction operators

项, 元素

项, 元素

Ex: Each term in the arithmetic series is obtained by adding a constant difference to the previous term.算术级数中的每个**项**是通过在前一项上加上一个常数差得到的。
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axis
axis
[名词]

a reference line used in coordinate systems to provide a framework for locating points

轴, 参考线

轴, 参考线

Ex: When solving equations , it 's common to plot the functions on a graph to visualize their behavior relative to the axes.解方程时,通常在图表上绘制函数以可视化它们相对于**轴**的行为。
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polynominal function

a mathematical function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power

多项式函数, 多项式功能

多项式函数, 多项式功能

Ex: The division algorithm for polynomials allows you to divide one polynomial function by another.多项式的除法算法允许你将一个**多项式函数**除以另一个多项式函数。
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to satisfy
to satisfy
[动词]

to fulfill the conditions or requirements of a mathematical statement, equation, or inequality

满足, 符合

满足, 符合

Ex: The inequality y>2x is satisfied by all points above the line represented by the equation y=2x.不等式 y > 2x 由方程 y = 2x 表示的线上方的所有点**满足**。
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coefficient
coefficient
[名词]

a numerical or constant factor that multiplies a variable in an algebraic term

系数, 乘数因子

系数, 乘数因子

Ex: When combining like terms in 3p+2p , the coefficients are added to get 5p .在3p + 2p中合并同类项时,**系数**相加得到5p。
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quadratic
quadratic
[名词]

an equation where the highest power of the variable is squared

二次方程

二次方程

Ex: The roots of the quadratic x2 − 4 = 0 are x=2 and x=−2.二次方程x2 − 4 = 0的根是x=2和x=−2。
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regression
regression
[名词]

a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables

回归

回归

Ex: Polynomial regression can model relationships that are not linear .多项式**回归**可以模拟非线性的关系。
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bimodal
bimodal
[形容词]

having or involving two distinct modes, peaks, or most frequent values

双峰的, 有两种模式的

双峰的, 有两种模式的

Ex: A bimodal curve on the graph suggests the presence of two dominant traits in the population .图表上的**双峰**曲线表明人群中存在两个主要特征。
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equidistant
equidistant
[形容词]

having equal distances from two or more points

等距的, 与两个或更多点距离相等的

等距的, 与两个或更多点距离相等的

Ex: The lighthouse was built at an equidistant point from the surrounding islands .灯塔建在离周围岛屿**等距**的点上。
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collinear
collinear
[形容词]

having points that lie on the same straight line

共线的, 位于同一直线上的

共线的, 位于同一直线上的

Ex: The architect ensured that the columns in the design were collinear for aesthetic balance .建筑师确保设计中的柱子是**共线的**以达到美学平衡。
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theorem
theorem
[名词]

a statement or proposition that has been proven to be true based on previously established axioms, definitions, and other theorems within a particular mathematical or logical system

定理

定理

Ex: Students often encounter various theorems while studying advanced mathematics .学生在学习高等数学时经常会遇到各种**定理**。
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period
period
[名词]

a recurring interval or length associated with a mathematical function or pattern

周期, 间隔

周期, 间隔

Ex: In the Fourier series expansion of a function , the period plays a fundamental role in determining the coefficients of the trigonometric terms .在函数的傅里叶级数展开中,**周期**在确定三角项的系数方面起着根本作用。
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to evaluate
to evaluate
[动词]

to find the numerical value of an expression, equation, or function by substituting specific values for the variables

评估

评估

Ex: To evaluate the expression 2x+3 when x=5 , substitute x=5 into the expression to get 2(5)+3=13 .要**评估**当x=5时的表达式2x+3,将x=5代入表达式得到2(5)+3=13。
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expanded notation

a way of representing numbers as the sum of each digit multiplied by its place value

扩展表示法, 数值分解

扩展表示法, 数值分解

Ex: In expanded notation, each digit of a number is represented by its place value , such as hundreds , tens , and ones .在**扩展表示法**中,数字的每一位都由其位值表示,如百位、十位和个位。
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scientific notation

a method of writing numbers as the product of a coefficient and a power of 10

科学记数法, 科学计数法

科学记数法, 科学计数法

Ex: Engineers employ scientific notation when describing the dimensions of nanoscale structures in microelectronics and materials science .工程师在描述微电子和材料科学中纳米级结构的尺寸时使用**科学记数法**。
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to diagram
to diagram
[动词]

to represent or illustrate something using a drawing, chart, or schematic

图解, 图示

图解, 图示

Ex: The project manager diagrammed the timeline to keep everyone on track with deadlines .项目经理**图解**了时间表,以确保每个人都能按时完成任务。
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matrix
matrix
[名词]

a rectangular array of numbers or symbols organized in rows and columns, commonly used in linear algebra for representing equations, transformations, and vector operations

矩阵, 表格

矩阵, 表格

Ex: Matrix addition and subtraction are performed element-wise , combining corresponding elements of two matrices.**矩阵**的加法和减法是按元素进行的,结合两个矩阵的相应元素。
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factorial
factorial
[名词]

the product of all positive whole numbers from 1 to a given number

阶乘, 阶乘

阶乘, 阶乘

Ex: Factorials are essential in the binomial theorem for expanding expressions .**阶乘**在二项式定理中对于展开表达式至关重要。
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vector
vector
[名词]

an ordered set of numbers that describes both magnitude and direction, commonly used to represent quantities like displacement, velocity, or force in physics and engineering

向量, 矢量

向量, 矢量

Ex: The force exerted by a tensioned rope can be represented as a vector in mechanics .由张紧的绳子施加的力可以在力学中表示为**矢量**。
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standard coordinate plane

a two-dimensional system used to represent points in space

标准坐标平面, 标准笛卡尔平面

标准坐标平面, 标准笛卡尔平面

Ex: In physics , vectors are often represented as arrows on the standard coordinate plane.在物理学中,向量通常表示为**标准坐标平面**上的箭头。
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trigonometric function

a mathematical function that relates the angles of a triangle to the lengths of its sides, commonly including sine, cosine, and tangent

三角函数

三角函数

Ex: By using the inverse trigonometric function, we can determine the angle from a given ratio of sides .通过使用反**三角函数**,我们可以从给定的边长比例确定角度。
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augmented matrix

a way of representing a system of linear equations in matrix form

增广矩阵, 扩展矩阵

增广矩阵, 扩展矩阵

Ex: The entries in the augmented matrix correspond to the coefficients of the variables and the constants in the system of equations .增广矩阵中的条目对应于方程组中变量的系数和常数。
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unit vector
unit vector
[名词]

a vector that has a magnitude of 1 and represents direction without regard to scale

单位向量, 大小为1的向量

单位向量, 大小为1的向量

Ex: To describe the direction of a force in physics , we often use a unit vector representing the direction without considering the magnitude .在物理学中描述力的方向时,我们经常使用一个**单位向量**来表示方向而不考虑大小。
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determinant
determinant
[名词]

a single number calculated from the elements of a square matrix that indicates important properties, like whether the matrix can be inverted

行列式

行列式

Ex: In linear algebra , the determinant is used to determine the volume scaling factor of the linear transformation described by the matrix .在线性代数中,**行列式**用于确定由矩阵描述的线性变换的体积缩放因子。
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