📚 Year 10 Edexcel Maths: Quick Guide to Key Vocabulary & Terminology | Year 10 Edexcel 数学：关键词汇与术语速记指南
Mastering the language of mathematics is the first step to solving problems with confidence. In Year 10 of the Edexcel course, you will meet a wide range of technical terms — from algebraic expressions and statistical measures to geometric transformations. This guide collects the essential vocabulary you need to know, explains each term clearly in English, and follows up immediately with its Chinese equivalent and definition. Use it as a quick reference whenever you revise a topic.
掌握数学语言是自信解题的第一步。在 Edexcel 10 年级课程中，你会遇到大量专业术语——从代数表达式和统计度量到几何变换。本文汇总了你必须掌握的核心词汇，每个术语先用英文清晰解释，紧接着给出对应的中文释义。复习每个专题时，都可以把它当作速查手册来用。
1. Algebraic Expressions | 代数表达式
In algebra, a variable is a symbol, typically a letter such as x or y, that stands for an unknown number. A term is either a single number, a variable, or a product of numbers and variables. For example, 4xy, -7, and x² are all terms. The coefficient is the numerical factor multiplying a variable — in 5a²b the coefficient of a²b is 5.
在代数中，变量是代表未知数的符号，通常是 x 或 y 这样的字母。项是一个单独的数、一个变量或数与变量的乘积。例如 4xy、–7 和 x² 都是项。系数是乘以变量的数字因子——在 5a²b 中，a²b 的系数是 5。
A constant is a term with a fixed value, such as 9 or –3.5, containing no variable part. An algebraic expression is a combination of terms linked by operations, like 3x + 2y – 5. To simplify an expression means to collect like terms (terms with exactly the same variable components) — for instance, 7a – 2a + 3b = 5a + 3b.
常数是具有固定值的项，如 9 或 –3.5，不含变量部分。代数表达式是由运算符号连接的项的组合，例如 3x + 2y – 5。化简一个表达式就是合并同类项（变量部分完全相同的项）——例如 7a – 2a + 3b = 5a + 3b。
Expanding ach term inside the bracket by the term outside: 2(x + 4) = 2x + 8. The reverse operation, factorising as a product of its factors. A common factor can be taken out, e.g. 6x + 9 = 3(2x + 3). A quadratic expression contains a variable raised to the power of 2, such as x² + 5x + 6.
展开括号是将括号内的每一项乘以括号外的项：2(x + 4) = 2x + 8。逆运算因式分解是将表达式写成因式的乘积。可以提取公因式，例如 6x + 9 = 3(2x + 3)。二次表达式含有变量的平方项，如 x² + 5x + 6。
2. Equations and Inequalities | 方程与不等式
An equation states that two expressions are equal, using the equals sign ‘=’. The solution e of an equation is the value (or values) of the variable that makes the statement true. For example, solving 5x – 2 = 13 gives x = 3. A linear equation has the variable raised only to the power of 1, such as 2y + 7 = 15.
方程用等号“=”陈述两个表达式相等。方程的解是使该陈述成立的变量值（或多个值）。例如，解方程 5x – 2 = 13 得到 x = 3。线性方程中变量的指数仅为 1，如 2y + 7 = 15。
An inequality eater than or equal to). The solution set of an inequality is often shown on a number line with open or closed circles. A formula is an equation showing a relationship between quantities, such as A = l × w for the area of a rectangle.
不等式使用符号比较两个表达式：<（小于）、>（大于）、≤（小于或等于）、≥（大于或等于）。不等式的解集常用空心或实心圆点画在数轴上。公式是显示量之间关系的方程，例如长方形的面积公式 A = l × w。
When you rearrange a formula, you change its subject. For instance, making r the subject of C = 2πr gives r = C / (2π). Substitution means replacing variables with specific values, e.g. putting a = 4 and b = –2 into 3a² + b.
变换公式时，你要改变公式的主项。例如，将 C = 2πr 中的 r 变为主项，得到 r = C / (2π)。代入是指用具体的值替换变量，比如将 a = 4 和 b = –2 代入 3a² + b。
3. Graphs and Functions | 图形与函数
A function is a rule that assigns each input exactly one output, often written as f(x). The gradient aight line measures its steepness; for the line y = mx + c, m is the gradient and c is the y-intercept where the line crosses the y-axis. A linear graph is a straight line, while a quadratic graph (y = ax² + bx + c) produces a smooth curve called a parabola.
函数是一种规则，为每个输入分配唯一输出，常记作 f(x)。直线的斜率衡量其倾斜程度；对于直线 y = mx + c，m 是斜率，c 是y 轴截距，即直线与 y 轴的交点。直线图是一条直线，而二次函数图（y = ax² + bx + c）会形成一条光滑曲线，称为抛物线。
The coordinates of a point are written as (x, y). You can find the gradient of a line segment by using the formula (change in y) ÷ (change in x). Parallel lines have the same gradient, whereas perpendicular lines have gradients that multiply to –1.
点用坐标 (x, y) 表示。可用公式 (y 的变化量) ÷ (x 的变化量) 求线段斜率。平行线斜率相同，而垂直线的斜率乘积为 –1。
A real-life graph can show how one quantity changes with another, such as a distance–time graph. The gradient of a distance–time graph represents speed. The point where two lines intersect is the simultaneous solution to their equations.
实际情境图可以展示一个量随另一个量变化的情况，如距离–时间图。距离–时间图的斜率代表速度。两条直线相交的点是它们方程组的联立解。
4. Ratio, Proportion and Rates of Change | 比、比例与变化率
A ratio compares the sizes of two or more quantities. The ratio 3 : 5 means for every 3 parts of the first quantity there are 5 parts of the second. To simplify a ratio, divide all sides by their highest common factor. Proportion compares a part to the whole, often written as a fraction or percentage.
比比较两个或多个数量的大小。比 3 : 5 表示每 3 份第一个量对应 5 份第二个量。要化简比，将所有项除以它们的最大公因数。比例比较部分与整体，常用分数或百分数表示。
Two quantities are in direct proportion if their ratio stays constant; as one doubles, the other doubles. In inverse proportion, the product of the two quantities remains constant — when one increases, the other decreases. The constant of proportionality , often denoted by k, links the variables: y = kx for direct, and y = k/x for inverse proportion.
若两个数量的比值保持不变，则它们成正比例；一个加倍，另一个也加倍。反比例中，两个数量的乘积保持不变——一个增大，另一个减小。比例常数常用 k 表示，联系两个变量：正比例 y = kx，反比例 y = k/x。
A rate of change describes how one quantity changes relative to another. Speed (distance per time) and density (mass per volume) are examples of compound measures that combine two units. The unitary method finds the value of a single unit before scaling up or down.
变化率描述一个量相对于另一个量的变化快慢。速度（距离/时间）和密度（质量/体积）是复合度量的例子，它们结合了两个单位。归一法先求出单一单位的值，再放大或缩小。
5. Geometry: Angles and Shapes | 几何：角与图形
An angle is formed when two lines meet at a vertex; it is measured in degrees (°). Angles are classified as acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), and reflex (greater than 180°). Adjacent angles share a common arm, and complementary angles sum to 90°, while supplementary angles sum to 180°.
当两条线在一个顶点相遇时就形成一个角，单位为度（°）。角分为锐角（小于 90°）、直角（恰好 90°）、钝角（介于 90° 和 180° 之间）以及优角（大于 180°）。邻角共用一条边，互余角之和为 90°，互补角之和为 180°。
When two lines cross, vertically opposite angles are equal. On parallel lines cut by a transversal, corresponding angles are equal, alternate angles are equal, and co-interior (allied) angles sum to 180°. A polygon is a closed shape with straight sides; a regular polygon has all sides and angles equal.
两直线相交时，对顶角相等。当平行线被一条截线切割时，同位角相等，内错角相等，同旁内角之和为 180°。多边形是由线段围成的封闭图形；正多边形的所有边和角都相等。
The sum of interior angles of an n-sided polygon is (n – 2) × 180°. The sum of exterior angles of any convex polygon is always 360°. A circle has a radius (distance from centre to edge), diameter (twice the radius), and circumference (perimeter). An arc is part of the circumference, and a chord joins two points on the circumference.
n 边形的内角和为 (n – 2) × 180°。任意凸多边形的外角和恒为 360°。圆有半径（圆心到圆周的距离）、直径（半径的两倍）和周长（圆周的长度）。弧是圆周的一部分，弦连接圆周上的两点。
6. Transformations and Symmetry | 变换与对称
A transformation moves or changes a shape. Translation slides a shape without rotating or reflecting it; it is described by a column vector, e.g. (3 –2) means 3 units right and 2 units down. Reflection flips a shape over a mirror line; the image is the same perpendicular distance from the mirror as the original.
变换是移动或改变一个图形。平移在不旋转、不反射的情况下滑动图形，用列向量描述，如 (3 –2) 表示向右 3 格、向下 2 格。反射将图形沿镜线翻转，映像到镜线的垂直距离与原图相同。
Rotation turns a shape about a fixed centre of rotation through a given angle (e.g. 90° clockwise). Enlargement changes the size of a shape by a scale factor; if the scale factor is greater than 1, the shape gets larger, and if it is between 0 and 1, the shape shrinks. A shape has rotational symmetry if it looks the same more than once during a full 360° turn.
旋转将图形绕固定的旋转中心转过一个给定角度（如顺时针 90°）。放大通过缩放因子改变图形的大小；若缩放因子大于 1，图形变大；若介于 0 和 1 之间，图形缩小。如果一个图形在旋转 360° 的过程中多次与自身重合，它就具有旋转对称性。
A shape has line symmetry if it can be folded along a line so that both halves match exactly. The number of such lines is called the order of line symmetry. A congruent shape has exactly the same size and shape as another; similar shapes have the same angles and proportional sides.
如果一个图形沿一条直线对折后两部分完全重合，它就具有线对称性。这样的直线数目称为线对称的阶。全等图形的大小和形状完全相同；相似图形的对应角相等、对应边成比例。
7. Pythagoras and Trigonometry | 勾股定理与三角学
Pythagoras' theorem applies to right-angled triangles: the square of the hypotenuse hypotenuse. You can use it to find a missing side or check if a triangle is right-angled.
勾股定理适用于直角三角形：斜边（最长的边，直角的对边）的平方等于另外两条边的平方和。记作 a² + b² = c²，其中 c 是斜边。你可以用它求未知边长或检验一个三角形是否为直角三角形。
Trigonometry in right-angled triangles uses three ratios: sine (sin = opposite/hypotenuse), cosine (cos = adjacent/hypotenuse), and tangent tan = opposite/adjacent). The side next to the given angle (and not the hypotenuse) is the adjacent side, and the side opposite the angle is the opposite side.
直角三角形中的三角学使用三个比：正弦（sin = 对边/斜边）、余弦（cos = 邻边/斜边）和正切（tan = 对边/邻边）。与给定角相邻（且不是斜边）的边是邻边，给定角的对边是对边。
The angle of elevation is the angle looking up from the horizontal; the angle of depression is looking down. When working with non-right-angled triangles, you may use the sine rule or cosine rule, though these often appear later in the course.
仰角是从水平线向上看的角度；俯角是向下看的角度。处理非直角三角形时，可能会用到正弦定理或余弦定理，不过这些通常出现在课程靠后的部分。
8. Probability | 概率
Probability is written as P(A) = number of favourable outcomes / total number of possible outcomes. An outcome is a possible result of a trial, and the sample space is the set of all possible outcomes.
概率度量事件发生的可能性，范围从 0（不可能）到 1（必然）。事件 A 的概率写作 P(A) = 有利结果数 / 所有可能结果的总数。结果是一次试验可能得到的结局，样本空间是所有可能结果的集合。
Two events are mutually exclusive ey if they cannot happen at the same time. For mutually exclusive events, P(A or B) = P(A) + P(B). Independent events utcome of one does not affect the other; for independent events, P(A and B) = P(A) × P(B).
如果两个事件不能同时发生，则它们互斥。对于互斥事件，P(A 或 B) = P(A) + P(B)。独立事件是指一个事件的结果不影响另一个事件的结果；对独立事件，P(A 且 B) = P(A) × P(B)。
A probability tree diagram helps to show all possible outcomes of combined events. The probabilities on each set of branches must sum to 1. The expected frequency of an event is the probability multiplied by the number of trials.
概率树形图有助于展示组合事件的所有可能结果。每组分枝上的概率之和必须为 1。事件的期望频数等于概率乘以试验次数。
9. Statistics: Averages and Charts | 统计：平均数与图表
In statistics, the mean is the sum of all data values divided by the number of values. The median is the middle value when the data are ordered; if there is an even number of values, the median is the mean of the two middle numbers. The mode is the value that appears most often, and the range is the difference between the largest and smallest values.
在统计学中，平均数（均值）是所有数据值的总和除以值的个数。中位数是数据排序后中间的值；如果有偶数个数据，中位数是中间两个数的均值。众数是出现次数最多的值，极差是最大值与最小值之差。
A frequency table organises data by showing how often each value or group occurs. The modal class is the group with the highest frequency. A grouped frequency table is used for continuous data, and you can estimate the mean using the midpoint of each class interval.
频数表通过显示每个值或每组出现的次数来整理数据。众数所在组是频数最高的组。对于连续数据，使用分组频数表，你可以用每组的组中值来估算平均数。
Common statistical diagrams include bar charts (for discrete or categorical data), pie charts (showing proportions as angles), stem-and-leaf diagrams (keeping original values), and scatter graphs (showing relationships between two variables). A line of best fit on a scatter graph indicates correlation, which can be positive, negative, or none.
Published by TutorHao | Year 10 Mathematics Revision Series | aleveler.com
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