📚 Year 11 Cambridge Mathematics: Key Terminology Quick Memory Guide | 11年级剑桥数学：核心术语速记指南
Mastering the language of mathematics is the first step towards success in the Year 11 Cambridge IGCSE Mathematics exam. This guide provides a bilingual collection of essential terms with clear definitions and memory tips, helping you recall key vocabulary quickly and accurately during revision and in the examination hall.
掌握数学语言是在11年级剑桥IGCSE数学考试中取得成功的第一步。本指南提供了双语核心术语合集，附有清晰的定义和记忆技巧，帮助你在复习和考试中快速准确地回忆关键词汇。
1. Algebra Basics | 代数基础术语
A variable is a symbol, usually a letter such as x or y, that represents an unknown number or a number that can vary.
变量是一个符号，通常是像x或y这样的字母，代表未知或可以变化的数值。
A constant is a fixed value that does not change. In the expression 5x + 3, the number 3 is a constant.
常数是一个固定不变的值。在表达式5x + 3中，数字3就是常数。
A coefficient is the number multiplied by a variable. In 7y, 7 is the coefficient of y.
系数是与变量相乘的数字。在7y中，7是y的系数。
A term is a single mathematical component, which can be a number, a variable, or the product of numbers and variables, separated by + or - signs.
项是单个数学组成部分，可以是数字、变量或数字与变量的乘积，由加号或减号分隔。
An expression is a combination of terms with operations but without an equals sign, such as 3a + 2b - 5.
表达式是由项和运算符号组合而成的式子，没有等号，例如3a + 2b - 5。
ation states that two expressions are equal, using an equals sign, for example 2x + 1 = 7.
方程表示两个表达式相等，使用等号，例如2x + 1 = 7。
ype of equation that shows the relationship between different quantities, like v = u + at.
公式是一种特殊的方程，展示不同量之间的关系，如 v = u + at。
Remember: Expression (no =), Equation (has =), Formula (relationship)
记住：表达式（无等号），方程（有等号），公式（展示关系）
2. Equations and Inequalities | 方程与不等式
highest power of the variable is 1, producing a straight line graph. Example: y = 2x + 3.
线性方程是变量的最高次数为1的方程，其图像是一条直线。例如 y = 2x + 3。
ble raised to the power of 2, typically written as ax² + bx + c = 0, producing a parabola.
二次方程包含一个变量的平方项，通常写作 ax² + bx + c = 0，其图像为抛物线。
Simultaneous equations are a set of two or more equations with the same variables, solved together to find common solutions.
联立方程组是两个或更多含有相同变量的方程，需要同时求解以找到共同解。
ke < (less than), > (greater than), ≤ (less than or equal), and ≥ (greater than or equal).
不等式使用 < （小于）、> （大于）、≤ （小于等于）和 ≥ （大于等于）等符号比较两个表达式。
e value of the variable that makes an equation true. For x - 3 = 5, the solution is x = 8.
解（或根）是使方程成立的变量取值。对于 x - 3 = 5，解为 x = 8。
es (< , >) exclude the boundary value, whereas non-strict inequalities (≤ , ≥) include it.
严格不等式（< , >）不包括边界值，而非严格不等式（≤ , ≥）包括边界值。
Tip: When multiplying or dividing an inequality by a negative number, reverse the sign.
提示：不等式两边同乘或除以负数时，要反转不等号。
3. Sequences | 序列术语
A sequence is an ordered list of numbers following a particular rule, for example 2, 4, 6, 8, ...
序列是按照特定规则排列的一组数，例如 2, 4, 6, 8, ...
Each number in a sequence is called a term, often denoted by a₁, a₂, a₃, ... aₙ.
序列中的每个数称为项，通常用 a₁, a₂, a₃, ... aₙ 表示。
The nth term is a formula that allows you to find any term in a sequence directly. For 3, 7, 11, 15, ..., the nth term is 4n - 1.
第n项是一个公式，可以直接求出序列中任意一项。对于 3, 7, 11, 15, ...，第n项为 4n - 1。
consecutive terms, called the common difference d. Example: 5, 9, 13, 17, ... with d = 4.
等差数列（AP）中相邻两项的差恒定，这个差称为公差 d。例如 5, 9, 13, 17, ...，公差 d = 4。
tween consecutive terms, called the common ratio r. Example: 2, 6, 18, 54, ... with r = 3.
等比数列（GP）中相邻两项的比恒定，这个比称为公比 r。例如 2, 6, 18, 54, ...，公比 r = 3。
The sum of the first n terms of an AP can be found using Sₙ = n/2 [2a + (n - 1)d].
等差数列前n项和公式为 Sₙ = n/2 [2a + (n - 1)d]。
AP: add/subtract; GP: multiply/divide
等差：加减；等比：乘除
4. Graphs and Functions | 图形与函数
The Cartesian plane (coordinate plane) is formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0).
笛卡尔平面（坐标平面）由两条互相垂直的数轴构成，横轴为x轴，纵轴为y轴，相交于原点 (0,0)。
A point is located by an ordered pair (x, y), where x is the horizontal distance from the origin and y is the vertical distance.
点用有序对 (x, y) 定位，x 表示离原点的水平距离，y 表示垂直距离。
The gradient (slope) measures the steepness of a line and is calculated as rise/run or (change in y)/(change in x). A horizontal line has gradient 0.
梯度（斜率）衡量一条直线的倾斜程度，计算公式为 垂直增量/水平增量 或 (y的增量)/(x的增量)。水平线的梯度为0。
he y-axis, found by setting x = 0. The x-intercept is where it crosses the x-axis (y = 0).
y截距是图形与y轴的交点，令 x=0 求得；x截距是图形与x轴的交点，令 y=0 求得。
ght line is often written as y = mx + c, where m is the gradient and c is the y-intercept.
直线方程通常写作 y = mx + c，其中 m 是梯度，c 是y截距。
its graph is a parabola, which is symmetrical and has a maximum or minimum turning point.
二次函数形式为 f(x) = ax² + bx + c，其图像是一条抛物线，具有对称性，且有一个最高点或最低点（转折点）。
The domain of a function is the set of all possible input (x) values, while the range is the set of all possible output (y) values.
函数的定义域是所有可能输入值 (x) 的集合，值域是所有可能输出值 (y) 的集合。
line that a curve approaches but never touches, common in reciprocal graphs like y = 1/x.
渐近线是曲线无限接近但永不触及的直线，常见于倒数函数图像如 y = 1/x。
5. Geometry | 几何术语
A point has position but no size, a line extends infinitely in both directions, and a line segment has two endpoints.
点有位置但没有大小；直线向两端无限延伸；线段有两个端点。
A ray starts at an endpoint and extends infinitely in one direction.
射线从一个端点开始，向一个方向无限延伸。
Angles are measured in degrees (°). Types include acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), and reflex (between 180° and 360°).
角度以度 (°) 为单位。类型包括锐角（小于90°）、直角（恰好90°）、钝角（90°到180°之间）和优角（180°到360°之间）。
Parallel lines are lines in a plane that never meet, no matter how far they are extended. Perpendicular lines intersect at a right angle (90°).
平行线是同一平面内永不相交的直线；垂直线相交成直角 (90°)。
A polygon is a closed 2D shape with straight sides. Triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides) and hexagons (6 sides) are common polygons.
多边形是由直线段围成的封闭二维图形。三角形（3条边）、四边形（4条边）、五边形（5条边）和六边形（6条边）是常见的多边形。
A circle is defined by its centre and radius. The diameter is twice the radius and passes through the centre. A chord is a line segment joining two points on the circle, not necessarily through the centre.
圆由圆心和半径定义。直径是半径的两倍并通过圆心。弦是连接圆上两点的线段，不一定通过圆心。
A tangent is a straight line that touches a circle at exactly one point, and is perpendicular to the radius at that point.
切线是一条与圆恰好在一点接触的直线，并且在该点与半径垂直。
An arc is a part of the circumference of a circle, and a sector is the region enclosed by two radii and an arc.
弧是圆周的一部分，扇形是由两条半径和一段弧围成的区域。
Pythagoras' theorem: a² + b² = c² (right-angled triangle)
勾股定理：a² + b² = c²（直角三角形）
6. Trigonometry | 三角学术语
In a right-angled triangle, the hypotenuse is the longest side, opposite the right angle. The opposite side is across from the given angle θ, and the adjacent side is next to θ.
在直角三角形中，斜边是最长边，对着直角。对边是给定角 θ 对面的边，邻边是紧挨着角 θ 的边。
nuse. Cosine (cos): cos θ = adjacent/hypotenuse. Tangent (tan): tan θ = opposite/adjacent.
正弦 (sin)：sin θ = 对边/斜边。余弦 (cos)：cos θ = 邻边/斜边。正切 (tan)：tan θ = 对边/邻边。
The angle of elevation is the angle measured upwards from the horizontal line of sight to an object. The angle of depression is measured downwards from the horizontal.
仰角是从水平视线向上测量到物体的角度；俯角是从水平视线向下测量的角度。
A bearing is a three-digit angle measured clockwise from north, used to describe direction. For example, east is 090°, south is 180°.
方位角是从正北方向按顺时针测量的三位数角度，用于描述方向。例如，正东为090°，正南为180°。
Memory aid: SOH CAH TOA (Sin = O/H, Cos = A/H, Tan = O/A)
记忆口诀：SOH CAH TOA
7. Measurement and Units | 测量与单位
Perimeter is the total distance around the outside of a 2D shape, measured in linear units such as metres (m).
周长是二维图形外边界的总长度，用线性单位如米 (m) 度量。
like m² or cm². Common formulas: rectangle = length × width, triangle = ½ × base × height.
面积是二维图形内部的区域大小，单位为平方单位如 m² 或 cm²。常见公式：矩形面积 = 长 × 宽，三角形面积 = ½ × 底 × 高。
ect, in cubic units like m³. For a cube or prism, volume = area of cross-section × length.
体积测量三维物体占据的空间，单位为立方单位如 m³。对于立方体或棱柱，体积 = 横截面积 × 长度。
Surface area is the total area of all faces of a 3D solid. Capacity refers to the amount a container can hold, often measured in litres or millilitres.
表面积是立体图形所有面的总面积。容量指容器能容纳的量，常用升或毫升度量。
0 cm, 1 cm = 10 mm. For area and volume, remember to square or cube the conversion factor.
公制单位换算：1 km = 1000 m，1 m = 100 cm，1 cm = 10 mm。面积和体积换算时，要平方或立方相应的换算因子。
f time: speed = distance / time. Density is mass per unit volume: density = mass / volume.
速度定义为单位时间内移动的距离：速度 = 距离/时间。密度是单位体积的质量：密度 = 质量/体积。
8. Vectors and Transformations | 向量与变换
A vector is a quantity that has both magnitude (size) and direction. A column vector (x over y) shows horizontal and vertical displacement.
向量是既有大小（模长）又有方向的量。列向量（x在上，y在下）表示水平和垂直位移。
The magnitude of a vector (a over b) is √a² + b², representing its length.
向量 (a, b) 的模为 √a² + b²，表示其长度。
Translation moves every point of a shape the same distance in the same direction, described by a vector.
平移是将图形每一点按相同方向和相同距离移动，用向量描述。
Reflection flips a shape over a mirror line, creating a mirror image. Every point is the same perpendicular distance from the mirror line.
反射将图形沿一条镜线翻转，产生镜像。每一点到镜线的垂直距离相等。
Rotation turns a shape about a fixed centre by a given angle and direction (clockwise or anticlockwise).
旋转是将图形绕一个固定中心旋转给定角度和方向（顺时针或逆时针）。
Enlargement changes the size of a shape by a scale factor from a centre of enlargement. A scale factor > 1 makes the shape larger; between 0 and 1 makes it smaller. Negative scale factors also invert the shape.
放大是以放大中心为基点，按比例因子改变图形的大小。比例因子 > 1 使图形变大；介于0和1之间使图形变小。负比例因子还会将图形倒转。
The image is the new shape after transformation, while the object is the original shape.
像是变换后的新图形，物体是变换前的原始图形。
9. Probability | 概率术语
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). It can be written as a fraction, decimal, or percentage.
概率衡量事件发生的可能性，用0（不可能）到1（必然）之间的数表示。可以写成分数、小数或百分数。
An experiment is an action with uncertain results. An outcome is a single possible result, and an event is a set of one or more outcomes.
试验是一个伴有不确定结果的动作；结果是一个可能发生的结果；事件是一个或多个结果的集合。
The sample space is the set of all possible outcomes, often shown in a grid or list.
样本空间是所有可能结果的集合，常用网格或列表表示。
favourable outcomes / total number of outcomes, assuming all outcomes are equally likely.
理论概率 = 有利结果数 /
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