Year 10 Cambridge Maths: Key Terminology Memorisation Guide | Year 10 剑桥数学：核心术语速记指南

📚 Year 10 Cambridge Maths: Key Terminology Memorisation Guide | Year 10 剑桥数学：核心术语速记指南

Building a strong command of mathematical vocabulary is vital for Cambridge Year 10 learners. Precise terms help you interpret exam questions correctly and express solutions clearly. In this guide, each key term is presented with a concise English definition immediately followed by its Chinese equivalent, supporting rapid memorisation and bilingual understanding.

掌握扎实的数学词汇对剑桥 Year 10 学生至关重要。精确的术语能帮助你正确理解考题、清晰表达解题过程。本指南中每个关键术语都先用简洁英文定义，紧接着给出中文对应释义，以促进快速记忆和双语理解。

1. Number and Arithmetic | 数与算术

Integer: A whole number that can be positive, negative or zero, without any fractional or decimal part, e.g. -3, 0, 7.

整数：可以是正数、负数或零的整数，没有分数或小数部分，例如 -3、0、7。

Rational number: Any number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0, including terminating and repeating decimals.

有理数：任何可以表示为 p/q 的数，其中 p、q 是整数且 q ≠ 0，包括有限小数和循环小数。

Irrational number: A number that cannot be written as a simple fraction; its decimal form is non‑terminating and non‑repeating, e.g. π, √2.

无理数：无法写成简单分数的数，其小数形式无限不循环，例如 π、√2。

Prime number: A natural number greater than 1 that has exactly two distinct factors: 1 and itself, e.g. 2, 3, 5, 7, 11.

质数（素数）：大于 1 的自然数，恰好有两个不同的因数：1 和它本身，例如 2、3、5、7、11。

Factor: A number that divides another number exactly without leaving a remainder, e.g. factors of 12 are 1, 2, 3, 4, 6, 12.

因数（因子）：能整除另一个数且不留余数的数，例如 12 的因数有 1、2、3、4、6、12。

Multiple: The product of a given number and any integer, e.g. multiples of 5 are 5, 10, 15, 20, …

倍数：一个给定数与任意整数的乘积，例如 5 的倍数有 5、10、15、20……

LCM (Lowest Common Multiple): The smallest positive number that is a multiple of two or more given numbers.

最小公倍数 (LCM)：两个或多个数共有的倍数中最小的正数。

HCF (Highest Common Factor) / GCD: The largest positive number that divides two or more numbers without a remainder.

最大公因数 (HCF/GCD)：能同时整除两个或多个数的最大正数。

Surd: An irrational number expressed using a root sign, e.g. √3, 5√2, left in exact form without decimal approximation.

根式（不尽根）：用根号表示的无理数，例如 √3、5√2，保留精确形式而不用小数近似。

Standard form (scientific notation) writing very large or very small numbers as a × 10ⁿ where 1 ≤ a < 10 and n is an integer.

标准形式（科学计数法）：将很大或很小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n 是整数。

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2. Algebra Basics | 代数基础

Variable: A symbol, usually a letter, that represents an unknown or changing value, e.g. x, y in 2x + 3.

变量：通常用字母表示的符号，代表未知或变化的值，例如 2x + 3 中的 x、y。

Coefficient: The numerical factor multiplying a variable in a term, e.g. in 5x² the coefficient is 5.

系数：项中乘以变量的数字因数，例如 5x² 的系数是 5。

Constant: A fixed number that does not change its value, e.g. in 3x + 7 the constant is 7.

常数：数值固定的数，例如 3x + 7 中的常数项是 7。

Term: A single number, variable or product of numbers and variables, separated by + or − signs, e.g. 4xy, -2a, 9.

项：一个数、变量或数与变量的乘积，由 + 或 − 号分隔，例如 4xy、−2a、9。

Expression: A collection of terms linked by operations but without an equals sign, e.g. 3x² − 2x + 5.

表达式：由运算符号连接的一组项，没有等号，例如 3x² − 2x + 5。

Equation cal statement that two expressions are equal, containing an equals sign, e.g. 2x − 4 = 10.

方程：表示两个表达式相等的数学语句，包含等号，例如 2x − 4 = 10。

Identity: An equation that is true for all values of the variable, often written with ≡, e.g. (x + 1)² ≡ x² + 2x + 1.

恒等式：对变量所有取值都成立的等式，常用 ≡ 表示，例如 (x + 1)² ≡ x² + 2x + 1。

Formula: A rule or relationship written in symbols, e.g. A = πr² for the area of a circle.

公式：用符号表示的规则或关系，例如圆的面积公式 A = πr²。

Expand: To multiply out brackets in an expression, e.g. expanding 2(x + 3) gives 2x + 6.

展开：将表达式中的括号乘开，例如将 2(x + 3) 展开得 2x + 6。

Factorise: To rewrite an expression as a product of its factors, e.g. x² − 9 factorises to (x + 3)(x − 3).

因式分解：将表达式重写为因式的乘积，例如 x² − 9 分解为 (x + 3)(x − 3)。

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3. Equations and Inequalities | 方程与不等式

Linear equation: An equation in which the highest power of the variable is 1, producing a straight‑line graph, e.g. 2x + 5 = 13.

线性方程：变量最高次幂为 1 的方程，图像为一条直线，例如 2x + 5 = 13。

Quadratic equation: An equation where the highest power is 2, usually written ax² + bx + c = 0 with a ≠ 0.

二次方程：最高次幂为 2 的方程，一般写作 ax² + bx + c = 0，其中 a ≠ 0。

Root / Solution: A value that satisfies an equation, making it true when substituted.

根 / 解：满足方程的值，代入后使方程成立。

Simultaneous equations: A set of two or more equations with the same variables, solved together to find the values that satisfy all equations simultaneously.

联立方程组：含有相同变量的两个或多个方程，需同时求解以找到满足所有方程的变量值。

Inequality: A statement comparing two expressions using signs <, >, ≤, ≥, ≠, e.g. 3x − 1 > 5.

不等式：使用 <, >, ≤, ≥, ≠ 比较两个表达式的语句，例如 3x − 1 > 5。

Strict inequality: Uses < or > and excludes the boundary value.

严格不等式：使用 < 或 >，不包括边界值。

Non‑strict inequality: Uses ≤ or ≥ and includes the boundary value.

非严格不等式：使用 ≤ 或 ≥，包括边界值。

Interval notation: A way of writing sets of numbers, e.g. −2 < x ≤ 3 is written as (−2, 3].

区间表示法：表示数集的方法，例如 −2 < x ≤ 3 写作 (−2, 3]。

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4. Sequences | 数列

Sequence: An ordered list of numbers that often follows a rule, e.g. 2, 4, 6, 8, …

数列：按一定次序排列的一列数，通常遵循某种规则，例如 2, 4, 6, 8……

Term: Each individual number in a sequence; the first term is often called u₁ or T₁.

项：数列中的每一个数；第一项常记为 u₁ 或 T₁。

nth term term in a sequence using its position n, e.g. nth term = 3n + 1 for the sequence 4, 7, 10, …

第 n 项（通项）：使用位置 n 计算数列中任意一项的公式，例如数列 4, 7, 10…… 的通项为 3n + 1。

Arithmetic progression (AP) difference between consecutive terms is constant (common difference d), e.g. 3, 7, 11, 15… with d = 4.

等差数列 (AP)：相邻两项的差为常数（公差 d）的数列，例如 3, 7, 11, 15…… 公差 d = 4。

Geometric progression (GP) s found by multiplying the previous term by a constant (common ratio r), e.g. 2, 6, 18, 54… with r = 3.

等比数列 (GP)：每一项等于前一项乘以常数（公比 r）的数列，例如 2, 6, 18, 54…… 公比 r = 3。

Recursive formula: Defines a term by relating it to previous terms, e.g. uₙ₊₁ = uₙ + 5 with u₁ = 2.

递推公式：通过与前一项的关系定义某一项，例如 uₙ₊₁ = uₙ + 5，且 u₁ = 2。

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5. Geometry: Angles, Lines and Shapes | 几何：角、线与形

Acute angle: An angle measuring between 0° and 90°.

锐角：度数在 0° 到 90° 之间的角。

Obtuse angle: An angle between 90° and 180°.

钝角：度数在 90° 到 180° 之间的角。

Reflex angle: An angle between 180° and 360°.

优角（反角）：度数在 180° 到 360° 之间的角。

Complementary angles: Two angles that sum to 90°.

余角：和为 90° 的两个角。

Supplementary angles: Two angles that sum to 180°.

补角：和为 180° 的两个角。

Vertically opposite angles: Angles opposite each other when two lines intersect; they are equal.

对顶角：两条直线相交时相对的两个角，它们相等。

Parallel lines: Lines in a plane that never meet, marked with arrows. Transversal creates corresponding, alternate and co‑interior angle pairs.

平行线：平面上永不相交的直线，用箭头标记。截线产生同位角、内错角和同旁内角。

Corresponding angles: Angles in matching positions when a transversal crosses parallel lines; they are equal.

同位角：截线与平行线相交时位置相同的一对角，它们相等。

Alternate angles: Angles inside parallel lines but on opposite sides of the transversal; they are equal.

内错角：在平行线内侧但位于截线两侧的角，它们相等。

Co‑interior angles (allied angles): Angles inside parallel lines on the same side of the transversal; they sum to 180°.

同旁内角：在平行线内侧且位于截线同侧的角，和为 180°。

Interior angle of a polygon: The angle inside the shape formed by two adjacent sides.

多边形的内角：由两条相邻边在图形内部形成的角。

Exterior angle of a polygon: The angle formed by extending one side; for regular polygons, it equals 360° ÷ n.

多边形的外角：延长一条边形成的角；对于正多边形，外角 = 360° ÷ n。

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6. Circles and Symmetry | 圆与对称

Circumference: The perimeter (distance around) a circle, given by C = 2πr or πd.

圆周：圆的周长（外围距离），公式 C = 2πr 或 πd。

Radius (r): Distance from the centre of a circle to any point on the circumference.

半径 (r)：从圆心到圆周上任意一点的距离。

Diameter (d) raight line passing through the centre connecting two points on the circumference; d = 2r.

直径 (d)：通过圆心连接圆周上两点的直线；d = 2r。

Chord: A line segment joining any two points on the circumference; the diameter is the longest chord.

弦：连接圆周上任意两点的线段；直径是最长的弦。

Tangent: A straight line that touches a circle at exactly one point, perpendicular to the radius at that point.

切线：与圆恰好相切于一点的直线，在该点与半径垂直。

Arc: A part of the circumference of a circle.

弧：圆周的一部分。

Sector: A region enclosed by two radii and an arc, like a 'pizza slice'.

扇形：由两条半径和一段弧围成的区域，形似“披萨切片”。

Segment: The region between a chord and an arc.

弓形：由一条弦和一段弧围成的区域。

Line symmetry: A shape has line symmetry if it can be folded along a line so that both halves match exactly.

线对称：如果一个图形可以沿一条线对折后两部分完全重合，则它具有线对称。

Rotational symmetry: A shape has rotational symmetry if it looks the same more than once when rotated through a full turn. The order is the number of matching positions.

旋转对称：如果图形旋转一周时能多次与自身重合，则具有旋转对称。重合的次数即为旋转对称的阶数。

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7. Mensuration: Area and Volume | 测量：面积与体积

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

周长：二维图形外边界线的总长度。

Area: The amount of surface covered by a 2D shape, measured in square units (cm², m², etc.).

面积：二维图形所覆盖的表面大小，单位为平方单位（cm², m² 等）。

Volume: The space occupied by a 3D object, measured in cubic units (cm³, m³, etc.).

体积：三维物体占据的空间，单位为立方单位（cm³, m³ 等）。

Surface area: The total area of all faces (and curved surfaces) of a 3D solid.

表面积：三维立体所有面（和曲面）的总面积。

Prism: A solid with a constant cross‑section along its length, e.g. triangular prism, cuboid. Volume = area of cross‑section × length.

棱柱：具有恒定横截面的立体，例如三棱柱、长方体。体积 = 横截面积 × 长度。

Cylinder: A prism with a circular cross‑section. Volume = πr²h; curved surface area = 2πrh.

圆柱：横截面为圆的棱柱。体积 = πr²h；侧面积 = 2πrh。

Pyramid h a polygon base and triangular faces meeting at an apex. Volume = ⅓ × base area × height.

棱锥：底面为多边形、侧面为三角形且交于顶点的立体。体积 = ⅓ × 底面积 × 高。

Cone yramid with a circular base. Volume = ⅓πr²h; curved surface area = πrl (l = slant height).

圆锥：类似于底面为圆的棱锥。体积 = ⅓πr²h；侧面积 = πrl（l 为斜高）。

Sphere: A perfectly round 3D object. Volume = ⁴⁄₃πr³; surface area = 4πr².

球体：完美的圆形三维物体。体积 = ⁴⁄₃πr³；表面积 = 4πr²。

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8. Coordinate Geometry | 坐标几何

Cartesian plane: A grid defined by two perpendicular number lines (x‑axis and y‑axis) intersecting at the origin (0, 0).

笛卡尔平面：由两条相互垂直的数轴（x 轴和 y 轴）相交于原点 (0, 0) 形成的网格。

Coordinates (x, y): An ordered pair showing a point's horizontal (x) and vertical (y) position from the origin.

坐标 (x, y)：有序数对，表示点相对于原点的水平 (x) 和垂直 (y) 位置。

Gradient (slope) ulated as m = (y₂ − y₁) / (x₂ − x₁). Positive gradient slopes upwards, negative downwards.

斜率（梯度）：衡量直线倾斜程度的量，计算公式 m = (y₂ − y₁) / (x₂ − x₁)。正斜率向上倾斜，负斜率向下倾斜。

m = (y₂ − y₁) / (x₂ − x₁)

Intercept: The point where a line crosses an axis. The y‑intercept is the value of y when x = 0.

截距：直线与坐标轴的交点。y 轴截距是当 x = 0 时的 y 值。

Equation of a straight line: Commonly 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 为斜率，c 为 y 轴截距。

Midpoint oint exactly halfway between two points (x₁, y₁) and (x₂, y₂): M = ((x₁+x₂)/2, (y₁+y₂)/2).

中点：位于两点 (x₁, y₁) 和 (x₂, y₂) 正中间的点：M = ((x₁+x₂)/2, (y₁+y₂)/2)。

Parallel lines: Have equal gradients (m₁ = m₂).

平行直线：斜率相等 (m₁ = m₂)。

Perpendicular lines: Product of gradients equals −1 (m₁ × m₂ = −1).

垂直直线：斜率乘积为 −1 (m₁ × m₂ = −1)。

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9. Statistics | 统计

Discrete data: Data that can only take specific, separate values (often whole numbers), e.g. number of cars in a family.

离散数据：只能取特定、分离数值的数据（常为整数），例如家庭拥有的汽车数。

Continuous data: Data that can take any value within a range, e.g. height, time, mass.

连续数据：在某个范围内可取任意值的数据，如身高、时间、质量。

Frequency: The number of times a particular value occurs in a data set.

频数：某个数值在数据集中出现的次数。

Mean: The average, found by summing all values and dividing by the number of values.

平均数（均值）：所有数值之和除以数值个数。

Median: The middle value when data is arranged in order; for an even number of values, it is the mean of the two middle numbers.

中位数：将数据按顺序排列后位于中间的值；若数据个数为偶数，则取中间两个数的均值。

Mode: The value that appears most frequently in a data set.

众数：数据集中出现次数最多的值。

Range: A measure of spread: largest value minus smallest value.

极差（范围）：衡量离散程度的量：最大值减最小值。

Quartiles: Values that divide an ordered data set into four equal parts. The lower quartile (Q₁) is the median of the lower half, the upper quartile (Q₃) is the median of the upper half.

四分位数：将有序数据集分成四等份的数值。下四分位数 (Q₁) 是下半部分数据的中位数，上四分位数 (Q₃) 是上半部分数据的中位数。

Interquartile range (IQR): Q₃ − Q₁; measures the spread of the middle 50% of data, resistant to outliers.

四分位距 (IQR)：Q₃ − Q₁；衡量中间 50% 数据的离散程度，不受极端值影响。

Correlation: The relationship between

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