📚 Year 10 SQA Advanced Mathematics: Quick Memorisation Guide to Vocabulary & Terminology | Year 10 SQA 进阶数学：词汇术语速记指南
Welcome to this targeted vocabulary guide for Year 10 SQA Advanced Mathematics. In the Scottish curriculum, mastering precise mathematical language is just as important as solving problems. This guide pairs each key term with its Chinese translation, helping bilingual learners build confidence and avoid misunderstandings in exams. Use it as a quick reference, a revision checklist, or a daily drill – the dual-language format makes memorisation faster and more effective.
欢迎使用本 Year 10 SQA 进阶数学词汇速记指南。在苏格兰课程体系中，熟练掌握精确的数学语言与解题能力同等重要。本指南为每一个关键术语提供中英双语对照，帮助双语学习者建立自信，避免考试中的理解偏差。你可以把它当作快速查阅手册、复习清单或每日操练材料——双语格式能让记忆更快、更牢固。
1. Algebraic Expressions | 代数表达式
Expression s, variables and operators (such as +, −, ×, ÷) without an equals sign, e.g. 3x² + 5x − 7.
表达式：由数字、变量和运算符（如 +、−、×、÷）组成的式子，不含等号，例如 3x² + 5x − 7。
Equation atement that shows two expressions are equal, containing an equals sign, e.g. 2x + 3 = 11.
方程：表明两个表达式相等的数学陈述，含有等号，例如 2x + 3 = 11。
Term: A single number, variable, or product of numbers and variables separated by + or − signs, e.g. in 4x² − 3x + 2, the terms are 4x², −3x and 2.
项：由加号或减号分隔的单个数字、变量或数字与变量的乘积，例如在 4x² − 3x + 2 中，项分别为 4x²、−3x 和 2。
Coefficient: The numerical factor multiplying a variable in a term, e.g. the coefficient of x² in 5x² is 5.
系数：项中与变量相乘的数值因子，例如在 5x² 中，x² 的系数是 5。
Factorise s, often by taking out common factors or using special products, e.g. x² − 9 = (x+3)(x−3).
因式分解：把一个表达式写成其因子的乘积，常通过提取公因子或利用特殊乘积实现，例如 x² − 9 = (x+3)(x−3)。
2. Quadratic Equations & Functions | 二次方程与二次函数
Quadratic equation n equation of the form ax² + bx + c = 0 where a ≠ 0, representing a parabola when graphed.
二次方程：形如 ax² + bx + c = 0 且 a ≠ 0 的方程，其图像是一条抛物线。
Discriminant two distinct real roots (Δ > 0), one repeated real root (Δ = 0), or no real roots (Δ < 0).
判别式：表达式 Δ = b² − 4ac，用于判定二次方程根的性质：两个不等实根（Δ > 0），一个重根（Δ = 0），或无实根（Δ < 0）。
Root: A solution to an equation; for a quadratic, the x-values where the graph crosses or touches the x-axis.
根：方程的解；对二次方程而言，即图像与 x 轴相交或相切的 x 值。
Parabola ntation depends on the sign of a in y = ax² + bx + c (upward if a > 0, downward if a < 0).
抛物线：二次函数的 U 形图像；开口方向取决于 y = ax² + bx + c 中 a 的符号（a > 0 时开口向上，a < 0 时开口向下）。
Completing the square: A method of rewriting a quadratic expression in the form a(x+p)² + q, which reveals the vertex and helps in solving equations.
配方法：将二次表达式改写成 a(x+p)² + q 形式的方法，能揭示顶点坐标并帮助解方程。
3. Functions & Graph Transformations | 函数与图像变换
Function: A rule that assigns each input (x) exactly one output (y), often written as f(x). The vertical line test confirms a graph represents a function.
函数：为每一个输入值 x 指定唯一输出值 y 的规则，常写作 f(x)。可通过垂直线检验判断图形是否为函数的图像。
Domain: The complete set of possible input values (x) for which a function is defined.
定义域：函数有定义的所有可能输入值（x）的集合。
Range: The set of all output values (y) that a function can produce.
值域：函数能产生的所有输出值（y）的集合。
Translation: A transformation that shifts a graph horizontally or vertically without changing its shape; f(x) + k moves it k units up, f(x + h) moves it h units left.
平移：将图像水平或垂直移动而不改变其形状的变换；f(x) + k 向上移动 k 个单位，f(x + h) 向左移动 h 个单位。
Reflection: A flip of a graph over a line, such as −f(x) reflecting in the x-axis or f(−x) reflecting in the y-axis.
反射：图像关于某一直线的翻转，例如 −f(x) 关于 x 轴反射，f(−x) 关于 y 轴反射。
4. Trigonometric Functions | 三角函数
Sine (sin): For an acute angle in a right-angled triangle, the ratio of the length of the opposite side to the hypotenuse. Extended using the unit circle to all real numbers.
正弦（sin）：在直角三角形中，锐角的对边长度与斜边长度的比值。利用单位圆可推广至全体实数。
Cosine (cos): The ratio of the adjacent side to the hypotenuse in a right-angled triangle; also the x-coordinate on the unit circle.
余弦（cos）：直角三角形中邻边与斜边的比值；也是单位圆上的 x 坐标。
Tangent (tan): The ratio of the opposite side to the adjacent side, equivalently sinθ/cosθ.
正切（tan）：对边长度与邻边长度的比值，等同于 sinθ/cosθ。
Radian a full circle is 2π radians; 180° = π rad. Key to calculus operations with trig functions.
弧度：角度度量单位，一周角对应 2π 弧度；180° = π 弧度。这是用三角函数进行微积分运算的关键。
Period: The length of the smallest interval over which a trigonometric function repeats its pattern; for sin(x) and cos(x) the period is 2π, for tan(x) it is π.
周期：三角函数重复其模式的最小间隔长度；sin(x) 和 cos(x) 的周期为 2π，tan(x) 的周期为 π。
5. Exponential & Logarithmic Functions | 指数与对数函数
Exponential function: A function of the form f(x) = a·bˣ where the variable appears in the exponent; often refers to base e, written exp(x) or eˣ.
指数函数：形如 f(x) = a·bˣ 的函数，其中变量出现在指数位置上；常指以 e 为底的函数，写作 exp(x) 或 eˣ。
Base: In an exponential expression bˣ, the number b that is raised to a power; in logarithms, the subscript in logₐ(x) is the base.
底数：指数表达式 bˣ 中被乘方的数 b；在对数中，logₐ(x) 的下标 a 即为底数。
Logarithm: The inverse of exponentiation: logₐ(y) = x means aˣ = y. Common bases are 10 (common log) and e (natural log, written ln).
对数：指数运算的逆运算：logₐ(y) = x 意味着 aˣ = y。常用底数为 10（常用对数）和 e（自然对数，写作 ln）。
Natural logarithm (ln): Logarithm with base e ≈ 2.718; it satisfies ln(eˣ) = x and eln x = x for x > 0.
自然对数（ln）：以 e ≈ 2.718 为底的对数；满足 ln(eˣ) = x 且当 x > 0 时 eln x = x。
6. Sequences & Series | 数列与级数
Arithmetic sequence: A sequence where the difference between consecutive terms is constant; this fixed value is called the common difference d.
等差数列：相邻两项之差为常数的数列；该固定差值称为公差 d。
Geometric sequence: A sequence where the ratio of consecutive terms is constant; this fixed multiplier is the common ratio r.
等比数列：相邻两项之比为常数的数列；该固定倍数称为公比 r。
Common difference / Common ratio: The constant d added or r multiplied to move from one term to the next in an arithmetic or geometric sequence respectively.
公差 / 公比：在等差数列或等比数列中，从前一项得到后一项分别所加的常数 d 或所乘的常数 r。
Series: The sum of the terms of a sequence; often denoted by sigma (Σ) notation, e.g. Σ (a₁ + ... + aₙ).
级数：数列各项的和；常用总和符号 Σ 表示，例如 Σ (a₁ + ... + aₙ)。
Summation (Sigma notation): A compact way to write a long sum using the Greek letter Σ; the lower and upper bounds indicate the starting and ending indices.
求和（西格玛记法）：用希腊字母 Σ 简洁表示长加法式子的方法；上下界指示起始与结束的索引。
7. Differentiation | 微分
Derivative: The instantaneous rate of change of a function, denoted by f'(x) or dy/dx; it gives the gradient of the tangent to the curve at any point.
导数：函数的瞬时变化率，记作 f'(x) 或 dy/dx；它给出曲线上任意点处切线的斜率。
Power rule: A basic differentiation rule: if f(x) = xⁿ then f'(x) = n xⁿ⁻¹, where n is a real constant.
Power rule: d/dx (xⁿ) = n xⁿ⁻¹
幂法则：基本求导法则：若 f(x) = xⁿ，则 f'(x) = n xⁿ⁻¹，其中 n 为实常数。
Stationary point: A point on a curve where the gradient is zero (f'(x) = 0); can be a maximum, minimum or point of inflection.
驻点：曲线上斜率为零的点（f'(x) = 0）；可能是极大值点、极小值点或拐点。
Second derivative: The derivative of the derivative, denoted f'' ity of a graph and to classify stationary points (positive → minimum, negative → maximum).
二阶导数：导数的导数，记作 f''(x)；用于判断图像的凹凸性并对驻点进行分类（二阶导数为正时为极小值点，为负时为极大值点）。
8. Integration | 积分
Integral: The reverse operation of differentiation; the general antiderivative F(x) + C represents a family of functions whose derivative is f(x).
积分：微分的逆运算；一般反导数 F(x) + C 表示导数为 f(x) 的一族函数。
Published by TutorHao | Year 10 进阶数学 Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图