📚 Year 11 AQA Maths: Key Terms Memory Guide | Year 11 AQA 数学：词汇术语速记指南
This guide is designed to help Year 11 students master the essential mathematical vocabulary required for the AQA GCSE exam. Quick and accurate recall of key terms can make a significant difference in understanding questions and communicating solutions effectively. Each section pairs concise definitions with memory tips to keep you exam-ready.
本指南旨在帮助 Year 11 学生掌握 AQA GCSE 数学考试所需的基本词汇。快速准确地回忆关键术语对于理解题目和有效表达解题过程至关重要。每个部分都搭配简明定义与记忆技巧，帮助你在考场上游刃有余。
1. Number Essentials: Factors, Multiples & Primes | 数字基础：因数、倍数与质数
Factor: iven number with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, 12. Think 'factor = fits exactly'.
因数：一个数的因数是能够整除该数且没有余数的整数。例如，12的因数有1、2、3、4、6、12。记法：因数就是刚好“塞得进”的数。
Prime Number: A prime number is a whole number greater than 1 whose only factors are 1 and itself. Examples: 2, 3, 5, 7, 11. 2 is the only even prime – keep that in mind.
质数：质数是大于1且只有1和它本身两个因数的整数。例如2、3、5、7、11。2是唯一的偶质数，很容易考到。
Prime Factor Decomposition: ing a factor tree. 24 = 2³ × 3. The index form uses powers to show repeated prime factors.
质因数分解：将一个数写成其质因数的乘积，常用“因子树”完成。24 = 2³ × 3。指数形式用来简写重复的质因数。
Highest Common Factor (HCF): The largest number that divides exactly into two or more numbers. Find it by listing common factors or comparing prime factor products. HCF of 24 and 36 is 12.
最大公因数 (HCF)：两个或多个数共有的最大因数。可以通过列举公因数或比较质因数乘积来找到。24和36的HCF是12。
Lowest Common Multiple (LCM): The smallest number that is a multiple of two or more given numbers. Use a Venn diagram of prime factors or list multiples. LCM of 6 and 8 is 24.
最小公倍数 (LCM)：两个或多个数的最小公倍数。可以使用质因数维恩图或数列法。6和8的LCM是24。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
Numerator & Denominator: The top number (numerator) tells how many parts you have; the bottom number (denominator) tells how many equal parts the whole is divided into. In 3/4, 3 is numerator, 4 is denominator.
分子与分母：上方的数（分子）表示你拥有几份；下方的数（分母）表示整体被分成几等份。在3/4中，3是分子，4是分母。
Equivalent Fractions: ultiplying or dividing both numerator and denominator by the same number. 1/2 = 2/4 = 4/8.
等价分数：表示相同值的分数，将分子和分母同时乘以或除以同一个数即可得到。1/2 = 2/4 = 4/8。
Percentage Increase/Decrease: To increase by 15%, multiply by 1.15; to decrease by 15%, multiply by 0.85. The multiplier directly links to the percentage change – remember 'increase = 1 + decimal, decrease = 1 - decimal'.
百分数增减：增加15%即乘以1.15；减少15%则乘以0.85。乘数直接对应百分比变化 —— 记忆口诀：增加是1加小数，减少是1减小数。
Reverse Percentage: nd : To find the original amount before a percentage change, divide by the multiplier. If a price is £92 after a 15% reduction, original = 92 ÷ 0.85.
逆向百分数：要找回百分数变化前的原始数值，只需除以对应的乘数。若降价15%后价格为£92，原价 = 92 ÷ 0.85。
Significant Figures: A way of rounding that starts at the first non-zero digit. 0.00456 to 2 significant figures is 0.0046. The zero before the 4 are not significant.
有效数字：一种从第一个非零数字开始计数的舍入方式。0.00456保留两位有效数字为0.0046。前面的零不计入有效数字。
3. Algebraic Expressions & Formulae | 代数表达式与公式
Term, Coefficient, Constant: In 4x + 7, 4x is a term, 4 is the coefficient of x, and 7 is a constant term. Terms are separated by + or - signs.
项、系数、常数：在4x + 7中，4x是一项，4是x的系数，7是常数项。项由加号或减号分隔。
Expression vs Equation: ion states that two expressions are equal and includes an equals sign (e.g. 3a + 2b = 10).
表达式与方程：表达式是由项构成的式子，没有等号（如3a + 2b）。方程则表示两个表达式相等，包含等号（如3a + 2b = 10）。
Like Terms: Terms that have exactly the same variable part can be combined. 3x and 5x are like terms; 3x and 3x² are not. Simplify by adding/subtracting coefficients.
同类项：变量部分完全相同的项可以合并。3x和5x是同类项；3x和3x²不是。合并时只需加减系数。
Expanding Brackets: 4) = 3x + 12. For double brackets, use FOIL (First, Outer, Inner, Last) or a grid method.
展开括号：将括号外的项乘以括号内的每一项。3(x+4) = 3x+12。双括号展开可用FOIL法则（首、外、内、末）或网格法。
Factorising: uadratic trinomials, look for two numbers that multiply to the constant and add to the coefficient of x.
因式分解：展开的逆过程；提取公因数。6x+9 = 3(2x+3)。对二次三项式，寻找两个数，它们的乘积等于常数项，加和等于x的系数。
4. Equations & Inequalities | 方程与不等式
Linear Equation: e : An equation where the highest power of the unknown is 1. Solve by performing inverse operations on both sides. 2x + 5 = 11 → x = 3.
线性方程：未知数的最高次幂为1的方程。通过两边执行逆运算求解。2x+5=11 → x=3。
Solving Simultaneous Equations: Two equations with two unknowns can be solved by elimination (add/subtract to remove a variable) or substitution. The solution is the point of intersection of their graphs.
解联立方程组：含有两个未知数的两个方程可用消元法（加减消去一个变量）或代入法求解。解的几何意义是两条直线图像的交点。
Inequality Symbols: open circle on a number line indicates strict inequality; closed circle includes the value.
不等式符号：< 表示小于，> 表示大于，≤ 表示小于或等于，≥ 表示大于或等于。数轴上空心点表示严格不等号，实心点表示包括该值。
Integer Solutions to Inequalities: possible integer values of x are -1, 0, 1, 2, 3. List all whole numbers within the range.
不等式的整数解：对于-2 < x ≤ 3，x可能的整数值为-1, 0, 1, 2, 3。列出范围内的所有整数即可。
5. Sequences | 数列
Term: Each number in a sequence is called a term. The first term is often denoted U₁ or T₁. The position of the term is n.
项：数列中的每一个数都称为一项。第一项常用U₁或T₁表示，项的位置记为n。
nth Term Rule: An algebraic expression that generates any term of a sequence based on its position n. For the arithmetic sequence 5, 8, 11, 14, ..., the nth term is 3n + 2.
第n项公式：一个根据位置n生成数列任意一项的代数式。对于等差数列5, 8, 11, 14, ...，第n项公式为3n+2。
Arithmetic Sequence: A sequence with a constant difference (d) between consecutive terms. The nth term is given by a + (n-1)d, where a is the first term. The linear pattern is easy to spot.
等差数列：相邻两项之差为常数d的数列。第n项公式为a+(n-1)d，a为首项。这种线性规律很容易识别。
Fibonacci Sequence: 1, 2, 3, 5, 8, ... The rule is Uₙ = Uₙ₋₁ + Uₙ₋₂. It appears in nature and exam questions.
斐波那契数列：每一项是前两项之和：1, 1, 2, 3, 5, 8, ... 递推规则为Uₙ = Uₙ₋₁ + Uₙ₋₂。它在自然界和考试题中经常出现。
6. Geometry: Angles & Polygons | 几何：角与多边形
Acute, Obtuse, Reflex: An acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is between 90° and 180°, and a reflex angle is between 180° and 360°.
锐角、钝角、优角：锐角小于90°，直角等于90°，钝角在90°与180°之间，优角在180°与360°之间。
Angles on a Straight Line: Sum to 180°. Angles around a point sum to 360°. Vertically opposite angles (where two lines cross) are equal.
直线上的角：和为180°。绕一点的角周和为360°。对顶角（两条直线交叉处）相等。
Parallel Line Angles: Alternate angles are equal (Z-shape), corresponding angles are equal (F-shape), co-interior (allied) angles sum to 180° (C-shape). Remember the letter shapes to identify them.
平行线中的角：内错角相等（Z形），同位角相等（F形），同旁内角之和为180°（C形）。用字母形状来辨认这些角非常方便。
Interior & Exterior Angles of Polygons: of interior angles = (n-2) × 180°. For a regular polygon, each exterior angle = 360° ÷ n.
多边形的内角与外角：任意凸多边形的外角和为360°。内角和 = (n-2) × 180°。对于正多边形，每个外角 = 360° ÷ n。
Circle Theorem Keywords: Chord, tangent, radius, diameter, arc, sector, segment. The angle in a semicircle is 90°. The perpendicular from the centre to a chord bisects the chord.
圆定理关键词：弦、切线、半径、直径、弧、扇形、弓形。半圆内的圆周角是90°。从圆心垂直于弦的直线平分该弦。
7. Pythagoras & Trigonometry | 毕达哥拉斯与三角学
Hypotenuse: he : The longest side of a right-angled triangle, always opposite the right angle. In Pythagoras' theorem, a² + b² = c², where c is the hypotenuse.
斜边：直角三角形中最长的边，总是直角的对边。在毕达哥拉斯定理中，a² + b² = c²，其中c为斜边。
SOHCAHTOA: s = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Use it to find missing sides and angles.
SOHCAHTOA：三角比的口诀：正弦 = 对边/斜边，余弦 = 邻边/斜边，正切 = 对边/邻边。用它来求缺失的边长或角度。
Angle of Elevation & Depression: Elevation is the angle up from the horizontal; depression is the angle down from the horizontal. They are equal when measured from parallel lines of sight.
仰角与俯角：仰角是从水平线向上看的角度；俯角是从水平线向下看的角度。当视线平行时，两者相等。
Bearings: Measured clockwise from North, always given as three figures (e.g. 045°). Solving bearing problems often involves constructing right-angled triangles and applying SOHCAHTOA or Pythagoras.
方位角：从正北方向顺时针测量，始终用三位数字表示（如045°）。解方位角问题常需构造直角三角形并应用SOHCAHTOA或毕达哥拉斯定理。
8. Transformations & Vectors | 图形变换与向量
Translation: A sliding movement described by a column vector (x above y). The shape stays congruent (same size and orientation). The vector (3, -2) means move 3 right, 2 down.
平移：由列向量（上方x，下方y）描述的滑动移动。变换后图形全等（大小和方向不变）。向量 (3, -2) 表示向右3格，向下2格。
Reflection: endicular distance from the mirror line. Common mirror lines: x = a, y = b, y = x, y = -x.
反射：关于给定直线（镜线）的镜像翻转。每一点到镜线的垂直距离相等。常见镜线：x = a、y = b、y = x、y = -x。
Rotation: Turning a shape about a centre of rotation through a specified angle and direction (clockwise/anticlockwise). The shape remains congruent. Use tracing paper to help.
旋转：绕旋转中心按指定角度和方向（顺时针/逆时针）转动图形。图形保持全等。用描图纸辅助作图。
Enlargement: A transformation that changes size by a scale factor k from a centre of enlargement. Distances are multiplied by k. For negative scale factors, the image appears on the opposite side of the centre.
放大：以放大中心为基准、按比例因子k改变大小的变换。距离乘以k。若比例因子为负，像出现在中心的另一侧。
Vector Notation: A vector has magnitude (length) and direction. Column vectors are written as (a b). Scalar multiplication changes the magnitude; adding vectors is done component-wise.
向量记号：向量具有大小（长度）和方向。列向量写成 (a b) 形式。标量乘法改变大小；向量相加按分量对应相加。
9. Statistics: Averages & Charts | 统计：平均数与图表
Mean, Median, Mode, Range: Median is the middle value when ordered. Mode is the most frequent value. Range = highest – lowest, measures spread.
平均数、中位数、众数、极差：平均数 = 数据和 ÷ 数据个数。中位数是将数据排序后位于中间的值。众数是出现频率最高的值。极差 = 最大值 – 最小值，衡量离散程度。
Frequency Polygon & Histogram: A frequency polygon plots frequencies at midpoints of intervals and connects them with straight lines. A histogram uses area of bars to represent frequency – crucial when class widths are unequal.
频数多边形与直方图：频数多边形以组中值为横坐标、频数为纵坐标描点并连线。直方图用条形的面积表示频数 —— 当组距不等时这一点至关重要。
Cumulative Frequency: A running total of frequencies. Plot upper class boundary against cumulative frequency to get an S-shaped curve. Use it to estimate median, quartiles and interquartile range (IQR).
累积频数：频数的累加。以组上界为横轴、累积频数为纵轴画出S形曲线。用以估计中位数、四分位数和四分位距(IQR)。
Box Plot: Displays minimum, lower quartile (Q1), median (Q2), upper quartile (Q3) and maximum. The box shows the IQR. Used to compare distributions visually.
箱线图：显示最小值、下四分位数Q1、中位数Q2、上四分位数Q3和最大值。箱体表示四分位距IQR。用于直观比较数据分布。
Scatter Graph & Correlation: Shows relationship between two variables. Positive correlation: as one increases, the other tends to increase. Line of best fit can be drawn for predictions. Correlation does not imply causation.
散点图与相关性：展示两个变量之间的关系。正相关表示一个增大，另一个也趋于增大。可绘制最佳拟合线用于预测。相关性不意味着因果关系。
10. Probability | 概率
Probability Scale: Ranges from 0 (impossible) to 1 (certain), often written as a fraction, decimal or percentage. An event with probability 0.5 has an even chance.
概率标度：从0（不可能）到1（必然），常以分数、小数或百分数表示。概率为0.5的事件表示机会均等。
Mutually Exclusive Events: the other happening is the sum of their individual probabilities: P(A or B) = P(A) + P(B).
互斥事件：不能同时发生的两个事件。其中一个或另一个发生的概率为其概率之和：P(A或B) = P(A) + P(B)。
Independent Events: ther. The probability of both happening is found by multiplying: P(A and B) = P(A) × P(B).
独立事件：一个事件的结果不影响另一个事件的结果。两者同时发生的概率相乘：P(A且B) = P(A) × P(B)。
Tree Diagrams: Used to show all possible outcomes of sequential events. Multiply along branches for 'and', add the relevant end probabilities for 'or'. Remember to update probabilities when items are not replaced.
树形图：用于显示连续事件的所有可能结果。沿分支相乘表示“且”，将相关的终端概率相加表示“或”。当物品不放回时，注意更新概率。
Venn Diagrams: Show sets and their overlaps. The intersection (∩) represents elements in both sets; union (∪) represents elements in either set. The universal set (ξ) contains all elements.
维恩图：表示集合及其重叠区域。交集(∩)代表两集合共有的元素；并集(∪)代表两集合中所有的元素。全集(ξ)包含所有元素。
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