📚 Year 9 Edexcel Maths: Quick Memory Guide for Key Terms | Year 9 Edexcel 数学：词汇术语速记指南
Mastering mathematical vocabulary is the secret weapon for excelling in Edexcel Year 9 Mathematics. Once you can speak the language of maths fluently, problem-solving becomes much faster and far less intimidating. This guide breaks down all the essential terms you need into bite-sized chunks, pairing concise English definitions with their Chinese equivalents and throwing in memory hacks to help you lock them in for good.
掌握数学词汇是攻克 Edexcel Year 9 数学的秘密武器。一旦你能流利使用数学语言，解题速度会大大加快，题目也不再那么令人生畏。本指南将所有你需要的核心术语拆分成小块，用简洁的英文定义与对应的中文解释相配对，并附上记忆技巧，帮助你牢固掌握它们。
1. Number Basics | 数字基础
Integer: A whole number that can be positive, negative or zero, with no fractional or decimal part. Examples: –7, 0, 15.
整数：可以是正数、负数或零的完整数字，没有分数或小数部分。例如：–7, 0, 15。
Factor: A number that divides exactly into another number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.
因数：能够整除另一个数（无余数）的数。例如，12 的因数有 1, 2, 3, 4, 6 和 12。
Multiple: The result of multiplying a number by any positive integer. The first few multiples of 5 are 5, 10, 15, 20…
倍数：一个数乘以任意正整数得到的结果。5 的前几个倍数是 5, 10, 15, 20…
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself. Examples: 2, 3, 5, 7, 11.
质数（素数）：大于 1 且只有两个不同因数的数：1 和它本身。例如：2, 3, 5, 7, 11。
Highest Common Factor (HCF): The largest factor shared by two or more numbers. For 8 and 12, the HCF is 4.
最高公因数（HCF）：两个或多个数共有的最大因数。对于 8 和 12，HCF 是 4。
Lowest Common Multiple (LCM): The smallest multiple two or more numbers have in common. The LCM of 4 and 6 is 12.
最小公倍数（LCM）：两个或多个数共有的最小倍数。4 和 6 的 LCM 是 12。
Square number ying an integer by itself. 9 is a square number because 3 × 3 = 9, usually written 3² = 9.
平方数：一个整数与自己相乘得到的数。9 是平方数，因为 3 × 3 = 9，通常记作 3² = 9。
Square root: A value that, when multiplied by itself, gives the original number. The square root of 25 is 5, shown as √25 = 5.
平方根：与自己相乘得到原数的数值。25 的平方根是 5，记作 √25 = 5。
Memory tip: Think of 'prime' as a prime minister who works alone – just like a prime number has only 'one and itself'.
记忆技巧：把 'prime' 想象成一个独自工作的首相——就像质数只有 '1 和自身' 两个因数。
2. Fractions, Decimals and Percentages | 分数、小数和百分比
Numerator: The top number in a fraction, showing how many parts are taken. In ¾, the numerator is 3.
分子：分数中上方的数，表示取了多少份。在 ¾ 中，分子是 3。
Denominator: The bottom number in a fraction, showing the total number of equal parts. In ¾, the denominator is 4.
分母：分数中下方的数，表示总共分成了几等份。在 ¾ 中，分母是 4。
Equivalent fractions: Fractions that represent the same value, even though they look different. For instance, ½ and ²⁄₄ are equivalent.
等值分数：虽然形式不同但值相等的分数。例如，½ 和 ²⁄₄ 是等值分数。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, such as ⁷⁄₄ or ³⁄₂.
假分数：分子大于或等于分母的分数，例如 ⁷⁄₄ 或 ³⁄₂。
Mixed number: A number made up of a whole number and a proper fraction, like 1 ½.
带分数：由一个整数和一个真分数组成的数，如 1 ½。
Decimal: A number written with a decimal point to separate the whole part from the fractional part. 0.75 is a decimal equivalent of ¾.
小数：用小数点将整数部分与分数部分分开的数。0.75 是 ¾ 的等值小数。
Percentage: A fraction out of 100, denoted by %. 75% means 75 out of 100, equal to 0.75.
百分比：以 100 为分母的分数，用 % 表示。75% 表示 100 份中的 75 份，等于 0.75。
Quick conversion trick: Remember FDP – Fraction to Decimal divide numerator by denominator; Decimal to Percent multiply by 100; Percent to Fraction write over 100 and simplify.
快速转换技巧：记住 FDP——分数转小数用分子除以分母；小数转百分比乘以 100；百分比转分数写上分母 100 然后化简。
3. Ratio and Proportion | 比和比例
Ratio: A way of comparing two or more quantities, showing the relative sizes. It can be written as 2 : 3 or as a fraction ⅔.
比：用来比较两个或多个量，显示相对大小。可以写成 2 : 3 或分数 ⅔。
Proportion ratios are equal. For example, ¼ = 25/100 shows proportion; we also say two quantities are 'in proportion' if they change together.
比例：表示两个比相等的陈述。例如，¼ = 25/100 展示了比例关系；如果两个量一起变化，我们也会说它们 '成比例'。
Direct proportion: When two quantities increase or decrease at the same rate, so their ratio stays constant. If you double one, you double the other.
正比例：两个量以相同速率增加或减少，使得它们的比值保持不变。如果其中一个翻倍，另一个也翻倍。
Scale factor: The multiplier used to enlarge or reduce a shape or quantity in a proportional way. A scale factor of 3 means every length becomes 3 times larger.
比例因子：用来按比例放大或缩小形状或数量的乘数。比例因子为 3 表示每个长度变为原来的 3 倍。
Unitary method: Finding the value of one unit first, then multiplying to find the required amount. If 5 pens cost £2, first find the cost of 1 pen, then multiply.
单位换算法：先求出一个单位的量，再乘以所需的单位数。例如，若 5 支笔 £2，先求 1 支笔的价格，再乘以需要的数量。
4. Algebraic Expressions | 代数表达式
Variable: A letter or symbol that represents a number we don't know yet, often x, y or n.
变量：一个字母或符号，代表我们尚不知道的数字，常见的有 x, y, n。
Term: A single number, variable or the product of numbers and variables, separated by + or – signs. In 5x + 3y – 7, there are three terms.
项：一个单独的数字、变量，或数字与变量的乘积，由 + 或 – 分隔。在 5x + 3y – 7 中有三项。
Coefficient: The number part of a term that multiplies the variable. In 7a², the coefficient is 7.
系数：项中与变量相乘的数字部分。在 7a² 中，系数是 7。
Constant: A term that is just a number, without any variable. Its value stays the same. In 2x + 9, 9 is the constant.
常数：只是一个数字的项，不含变量，其值保持不变。在 2x + 9 中，9 是常数。
Expression: A collection of terms joined by operations (+, –, ×, ÷) but without an equals sign. 4n – 1 is an expression.
表达式：用运算符号（+, –, ×, ÷）连接起来的项的集合，不含等号。4n – 1 是一个表达式。
Simplify (collect like terms): Combining terms that have exactly the same variable part. 3a + 5a simplifies to 8a.
化简（合并同类项）：将变量部分完全相同的项合并。3a + 5a 化简为 8a。
Expand: To multiply out brackets, often using the distributive law. 2(x + 3) expands to 2x + 6.
展开：用乘法运算去括号，通常使用分配律。2(x + 3) 展开为 2x + 6。
Factorise: The reverse of expanding – putting brackets back in by taking out a common factor. 2x + 6 factorises to 2(x + 3).
因式分解：展开的逆过程——通过提取公因数把表达式放回括号内。2x + 6 因式分解为 2(x + 3)。
5. Equations and Inequalities | 方程和不等式
Equation l statement that two expressions are equal, shown by an equals sign. Example: 2x + 5 = 11.
方程：表明两个表达式相等的数学陈述，用等号表示。例如：2x + 5 = 11。
Inequality: A statement that one expression is less than, greater than, less than or equal to, or greater than or equal to another.
不等式：表明一个表达式小于、大于、小于等于或大于等于另一个表达式的陈述。
Solve: To find the value(s) of the variable that make the equation or inequality true.
求解：找出使方程或不等式成立的变量的值。
Solution: The answer obtained by solving an equation. For x + 4 = 7, the solution is x = 3.
解：通过解方程得到的答案。对于 x + 4 = 7，解是 x = 3。
Balance method: Keeping the equation balanced by performing the same operation (add, subtract, multiply, divide) on both sides.
等量公理法：通过在等式两边进行相同的运算（加、减、乘、除）来保持等式平衡。
Inequality symbols: ' < ' means less than; ' > ' means greater than; ' ≤ ' means less than or equal to; ' ≥ ' means greater than or equal to; ' ≠ ' means not equal to.
不等式符号：' < ' 表示小于；' > ' 表示大于；' ≤ ' 表示小于等于；' ≥ ' 表示大于等于；' ≠ ' 表示不等于。
6. Sequences and Functions | 数列和函数
Sequence: An ordered list of numbers that often follows a rule. 2, 5, 8, 11… is a sequence.
数列：一组有序的数字，通常遵循某种规则。2, 5, 8, 11… 就是一个数列。
Term-to-term rule: A rule that tells you how to get from one term to the next. In the sequence above, the rule is 'add 3'.
逐项规则：告诉你如何从前一项得到下一项的规则。在上述数列中，规则是 '加 3'。
nth term: A formula that allows you to find any term in a sequence directly from its position number, n. For 3, 6, 9, 12… the nth term is 3n.
第 n 项公式：一个公式，让你能够根据项的位置编号 n 直接求出数列中任意一项。对于 3, 6, 9, 12…，第 n 项公式是 3n。
Arithmetic sequence: A sequence where the difference between consecutive terms is constant. This difference is called the common difference.
等差数列：相邻两项的差是常数的数列。这个差称为公差。
Function machine: A visual way of thinking about functions: you input a number, apply a set of operations, and get an output. It's like a number processing box.
函数机器：一种将函数可视化的方法：你输入一个数字，应用一组运算，然后得到一个输出。它就像一个数字加工盒。
7. Geometry: Angles and Lines | 几何：角与线
Acute angle: An angle that measures between 0° and 90°.
锐角：度数在 0° 到 90° 之间的角。
Obtuse angle: An angle greater than 90° but less than 180°.
钝角：大于 90° 但小于 180° 的角。
Reflex angle: An angle between 180° and 360°.
优角：角度在 180° 到 360° 之间的角。
Right angle: Exactly 90°, often marked with a small square.
直角：恰好 90°，常用一个小方框标记。
Complementary angles: Two angles that add up to 90°.
余角：两个角之和为 90°。
Supplementary angles: Two angles that add up to 180°.
补角：两个角之和为 180°。
Vertically opposite angles: When two lines cross, the angles opposite each other are equal. They are vertically opposite.
对顶角：当两条直线相交时，彼此相对的角相等。它们被称为对顶角。
Parallel lines: Lines in the same plane that never meet, no matter how far they extend.
平行线：在同一平面内无论怎样延长都不会相交的线。
Corresponding angles: Angles in matching corners when a line crosses parallel lines; they are equal.
同位角：一条直线截两条平行线时，位置相同的角；它们相等。
Alternate angles: Angles inside the parallel lines but on opposite sides of the transversal; they are equal.
内错角：在两条平行线内部，在截线两侧的角；它们相等。
Co-interior (or allied) angles: Angles inside parallel lines on the same side of the transversal; they add up to 180°.
同旁内角：在平行线内部，截线同一侧的角；它们的和为 180°。
8. Properties of Shapes | 形状的性质
Polygon: A closed 2D shape with straight sides. Triangles, quadrilaterals and hexagons are all polygons.
多边形：由直线段围成的封闭二维图形。三角形、四边形和六边形都是多边形。
Regular polygon: All sides and all interior angles are equal. A square and an equilateral triangle are regular.
正多边形：所有边长和内角都相等的多边形。正方形和等边三角形是正多边形。
Equilateral triangle: Three equal sides and three equal angles of 60°.
等边三角形：三条边相等，三个角均为 60°。
Isosceles triangle: Two equal sides and two equal base angles.
等腰三角形：两条边相等，两个底角相等。
Scalene triangle: All sides and angles are different.
不等边三角形：所有边长和角都不相等。
Quadrilateral: Any 2D shape with four straight sides. Examples: square, rectangle, parallelogram, rhombus, trapezium, kite.
四边形：任何有四条直线边的二维图形。例如：正方形、长方形、平行四边形、菱形、梯形、风筝形。
Circle parts: Radius (from centre to circumference), Diameter (across the centre, twice the radius), Circumference (perimeter of the circle), Chord (a line segment joining two points on the circle), Tangent (a line touching the circle at exactly one point), Arc (part of the circumference), Sector (region between two radii and an arc).
圆的部分：半径（从圆心到圆周）、直径（穿过圆心，半径的两倍）、圆周（圆的周长）、弦（圆上两点间的线段）、切线（恰好与圆交于一点的直线）、弧（圆周的一部分）、扇形（两条半径和一段弧围成的区域）。
9. Perimeter, Area and Volume | 周长、面积和体积
Perimeter: The total distance around the edge of a 2D shape. For a rectangle, add the lengths of all four sides.
周长：围绕二维图形边缘的总距离。对于长方形，将四条边的长度相加。
Area shape, measured in square units (cm², m²). Formula for a rectangle: Area = length × width.
面积：二维图形内部空间的大小，以平方单位（cm², m²）计量。长方形公式：面积 = 长 × 宽。
Area of triangle: ½ × base × perpendicular height. Always use the height at a right angle to the base.
三角形面积：½ × 底 × 垂直高。始终使用与底垂直的高。
Area of circle: π × radius², expressed as A = πr². The radius must be squared first.
圆的面积：π × 半径²，表示为 A = πr²。先计算半径的平方。
Circumference: The distance around a circle. Formula: C = π × diameter or C = 2πr.
圆周长：绕圆一圈的距离。公式：C = π × 直径 或 C = 2πr。
Volume: The amount of 3D space an object occupies, measured in cubic units (cm³, m³). Volume of
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