📚 Year 10 Eduqas Maths: Glossary & Terminology Fast-Track Guide | Year 10 Eduqas 数学：词汇术语速记指南
Building a strong mathematical vocabulary is like learning the language of numbers, shapes, and logic. In Year 10 Eduqas Maths, you need to quickly recall and apply key terms across number, algebra, geometry, statistics, and probability. This guide presents essential terms with clear explanations and memory hooks to help you master them efficiently.
建立扎实的数学词汇就像学习数字、形状和逻辑的语言。在 Year 10 Eduqas 数学中，你需要快速回忆并应用涉及数、代数、几何、统计和概率的关键术语。本指南通过清晰的解释和记忆钩子呈现基本术语，帮助你高效掌握它们。
1. Number & Arithmetic | 数与算术
Integer: An integer is any whole number, positive, negative, or zero. Examples: -3, 0, 7. Integers are the building blocks of arithmetic and appear on number lines marked with equally spaced tick marks. Memory tip: "Integer equals intact whole number, no fractions hiding inside."
整数：整数是任何正整数、负整数或零。例如：-3、0、7。整数是算术的基石，出现在等分刻度的数轴上。记忆窍门：“整数就是完整的数，里面不藏分数。”
Prime number: A prime number is a whole number greater than 1 that has exactly two distinct factors: 1 and itself. The first five primes are 2, 3, 5, 7, 11. Note that 1 is not prime. Think: "Prime has only 1 and me, no other family."
质数（素数）：质数是大于1的整数，且只有两个不同的因数：1和它本身。前五个质数是2，3，5，7，11。注意1不是质数。记忆：“质数只有1和自己，没有别的亲戚。”
Square number: 4² = 16, 7² = 49. Square numbers can be represented as geometrical squares. Quick recall: "Square means making a square array of dots."
平方数：平方数是一个整数乘以自身的积，例如1² = 1，4² = 16，7² = 49。平方数可以用几何上的正方形表示。快速回忆：“平方就是摆成正方形的点阵。”
Cube number: er by itself twice, e.g. 2³ = 8, 3³ = 27. Visualise a 3D cube of unit blocks. Memory hook: "Cube is volume, three times the same number."
立方数：立方数是一个整数乘以自身两次得到的数，例如2³ = 8，3³ = 27。想象一个由单位方块构成的立体正方体。记忆钩子：“立方是体积，同一个数乘三次。”
Factor: A factor of a number divides it exactly with no remainder. For 12, factors are 1, 2, 3, 4, 6, 12. Factors come in pairs that multiply to the number. Tip: "A factor is a friend that fits perfectly."
因数：一个数的因数是可以整除该数而没有余数的数。例如12的因数有1, 2, 3, 4, 6, 12。因数成对出现，相乘得原数。窍门：“因数就是完美契合的朋友。”
Multiple: A multiple of a number is the result of multiplying it by any integer. Multiples of 5 include 5, 10, 15, 20 ... Think of the multiplication table. "Multiples are what you say when skip-counting."
倍数：一个数的倍数是用任何整数乘以该数得到的结果。5的倍数包括5, 10, 15, 20 ... 想想乘法表。“倍数就是跳着数数时念出的数。”
Highest Common Factor (HCF): tors or use prime factorisation and multiply the smallest powers of common primes. Memory: "HCF = biggest value that divides both cleanly."
最大公因数 (HCF)：两个或多个数的最大公因数是它们共有的最大因数。求法：列出所有因数或使用质因数分解，取公共质数的最小幂次相乘。记忆：“HCF = 能整除所有数的最大值。”
Lowest Common Multiple (LCM): 6, LCM is 12. Use prime factors, taking the highest powers of all primes present. Slogan: "LCM = smallest shared timetable entry."
最小公倍数 (LCM)：最小公倍数是每个给定数的倍数中最小的一个。对于4和6，LCM是12。求法：用质因数，取所有出现质数的最高幂次。口诀：“LCM = 共享时刻表里最小的那一项。”
2. Fractions, Decimals & Percentages | 分数、小数与百分数
Numerator and Denominator: In a fraction a/b, a is the numerator (top), b is the denominator (bottom). The denominator tells how many equal parts make a whole. Remember: "Denominator is the name (like thirds), numerator counts how many."
分子与分母：在分数a/b中，a是分子（上），b是分母（下）。分母表示一个整体被分成多少等份。记忆：“分母是名字（如‘四分之一’），分子报数。”
Equivalent fractions: plying or dividing numerator and denominator by the same number. Example: 1/2 = 2/4 = 3/6. "What you do to the top, do to the bottom."
等值分数：表示相同数值的分数，可通过将分子和分母同时乘以或除以相同的数得到。例如：1/2 = 2/4 = 3/6。“上下同乘除，值不变。”
Terminating and recurring decimals: of digits (0.25 = 1/4). A recurring decimal repeats forever with a dot notation, e.g. 0.3̅ = 1/3. Memory: "Terminating means it ends; recurring has a repeating pattern."
有限小数与循环小数：有限小数在有限位数后终止（如0.25 = 1/4）。循环小数永远重复，用点表示，如0.3̅ = 1/3。记忆：“终止即结束；循环模式不断重复。”
Percentage: A percentage is a fraction out of 100. The symbol % means /100. To convert a decimal to a percentage, multiply by 100. "Percent = per century (per hundred)."
百分数：百分数是分母为100的分数。符号%表示/100。要将小数转化为百分数，乘以100。“百分数就是每一百。”
3. Indices & Standard Form | 指数与标准形式
Index (power): base by itself. In 5³, 5 is the base and 3 is the index (power), meaning 5 × 5 × 5 = 125. "Index = number of repeats in the multiplication."
指数（幂）：指数表示底数自乘的次数。在5³中，5是底数，3是指数，表示5 × 5 × 5 = 125。“指数就是乘法中重复的次数。”
Key index laws are best memorised with numerical patterns:
Multiplying same base: a² × a³ = a²⁺³ = a⁵. "Add the powers."
同底数幂相乘：a² × a³ = a²⁺³ = a⁵。“指数相加。”
Dividing same base: a⁵ ÷ a² = a⁵⁻² = a³. "Subtract the powers."
同底数幂相除：a⁵ ÷ a² = a⁵⁻² = a³。“指数相减。”
Power of a power: (a²)³ = a²×³ = a⁶. "Multiply the powers."
幂的乘方：(a²)³ = a²×³ = a⁶。“指数相乘。”
Zero index: a⁰ = 1 (a ≠ 0). "Anything to the power zero equals 1."
零指数：a⁰ = 1 (a ≠ 0)。“任何非零数的零次幂等于1。”
a⁰ = 1
Negative indices: A negative index represents a reciprocal. a⁻ⁿ = 1 / aⁿ. Example: 2⁻³ = 1/2³ = 1/8. Think: "Negative power flips the fraction."
负指数：负指数表示倒数。a⁻ⁿ = 1 / aⁿ。例如：2⁻³ = 1/2³ = 1/8。想成：“负指数，分数倒过来。”
Standard form: where 1 ≤ A < 10 and n is an integer. e.g. 4500 = 4.5 × 10³; 0.0023 = 2.3 × 10⁻³. Memory: "A between 1 and 10, n counts how many places the decimal moved."
标准形式：标准形式用A × 10ⁿ表示极大或极小的数，其中1 ≤ A < 10，n为整数。例如：4500 = 4.5 × 10³；0.0023 = 2.3 × 10⁻³。记忆：“A在1到10之间，n记录小数点移动位数。”
4. Algebra: Expressions & Equations | 代数：表达式与方程
Variable and coefficient: A variable is a symbol, usually a letter, that represents an unknown number. A coefficient is the number multiplied by the variable. In 3x + 2y, variables are x and y; coefficients are 3 and 2. "Coefficient stands before the letter like a bodyguard."
变量与系数：变量是一个符号，通常是字母，代表未知数。系数是乘以变量的数。在3x + 2y中，变量是x和y，系数是3和2。“系数就像变量前面的保镖。”
Expression, equation, identity, formula: ity is true for all values (x + x = 2x). A formula shows a relationship between variables (A = πr²). "Expression – no equals; Equation – solve me; Identity – always equal; Formula – rule that links variables."
表达式、方程、恒等式、公式：表达式是没有等号的项集合（3x + 5）。方程表示对特定值成立的等式（2x + 1 = 9）。恒等式对所有值都成立（x + x = 2x）。公式展示了变量间的关系（A = πr²）。“表达式无等号；方程要求解；恒等式永远等；公式是规则。”
Expanding brackets: inside by the term outside. For (x + 2)(x + 3), expand as x² + 3x + 2x + 6 = x² + 5x + 6. "Everyone inside shakes hands with the outsider."
展开括号：使用分配律：a(b + c) = ab + ac。括号内每一项乘以括号外的项。例如(x + 2)(x + 3) 展开为 x² + 3x + 2x + 6 = x² + 5x + 6。“里面的每个人都要和外面的人握手。”
Factorising: nd : The reverse of expanding. Find the highest common factor of terms and write as a product. Example: 6x + 9 = 3(2x + 3). "Factorising is pulling out the common ingredient."
因式分解：展开的逆运算。找出各项的最大公因数，写成乘积形式。例如：6x + 9 = 3(2x + 3)。“因式分解就是提取公共的原材料。”
5. Inequalities & Sequences | 不等式与数列
Inequality symbols: ater than or equal to. The open end of the symbol always faces the larger quantity. Think: "The
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