📚 Year 10 CCEA Maths: Essential Vocabulary Mnemonic Guide | Year 10 CCEA 数学：词汇术语速记指南
Mastering mathematical terminology is the foundation of success in CCEA Year 10 Maths. When you understand the language of numbers, algebra and shapes, problem-solving becomes much clearer. This guide pairs every key term with a simple definition, followed immediately by its Chinese equivalent, plus memory tricks where helpful. Use it to build your maths vocabulary and boost your confidence for class tests, homework and end-of-year assessments.
掌握数学术语是 CCEA Year 10 数学成功的基石。当你真正理解数字、代数和图形的语言时，解题思路会变得清晰很多。本指南为每个核心术语提供了简明定义，并紧跟对应的中文解释，同时还附上了实用的记忆窍门。用它来积累你的数学词汇，为课堂测验、家庭作业和年终考试增添信心。
1. Core Number Terms | 核心数字术语
Numbers are the building blocks of all maths topics. CCEA expects you to know the difference between types of numbers and how they relate to each other. Let's start with the most fundamental vocabulary.
数是所有数学主题的基石。CCEA 要求你了解不同类型数字之间的区别以及它们的相互关系。我们从最基础的词汇开始。
Integer: A whole number that can be positive, negative or zero, with no fractional part. For example, -3, 0 and 15 are all integers.
整数：可以是正数、负数或零的整数，没有小数部分。例如 -3、0 和 15 都是整数。
Natural number: The counting numbers starting from 1: 1, 2, 3, 4 and so on. Sometimes zero is included, but in CCEA questions natural numbers usually mean positive integers.
自然数：从 1 开始的计数数字：1、2、3、4 等等。有时也包含零，但在 CCEA 的题目中，自然数通常指正整数。
Prime number: A number greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are the first few primes. Memory tip: 'Prime' suggests 'first quality' — the number cannot be broken down further by multiplication.
质数：大于 1 且恰好只有两个不同因数——1 和它本身——的数。前几个质数是 2、3、5、7、11。记忆技巧：'质'表示基本，这个数无法通过乘法进一步分解。
Composite number: A whole number greater than 1 that is not prime — it has more than two factors. 4, 6, 8, 9 are composites.
合数：大于 1 但不是质数的整数，它有两个以上的因数。例如 4、6、8、9 都是合数。
Factor: A whole number that divides exactly into another number with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12.
因数：能够整除另一个数而没有余数的整数。12 的因数包括 1、2、3、4、6 和 12。
Multiple: The result of multiplying a number by an integer. The multiples of 5 are 5, 10, 15, 20 and so on. Essentially, multiples are the 'times table' of a number.
倍数：将一个数乘以整数所得到的结果。5 的倍数有 5、10、15、20 等。本质上，倍数就是某个数的“乘法表”。
Highest Common Factor (HCF): The largest factor shared by two or more numbers. For 12 and 18, the HCF is 6. Mnemonic: 'Highest' reminds you to look for the biggest shared divisor.
最大公因数 (HCF)：两个或多个数共有的最大因数。12 和 18 的最大公因数是 6。助记：'最大'提醒你要找共有因数中最大的那一个。
Lowest Common Multiple (LCM): The smallest multiple that two or more numbers share. For 4 and 5, the LCM is 20. Think of it as the first number that appears in both times tables.
最小公倍数 (LCM)：两个或多个数共有的最小倍数。4 和 5 的最小公倍数是 20。可以把它想象成同时出现在两个乘法表中的第一个数。
itself. 9 is a square number because 3 × 3 = 9. The first few squares are 1, 4, 9, 16, 25.
平方数：一个整数乘以自身的结果。9 是一个平方数，因为 3 × 3 = 9。前几个平方数是 1, 4, 9, 16, 25。
esult of multiplying an integer by itself twice. 8 is a cube number because 2 × 2 × 2 = 8.
立方数：一个整数乘以自身两次的结果。8 是立方数，因为 2 × 2 × 2 = 8。
2. Fractions, Decimals & Percentages | 分数、小数与百分比
Being able to move confidently between fractions, decimals and percentages is a vital skill. CCEA questions often ask you to compare quantities in different forms, so you need to know the language of each representation.
能够在分数、小数和百分比之间熟练转换是一项关键技能。CCEA 的题目经常会要求你比较不同形式的数量，因此你需要掌握每种表示方式的术语。
Numerator: The top number in a fraction, showing how many parts we have. In 3/4, 3 is the numerator.
分子：分数中位于上方的数字，表示我们拥有多少份。在 3/4 中，3 是分子。
Denominator: The bottom number in a fraction, indicating how many equal parts the whole is split into. In 3/4, 4 is the denominator.
分母：分数中位于下方的数字，表示整体被等分成多少份。在 3/4 中，4 是分母。
Proper fraction: A fraction where the numerator is smaller than the denominator, such as 2/5 or 7/8. Its value is always less than 1.
真分数：分子小于分母的分数，例如 2/5 或 7/8。它的值始终小于 1。
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, such as 9/4 or 5/5. The value is at least 1.
假分数：分子大于或等于分母的分数，例如 9/4 或 5/5。其值至少为 1。
Mixed number: A whole number combined with a proper fraction, like 2½. It is another way to express an improper fraction.
带分数：由一个整数和一个真分数组合而成，例如 2½。它是假分数的另一种表达形式。
Equivalent fractions: Different fractions that represent the same value, such as 1/2, 2/4 and 3/6. You can generate them by multiplying or dividing numerator and denominator by the same whole number.
等值分数：表示相同数值的不同分数，例如 1/2、2/4 和 3/6。你可以通过将分子和分母同时乘或除以同一个整数来得到等值分数。
Terminating decimal: A decimal number that ends after a finite number of digits, such as 0.75 or 3.2. All terminating decimals can be written as fractions with denominators that are powers of 10 or 2 and 5.
有限小数：位数有限的小数，例如 0.75 或 3.2。所有有限小数都可以写成分母为 10、2 和 5 的幂的分数。
Recurring decimal: A decimal in which a digit or group of digits repeats forever, often marked with a dot or bar, for example 0.333… or 0.142857142857…
循环小数：一个数字或一组数字无限重复出现的小数，通常用点或横线标记，例如 0.333… 或 0.142857142857…
Percentage: A fraction expressed out of 100. The symbol % means 'per hundred', so 45% means 45/100.
百分比：以 100 为分母的分数。符号 % 表示“每百”，因此 45% 就是 45/100。
ecrease expressed as a percentage of the original amount. Formula: change ÷ original × 100%.
百分比变化：相对于原始数量的增减，用百分比表示。公式：变化量 ÷ 原始量 × 100%。
3. Powers, Roots & Standard Form | 幂、根与标准形式
Year 10 brings more work with indices and standard form, which appear frequently in CCEA non-calculator and calculator papers. The vocabulary here is compact but powerful.
Year 10 会接触更多指数和标准形式的运算，它们在 CCEA 非计算器和计算器试卷中都十分常见。这部分术语虽然精炼，但威力很大。
many times the base is multiplied by itself. In 5³, 3 is the exponent and means 5 × 5 × 5.
指数（indices）或幂：位于底数右上角的小数字，表示底数乘以自身的次数。在 5³ 中，3 是指数，表示 5 × 5 × 5。
Base: The main number that is being raised to a power. In 5³, 5 is the base.
底数：被乘方运算的那个主要数字。在 5³ 中，5 是底数。
Square root: A value that, when multiplied by itself, gives the original number. The square root of 25 is 5, written as √25 = 5.
平方根：一个与自己相乘能够得到原数的值。25 的平方根是 5，记作 √25 = 5。
times in a multiplication, gives the original number. The cube root of 8 is 2, written as ∛8 = 2.
立方根：一个在乘法中使用三次能够得到原数的值。8 的立方根是 2，记作 ∛8 = 2。
small numbers as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. So 6500 becomes 6.5 × 10³.
标准形式（科学记数法）：将极大或极小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10，n 为整数。例如 6500 写成 6.5 × 10³。
Surd: An expression containing a root that cannot be simplified to a whole number, such as √2 or √5. Surds are left in root form to keep exact values.
根式（无理根）：含有无法化简为整数的根号的表达式，例如 √2 或 √5。根式保留根号形式以保持精确值。
Laws of indices: Quick rules for multiplying and dividing powers. Key examples:
指数运算法则：乘除幂的快捷规则。关键示例：
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
When multiplying like bases, add the indices. When dividing, subtract them. When raising a power to another power, multiply the indices.
同底数幂相乘时，指数相加；相除时，指数相减；幂的乘方时，指数相乘。
4. Algebraic Expressions & Identities | 代数表达式与恒等式
Algebra is the language of patterns and generalisations. CCEA papers will ask you to manipulate expressions, so knowing the difference between an expression, an equation and a formula is essential.
代数是模式和一般化的语言。CCEA 试卷会要求你操作各种式子，因此理解表达式、方程和公式之间的区别至关重要。
Variable: A symbol, usually a letter, that represents an unknown or changing value in an expression. In 3x + 7, x is the variable.
变量：通常用字母表示的符号，代表表达式中未知或变化的值。在 3x + 7 中，x 是变量。
Coefficient: The number multiplied by a variable. In 3x + 7, 3 is the coefficient of x.
系数：与变量相乘的数字。在 3x + 7 中，3 是 x 的系数。
Constant: A fixed term that does not change. In 3x + 7, 7 is the constant.
常数：不变的固定项。在 3x + 7 中，7 是常数。
Term: A single number, variable or the product of numbers and variables. In the expression 5x² − 3x + 2, there are three terms.
项：一个单独的数、变量或数与变量的乘积。在表达式 5x² − 3x + 2 中，共有三项。
Expression: A collection of terms combined by mathematical operations, but with no equals sign. For example, 4y − 9 or 2a² + 3a − 5.
表达式：通过数学运算将项组合在一起的式子，但没有等号。例如 4y − 9 或 2a² + 3a − 5。
ent that two expressions are equal, containing an equals sign. 2x + 3 = 11 is an equation.
方程：表明两个表达式相等的陈述，含有等号。2x + 3 = 11 是一个方程。
onship between different quantities. For example, A = l × w gives the area of a rectangle.
公式：一种展示不同量之间关系的特殊方程。例如 A = l × w 给出了矩形的面积。
Identity: An equation that is true for all values of the variable, often written with an '≡' sign. For instance, (x + 1)² ≡ x² + 2x + 1.
恒等式：对于变量的所有取值都成立的方程，常用 '≡' 符号表示。例如 (x + 1)² ≡ x² + 2x + 1。
Like terms: Terms that contain exactly the same variable raised to the same power. 3x and −5x are like terms and can be combined; 3x² and 4x are not like terms.
同类项：含有完全相同变量且指数相同的项。3x 和 −5x 是同类项，可以合并；而 3x² 和 4x 则不是同类项。
Expand: To multiply out brackets. Expanding 3(x + 2) gives 3x + 6.
展开：将括号乘开。将 3(x + 2) 展开得到 3x + 6。
Factorise: The reverse of expanding — writing an expression as a product of its factors. 3x + 6 factorises to 3(x + 2).
因式分解：展开的逆运算，将表达式写成其因式的乘积。3x + 6 因式分解为 3(x + 2)。
FOIL: A mnemonic for expanding two binomials: First, Outer, Inner, Last. For (x + 3)(x + 5), multiply First terms, then Outer, Inner and Last, then simplify.
FOIL法则：展开两个二项式的助记法：首项、外项、内项、末项。对于 (x + 3)(x + 5)，依次乘开并化简。
5. Equations & Inequalities | 方程与不等式
Solving equations is at the heart of Year 10 algebra. You will also meet inequalities, where the answer is a range of values rather than a single number. Knowing the notation helps you present solutions accurately.
解方程是 Year 10 代数的核心内容。你还会遇到不等式，答案往往是一个范围而不是单个数值。熟悉这些符号能帮助你准确呈现解答。
iable is only raised to the power of 1, such as 2x + 5 = 13. Its graph is a straight line.
线性方程：变量只带一次幂的方程，例如 2x + 5 = 13。它的图像是一条直线。
aining a term with the variable squared, such as x² − 4x − 5 = 0. Its graph is a parabola.
二次方程：含有变量平方项的方程，例如 x² − 4x − 5 = 0。它的图像是一条抛物线。
ame time. You solve them to find values that satisfy both, like y = 2x + 1 and x + y = 10.
联立方程组：一组同时成立的两个或多个方程。你需要求出同时满足所有方程的解，例如 y = 2x + 1 和 x + y = 10。
< (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式：使用 < (小于)、> (大于)、≤ (小于等于)、≥ (大于等于) 符号比较两个表达式的数学语句。
Solution set: The range of values that makes an inequality true. For x > 3, the solution set is all numbers greater than 3, often shown on a number line with an open circle at 3.
解集：使不等式成立的所有数值范围。对于 x > 3，解集是所有大于 3 的数，通常在数轴上用空心圆点表示 3。
both sides, keeping the scales balanced. If 2x = 10, divide both sides by 2 to get x = 5.
等量平衡法：解方程时通过对等号两边同时进行相同操作来保持平衡的方法。如果 2x = 10，两边同除以 2 得到 x = 5。
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