📚 Year 7 CAIE Advanced Mathematics: Vocabulary Quick-Memorisation Guide | Year 7 CAIE 进阶数学词汇术语速记指南
Mastering mathematical vocabulary is essential for solving problems confidently at Year 7 CAIE Advanced Mathematics. This guide presents key terms with simple definitions and memory tricks to help you remember them easily. Each term appears in English followed by a clear Chinese explanation – ideal for bilingual learners aiming to strengthen their maths language skills.
掌握数学词汇是自信解决 Year 7 CAIE 进阶数学问题的基础。本指南通过简单的定义和记忆技巧，帮助你轻松记住关键术语。每个术语先给出英文说明，再提供清晰的中文解释，非常适合希望强化数学语言能力的双语学习者。
1. Number Types and Place Value | 数的类型与位值
Numbers form the foundation of all mathematics. Recognising different types of numbers and understanding place value prevents confusion in calculations and word problems.
数是数学的基础。认识不同类型的数并理解位值，可以避免在计算和应用题中混淆。
Integer: Any positive whole number, negative whole number, or zero. Examples: −7, 0, 4. Integers never contain fractions or decimals. Tip: 'Integer' sounds like 'integrity' – it stays whole and unbroken.
整数：任何正整数、负整数或零。例如 −7, 0, 4。整数绝不包含分数或小数。技巧：“整数”就是保持完整的数。
Whole Number: A non‑negative integer: 0, 1, 2, 3, … Whole numbers include zero. Tip: 'Whole' begins with zero – think of a whole cake that hasn't been touched yet (zero slices eaten).
非负整数：0, 1, 2, 3, … 包含零的非负整数。技巧：“非负”意味着不小于零，就像一整块蛋糕还没动过。
Natural Number: A positive integer used for counting: 1, 2, 3, … In CAIE, natural numbers start at 1. Tip: Natural counting always begins with 1 – you start counting from one item, not zero.
自然数：用于计数的正整数：1, 2, 3, … CAIE 体系中自然数从 1 开始。技巧：自然数就是数数，总是从 1 开始。
Negative Number: A number less than zero, shown with a minus sign. Example: −3 is three units below zero. Tip: Picture a thermometer in winter – temperatures drop into negative values.
负数：小于零的数，带有减号。例如 −3 比零小三。技巧：想象冬天的温度计，降到零下。
Place Value: The value given to a digit by its position in a number. In 2 836, the digit 8 has place value 800 (hundreds). Tip: 'Place' means column – units, tens, hundreds, thousands.
位值：数字在数中因所处位置而具有的值。在 2 836 中，数字 8 的位值是 800（百位）。技巧：位置决定了价值 – 个位、十位、百位、千位。
Digit: A single numerical symbol from 0 to 9. The number 1 042 uses four digits. Tip: Digits are the building blocks of numbers, just as letters are for words.
数字：从 0 到 9 的单个数字符号。数字 1 042 使用了四个数字。技巧：数字是组成数的字母。
Ascending Order: Arranging values from smallest to largest. Example: −5, 0, 3, 12. Tip: 'Ascend' means climb up – the numbers go upward.
升序：从小到大排列。如 −5, 0, 3, 12。技巧：“升”就是向上走。
Descending Order: Arranging values from largest to smallest. Example: 12, 3, 0, −5. Tip: 'Descend' means go down – the numbers drop.
降序：从大到小排列。如 12, 3, 0, −5。技巧：“降”就是向下滑。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions, decimals and percentages are three ways of showing parts of a whole. Being able to switch between them quickly is a key skill for Year 7 Advanced Mathematics.
分数、小数和百分数是表示整体的一部分的三种方式。能够在它们之间快速转换是 Year 7 进阶数学的一项关键技能。
Fraction: A part of a whole written with a numerator and denominator, e.g. 3/4. The bar means division. Tip: Think of a pizza sliced into 4 equal pieces – 3/4 means 3 slices.
分数：用分子和分母表示的整体的一部分，如 3/4。分数线表示除法。技巧：想象一张比萨分成 4 等份，3/4 就是 3 块。
Numerator: The top number in a fraction – shows how many parts we have. In 5/8, 5 is the numerator. Tip: 'Numerator' begins with 'Numer' like 'number' – it counts the parts.
分子：分数中上面的数，表示取了多少份。5/8 中 5 是分子。技巧：“分子”就是数出有多少份。
Denominator: The bottom number in a fraction – tells the total number of equal parts. In 5/8, 8 is the denominator. Tip: 'Denominator' starts with 'Denom' – think of 'denomination' of parts, like the type of coin.
分母：分数中下面的数，表示总共有多少等份。5/8 中 8 是分母。技巧：“分母”就像总类别的名称。
Proper Fraction: A fraction where the numerator is smaller than the denominator. Value is less than 1, e.g. 2/5. Tip: 'Proper' means smaller on top – modest fraction.
真分数：分子小于分母的分数。值小于 1，如 2/5。技巧：真分数上面小，有“谦虚”的大小。
Improper Fraction: A fraction where the numerator is greater than or equal to the denominator. Value is 1 or more, e.g. 9/4. Tip: 'Improper' because it looks top‑heavy – ready to become a mixed number.
假分数：分子大于或等于分母的分数。值等于或大于 1，如 9/4。技巧：假分数看起来上重下轻，常可化为带分数。
Mixed Number: A whole number combined with a proper fraction, e.g. 2 1/3. Tip: 'Mix' a whole and a fraction together – like a mixed fruit bowl.
带分数：由整数和真分数合成的数，如 2 1/3。技巧：把整数和分数“混合”在一起。
Equivalent Fractions: sent the same amount but have different numerators and denominators, e.g. 1/2 = 2/4 = 4/8. Tip: Multiply or divide the top and bottom by the same number.
等值分数：值相同但分子分母不同的分数，如 1/2 = 2/4 = 4/8。技巧：分子分母同时乘或除同一个数。
Decimal: A number expressed with a decimal point to show tenths, hundredths, etc. Example: 0.75 means 75 hundredths. Tip: The decimal point separates whole units from parts.
小数：用小数点表示十分位、百分位等的数。例如 0.75 表示 75 个百分之一。技巧：小数点把整数部分和部分隔开。
Percentage: A fraction out of 100, written with a % sign. 45% means 45 per 100. Tip: 'Per cent' means 'per hundred' – always compare to 100.
百分数：分母为 100 的分数，用 % 表示。45% 即每一百里的 45。技巧：“百分”就是每一百。
Recurring Decimal: A decimal in which one or more digits repeat endlessly, e.g. 0.
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