Year 7 AQA Further Maths: Vocabulary Terminology Quick-Memorisation Guide | 7年级AQA进阶数学：词汇术语速记指南

📚 Year 7 AQA Further Maths: Vocabulary Terminology Quick-Memorisation Guide | 7年级AQA进阶数学：词汇术语速记指南

Mastering the vocabulary of further mathematics is the first step to solving problems confidently. In Year 7, building a strong terminology foundation will help you understand questions, explain your reasoning, and connect different topics. This guide provides clear definitions and memory tricks for essential terms used in AQA Further Maths for Year 7, all in a bilingual format to reinforce learning. Let's turn tricky words into easy-to-remember ideas.

掌握进阶数学的词汇是自信解题的第一步。在7年级，打下坚实的术语基础将有助于你理解题目、解释推理过程，并串联不同知识点。本指南为AQA 7年级进阶数学中的必备术语提供清晰的定义和速记技巧，采用中英双语形式来加深记忆。让我们把难记的词变成容易记住的概念。

1. Number and Place Value | 数字与位值

Numbers are built from digits and their positions hold real value. Getting comfortable with place value and comparisons makes everything else easier.

数字由数字符号构成，符号所在的位置决定其实际值。熟悉位值和大小比较，能让后续学习更加轻松。

Digit: A single numerical symbol (0,1,2,3,4,5,6,7,8,9) used to build numbers. Think of 'digit' as a finger – we count on our fingers and each finger is a digit, just like each symbol is a digit.

数字符号 (Digit): 用来组成数字的单个符号（0–9）。联想记忆：digit 也有“手指”的意思，我们最初用十根手指计数，每个手指就像一个个数字符号。

Place value: The value a digit has because of its position in a number. In 472, the place value of 7 is 70. Remember: the 'place' gives the 'value'.

位值 (Place value): 数字在数中的位置所决定的值。在472中，数字7的位值是70。记住：“位置”决定“价值”。

Integer: Any whole number that can be positive, negative, or zero. The word sounds like 'in-te-ger', think 'intact' whole number, nothing broken.

整数 (Integer): 任何正整数、负整数或零。英语单词和“intact（完整）”同源，代表完整的数，没有小数部分。

Less than (<): A comparison showing one number is smaller than another. 3 < 7. Imagine the smaller end of the symbol points to the smaller number.

小于 (<): 表示一个数比另一个数小。3 < 7。想象符号的尖头一端指向较小的数，像嘴巴吃大数，这样就不会搞错方向。

Greater than (>): A comparison showing one number is larger than another. 9 > 2. The wide opening faces the bigger number.

大于 (>): 表示一个数比另一个数大。9 > 2。开口大的那一边朝着较大的数，仿佛大嘴吞下大数。

Rounding: Changing a number to the nearest given place value to make it simpler. If the next digit is 5 or more, round up. Think '5 or above, give it a shove'.

四舍五入 (Rounding): 将数字简化为指定位值最近的近似值。口诀“五以上，往上推；四以下，往后丢”，看到下一位≥5就进1，否则舍去。

Significant figures: The meaningful digits in a number starting from the first non-zero digit. In 0.0560, the first significant figure is 5. Think 'significant' means the digits that really matter.

有效数字 (Significant figures): 一个数中从第一个非零数字开始的有意义的数字。0.0560的第一个有效数字是5。有效数字就是那些真正“起作用”的数字。

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2. Factors, Multiples and Primes | 因数、倍数与质数

These words describe how numbers relate to each other through multiplication and division. They are the secret codes of number theory.

这些词通过乘法和除法描述了数字之间的关联，是数论的秘密代码。

Factor: A number that divides exactly into another number without a remainder. 3 is a factor of 12. Think 'factory' – factors produce the number by multiplying together.

因数 (Factor): 能整除另一个数而没有余数的数。3是12的因数。联想“工厂”：因数之间相乘就能“生产”出这个数。

Multiple : The result of multiplying a number by an integer. 20 is a multiple of 5 because 5×4=20. Think 'many times' – you get multiples by adding the number over and over.

倍数 (Multiple): 一个数乘以整数得到的结果。20是5的倍数，因为5×4=20。想象“多次叠加”：不断加上自己就能得到倍数。

Prime number: A whole number greater than 1 with exactly two distinct factors: 1 and itself. 7 is prime (factors: 1,7). Remember: prime sounds like 'prime time' – only the main show (1 and itself).

质数 (Prime number): 大于1且只有两个不同因数的整数：1和它本身。7是质数。联想：“质”有“本质”之意，它的因数只有最本质的1和自身，非常纯粹。

Composite number: A whole number greater than 1 that has more than two factors. 8 is composite (factors: 1,2,4,8). Think 'composed' of many parts.

合数 (Composite number): 大于1且拥有两个以上因数的整数。8是合数。联想“组合”：由多个因数组合而成。

Highest common factor (HCF): The largest factor that two or more numbers share. The HCF of 12 and 18 is 6. Think of 'highest' on a ladder of common factors.

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。想象在公因数的梯子上，爬到最高那一级。

Lowest common multiple (LCM): The smallest multiple that two or more numbers share. The LCM of 4 and 6 is 12. 'Lowest' common meeting point on the multiple train.

最小公倍数 (LCM): 两个或多个数共有的最小倍数。4和6的最小公倍数是12。可以想象倍数火车在12站第一次相遇。

Prime factorisation reaking down a composite number into a product of prime numbers. 20 = 2×2×5. Like a number's DNA made of primes only.

质因数分解 (Prime factorisation): 将一个合数分解成质数相乘的形式。20 = 2×2×5。就像把数字拆成最基本的质数“DNA”。

Square number itself. 9 is a square number because 3×3=9. Visualise a square made of dots: 3 rows of 3.

平方数 (Square number): 一个数自乘的结果。9是平方数，因为3×3=9。可以想象由点组成的正方形阵列，3行3列。

Cube number a multiplication. 8 is a cube number because 2×2×2=8. Picture a 2×2×2 cube of sugar cubes.

立方数 (Cube number): 一个数自乘三次的结果。8是立方数，因为2 × 2 × 2 = 8。可以想象 2×2×2 的方糖堆。

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3. Fractions, Decimals and Percentages | 分数、小数和百分比

These three forms all represent parts of a whole. Being able to switch between them is essential for advanced maths.

这三种形式都表示整体的一部分。能在它们之间自由转换是进阶数学的基本功。

Numerator: The top number in a fraction; it tells how many parts we have. In ¾, 3 is the numerator. Think 'NUmerator' is 'NUmber of parts Up'.

分子 (Numerator): 分数线上方的数，表示我们拥有几份。¾中，3是分子。联想记忆：分子在“分”的上面，像一颗草莓顶在蛋糕上。

Denominator: The bottom number in a fraction; it tells how many equal parts the whole is divided into. In ¾, 4 is the denominator. Think 'Denominator' sits 'Down'.

分母 (Denominator): 分数线下方的数，表示整体被等分成几份。¾中，4是分母。英语“Denominator”和下“Down”发音相似，永远在底部。

Proper fraction: A fraction where the numerator is less than the denominator, so the value is less than 1. Example: ⅔. It's 'proper' because the top is smaller and well-behaved.

真分数 (Proper fraction): 分子小于分母的分数，值小于1。例如⅔。它很“安分”，因为上面比下面小。

Improper fraction numerator is greater than or equal to the denominator, value ≥1. ⁵⁄₃ is improper. It looks 'top-heavy', like an improper stack.

假分数 (Improper fraction): 分子大于或等于分母的分数，值≥1。⁵⁄₃是假分数。因为头重脚轻，像个不稳定的堆积。

Mixed number: A whole number and a proper fraction combined, like 2 ½. It mixes two types of numbers together.

带分数 (Mixed number): 由一个整数和一个真分数组合而成，如2½。它把整数和分数“混合”在一起。

Equivalent fractions ok different. ½ = ²⁄₄ = ⁴⁄₈. Just multiplied numerator and denominator by the same number.

等值分数 (Equivalent fractions): 看起来不同但值相等的分数。½ = ²⁄₄ = ⁴⁄₈，只要分子分母同乘一个数即可。

Simplify: Reducing a fraction to its simplest form by dividing the numerator and denominator by their HCF. ⁶⁄₈ simplifies to ¾. Make it as simple as possible.

约分 (Simplify): 用分子分母的最大公因数去除，化为最简分数。⁶⁄₈ 约分为 ¾。目标是让它“简单到不能再简单”。

Decimal: A number written with a decimal point to show values smaller than 1. Think 'dec' meaning ten, based on tenths, hundredths etc.

小数 (Decimal): 带有小数点的数，表示小于1的值。decimal 的词根是“十”，因为小数是按十分位、百分位来计数的。

Percentage: A fraction out of 100. 45% means 45 out of 100. The symbol % splits the two zeros in 100 – a visual reminder.

百分比 (Percentage): 以100为分母的分数。45% 表示 100份里的45份。% 符号像是由100这个数中间分割而来，便于记忆。

Recurring decimal: A decimal that has a repeating pattern of digits forever. 0.333... is recurring. Think of 'recurring' as a broken record that keeps repeating.

循环小数 (Recurring decimal): 小数部分有一段数字不断重复。0.333... 就是循环小数。就像一张卡碟的唱片，不停重复。

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4. Algebraic Expressions | 代数表达式

Algebra uses letters to stand for unknown numbers. Understanding the vocabulary makes writing and simplifying expressions a lot smoother.

代数用字母代表未知数。理解这些词汇能让书写和化简表达式变得顺畅。

Variable: A symbol, usually a letter, that represents a number we don't know yet. x and y are common variables. Think 'vary' – its value can vary.

变量 (Variable): 通常用字母表示未知数量的符号。x 和 y 是常见的变量。联想“变化”：它的值是可以改变的。

Coefficient: The number multiplied by a variable. In 5x, 5 is the coefficient. 'Co' means together, it works with the variable.

系数 (Coefficient): 变量前面的数字因子。在5x中，5是系数。系数和变量一起“配合”工作。

Term: A single number, variable, or number multiplied by variables. 3, x, 4xy are all terms. Think of terms as individual pieces of a mathematical phrase.

项 (Term): 一个单独的数、变量或数与变量的乘积。3, x, 4xy 都是项。可以把项看作数学短语中的单个单词。

Expression: A combination of terms using operations like addition and subtraction, but with no equals sign. 3x + 2y - 7 is an expression. It's a phrase, not a full sentence.

表达式 (Expression): 通过运算符号连接起来的项的组合，没有等号。3x + 2y - 7 就是表达式。它是一个短语，不是完整的句子。

Like terms: Terms that have exactly the same variable part. 2x and 5x are like terms; 2x and 2y are unlike. 'Like' means they match, so you can combine them.

同类项 (Like terms): 变量部分完全相同的项。2x 和 5x 是同类项；2x 和 2y 不是。它们是“同类”，所以能合并。

Simplify an expression: Collect like terms to write an expression in its shortest form. 2a + 3a simplifies to 5a. Just counting 'a's.

化简表达式 (Simplify an expression): 合并同类项，把表达式写成最简形式。2a + 3a 化简为 5a。就像数有多少个 a。

Expand: Multiply out brackets by distributing each term inside. 2(x + 3) expands to 2x + 6. Think 'expanding' the brackets like opening a folding fan.

展开 (Expand): 用乘法分配律去掉括号。2(x + 3) 展开为 2x + 6。想象把折叠扇子“展开”，每一项都露出来。

Factorise: The reverse of expanding; put brackets back in by taking out a common factor. 2x + 6 factorises to 2(x + 3). Think 'factory' – put the common part outside.

因式分解 (Factorise): 展开的逆运算，提取公因数放回括号。2x + 6 分解为 2(x + 3)。像工厂将公因数打包到括号外。

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5. Equations and Inequalities | 方程与不等式

When we set expressions equal to something or compare them, the language shifts. These terms help you describe and solve mathematical sentences.

当我们让表达式等于某个值或进行比较时，用语就不同了。这些术语帮助你描述和求解数学句子。

Equation al statement that shows two expressions are equal, using an equals sign. 2x + 1 = 7. Think 'equa' like 'equal' – both sides balance.

方程 (Equation): 用等号表示两个表达式相等的数学语句。2x + 1 = 7。关键词是“相等”，方程左右两边是平衡的。

Solution : The value of the variable that makes an equation true. The solution to 2x + 1 = 7 is x = 3. It 'solves' the puzzle.

解 (Solution): 使方程成立的变量的值。2x + 1 = 7 的解是 x = 3。它解开了谜题。

Solve s : To find the value of the unknown that satisfies the equation. To solve 2x = 10, we divide both sides by 2 to get x = 5. Keep the balance!

求解 (Solve): 找出使方程成立的未知数的值。解 2x = 10，两边同除以2得到 x=5。始终记住保持天平平衡！

Inequality , >, ≤ or ≥. x > 4 means x can be any value greater than 4. Not equal, just related.

不等式 (Inequality): 用 <, >, ≤, ≥ 等符号比较两个表达式的语句。x > 4 表示 x 可以是大于4的任意值。不相等，但有大小关系。

Unknown: The variable or missing number we are trying to find. Often represented by x. Until solved, it's 'unknown'.

未知数 (Unknown): 我们试图找出的变量或缺失的数。通常用 x 表示。在解出之前，它始终是“未知”的。

Balance method: A method of solving equations by doing the same operation to both sides to keep the equation balanced. If you add 3 to one side, add 3 to the other.

平衡法 (Balance method): 通过对方程两边同时进行相同操作来求解的方法。如果一边加3，另一边也必须加3，天平才不会倾斜。

Satisfy true, it satisfies it. x = 2 satisfies x + 3 = 5. Think of satisfying a condition or rule.

满足 (Satisfy): 当一个值使方程或不等式成立时，就说它满足该式。x=2 满足 x+3=5。像是符合某个条件。

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6. Geometry – Angles and Shapes | 几何 – 角度与形状

Geometry is full of special words for lines, angles and shapes. Learning them lets you describe the world around you with precision.

几何中有大量描述线、角和形状的专用词。掌握它们，你就能精确描述周围的世界。

Acute angle: An angle less than 90°. Think 'a cute' little angle, small and sharp.

锐角 (Acute angle): 小于90°的角。英文 acute 与 “a cute” 同音，可以想象成一个“可爱的小角”。

Obtuse angle: An angle greater than 90° but less than 180°. Think 'obtuse' sounds like 'obese' – a big fat angle.

钝角 (Obtuse angle): 大于90°但小于180°的角。英语 obtuse 有点像 obese（肥胖），是一个“大胖角”。

Reflex angle: An angle greater than 180° but less than 360°. It 'reflects' back past the straight line, like a reflex action.

优角 (Reflex angle): 大于180°小于360°的角。它像反射一样越过直线，反应（reflex）迅速，张开很大。

Right angle: An angle of exactly 90°, often marked with a small square. It's the 'right' corner for builders.

直角 (Right angle): 恰好90°的角，通常用一个小方框标记。它是建筑工人眼中的“标准角”

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