📚 Year 7 Edexcel Further Maths: Key Terminology Quick Study Guide | 七年级 Edexcel 进阶数学：词汇术语速记指南
Mastering the key vocabulary of Year 7 Further Maths is essential to understanding problems and communicating solutions clearly. This quick study guide presents the most important terms you will meet, each paired with a memory tip to help you remember them fast. Whether you are learning about integers, algebra or angles, the right words will unlock your confidence in every topic.
掌握七年级进阶数学的关键词汇对于理解题目和清晰表达解题过程至关重要。本速记指南将呈现你将遇到的最重要术语，每个术语都配有记忆技巧，帮助你快速记住它们。无论你正在学习整数、代数还是角度，正确的词汇都能为你打开每道题的自信之门。
1. Number & Place Value | 数字与位值
Integer: A whole number that can be positive, negative or zero. The word comes from Latin meaning 'whole' or 'untouched'. Memory tip: Think of an 'integer' as an 'intact' number – no fractions or decimals.
整数：可以是正数、负数或零的整数。这个词来自拉丁语，意为“完整的”。记忆技巧：把“整数”想象成“完整的”数——没有分数或小数部分。
Place value: The value of a digit based on its position in a number. In 345, the 3 is worth 300 because it is in the hundreds place. Memory tip: Each place is ten times larger than the place to its right, like a set of boxes growing ten times each step.
位值：一个数字中某位数因其位置而代表的值。在345中，3代表300，因为它位于百位。记忆技巧：每向左移动一位，数值就扩大十倍，就像一排盒子，每步放大十倍。
Negative number: A number less than zero, written with a minus sign. Memory tip: Imagine a lift going below ground level – negative numbers are floors below zero.
负数：小于零的数，用减号表示。记忆技巧：想象一部电梯降到地平面以下——负数就是零以下的楼层。
2. Arithmetic Operations | 算术运算
Addition (+) and subtraction (−) are inverse operations. The result of addition is called the sum; the result of subtraction is the difference. Memory tip: 'Sum' and 'some' sound alike – when you add, you get some total.
加法（+）和减法（−）互为逆运算。加法得到的结果叫和，减法得到的叫差。记忆技巧：'Sum' 听起来像 'some'——把数合起来得到总量。
are also inverses. The result of multiplication is the product; the result of division is the quotient. Memory tip: 'Product' reminds you of 'produce' – multiplying 'produces' a bigger number (unless by fractions).
乘法（×）和除法（÷）也互为逆运算。乘法得到的结果叫积，除法的结果叫商。记忆技巧：'Product' 让你想到 'produce'（产生）——乘法“产生”一个更大的数（乘以分数除外）。
BIDMAS / BODMAS: The order of operations – Brackets, Indices (or Orders), Division, Multiplication, Addition, Subtraction. Memory tip: Learn the phrase 'Big Ideas Drive My Algebraic Success' to remember the order.
BIDMAS / BODMAS：运算顺序——括号、指数（或阶）、除法、乘法、加法、减法。记忆技巧：记住口诀“括号指数先算，再乘除后加减”，就能轻松掌握顺序。
3. Factors, Multiples & Primes | 因数、倍数与质数
r number. For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly. Memory tip: Factors 'fit into' a number with no remainder.
因数：能整除另一个数的数。例如，3是12的因数，因为12÷3=4没有余数。记忆技巧：因数能“刚好装进”那个数里。
Multiple: The result of multiplying a number by an integer. The multiples of 5 are 5, 10, 15, 20, … Memory tip: A multiple is what you 'get' when you multiply – think 'times table'.
倍数：一个数与整数相乘得到的结果。5的倍数有5、10、15、20……。记忆技巧：倍数就是你做乘法时“得到”的数——想想乘法口诀表。
Prime number: A whole number greater than 1 that has exactly two factors – 1 and itself. Examples: 2, 3, 5, 7, 11. Memory tip: Prime numbers are like 'prime' cuts of meat – they cannot be divided into smaller equal chunks (except by 1 and itself).
质数：大于1且只有两个因数（1和它本身）的整数。如2、3、5、7、11。记忆技巧：质数就像“不可分割”的原子——除了1和本身，没法再平分。
HCF (Highest Common Factor) and LCM (Lowest Common Multiple): HCF is the biggest factor shared by two or more numbers; LCM is the smallest multiple they share. Memory tip: HCF sounds like 'highest shared fence', LCM like 'lowest shared meeting point'.
最大公因数（HCF）和最小公倍数（LCM）：HCF是两个或多个数共有的最大因数；LCM是它们共有的最小倍数。记忆技巧：把HCF想象成“最高的共同围栏”，LCM想象成“最低的共同相遇点”。
4. Fractions | 分数
Numerator: The top part of a fraction, showing how many parts are taken. Denominator: The bottom part, showing the total number of equal parts. Memory tip: 'Numerator' has an 'u' as in 'up', so it's upstairs. Denominator starts with 'd' as in 'down', so it's downstairs.
分子：分数线上方的数，表示取了多少份。分母：分数线下方的数，表示总共有多少等份。记忆技巧：Numerator 带 'u' 像 'up'（上），所以住楼上；Denominator 开头是 'd'，像 'down'（下），所以住楼下。
/4 = 3/6. Memory tip: Multiply or divide both numerator and denominator by the same number – the fraction stays the same, just like scaling a picture.
等值分数：表示相同量值的分数，如1/2 = 2/4 = 3/6。记忆技巧：分子和分母同时乘或除以相同的数，分数的值不变，就像把图片按比例缩放。
Mixed number and improper fraction: A mixed number has a whole number and a fraction (e.g. 2 1/3). An improper fraction has a numerator larger than the denominator (e.g. 7/3). Memory tip: 'Improper' means it's 'top-heavy', like carrying too many parcels upstairs.
带分数和假分数：带分数由整数和分数组成（如2 1/3）。假分数的分子比分母大（如7/3）。记忆技巧：'Improper' 意味着“头重脚轻”，就像楼上装了太多包裹。
5. Decimals & Percentages | 小数与百分数
Decimal point: The dot separating whole numbers from fractional parts. The first place after the point is tenths, the second is hundredths. Memory tip: The decimal point is like a 'full stop' – everything to its right is less than 1.
小数点：分隔整数部分与小数部分的点。小数点后第一位是十分位，第二位是百分位。记忆技巧：小数点就像一个“句号”——它右边的数都小于1。
Percentage: A fraction out of 100, symbol %. 25% means 25/100 = 1/4. Memory tip: 'Cent' means 100, like in 'century' (100 years) – percentage is per hundred.
百分数：分母为100的分数，符号为%。25%表示25/100 = 1/4。记忆技巧：'Cent' 意为100，如 'century'（世纪百年）——百分数就是每百份中的份数。
Convert between fractions, decimals and percentages: 1/2 = 0.5 = 50%. Memory tip: Think of the three forms as different languages saying the same amount – learn the translation shortcuts.
分数、小数和百分数之间的转换：1/2 = 0.5 = 50%。记忆技巧：把这三种形式看作表达同一数量的三种语言——学会翻译捷径即可。
6. Ratio & Proportion | 比与比例
Ratio: A way to compare two or more quantities, e.g. 2:3. The order matters. Memory tip: A ratio is like a recipe – '2 parts flour to 3 parts sugar' – it tells you the mix.
比：比较两个或以上数量的方式，如2:3。顺序很重要。记忆技巧：比就像一份配方——“2份面粉配3份糖”——它给出混合比例。
Simplify a ratio: Divide all parts by their HCF. 4:6 simplifies to 2:3. Memory tip: Simplifying a ratio is like scaling down a photo – keep the same shape, just smaller terms.
化简比：将所有项除以它们的最大公因数。4:6化简为2:3。记忆技巧：化简比就像缩小照片——保持相同形状，只是数字变小了。
g two ratios are equal. If 2:3 = 4:6, they are in proportion. Memory tip: Proportion means 'equal portions' – the balance stays the same.
比例：表示两个比相等的等式。若2:3 = 4:6，则它们成比例。记忆技巧：比例意味着“相等份数”——天平始终平衡。
7. Algebra – Expressions | 代数——表达式
Variable: A letter or symbol that stands for an unknown number, often x or y. Memory tip: Think of a variable as a 'mystery box' – you don't know what's inside until you solve it.
变量：代表未知数的字母或符号，常用x或y。记忆技巧：把变量想象成一个“神秘盒子”——在解开之前，你不知道里面是什么。
Coefficient: The number multiplying the variable in a term. In 3x, 3 is the coefficient. Memory tip: 'Coefficient' sounds like 'co-pilot' – it goes with the variable, helping to define it.
系数：项中与变量相乘的数。在3x中，3是系数。记忆技巧：Coefficient 听起来像 'co-pilot'（副驾驶）——它和变量一起出现，帮助确定变量的大小。
nd power, e.g. 5x and 2x. You can combine them: 5x + 2x = 7x. Memory tip: You can only add 'apples with apples' – x with x, y with y.
同类项：变量和指数完全相同的项，如5x和2x。你可以合并它们：5x + 2x = 7x。记忆技巧：只能“苹果加苹果”——x和x能加，y和y能加，不能混着加。
Expand: To multiply out brackets, e.g. 3(x + 4) = 3x + 12. Memory tip: Expand means 'spread out' – the bracket opens like a door and the outside number visits each term inside.
展开：将括号乘开，如3(x+4)=3x+12。记忆技巧：Expand 就是“展开”——括号像一扇门被推开，外面的数去拜访括号里的每一项。
8. Algebra – Equations | 代数——方程
g the equals sign. Example: 2x + 3 = 11. Memory tip: An equation is like a balanced seesaw – both sides have the same weight.
方程：用等号表示两个表达式相等的数学陈述。例如：2x+3=11。记忆技巧：方程就像一个平衡的跷跷板——两边重量相等。
Solve: To find the value of the unknown that makes the equation true. Memory tip: Solving is 'detective work' – you follow clues (inverse operations) to find the hidden number.
解：求出使方程成立的未知数的值。记忆技巧：解方程就像“侦探工作”——你按照线索（逆运算）找出隐藏的数。
Inverse operation: The opposite operation, e.g. addition and subtraction, multiplication and division. You use inverses to isolate the variable. Memory tip: If you 'go backwards', you undo the steps – like unwrapping a present.
逆运算：相反的运算，如加与减、乘与除。你使用逆运算来分离变量。记忆技巧：“倒着走”就撤消了步骤——就像拆开礼物包装。
9. Sequences | 数列
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