📚 Year 7 SQA Advanced Math: Vocabulary & Terminology Memorization Guide | Year 7 SQA 进阶数学：词汇术语速记指南
Mastering mathematical vocabulary is the cornerstone of success in Year 7 Advanced Math. This guide presents essential SQA-aligned terms with bilingual explanations and clever memory tips to help you recall definitions quickly and apply them confidently.
掌握数学词汇是 Year 7 进阶数学成功的基石。本指南提供与 SQA 对齐的核心术语，附有双语解释及巧妙的记忆技巧，帮助你快速回忆定义并自信地运用它们。
1. Number and Place Value | 数字与数位
Understanding the language surrounding whole numbers and their positions allows you to work with large and small values accurately. The key terms include integer, digit, place value, and order of magnitude.
理解描述整数及其位置的语言，可以让你准确处理大数值和小数值。关键术语包括整数、数字、数位和数量级。
Integer – An integer is any whole number, positive or negative, including zero. Think ‘integer = intact number’, no fractions or decimals. Memory tip: Imagine a number line; every mark that can be a whole person is an integer.
整数 – 整数是任何正整数、负整数和零。记住“整数就是完整的数”，不含分数或小数。记忆技巧：想象一条数轴，上面每一个能代表完整个体的人就是整数。
Place value – Place value tells us the value of a digit based on its position in a number. For example, in 3,524, the digit 5 is in the hundreds place, so its value is 500. Use a place value chart to visualize units, tens, hundreds, and thousands.
数位 – 数位告诉我们一个数字在数字中的位置所代表的值。例如，在 3,524 中，数字 5 在百位上，所以它的值是 500。借助数位表可以直观地看到个、十、百、千。
Digit – A digit is a single symbol used to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number can have multiple digits. Memory hook: ‘Dig-it’ into the ten symbols.
数字 – 数字是用来书写数字的单个符号：0、1、2、3、4、5、6、7、8、9。一个数可以包含多个数字。记忆法：从十个符号中“挖出”数字来。
Order of magnitude – This term refers to the power of ten that a number rounds to. For instance, 279 has an order of magnitude of 10² (hundreds). It helps you compare sizes quickly.
数量级 – 这个术语指一个数四舍五入后对应的 10 的幂。例如，279 的数量级是 10²（百）。它能帮你快速比较数值的大小。
2. Factors, Multiples and Primes | 因数、倍数与质数
These building blocks of number theory appear repeatedly in fractions, algebra, and problem-solving. Grasp factor, multiple, HCF, LCM, and prime number firmly.
这些数论的基石在分数、代数和解题中反复出现。牢牢掌握因数、倍数、最大公因数、最小公倍数和质数。
Factor – A factor is a number that divides another exactly without leaving a remainder. Factors of 12 are 1, 2, 3, 4, 6, 12. Tip: Factors ‘fit in’ evenly.
因数 – 因数是可以整除另一个数的数。12 的因数有 1、2、3、4、6、12。技巧：因数能“刚好装下”。
Multiple – A multiple is what you get when you multiply a number by an integer. Multiples of 4: 4, 8, 12, 16… Recall: Multiples are ‘many folds’ of the original number.
倍数 – 倍数是当一个数乘以整数后得到的结果。4 的倍数：4、8、12、16… 记住：倍数是原数的“许多倍”。
Highest Common Factor (HCF) – The largest factor that two or more numbers share. For 8 and 12, HCF is 4. Strategy: List factors and spot the biggest common one.
最大公因数 (HCF) – 两个或多个数共有的最大的因数。8 和 12 的最大公因数是 4。策略：列出因数并找出最大的共有项。
Lowest Common Multiple (LCM) – The smallest multiple that two or more numbers share. For 4 and 6, LCM is 12. Think: LCM is used when finding a common denominator for fractions.
最小公倍数 (LCM) – 两个或多个数共有的最小的倍数。4 和 6 的最小公倍数是 12。联想：求分数公分母时就用 LCM。
Prime number – A prime number has exactly two distinct factors: 1 and itself. E.g., 2, 3, 5, 7, 11. Memory aid: ‘Prime’ = simply two factors, like a prime minister has one main office and a backup.
质数 – 质数恰好有两个不同的因数：1 和它本身。例如 2、3、5、7、11。记忆法：“质数”像一位孤高的首相，只有两个支持者。
3. Fractions | 分数
Fractions represent parts of a whole. Key vocabulary: numerator, denominator, proper fraction, improper fraction, and mixed number.
分数代表整体的部分。核心词汇：分子、分母、真分数、假分数和带分数。
Numerator – The top number of a fraction; it tells how many parts we have. In ⅗, 3 is the numerator. Think ‘NUmerator = Number Up’.
分子 – 分数线上面的数字；它表示我们有多少份。在 ⅗ 中，3 是分子。联想：“分子”就像“分的子女”，站得高。
Denominator – The bottom number; it shows how many equal parts the whole is divided into. In ⅗, 5 is the denominator. Recall ‘Denominator = Down’.
分母 – 分数线下面的数字；它表示整体被分成了多少等份。在 ⅗ 中，5 是分母。记住：“分母”在下方。
Proper fraction – A fraction whose numerator is smaller than the denominator, e.g., ⅔. Its value is less than 1.
真分数 – 分子小于分母的分数，例如 ⅔。它的值小于 1。
Improper fraction – The numerator is greater than or equal to the denominator, e.g., 7/4. It represents a value of 1 or more.
假分数 – 分子大于或等于分母的分数，例如 7/4。它表示的值大于或等于 1。
Mixed number – A whole number combined with a proper fraction, like 1½. Converting between improper fractions and mixed numbers is a core skill.
带分数 – 一个整数和一个真分数组合在一起，如 1½。假分数与带分数的互化是核心技能。
4. Decimals and Percentages | 小数和百分数
Decimals and percentages are alternative ways of representing fractions. Comprehending decimal point, decimal place, and percent will let you move between these forms effortlessly.
小数和百分数是分数的另一种表示方式。理解小数点、小数位和百分比将使你在这几种形式之间轻松转换。
Decimal point – The dot separating the whole number part from the fractional part. In 3.75, the dot is the decimal point. Memory: ‘Point punctuates the whole and the part.’
小数点 – 将整数部分与小数部分隔开的点。在 3.75 中，这个点就是小数点。记忆：“点点分隔整体与部分”。
Decimal place – The position of a digit to the right of the decimal point, showing tenths, hundredths, thousandths. The number 0.06 has a 6 in the hundredths place.
小数位 – 小数点右侧的数字位置，表示十分位、百分位、千分位。数字 0.06 中的 6 在百分位上。
Percent (%) – Per cent means ‘out of 100’. 45% equals 45/100 or 0.45. Quick conversion: percent → fraction over 100; percent → decimal by shifting the point two places left.
百分数 (%) – Percent 的意思是“每一百”。45% 等于 45/100 或 0.45。快速转换：百分数写成分母为 100 的分数；百分数转小数则将小数点左移两位。
5. Order of Operations | 运算顺序
To avoid confusion when an expression has multiple operations, we follow the BODMAS/BIDMAS rule. Familiarity with brackets, indices, and the four operations is vital.
当一个表达式中有多个运算时，为了避免混淆，我们遵循 BODMAS/BIDMAS 规则。熟悉括号、指数和四种基本运算至关重要。
BODMAS – Brackets, Orders (Indices), Division, Multiplication, Addition, Subtraction. Use this sequence to evaluate expressions. Variant BIDMAS replaces ‘Orders’ with ‘Indices’.
BODMAS – 括号 (Brackets)、指数 (Orders/Indices)、除法 (Division)、乘法 (Multiplication)、加法 (Addition)、减法 (Subtraction)。按照这个顺序计算表达式。BIDMAS 只是将“Orders”改为了“Indices”。
Brackets – ( ) or [ ] indicate that the operation inside must be done first. Memory: ‘Brackets break in first.’
括号 – ( ) 或 [ ] 表示必须先计算里面的运算。记住：“括号总是抢先”。
Indices / Orders – Powers like 3² or 5³. 3² means 3 × 3 = 9. Solve these right after brackets.
指数 / 阶 – 像 3² 或 5³ 这样的幂。3² 表示 3 × 3 = 9。紧跟在括号之后就计算指数。
Example: 10 – 2 × ( 3 + 1 )² = 10 – 2 × 4² = 10 – 2 × 16 = 10 – 32 = -22
示例: 10 – 2 × ( 3 + 1 )² = 10 – 2 × 4² = 10 – 2 × 16 = 10 – 32 = -22
6. Algebraic Expressions | 代数表达式
Algebra uses letters to stand for unknown values. We collect, manipulate, and simplify expressions using terms, coefficients, and like terms.
代数用字母表示未知值。我们利用项、系数和同类项来收集、操作和简化表达式。
Variable – A letter that represents a number we don’t yet know, such as x or y. Think of it as a ‘varying’ placeholder.
变量 – 一个代表未知数的字母，例如 x 或 y。可以把它看作是“变化的”占位符。
Coefficient – The number multiplying the variable. In 7x, 7 is the coefficient. Memory: ‘Coefficient co-operates with the variable.’
系数 – 与变量相乘的数字。在 7x 中，7 是系数。记忆：“系数与变量合作”。
Term – A term is a single number, a variable, or numbers and variables multiplied together. E.g., 5, x, -3xy. Expressions are made of terms joined by + or -.
项 – 项是一个单独的数字、一个变量或数字与变量的乘积。例如 5、x、-3xy。表达式由各项通过 + 或 – 连接组成。
Like terms – Terms with exactly the same variable part and exponent can be combined. 2a and 5a are like terms; 2a and 3a² are not. Simplify by adding or subtracting coefficients.
同类项 – 变量部分和指数完全相同的项可以合并。2a 和 5a 是同类项；2a 和 3a² 则不是。通过加减系数进行化简。
7. Solving Equations | 解方程
An equation shows that two expressions are equal. Solving means finding the unknown value that makes the statement true. Key words: balance, inverse, unknown.
方程表示两个表达式相等。求解意味着找到使等式成立的未知值。关键术语：平衡、逆运算、未知数。
Equation – A mathematical sentence with an equals sign, like 2x + 3 = 11. It declares balance. Think of scales with the = as the pivot.
方程 – 带有等号的数学语句，例如 2x + 3 = 11。它表示一种平衡。可以将等号想象成天平的中心支点。
Solve – To find the value of the variable. Solving 2x = 8 gives x = 4. Strategy: always do the opposite operation to both sides.
求解 – 找到变量的值。解 2x = 8 得到 x = 4。策略：始终对方程两边做相反的运算。
Inverse operation – The operation that reverses another. Addition and subtraction are inverses; multiplication and division are inverses. Use inverse to isolate the unknown.
逆运算 – 能够逆转另一种运算的运算。加减互逆；乘除互逆。利用逆运算来隔离未知数。
Balance method – Whatever you do to one side of an equation, you must do to the other to keep it balanced. This method underpins all formal equation solving.
平衡法 – 对方程一边所做的操作，必须同时对另一边执行以保持平衡。这一方法是所有规范解方程的基础。
8. Geometry: Lines and Angles | 几何：线与角
Geometry vocabulary describes shapes, lines, and their properties. Master the names of angles and line arrangements: acute, obtuse, right, reflex, parallel, perpendicular.
几何词汇描述形状、线及其性质。掌握角度和线排列的名称：锐角、钝角、直角、优角、平行、垂直。
Angle – The space between two intersecting lines measured in degrees (°). The corner point is the vertex.
角 – 两条相交线之间的空间，以度 (°) 为单位。两条线的交点是顶点。
Acute angle – An angle less than 90°, sharp and small. ‘Acute’ reminds you of a cute little angle.
锐角 – 小于 90° 的角，尖而小。’Acute’ 让你联想到“小巧可爱”。
Right angle – Exactly 90°, often marked with a small square. A right angle forms a perfect corner.
直角 – 恰好等于 90°，通常用一个小方框标记。直角构成完美的角。
Obtuse angle – Greater than 90° but less than 180°. It looks wide and ‘obtuse’/’obese’ helps recall it is a larger angle.
钝角 – 大于 90° 但小于 180° 的角。看起来宽大，“钝”可以联想成庞大迟钝。
Reflex angle – An angle between 180° and 360°. It is the ‘reflection’ of the acute/obtuse side around the vertex.
优角 – 大于 180° 且小于 360° 的角。它可以看作是跨越顶点另一侧的“反射”。
Parallel lines – Lines that never meet, staying the same distance apart. Think of railway tracks.
平行线 – 永不相交的线，始终保持等距。想象火车铁轨。
Perpendicular lines – Lines that intersect at a right angle (90°). Memory: ‘Perpendicular’ points precisely to a right angle.
垂直线 – 相交成直角 (90°) 的线。记忆：“垂直”指向一个精准的直角。
9. Perimeter, Area and Volume | 周长、面积与体积
Measuring space involves perimeter (the distance around), area (the surface covered), and volume (the space inside a 3D shape). Learn their units and formulas.
空间的测量涉及周长（外框距离）、面积（覆盖的表面）和体积（三维形状内的空间）。学习它们的单位和公式。
Perimeter – The total length around a 2D shape. For a rectangle, P = 2×(length + width). Units: cm, m, etc. ‘Peri’ means ‘around’, like perimeter fence.
周长 – 二维图形边界的总长度。对于长方形，周长 = 2×(长 + 宽)。单位：厘米、米等。“周”即环绕一圈。
Area – The amount of surface a shape covers. Measured in square units, e.g., cm². Rectangle area = length × width. Visualise counting squares inside.
面积 – 形状覆盖的表面大小。以平方单位计量，如 cm²。长方形面积 = 长 × 宽。想象在图形内部数方格。
Volume – The space a 3D object occupies. Units: cm³, m³. Cuboid volume = length × width × height. Think of filling a box with unit
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