📚 Year 8 OCR Further Maths: Key Terms Memory Guide | Year 8 OCR 进阶数学：词汇术语速记指南
Mastering the language of mathematics is essential for solving problems and communicating ideas clearly. This guide covers the key terminology you will meet in Year 8 OCR Further Mathematics, with concise definitions, worked examples and clever memory tips to help you lock each term into your long-term memory. Use it as a quick reference whenever you revise.
掌握数学语言对于解题和清晰地表达思想至关重要。本指南涵盖你在 Year 8 OCR 进阶数学中会遇到的关键术语，附有简明的定义、示例和巧妙的记忆技巧，帮助你把每一个术语牢牢印入长期记忆。复习时可随时查阅。
1. Algebra Basics | 代数基础
Variable: A variable is a symbol, usually a letter, that stands for a number that can change or is unknown. For example, in the expression 4x + 7, x is the variable. Memory tip: think of vary – a variable varies.
变量：变量是一个符号，通常是字母，代表可以改变或未知的数值。例如，在表达式 4x + 7 中，x 就是变量。记忆提示：联想到“变化”——变量会变化。
Constant: A constant is a fixed number that does not change. In the expression 4x + 7, the number 7 is the constant term. Memory tip: a constant stays constant, like the number of hours in a day.
常数：常数是一个固定不变的数。在表达式 4x + 7 中，数字 7 就是常数项。记忆提示：常数始终保持不变，就像一天的小时数一样。
Coefficient: A coefficient is the number multiplied by a variable. In 4x + 7, the coefficient of x is 4. If no number is written, the coefficient is 1 (e.g. x means 1x).
系数：系数是与变量相乘的数字。在 4x + 7 中，x 的系数是 4。如果没有写出数字，系数就是 1（例如 x 表示 1x）。
Term: A term is a single number, variable, or product of numbers and variables. In 5y² + 3y - 2, there are three terms: 5y², 3y, and -2. Terms are separated by addition or subtraction signs.
项：项是单个数字、变量或数字与变量的乘积。在 5y² + 3y - 2 中，有三个项：5y²、3y 和 -2。项之间由加号或减号分隔。
Expression: An expression is a combination of numbers, variables and operation signs, but it does not contain an equals sign. Examples: 2a + 3b, x² - 5. You simplify expressions, not solve them.
表达式：表达式是数字、变量和运算符号的组合，但不包含等号。例如：2a + 3b，x² - 5。表达式是化简，而不是求解。
Equation example, 3x + 2 = 11 is an equation. You solve equations to find the value of the unknown.
方程：方程表示两个表达式相等，使用等号（=）。例如，3x + 2 = 11 是一个方程。解方程就是求出未知数的值。
Formula different quantities. For example, the area of a rectangle is given by the formula A = lw.
公式：公式是一种特殊的方程，表示不同量之间的关系。例如，矩形的面积可以用公式 A = lw 表示。
2. Linear Equations and Inequalities | 线性方程与不等式
Solve r values) of the variable that make the equation true. For 2x = 10, the solution is x = 5.
求解：求解一个方程意味着找到使方程成立的变量的值。对于 2x = 10，解是 x = 5。
Solution / Root: The solution is the number that satisfies the equation. It is sometimes called a root, especially when dealing with polynomial equations. In Year 8, we can simply say 'solution'.
解 / 根：解是满足方程的数，有时也称为根，尤其是在处理多项式方程时。在 Year 8，我们可以简单地说“解”。
Inverse operation: An inverse operation is an operation that reverses the effect of another. Addition and subtraction are inverses; multiplication and division are inverses. Use inverse operations to isolate the variable.
逆运算：逆运算是一种能够撤销另一种运算效果的运算。加法和减法互为逆运算；乘法和除法互为逆运算。利用逆运算来分离变量。
Balance method: The balance method involves doing the same operation to both sides of an equation to keep it balanced, just like a weighing scale. It is the standard way to solve linear equations formally.
平衡法：平衡法是在方程两边进行相同的运算以保持平衡，就像天平一样。这是正式解线性方程的标准方法。
Inequality: An inequality compares two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to) or ≥ (greater than or equal to). For example, x > 3 means x can be any number greater than 3.
不等式：不等式使用 <（小于）、>（大于）、≤（小于或等于）或 ≥（大于或等于）等符号来比较两个表达式。例如，x > 3 表示 x 可以是任何大于 3 的数。
3. Powers and Roots | 幂与根
Power / Exponent / Index: A power tells you how many times to multiply a base number by itself. In 5³, the exponent is 3. Memory tip: The exponent 'exposes' how many copies of the base are multiplied.
幂 / 指数：幂告诉你一个底数要自乘多少次。在 5³ 中，指数是 3。记忆提示：指数“暴露”了有多少个底数在相乘。
Base: The base is the number that is being repeatedly multiplied. In 2⁵, the base is 2.
底数：底数是被重复相乘的那个数。在 2⁵ 中，底数是 2。
Square mber by itself. 6 squared = 6² = 6 × 6 = 36. The square of an integer is a perfect square.
平方：平方意味着一个数自乘。6 的平方 = 6² = 6 × 6 = 36。整数的平方是“完全平方数”。
Cube: Cubing means multiplying a number by itself twice. 4 cubed = 4³ = 4 × 4 × 4 = 64.
立方：立方意味着一个数自乘两次。4 的立方 = 4³ = 4 × 4 × 4 = 64。
Square root: The square root of a number is the value that, when squared, gives the original number. √25 = 5 because 5² = 25. The square root symbol is called a radical.
平方根：一个数的平方根是平方后得到原数的值。√25 = 5，因为 5² = 25。平方根符号叫做根号。
Cube root: The cube root reverses cubing. ³√64 = 4 because 4³ = 64.
立方根：立方根是立方的逆运算。³√64 = 4，因为 4³ = 64。
Index laws: When multiplying powers with the same base, add the exponents. When raising a power to another power, multiply the exponents.
指数法则：同底数的幂相乘，指数相加。幂的乘方，指数相乘。
aᵐ × aⁿ = aᵐ⁺ⁿ and (aᵐ)ⁿ = aᵐⁿ
4. Fractions, Decimals and Percentages | 分数、小数和百分比
Numerator: The top part of a fraction. In 3/4, 3 is the numerator; it tells how many equal parts we have. Memory tip: NUmerator is NUmber Up.
分子：分数的上部。在 3/4 中，3 是分子；它表示我们有多少个等份。记忆提示：分子就是上面的数。
Denominator: The bottom part of a fraction. In 3/4, 4 is the denominator; it tells into how many equal parts the whole is divided. Memory tip: Denominator starts with D for Down.
分母：分数的下部。在 3/4 中，4 是分母；它表示整体被分成了多少等份。记忆提示：分母在下面。
Equivalent fractions They are obtained by multiplying or dividing the numerator and denominator by the same non-zero number.
等值分数：表示相同数值但分子和分母不同的分数，如 1/2 = 2/4 = 4/8。它们是通过将分子和分母同时乘以或除以同一个非零数得到的。
Decimal show tenths, hundredths, etc. 0.75 means 7 tenths and 5 hundredths, equal to 75/100 = 3/4.
小数：用小数点表示十分位、百分位等的数。0.75 表示 7 个十分之一和 5 个百分之一，等于 75/100 = 3/4。
Percentage: A percentage is a fraction with denominator 100. Percent means 'per hundred'. 45% = 45/100 = 0.45. Use percentages to compare proportions easily.
百分比：百分比是分母为 100 的分数。百分表示“每一百”。45% = 45/100 = 0.45。用百分比可以方便地比较比例。
Proportion pares a part to the whole. If 15 out of 20 students passed, the proportion is 15/20 = 3/4.
比例：比例将部分与整体进行比较。如果 20 名学生中有 15 人通过，比例是 15/20 = 3/4。
Ratio: A ratio compares parts to parts. If a class has 12 boys and 8 girls, the ratio of boys to girls is 12:8, which simplifies to 3:2.
比：比是对部分与部分进行比较。如果一个班级有 12 名男生和 8 名女生，男生与女生的比是 12:8，化简后为 3:2。
5. Linear Graphs | 线性图像
Coordinate / Ordered pair: A pair of numbers (x, y) that locates a point on the coordinate plane. The first number is the horizontal (x) coordinate; the second is the vertical (y) coordinate.
坐标 / 有序数对：用来在坐标平面上定位点的一对数 (x, y)。第一个数是水平坐标 (x)，第二个数是垂直坐标 (y)。
Axes: The two perpendicular number lines on a graph. The horizontal line is the x-axis; the vertical line is the y-axis. They meet at the origin.
坐标轴：图形上两条互相垂直
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