📚 A Quick Guide to Memorising Key Maths Terminology for Year 10 Eduqas | Year 10 Eduqas 数学词汇术语速记指南
Mastering mathematical language is just as important as solving problems. When you understand the precise meaning of terms, you can interpret questions correctly and communicate your reasoning clearly. This guide breaks down essential Year 10 Eduqas terminology into manageable groups, with clear explanations and memory hooks to help you recall them quickly in your assessments.
掌握数学语言与解题同等重要。当你理解术语的精确含义时，就能正确理解题意并清晰地表达推理过程。本指南将 Year 10 Eduqas 必备术语分组整理，配合清晰的解释和记忆技巧，帮助你在考试中快速回忆。
1. Number Terminology | 数字术语
Integer: An integer is any whole number that can be positive, negative, or zero. It has no fractional or decimal part.
整数：整数是任何正整数、负整数或零，没有分数或小数部分。
Prime Number: A prime number has exactly two distinct factors: 1 and the number itself. The number 1 is not prime because it only has one factor.
质数（素数）：质数恰好有两个不同的因数：1 和它本身。数字 1 不是质数，因为它只有一个因数。
Factor: A factor of a given number divides it exactly without leaving a remainder. For instance, factors of 12 are 1, 2, 3, 4, 6, and 12.
因数：一个数的因数能整除该数，且没有余数。例如，12 的因数是 1、2、3、4、6 和 12。
Multiple: A multiple is the product of a number and any integer. The multiples of 5 are 5, 10, 15, 20, and so on.
倍数：倍数是一个数与任意整数的乘积。5 的倍数有 5、10、15、20 等等。
Highest Common Factor (HCF) & Lowest Common Multiple (LCM): The HCF is the largest factor shared by two or more numbers, while the LCM is the smallest multiple they share. Use prime factorisation to find them efficiently.
最大公因数（HCF）与最小公倍数（LCM）：最大公因数是两个或多个数共有的最大因数，最小公倍数是它们共有的最小倍数。用质因数分解可以高效求出。
2. Fractions, Decimals and Percentages | 分数、小数和百分比
Numerator and Denominator: In a fraction, the numerator is the top part showing how many parts we have, and the denominator is the bottom part showing the total number of equal parts.
分子与分母：在分数中，分子是上方的数字，表示我们有多少份；分母是下方的数字，表示整体被分成多少等份。
Equivalent Fractions: e value even though they use different numerators and denominators, such as ½ = ²/₄ = ⁴/₈.
等值分数：虽然分子和分母不同，但表示相同数值的分数，例如 ½ = ²/₄ = ⁴/₈。
Recurring Decimal: A decimal with a digit or group of digits that repeats indefinitely, like 0.333... or 0.142857142857... Use a dot or bar above the repeating part.
循环小数：小数点后有一位或一组数字无限重复出现的小数，如 0.333... 或 0.142857142857... 在重复部分上方加点或横线表示。
Percentage Increase and Decrease: nce to the original amount. A multiplier method makes calculations quicker: increase by 15% → multiplier 1.15; decrease by 15% → multiplier 0.85.
百分比增减：百分比变化是对原值的差值进行比较。用乘数法可以快速计算：增加 15% → 乘数 1.15；减少 15% → 乘数 0.85。
3. Order of Operations (BIDMAS) | 运算顺序
BIDMAS: This acronym reminds you of the correct sequence for calculations: Brackets, Indices (powers, roots), Division, Multiplication, Addition, Subtraction. Division and multiplication have equal priority and are worked left to right, as are addition and subtraction.
BIDMAS：这个首字母缩略词帮你记住正确的计算顺序：括号、指数（幂、根）、除法、乘法、加法、减法。除法和乘法优先级相同，从左到右计算；加法和减法同理。
Indices (Powers): elf. For example, 2³ = 2 × 2 × 2 = 8. A negative index means reciprocal: 2⁻² = 1/2² = 1/4.
指数（幂）：指数表示一个基数自乘的次数。例如 2³ = 2 × 2 × 2 = 8。负指数表示倒数：2⁻² = 1/2² = 1/4。
Roots: The square root of a number is a value that gives the original number when multiplied by itself, such as √25 = 5. The cube root works similarly: ∛8 = 2.
根：一个数的平方根是自乘后得到原数的值，例如 √25 = 5。立方根类似：∛8 = 2。
4. Algebraic Fundamentals | 代数基础
Variable, Coefficient, Constant: A variable is a letter representing an unknown quantity (e.g., x, y). A coefficient is the number multiplying a variable, like the '3' in 3x. A constant is a fixed number, such as the '+5' in 3x + 5.
变量、系数、常数：变量是用字母表示未知量（如 x、y）。系数是乘以变量的数，例如 3x 中的 “3”。常数是一个固定数值，例如 3x + 5 中的 “+5”。
Term, Expression, Equation, Identity: that two expressions are equal and can be solved (e.g., 2x + 7 = 15). An identity is true for all values, denoted by ≡ (e.g., (x + 1)² ≡ x² + 2x + 1).
项、表达式、方程、恒等式：项是单个数学元素（如 4xy）。表达式是项的集合，没有等号（如 2x + 7）。方程陈述两个表达式相等，可以求解（如 2x + 7 = 15）。恒等式对所有值都成立，用 ≡ 表示（如 (x + 1)² ≡ x² + 2x + 1）。
Formula: hows the relationship between different variables, such as the area of a triangle A = ½bh.
公式：公式是一种特殊的方程，表示不同变量之间的关系，例如三角形面积公式 A = ½bh。
5. Solving Equations and Inequalities | 解方程与不等式
Linear Equation: For example, 3x - 4 = 11. Solve by performing inverse operations to isolate the variable.
线性方程：变量的指数为 1 的方程，图像为一条直线。例如 3x - 4 = 11。通过逆运算分离变量来求解。
Quadratic Equation: 6 = 0. Solutions can be found by factorising, completing the square, or using the formula.
二次方程：变量最高次幂为 2 的方程，例如 x² + 5x + 6 = 0。可通过因式分解、配方法或求根公式求解。
Inequality Symbols: or equal to. On a number line, open circles exclude the value; closed circles include it.
不等号：< 表示小于，> 表示大于，≤ 表示小于等于，≥ 表示大于等于。在数轴上，空心圆圈表示不包含该值；实心圆点表示包含。
Solution Set: For inequalities, the solution is often a range of values, written using set notation like {x: x > 2} or displayed on a number line.
解集：对于不等式，解通常是一个范围，用集合符号表示，例如 {x: x > 2}，或在数轴上标出。
6. Sequences and Patterns | 数列与规律
Term-to-Term Rule: A rule that tells you how to get from one term to the next in a sequence, e.g., "add 4" for 3, 7, 11, 15. This is easy but inefficient for finding the 100th term.
项间递推规则：描述数列中如何从前一项得到后一项的规则，例如在 3, 7, 11, 15 中是“加 4”。这个方法简单，但用来求第 100 项效率很低。
Position-to-Term Rule (nth term): A formula that links the term's position n to its value. For an arithmetic sequence, the nth term is a + (n - 1)d, where a is the first term and d is the common difference.
通项公式（第 n 项）：将项的位置 n 与其值联系起来的公式。对于等差数列，第 n 项公式为 a + (n - 1)d，其中 a 为首项，d 为公差。
Arithmetic Sequence: A number sequence with a constant difference between consecutive terms, such as 2, 5, 8, 11 (difference +3).
等差数列：相邻项之间的差为常数的数列，例如 2、5、8、11（差为 +3）。
Geometric Sequence: d by multiplying the previous term by a constant ratio, e.g., 3, 6, 12, 24, 48 (ratio ×2).
等比数列：每一项由前一项乘以一个固定比值得到的数列，例如 3、6、12、24、48（比值为 ×2）。
7. Key Angle Facts | 重要角度事实
Acute, Obtuse, Right, Reflex, Straight: An acute angle is less than 90°, a right angle is exactly 90°, obtuse is between 90° and 180°, straight is 180°, and reflex is between 180° and 360°.
锐角、钝角、直角、优角、平角：锐角小于 90°，直角恰好 90°，钝角在 90° 到 180° 之间，平角为 180°，优角在 180° 到 360° 之间。
Complementary and Supplementary: Complementary angles sum to 90°, supplementary angles sum to 180°. Remember: "C" comes before "S" and 90 is less than 180.
互余与互补：互余角之和为 90°，互补角之和为 180°。记忆方法：互余（C 开头）对应较小的 90°，互补（S 开头）对应较大的 180°。
Angles on a Straight Line and Around a Point: Angles on a straight line always add up to 180°, and angles around a single point add up to 360°. Vertically opposite angles are equal when two lines intersect.
直线上的角与绕一点的角度：直线上的角之和总为 180°，绕一点的角度之和为 360°。当两直线相交时，对顶角相等。
8. Properties of Polygons | 多边形性质
Regular Polygon: A polygon where all sides are equal in length and all interior angles are equal. Examples include equilateral triangle and square.
正多边形：所有边等长且所有内角相等的多边形，例如等边三角形和正方形。
Interior and Exterior Angles: An interior angle is inside the shape; an exterior angle is formed by extending one side outward. At each vertex, the interior and exterior angles add to 180°.
内角与外角：内角在多边形内部；外角是延长一条边所形成的角。在每个顶点处，内角与外角之和为 180°。
Sum of Interior Angles: angles = (n - 2) × 180°. The sum of exterior angles is always 360° for any convex polygon.
内角和：对于 n 边形，内角和 = (n - 2) × 180°。对于任何凸多边形，外角和总是 360°。
Congruent and Similar: Congruent shapes are identical in size and shape; corresponding sides and angles are equal. Similar shapes have the same shape but may differ in size; corresponding angles are equal and sides are in proportion.
全等与相似：全等图形形状和大小完全相同，对应边和对应角均相等。相似图形形状相同但大小可能不同，对应角相等，对应边成比例。
9. Perimeter, Area and Volume | 周长、面积和体积
Perimeter: he : The total distance around the outside of a 2D shape. For a rectangle, perimeter = 2(l + w).
周长：围绕二维图形外边缘的总长度。对于矩形，周长 = 2(长 + 宽)。
Area of Common Shapes: × height; Trapezium: A = ½(a + b)h where a and b are the parallel sides; Circle: A = πr².
常见图形的面积：矩形：A = 长 × 宽；三角形：A = ½ × 底 × 高；梯形：A = ½(a + b)h，其中 a 和 b 是平行边；圆：A = πr²。
Circumference: The perimeter of a circle: C = 2πr or C = πd, where r is radius and d is diameter.
圆周：圆的周长：C = 2πr 或 C = πd，其中 r 为半径，d 为直径。
Volume of a Prism: th. This applies to cylinders, triangular prisms, and cuboids. Remember the cross-section is the uniform shape that runs through the object.
棱柱的体积：体积 = 横截面积 × 长度。这适用于圆柱、三棱柱和长方体。注意横截面是贯穿物体的统一形状。
10. Statistics and Probability Terms | 统计与概率术语
Mean, Median, Mode, Range: Mean is the average (sum ÷ count). Median is the middle value when data are ordered. Mode is the most frequent value. Range is the difference between the highest and lowest values.
平均数、中位数、众数、极差：平均数（均值）是总和除以个数；中位数是将数据排序后位于中间的值；众数是出现频率最高的值；极差是最大值与最小值之差。
Discrete and Continuous Data: Discrete data can only take specific, separate values (e.g., number of students). Continuous data can take any value within a range (e.g., height, time). Bar charts suit discrete; histograms suit continuous.
离散数据与连续数据：离散数据只能取特定的、分立的值（如学生人数）。连续数据可以在一个范围内取任何值（如身高、时间）。离散数据宜用条形图，连续数据宜用直方图。
Probability Scale: Probability is a number between 0 and 1, where 0 means impossible and 1 means certain. It can be written as a fraction, decimal, or percentage.
概率标度：概率是一个介于 0 到 1 之间的数，0 表示不可能，1 表示必然。可用分数、小数或百分比表示。
Mutually Exclusive and Independent Events: : the outcome of one does not affect the other (e.g., rolling a die twice). P(A and B) = P(A) × P(B).
互斥事件与独立事件：互斥事件不能同时发生（例如掷一枚硬币得到正面和反面）。P(A 或 B) = P(A) + P(B)。独立事件：一个事件的结果不影响另一个事件（例如掷两次骰子）。P(A 且 B) = P(A) × P(B)。
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