Year 8 Cambridge Advanced Mathematics: Quick Vocabulary and Terminology Memory Guide | Year 8 Cambridge 进阶数学：词汇术语速记指南

📚 Year 8 Cambridge Advanced Mathematics: Quick Vocabulary and Terminology Memory Guide | Year 8 Cambridge 进阶数学：词汇术语速记指南

Mastering advanced mathematics in Year 8 requires more than just solving problems — you must speak the language fluently. This guide presents essential terms across algebra, geometry, statistics, and more, with paired English-Chinese explanations and effective memory tricks. Use it to build confidence, ace your Cambridge assessments, and make revision painless.

在 Year 8 阶段学好进阶数学，不仅需要会解题，更要能流畅地“说”数学语言。本指南按代数、几何、统计等板块梳理必会术语，提供英中对照释义和实用记忆技巧。用它建立信心，轻松应对 Cambridge 测评，让复习不再痛苦。

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1. Algebraic Fundamentals | 代数基础术语

Variable: A letter or symbol that stands for an unknown number. In '3x + 5', x is the variable. Remember: a variable can 'vary', meaning its value can change.

变量：代表未知数的字母或符号。在“3x + 5”中，x 是变量。记忆：变量可以“变”，数值不固定。

Coefficient: The number multiplied by a variable. In 7y², 7 is the coefficient. Tip: 'Co-' means together; a coefficient works together with the variable.

系数：与变量相乘的数。在 7y² 中，7 是系数。提示：“系”表示联系，系数和变量紧密关联。

Constant: A fixed number that does not change. In '4m − 9', −9 is the constant. A constant stays 'constant'.

常数：不变的固定数值。在“4m − 9”中，−9 是常数。常数“恒定不变”。

Term: A single number, variable, or product of numbers and variables. '5ab', '−2x', and '7' are all terms. Think of a term as one piece of an expression.

项：单独的数、变量，或它们的乘积。“5ab”“−2x”“7”都是项。把项想象成表达式的一块积木。

Like Terms: Terms that have identical variable parts. 3x² and −5x² are like terms; 2x and 2y are not. You can only combine like terms.

同类项：变量部分完全相同的项。3x² 和 −5x² 是同类项；2x 和 2y 不是。只能合并同类项。

Expression: A combination of terms using operators (+, −, etc.) without an equals sign. '4a + 7 − b' is an expression. It does not state equality.

表达式：用运算符号连接起来、没有等号的式子。“4a + 7 − b”是表达式，不包含等量关系。

Equation: A mathematical statement that two expressions are equal, shown by an equals sign. '2n + 6 = 14' is an equation. Equations can be solved.

方程：含有等号、表示两式相等的数学陈述。“2n + 6 = 14”是方程，可以求解。

Simplify: To write an expression in its shortest form. Combining like terms turns 'x + 3x − 2' into '4x − 2'. Simplify means 'make simpler'.

化简：把表达式写成最简形式。合并同类项将“x + 3x − 2”变为“4x − 2”。“化简”即“变简单”。

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2. Numbers and Arithmetic | 数与算术术语

Integer: A whole number that can be positive, negative, or zero. ... −2, −1, 0, 1, 2 ... are integers. Fractions are not integers.

整数：可以是正数、负数或零的完整数字。…−2, −1, 0, 1, 2…是整数。分数不是整数。

Prime Number: A positive integer greater than 1 that has exactly two distinct factors: 1 and itself. 2, 3, 5, 7, 11 are primes. 1 is not prime.

质数（素数）：大于 1 且只有 1 和它本身两个不同因数的正整数。2, 3, 5, 7, 11 是质数。1 不是质数。

Composite Number: A positive integer that has more than two factors. 8 (factors: 1,2,4,8) is composite. 'Composite' means 'made of parts'.

合数：拥有两个以上因数的正整数。8（因数：1,2,4,8）是合数。“合”表示由多个部分构成。

Factor: A number that divides another exactly without leaving a remainder. 1, 2, 4, and 8 are factors of 8. Think of factors as 'factory parts'.

因数（因子）：能整除另一个数且没有余数的数。1, 2, 4, 8 是 8 的因数。可联想“因”字，有“组成部分”之意。

Multiple: of a number and any integer. 12 is a multiple of 3 (3 × 4). Multiples are like the number's 'time tables'.

倍数：一个数与任意整数的乘积。12 是 3 的倍数（3 × 4）。倍数就像乘法表里的结果。

Highest Common Factor (HCF): The largest factor shared by two or more numbers. The HCF of 12 and 18 is 6. Use factor trees to find it.

最大公因数（HCF）：两个或多个数共有的最大因数。12 和 18 的 HCF 是 6。可以用因子树求解。

Lowest Common Multiple (LCM): The smallest multiple that two or more numbers share. The LCM of 4 and 6 is 12. It helps when finding common denominators.

最小公倍数（LCM）：两个或多个数共有的最小倍数。4 和 6 的 LCM 是 12。找公分母时常用。

Square Number: : The result of multiplying an integer by itself. 16 is a square number because 4² = 4 × 4 = 16. Visualise a square grid.

平方数：一个整数与自身相乘的结果。16 是平方数，因为 4² = 4×4 = 16。可想象正方形格子。

Cube Number: uct of an integer used three times as a factor. 27 = 3 × 3 × 3 = 3³. Picture a 3×3×3 cube.

立方数：一个整数作为因数使用三次的乘积。27 = 3×3×3 = 3³。想象一个 3×3×3 的立方体。

Square Root (√): A value that, when multiplied by itself, gives the original number. √25 = 5. The symbol looks like a tick with a vinculum.

平方根 (√)：自身相乘后得到原数的值。√25 = 5。符号像带横线的对勾。

Index (Exponent): The small raised number indicating how many times the base is used as a factor. In 2⁵, 5 is the index. 'Index' means 'pointer'.

指数（幂）：标注底数作为因数使用次数的小型上标数字。在 2⁵ 中，5 是指数。“指数”即“指示次数”。

Standard Form (Scientific Notation): ing very large or very small numbers as a × 10ⁿ, where 1 ≤ a < 10. 4500 becomes 4.5 × 10³.

标准形式（科学记数法）：将很大或很小的数写成 a × 10ⁿ 的形式，其中 1 ≤ a < 10。4500 写作 4.5 × 10³。

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3. Lines and Angles | 线与角术语

Acute Angle: An angle greater than 0° and less than 90°. It looks sharp, like an 'acute' blade.

锐角：大于 0° 且小于 90° 的角。形状很尖，就像锋利的刀刃（acute 有“尖锐”之意）。

Right Angle: Exactly 90°, often marked with a small square. 'Right' comes from the Latin 'rectus', meaning upright.

直角：恰好 90°，常画一个小方格标示。拉丁词根意为“直立”。

Obtuse Angle: Greater than 90° but less than 180°. 'Obtuse' means blunt or dull, the opposite of sharp.

钝角：大于 90° 且小于 180°。“钝”与“锐”相对，指不尖锐。

Reflex Angle: An angle greater than 180° and less than 360°. It 'reflects' back past the straight line.

优角（反射角）：大于 180° 且小于 360° 的角。角“反”过来超过了平角。

Complementary Angles: Two angles that add up to 90°. They 'complete' each other to a right angle.

余角：两个角和为 90°。它们互相“补足”成一个直角。

Supplementary Angles: Two angles that sum to 180°. They 'supply' what is needed for a straight line.

补角：两个角和为 180°。它们“补充”成为一条直线。

Vertically Opposite Angles: When two lines cross, the angles opposite each other are equal. They form an 'X' shape and are 'vertically' aligned.

对顶角：两条直线相交，相对的两个角相等。构成“X”形，顶点相对。

Parallel Lines: : Lines that never meet, staying the same distance apart. The pair of lines on an equals sign is parallel: =.

平行线：永不相交、距离保持相等的直线。等号的上下两横就是平行线。

Corresponding Angles: Angles in matching corners when a transversal crosses parallel lines. They are equal. Imagine sliding one angle along the transversal.

同位角：截线与平行线相交时，处于相同位置的角度，彼此相等。可想象把角沿截线平移。

Alternate Angles: Angles inside the parallel lines but on opposite sides of the transversal. They are equal. Picture a 'Z' shape.

内错角：位于平行线内侧、截线两侧的角，彼此相等。可联想字母“Z”的形状。

Interior (Co‑interior) Angles: Angles inside the parallel lines on the same side of the transversal. They sum to 180°. Think of a 'C' or 'U' shape.

同旁内角：在平行线内侧且位于截线同侧的角，和为 180°。形状像字母“C”或“U”。

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4. Polygons and Shapes | 多边形与图形术语

Polygon: A closed 2D shape with straight sides. 'Poly' means many, 'gon' means angles. Triangles, quadrilaterals, pentagons are polygons.

多边形：由直边围成的封闭二维图形。“poly”是多，“gon”是角。三角形、四边形、五边形都是多边形。

Quadrilateral: Any polygon with exactly four sides. Squares, rectangles, parallelograms, and trapeziums are all quadrilaterals.

四边形：恰好有四条边的多边形。正方形、长方形、平行四边形、梯形都是四边形。

Parallelogram: A quadrilateral with two pairs of parallel sides. Opposite sides are equal; opposite angles are equal. 'Parallel' is in the name.

平行四边形：有两组平行边的四边形。对边相等，对角相等。名字里就有“平行”。

Rhombus: A parallelogram with all four sides equal. A square is a rhombus with right angles. Think of a diamond shape.

菱形：四条边都相等的平行四边形。正方形是含有直角的菱形。想象扑克牌的方块形状。

Trapezium (UK): A quadrilateral with exactly one pair of parallel sides. Think of a trapezium as a 'triangular gate' shape.

梯形（英式定义）：恰好有一组平行边的四边形。可联想阶梯的形状。

Kite: A quadrilateral with two pairs of adjacent equal sides. Its diagonals cross at right angles, and one diagonal bisects the other.

风筝形：两组邻边分别相等的四边形。对角线互相垂直，一条对角线平分另一条。形似风筝。

Pentagon (5), Hexagon (6), Heptagon (7), Octagon (8): Polygons named by the number of sides. 'Octo' means eight, like an octopus. Use the Greek number prefixes to recall.

五边形、六边形、七边形、八边形：按边数命名的多边形。希腊词根“octo”是八，与章鱼（octopus）同源，帮助记忆。

Perimeter: The total distance around the outside of a shape. Add all side lengths. 'Peri' means around, 'meter' means measure.

周长：图形外边界的总长度。将所有边长相加。“周”即一圈，“长”即长度。

Area: ount of surface a shape covers, measured in square units. Rectangle area = length × width.

面积：图形覆盖的表面大小，以平方单位计量。矩形面积 = 长 × 宽。

Congruent: he : Shapes that are exactly the same in size and shape. One can be rotated or reflected to match the other. Congruent = 'same'.

全等：大小和形状完全相同的图形。可以通过旋转或反射叠合。全等即“完全相等”。

Similar: Shapes with the same angles but possibly different sizes, with sides in proportion. Enlargements produce similar figures.

相似：角度相同、大小可能不同、对应边成比例的图形。放大产生相似图形。

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5. Circles and 3D Shapes | 圆与立体图形术语

Radius (r): The distance from the centre of a circle to any point on its circumference. Plural is radii. 'Radial' lines spread outward.

半径 (r)：从圆心到圆周上任一点的距离。复数形式是 radii。像车轮的辐条辐射向外。

Diameter (d): The longest chord passing through the centre; twice the radius. d = 2r. 'Dia' means across, 'meter' means measure.

直径 (d)：通过圆心的最长弦；等于半径的两倍，d = 2r。“直径”意为横贯测量的线。

Circumference: The perimeter of a circle. C = 2πr or πd. 'Circum' means around, like 'circle'.

圆周：圆的边界长度。C = 2πr 或 πd。“circum”有环绕之意。

Pi (π): The ratio of a circle's circumference to its diameter, approximately 3.14 or 22/7. π is an irrational number.

圆周率 (π)：圆周长与直径的比值，约等于 3.14 或 22/7。π 是一个无理数。

Prism: A 3D solid with a constant cross‑section throughout its length. Its two end faces are congruent and parallel. A cuboid is a rectangular prism.

棱柱：具有恒定横截面的三维立体，两端面平行且全等。长方体就是矩形棱柱。

Pyramid: nal base and triangular faces meeting at a common vertex. Volume = ⅓ × base area × height.

棱锥：底面为多边形、各个侧面为三角形且交于同一点的立体。体积 = ⅓ × 底面积 × 高。

Net: A flat 2D pattern that can be folded to form a 3D shape. 'Net' like a fishing net that can be opened out.

展开图：能折叠成立体图形的二维平面图。“net”原意是网，可以铺开。

Surface Area: The total area of all faces of a 3D solid. Add the area of each individual face from the net.

表面积：立体所有面的总面积。根据展开图把各面面积相加。

Volume: 3D object occupies, measured in cubic units. Volume of a cuboid = length × width × height.

体积：三维物体占据的空间大小，以立方单位计量。长方体体积 = 长 × 宽 × 高。

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6. Coordinates and Graphs | 坐标与图像术语

Coordinate Plane: A grid formed by two perpendicular number lines called axes. The horizontal axis is x, vertical is y. The plane is divided into four quadrants.

坐标平面：由两条互相垂直的数轴（坐标轴）构成的网格。横轴为 x 轴，纵轴为 y 轴。平面分为四个象限。

Origin: The point (0,0) where the x‑axis and y‑axis intersect. All coordinates are measured from here.

原点：点 (0,0)，x 轴和 y 轴的交点。所有坐标都从这里开始测量。

Ordered Pair (x, y): A pair of numbers showing horizontal position first, then vertical. (3, −2) means 3 right, 2 down.

有序数对 (x, y)：先写横向位置，再写纵向位置的一对数字。(3, −2) 表示向右 3，向下 2。

Gradient (Slope): A measure of steepness: change in y divided by change in x. Positive gradient slopes upward; negative slopes downward.

斜率（坡度）：陡峭程度的度量：y 的变化量 ÷ x 的变化量。正斜率向上倾斜，负斜率向下倾斜。

y-intercept: The point where a line crosses the y‑axis. Its x‑coordinate is always 0. In y = mx + c, c is the y‑intercept.

y 轴截距：直线与 y 轴的交点，其 x 坐标永远为 0。在 y = mx + c 中，c 就是 y 截距。

Linear Equation: An equation whose graph is a straight line. It can be written as y = mx + c. 'Linear' means line‑like.

线性方程：图像为一条直线的方程，通常写成 y = mx + c。“线性”即直线形态。

Plot: To mark points accurately on a coordinate grid. Start with a table of values, then 'plot' each (x, y) as a dot.

描点：在坐标网格上精确标出点的位置。先列表求值，再将每个 (x, y) 描成点。

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7. Statistics and Data | 统计学与数据术语

Mean: The average, found by summing all values and dividing by the number of values. The mean 'balances' the data set.

平均数（均值）：将所有数值相加再除以个数得到的平均值。均值能“平衡”数据集。

Median: The middle value when data is ordered. For an even number of values, it is the mean of the two middle numbers. 'Median' sounds like 'medium'.

中位数：将数据排序后位于中间的值。若数据个数为偶数，则取中间两数的均值。“中”即中间。

Mode: The most frequently occurring value. A data set may have one mode, more than one, or none. 'Mode' = most common.

众数：出现次数最多的值。一组数据可能有一个众数、多个众数或没有众数。“众”即众多。

Range: : The difference between the largest and smallest values. Range = maximum − minimum. It shows spread, not average.

极差（全距）：最大值与最小值的差。极差 = 最大值 − 最小值。它反映离散程度，而非平均水平。

Frequency: The number of times an item occurs. A frequency table organises data to show how often each value appears.

频数（频率）：某个项目出现的次数。频数表整理数据，显示每个值出现的次数。

Bar Chart: Uses bars of equal width to show frequency. The bars do not touch for categorical data. Ideal for comparing categories.

条形图：用等宽长条表示频数。分类数据中长条不相连。适合比较不同类别。

Pie Chart: o sectors proportional to frequency. Each slice represents a part of the whole. 360° = 100%.

饼图：按频数比例分成扇形的圆形图表。每块扇形都是整体的一部分。360° 代表 100%。

Scatter Graph: A plot of paired data points on a coordinate plane. It can show correlation — positive, negative, or none.

散点图：在坐标平面上绘制的成对数据点。可以显示相关关系：正相关、负相关或无相关。

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8. Probability Terminology | 概率术语

Probability: A measure of how likely an event is, ranging from 0 (impossible) to 1 (certain). Written as a fraction, decimal, or percentage.

概率：衡量事件发生可能性的数值，从 0（不可能）到 1（必然）。可用分数、小数或百分数表示。

Outcome: A single possible result of a trial. When you flip a coin, one outcome is 'heads'.

结果：一次试验中可能发生的单个情况。抛硬币时，“正面”就是一个结果。

Event: A set of one or more outcomes. Rolling an even number on a die is an event consisting of outcomes 2, 4, and 6.

事件：由一个或多个结果组成的集合。掷骰子掷出偶数是包含 2、4、6 的事件。

Sample Space: The list of all possible outcomes. For rolling a standard die, the sample space is {1,2,

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