Year 11 CIE Mathematics: Vocabulary & Terminology Quick Memory Guide | Year 11 CIE 数学：词汇术语速记指南

📚 Year 11 CIE Mathematics: Vocabulary & Terminology Quick Memory Guide | Year 11 CIE 数学：词汇术语速记指南

Mastering the precise meaning of mathematical terms is half the battle in CIE IGCSE Mathematics. This guide breaks down essential vocabulary into logical sections with simple explanations and memorable cues to help you recall them quickly under exam pressure.

在 CIE IGCSE 数学中，准确理解数学术语是成功的一半。本文将关键词汇分门别类，配以简明解释和记忆线索，助你在考试中快速回忆，轻松应对。

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1. Algebraic Expressions and Equations | 代数表达式与方程

Expression – A combination of numbers, variables (letters) and operations, such as 3x + 5 or 2a² − b. It never contains an equals sign. Think: 'Expression has no impression of equality.'

表达式 – 由数字、变量和运算符号构成的式子，例如 3x + 5，不含等号。记忆：表达式没有“等”的印象。

Equation – ment that two expressions are equal, indicated by an equals sign. For example, 2x + 1 = 7. 'Equation has EQUALS, so it balances.'

方程 – 表示两个表达式相等的数学陈述，用等号连接，如 2x + 1 = 7。方程含有“等”，意味平衡。

Identity – An equation that holds true for all values of the variable, often marked with a triple bar ≡. E.g., 2(x+1) ≡ 2x+2. 'Identity identifies identical expressions, always true.'

恒等式 – 对变量所有取值都成立的等式，常用 ≡ 表示。如 2(x+1) ≡ 2x+2。恒等式标识两式恒等，始终成立。

Inequality – Compares two values using <, >, ≤ or ≥. The open side faces the larger quantity. 'In me equality doesn't exist, hence inequality.'

不等式 – 用 <, >, ≤, ≥ 表示两个量的大小关系，开口朝向较大值。记忆：不相等的关系。

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2. Linear Functions and Graphs | 线性函数与图像

Gradient (slope) – calculated as (change in y)/(change in x) or rise / run. In y = mx + c, m is the gradient. 'Gradient measures how much you go up or down for each step across.'

斜率（梯度） – 直线的倾斜程度，计算为纵变化量/横变化量。直线方程 y = mx + c 中 m 即为斜率。助记：横走一格，竖变多少。

Intercept – ses the y-axis (y-intercept) or x-axis (x-intercept). In y = mx + c, c is the y-intercept. 'Intercept reminds of interrupting the axis.'

截距 – 直线与坐标轴的交点。y = mx + c 中 c 为 y 轴截距。截距即截断轴线之处。

Parallel lines – Lines that never meet and have identical gradients. 'Parallel lines share the same slope, so they stay apart.'

平行线 – 永不相交且斜率相同的直线。平行线斜率相等，永保距离。

Perpendicular lines – Lines that intersect at right angles (90°). Their gradients multiply to −1 (m₁ × m₂ = −1). 'Perpendicular means perfect corner, slopes are negative reciprocals.'

垂直线 – 相交成 90° 的直线，其斜率乘积为 −1 (m₁ × m₂ = −1)。垂直就是完美的直角，斜率互为负倒数。

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3. Quadratic Expressions and Equations | 二次表达式与方程

Quadratic – An expression or equation where the highest power of the variable is 2, such as x² + 3x − 4. From Latin 'quadratus' meaning square. 'Quad' links to four sides of a square, but really it's about raising to power 2.'

二次的 – 变量最高次数为 2 的表达式或方程，如 x² + 3x − 4，源自拉丁语“平方”。可联想正方形有四边，核心是平方。

Root (solution) – hat makes the quadratic equation true. For x² − 5x + 6 = 0, the roots are x = 2 and x = 3. 'Roots are where the parabola touches or crosses the x-axis.'

根（解） – 使二次方程成立的 x 值。x² − 5x + 6 = 0 的根为 2 和 3。记忆：根是抛物线与 x 轴的交点。

Completing the square – Rewriting a quadratic in the form a(x + p)² + q to find the vertex or solve equations. 'Complete the square to make a perfect square trinomial.'

配方法 – 将二次式改写成 a(x + p)² + q 的形式。记忆：配方即制造完全平方。

Discriminant – e of roots: positive → two real roots, zero → one repeated root, negative → no real roots. 'Discriminant discriminates between real and complex roots.'

判别式 – 二次公式中的 b² − 4ac。判别式判别根的性质：正→两实根，零→一重根，负→无实根。记忆：判别根的真伪。

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4. Geometry: Angles and Shapes | 几何：角与图形

Acute, Obtuse and Reflex angles – Acute < 90°, Obtuse between 90° and 180°, Reflex > 180° but < 360°. 'A small angle is a cute acute angle; obtuse sounds like obese, large; reflex bends back beyond a straight line.'

锐角、钝角与优角 – 锐角 < 90°；钝角介于 90° 与 180° 之间；优角 > 180° 且 < 360°。记忆：锐角小巧，钝角肥胖，优角反折。

Vertically opposite angles – When two lines cross, the opposite angles are equal. Imagine the letter X. 'Vertically opposite: top equals bottom, left equals right.'

对顶角 – 两直线相交，对顶的角相等。想象 X 形，上下角相等，左右角相等。

Alternate angles (Z-angles) – When a transversal cuts parallel lines, alternate interior angles are equal. Look for a Z or reversed Z shape. 'Alternate angles are equal on parallel lines.'

内错角（Z角） – 截线穿过平行线，内错角相等。寻找 Z 形。内错角相等。

Corresponding angles (F-angles) – On parallel lines, angles in matching corners are equal. Look for an F shape. 'Corresponding angles correspond in position.'

同位角（F角） – 平行线截线中位置相应的角相等。想象 F 形。同位角位置对应。

Complementary and Supplementary angles – Complementary add up to 90°, Supplementary add up to 180°. 'C before S, 90 before 180. A supplement adds extra.'

余角与补角 – 余角和为 90°，补角和为 180°。C 在 S 前，90 在 180 前。补角需要“补充”更多。

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5. Trigonometry Basics | 三角学基础

Hypotenuse – The longest side of a right-angled triangle, opposite the right angle. 'Hypotenuse holds the right angle away.'

斜边 – 直角三角形中最长的边，正对直角。记忆：斜边与直角相对。

Sine (SOH) – sin θ = Opposite / Hypotenuse. 'SOH: Some Old Horses, or simply sin = O/H.'

正弦 (SOH) – sin θ = 对边/斜边。口诀：SOH，正弦对斜。

Cosine (CAH) – cos θ = Adjacent / Hypotenuse. 'CAH: Can Always Hide, cos = A/H.'

余弦 (CAH) – cos θ = 邻边/斜边。口诀：CAH，余弦邻斜。

Tangent (TOA) – tan θ = Opposite / Adjacent. 'TOA: Take Over Australia, tan = O/A.'

正切 (TOA) – tan θ = 对边/邻边。TOA，正切对邻。

Angle of elevation and depression – Elevation: measured upwards from the horizontal; Depression: measured downwards from the horizontal. 'When you feel elevated you look up; when depressed you look down.'

仰角与俯角 – 仰角从水平线向上看；俯角从水平线向下看。记忆：仰视，俯视。

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6. Perimeter, Area and Volume | 周长、面积与体积

Perimeter – The total distance around a 2D shape. 'Peri- means around, meter means measure. Think of fencing a garden.'

周长 – 二维图形边界总长。记忆：围绕一周的长度。

Area – The amount of surface enclosed within a 2D shape, measured in square units. 'Area fills the inside.'

面积 – 二维图形内部区域的大小，单位是平方单位。记忆：内部区域。

Volume – The space occupied by a 3D object, measured in cubic units. 'Volume answers how much fits inside a box.'

体积 – 三维物体占据的空间，单位是立方单位。记忆：容纳量。

Surface area – The total area of all faces of a solid. 'Surface area is the sum of the area of the wrapping.'

表面积 – 立体所有面的总面积。记忆：包裹它的总面积。

Prism – lid with a uniform cross-section along its length. Volume = area of cross-section × length

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