IB Formula Booklet SL and HL May 2021 | IB 公式手册 SL 与 HL 2021 年 5 月版

📚 IB Formula Booklet SL and HL May 2021 | IB 公式手册 SL 与 HL 2021 年 5 月版

The IB Mathematics formula booklet issued for the May 2021 session is a compact but powerful tool for both Standard Level and Higher Level candidates. It separates SL and HL content and gives you the exact notation the examiners expect. Used correctly, it saves time and avoids recall errors.

2021 年 5 月考试所用的 IB 数学公式手册是一份精简而实用的工具，适用于标准水平（SL）与高级水平（HL）考生。它将 SL 与 HL 内容分开，并给出考官期望的准确记号。使用得当，它能节省时间并减少记忆错误。

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1. What the May 2021 Booklet Is | 2021 年 5 月公式手册是什么

The May 2021 booklet supports the first assessment of the new IB Mathematics courses: Analysis and Approaches (AA) and Applications and Interpretation (AI). You receive a clean copy in the exam, so every formula is available without memorisation.

2021 年 5 月的手册服务于新 IB 数学课程的首次评估：分析与方法（AA）以及应用与解释（AI）。考试中你会拿到干净副本，因此所有公式都可查阅，无需死记硬背。

There are separate booklets for AA and AI. The SL booklet is shorter and focuses on core skills; the HL booklet adds advanced topics such as vectors, complex numbers, further calculus, and extra statistical distributions.

AA 与 AI 分别有各自的手册。SL 手册较短，侧重核心技能；HL 手册增加了向量、复数、进一步的微积分以及额外的统计分布等高级主题。

Because the booklet is provided, examiners test application and interpretation more than recall. You should practise locating formulas quickly and combining them with your GDC.

由于考试会提供手册，考官更侧重应用与解释，而非单纯记忆。你应当练习快速定位公式，并将它们与图形计算器结合使用。

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2. SL and HL Booklet Structure | SL 与 HL 手册结构

Each booklet opens with a contents page and groups formulas by topic: number and algebra, functions, geometry and trigonometry, statistics and probability, and calculus. HL sections are usually shaded or marked 'HL only'.

每本手册开头是目录，并按主题将公式分组：数与代数、函数、几何与三角、统计与概率、微积分。HL 部分通常加阴影或标注 'HL only'（仅 HL）。

In the exam, do not waste time flipping randomly. Know whether the formula you need is in the SL block or the HL block before you start. The contents page is your fastest route.

考试时不要随机翻页浪费时间。开考前就要知道自己需要的公式在 SL 区块还是 HL 区块。目录页是查找公式最快的路径。

AA and AI booklets differ slightly. For example, product and quotient rules appear in AA SL and HL, but the AI SL booklet may only show simpler derivative rules. Always check the exact booklet for your course.

AA 与 AI 手册略有不同。例如，乘法法则与除法法则出现在 AA SL 和 HL 中，但 AI SL 手册可能只给出较简单的导数法则。请务必核对你所学课程对应的手册。

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3. Number and Algebra | 数与代数

The booklet gives the quadratic formula in its standard form. It is one of the most commonly used tools across Papers 1 and 2.

手册给出标准形式的二次方程求根公式。这是试卷一和试卷二中最常用的工具之一。

x = (-b ± √b² - 4ac) / 2a

For exponents and logarithms, the key identities are aˣ × aʸ = aˣ⁺ʸ and logₐ(xy) = logₐx + logₐy. These appear in both SL and HL booklets.

对于指数与对数，核心恒等式为 aˣ × aʸ = aˣ⁺ʸ 以及 logₐ(xy) = logₐx + logₐy。这些同时出现在 SL 和 HL 手册中。

HL AA and HL AI also list the binomial theorem, including the general term C(n, r) aⁿ⁻ʳ bʳ. Make sure you can identify r from the term you need.

HL AA 与 HL AI 还列出二项式定理，包括通项 C(n, r) aⁿ⁻ʳ bʳ。务必确保你能根据所需项确定 r 的值。

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4. Functions | 函数

Function notation in the booklet uses f(x), with domain and range given in set notation. The inverse function is written f⁻¹(x), not 1/f(x).

手册中的函数记号使用 f(x)，定义域和值域用集合记号表示。反函数写作 f⁻¹(x)，而不是 1/f(x)。

ical stretch, b controls horizontal stretch, h shifts horizontally, and k shifts vertically.

函数变换概括为 y = a f(b(x - h)) + k。其中 a 控制纵向伸缩，b 控制横向伸缩，h 控制水平平移，k 控制垂直平移。

rtex (h, k). The booklet expects you to move between standard, factored, and vertex forms.

二次函数顶点式 y = a(x - h)² + k 的图像顶点为 (h, k)。手册要求你能在标准式、因式式和顶点式之间转换。

For exponential models, the general forms are f(x) = a bˣ and f(x) = a e^kx. These are especially important in AI applications.

对于指数模型，一般形式为 f(x) = a bˣ 和 f(x) = a e^kx。这些在 AI 应用问题中尤为重要。

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5. Geometry and Trigonometry | 几何与三角

le sector, the arc length is l = rθ and the area is A = ½ r²θ, where θ must be in radians.

对于扇形，弧长公式为 l = rθ，面积公式为 A = ½ r²θ，其中 θ 必须以弧度为单位。

ne rule appear in the booklet as a/sin A = b/sin B = c/sin C and c² = a² + b² - 2ab cos C.

正弦定理和余弦定理在手册中记为 a/sin A = b/sin B = c/sin C 以及 c² = a² + b² - 2ab cos C。

θ / cos θ. Double-angle formulas are listed for HL and often useful in SL trig equations.

核心恒等式包括 sin²θ + cos²θ = 1 以及 tan θ = sin θ / cos θ。倍角公式列在 HL 中，但 SL 解三角方程时也常会用到。

Exact values for 0°, 30°, 45°, 60°, and 90° are expected to be used with radian equivalents. The booklet may show them in a small table, but quick recall is still an advantage.

0°、30°、45°、60°、90° 的三角精确值需要与弧度制等价使用。手册可能以小型表格列出，但快速记忆仍然是优势。

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6. Statistics and Probability | 统计与概率

The binomial distribution is given by P(X = r) = C(n, r) pʳ (1 - p)ⁿ⁻ʳ. Its mean is μ = np and variance is σ² = np(1 - p).

二项分布由 P(X = r) = C(n, r) pʳ (1 - p)ⁿ⁻ʳ 给出。其均值为 μ = np，方差为 σ² = np(1 - p)。

the standardised variable z = (x - μ) / σ. You still need your GDC to find probabilities.

对于正态分布，手册给出标准化变量 z = (x - μ) / σ。你仍需要使用图形计算器来求概率。

HL AI includes the Poisson distribution P(X = r) = e⁻λ λʳ / r!. HL AA and HL AI both list unbiased estimators for sample variance.

HL AI 包含泊松分布 P(X = r) = e⁻λ λʳ / r!。HL AA 与 HL AI 都列出样本方差的无偏估计量。

Conditional probability appears as P(A|B) = P(A ∩ / P(B). Identifying the reduced sample space is usually faster than substituting blindly.

条件概率公式为 P(A|B) = P(A ∩ B) / P(B)。识别缩减后的样本空间通常比盲目代入更快。

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7. Calculus | 微积分

e derivative of xⁿ is nxⁿ⁻¹. The integral is ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C, valid for n ≠ -1.

xⁿ 的导数为 nxⁿ⁻¹。积分为 ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C，且 n ≠ -1。

Chain rule, product rule, and quotient rule are listed in words and symbols. For example,

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