📚 Review set 11B - CALCULATOR | 复习集 11B - 计算器使用
Review set 11B is designed to reinforce key IB Mathematics concepts while sharpening your skills with a graphic display calculator (GDC). Whether you are working through functions, calculus, statistics, or algebra, this set expects you to apply efficient calculator techniques to model, solve, and verify. Mastering these tools not only saves time but also reduces careless mistakes, making your exam performance more reliable.
复习集 11B 旨在巩固 IB 数学的核心概念，同时提升你使用图形显示计算器（GDC）的技能。无论你正在处理函数、微积分、统计还是代数，这套练习都要求你使用高效的计算器技巧来建模、求解和验证。掌握这些工具不仅能节省时间，还能减少粗心错误，让你的考试表现更加可靠。
1. Overview of Review Set 11B | 复习集 11B 概览
Review set 11B typically covers topics from the later part of the IB syllabus, including advanced functions, differential and integral calculus, probability distributions, and statistical inference. The 'CALCULATOR' tag indicates that you are allowed – and expected – to use your GDC for graphing, numerical solving, statistical calculations, and for checking analytical work.
复习集 11B 通常覆盖 IB 教学大纲后半部分的内容，包括高级函数、微分与积分、概率分布以及统计推断。“计算器”的标注意味着你被允许——并且预计需要——使用 GDC 来作图、数值求解、统计计算以及检验分析结果。
2. GDC Basics: Mode, Angle, and Format | GDC 基础：模式、角度与格式
Before starting any problem, confirm that your calculator is in the correct mode. For calculus and algebra, use Radian mode unless the question specifies degrees. Set the number format to Float or a suitable decimal place. In the TI‑Nspire, go to Settings > Document Settings; on the Casio fx‑CG50, use SHIFT > SETUP.
在开始任何题目之前，确认你的计算器处于正确的模式。对于微积分和代数，除非题目明确指定角度制，否则请使用弧度制。将数字格式设置为浮点或合适的小数位数。在 TI‑Nspire 中，进入 Settings > Document Settings；在 Casio fx‑CG50 上，使用 SHIFT > SETUP。
Always store intermediate values using the memory function (e.g. STO> on TI or the variable assignment on Casio) to maintain full precision. Clearing the calculator's memory before a mock exam is also a good habit.
总是使用记忆功能保存中间值（例如 TI 上的 STO> 或 Casio 上的变量赋值），以保持完整精度。在模拟考试前清空计算器内存也是一个好习惯。
3. Solving Equations Graphically | 图形法解方程
For an equation such as ex − 3x = 0, you can graph the two sides or set up a single function and find the zero. On the TI‑Nspire, press Menu > Analyze Graph > Zero. On the Casio, use G‑Solv > ROOT. Adjust the window to ensure all intersections are visible.
对于像 ex − 3x = 0 这样的方程，你可以将两边分别作图，或设置单个函数并求零点。在 TI‑Nspire 上，按 Menu > Analyze Graph > Zero。在 Casio 上，使用 G‑Solv > ROOT。调整视窗以确保所有交点都可见。
If the question asks for solutions to three significant figures, use the GDC's trace or table function to refine the value. Always quote answers within the accuracy expected.
如果题目要求答案精确到三位有效数字，使用 GDC 的追踪或表格功能来细化数值。始终按要求的精度给出答案。
4. Calculus with Calculator: Derivatives at a Point | 计算器做微积分：某点处的导数
ting a derivative numerically, such as finding the gradient of a curve at x = a. On the TI‑Nspire, use Menu > Calculus > Numerical Derivative at a Point. Enter the function and the point. The result is the instantaneous rate of change.
复习集 11B 中的许多任务要求对导数进行数值计算，例如求曲线在 x = a 处的斜率。在 TI‑Nspire 上，使用 Menu > Calculus > Numerical Derivative at a Point。输入函数和该点，结果即为瞬时变化率。
Example: f(x) = ln(x² + 1), find f'(2) → GDC gives 0.800 (3 s.f.)
示例： f(x) = ln(x² + 1)，求 f'(2) → GDC 给出 0.800（3位有效数字）
For symbolic differentiation, you can also use the derivative template to check your manual work. This is particularly useful when verifying the simplified form of a derivative before setting up an optimization problem.
对于符号微分，你也可以使用导数模板来检查手算结果。这在验证导数的简化形式后再建立优化问题时尤其有用。
5. Definite Integrals and Area Under a Curve | 定积分与曲线下面积
To compute the area bounded by a curve and the x‑axis, use the definite integral function. On the TI‑Nspire, choose Menu > Calculus > Numerical Integral. On Casio, use ∫dx from the Run‑Matrix menu. Ensure the limits are entered correctly – upper limit first on some models.
要计算曲线与 x 轴围成的面积，使用定积分功能。在 TI‑Nspire 上，选择 Menu > Calculus > Numerical Integral。在 Casio 上，在 Run‑Matrix 菜单中使用 ∫dx。确保正确输入上下限——某些型号需先输入上限。
If the curve crosses the x‑axis, you must split the integral at the roots to find total area. Plot the absolute value of the function or sum the absolute values of each part.
如果曲线与 x 轴相交，你必须在根处分段积分以求出总面积。绘制函数的绝对值图，或将各部分的绝对值相加。
6. Statistical Analysis Tools | 统计分析工具
Review set 11B often includes tasks involving a data set or frequency table. Enter your data into lists: on TI‑Nspire, open a Lists & Spreadsheet page; on Casio, use the Statistics app. From there, you can calculate the mean, standard deviation (σₙ or sₙ₋₁), quartiles, and more.
复习集 11B 经常包含涉及数据集或频率表的任务。将数据输入列表：在 TI‑Nspire 上，打开 Lists & Spreadsheet 页面；在 Casio 上，使用 Statistics 应用程序。从那里你可以计算均值、标准差（σₙ 或 sₙ₋₁）、四分位数等。
Make sure you are using the correct standard deviation: σₙ for population, sₙ₋₁ for sample. The IB typically expects sample standard deviation unless stated otherwise.
确保使用正确的标准差：σₙ 用于总体，sₙ₋₁ 用于样本。除非另有说明，IB 通常要求样本标准差。
7. Normal Distributions and Inverse Normal | 正态分布与逆正态
lative distribution function (normalcdf). For example, P(X < k) given μ = 50, σ = 7. On TI‑Nspire, Menu > Statistics > Distributions > Normal Cdf. Set lower bound to −10⁹⁹ and upper bound to k.
正态分布的概率可通过正态累积分布函数（normalcdf）求出。例如，给定 μ = 50, σ = 7，求 P(X < k)。在 TI‑Nspire 上，Menu > Statistics > Distributions > Normal Cdf。将下限设为 −10⁹⁹，上限设为 k。
Inverse normal problems ask for the value k given a left‑tail probability. Use Inverse Normal on your GDC. Enter the area, mean, and standard deviation. Always sketch the bell curve to confirm the direction of the tail.
逆正态问题要求根据左侧尾部概率求出 k。在 GDC 上使用 Inverse Normal。输入面积、均值和标准差。始终画出钟形曲线以确认尾部方向。
8. Hypothesis Testing Using p‑values | 使用 p 值进行假设检验
In Review set 11B, you may encounter a one‑sample z‑test or t‑test. The calculator can generate the test statistic and p‑value directly. Navigate to the statistics inference menu: on TI‑Nspire, Menu > Statistics > Stat Tests. Enter the summary statistics and choose the correct alternative hypothesis.
在复习集 11B 中，你可能会遇到单样本 z 检验或 t 检验。计算器可以直接生成检验统计量和 p 值。进入统计推断菜单：在 TI‑Nspire 上，Menu > Statistics > Stat Tests。输入汇总统计量并选择正确的备择假设。
Compare the p‑value to the significance level (commonly 5%). If p < 0.05, reject H₀. State your conclusion in context, not just 'reject H₀'.
将 p 值与显著性水平（通常为 5%）比较。如果 p < 0.05，则拒绝 H₀。在上下文中陈述结论，而不仅仅是“拒绝 H₀”。
9. Regression and Correlation | 回归与相关
After entering bivariate data, the GDC provides the equation of the least‑squares regression line (y = a + bx) and Pearson's product– ne. Use the Stats app to compute r² as well to interpret the coefficient of determination.
输入双变量数据后，GDC 给出最小二乘回归线方程（y = a + bx）以及皮尔逊积矩相关系数 r。注意哪个是自变量；交换变量会改变直线。使用 Stats 应用程序计算 r²，以解读决定系数。
Always plot the scatter diagram to check for outliers or non‑linear patterns. The calculator's residual plot can help verify the model's appropriateness.
始终绘制散点图以检查异常值或非线性模式。计算器的残差图有助于验证模型的适用性。
10. Financial Calculations: TVM Solver | 金融计算：TVM 求解器
If Review set 11B includes compound interest, annuities, or amortization, use the Time‑Value‑of‑Money (TVM) solver. On TI‑Nspire, Menu > Finance > TVM Solver. Set PV, FV, PMT, n, and I% carefully. Remember to follow the cash flow sign convention: money you pay is negative, money you receive is positive.
如果复习集 11B 包含复利、年金或摊还，使用资金时间价值（TVM）求解器。在 TI‑Nspire 上，Menu > Finance > TVM Solver。仔细设置 PV、FV、PMT、n 和 I%。记住遵循现金流符号惯例：你付出的钱为负，收到的钱为正。
For credit calculations, set P/Y and C/Y to match the compounding frequency. Interpret the results in the context of the loan or investment scenario.
对于信贷计算，设置 P/Y 和 C/Y 以匹配复利频率。在贷款或投资情景中解读结果。
11. Common Errors and Troubleshooting | 常见错误与排查
A frequent mistake is using the wrong angle unit. Functions like sin(x) give radically different values in radians vs degrees. Always check the angle symbol (if any) and the problem context. Another common slip is forgetting to clear the memory of previous definitions, causing unexpected graphs or results.
一个常见错误是使用了错误的角度单位。像 sin(x) 这样的函数在弧度和度数下得出的值截然不同。经常检查角度符号（如有）和题目背景。另一个常见疏忽是忘记清除先前定义的记忆，导致出现意外的图形或结果。
If the GDC returns an 'Error: Domain', verify that the argument is within the valid range (e.g., ln of negative number). For 'Error: Syntax', re‑enter parentheses and check the order of operations.
如果 GDC 返回 'Error: Domain'，验证参数是否在有效范围内（例如，负数的 ln）。对于 'Error: Syntax'，重新输入括号并检查运算顺序。
12. Exam Tips for Calculator Use | 考试中使用计算器的技巧
Show your exact set‑up on paper before using the calculator, so examiners can follow your reasoning. If a question requires 'hence' or analytical proof, the GDC should only be used for verification, not as a substitute for written work. In the 'CALCULATOR' paper, however, you are expected to use GDC as the primary tool.
在使用计算器之前在卷面上写出你的具体设置，以便考官能理解你的推理。如果题目要求“因此”或分析证明，GDC 应仅用于验证，而不是替代书面步骤。但在“计算器”试卷中，要求你将 GDC 作为主要工具。
Manage your time by storing results in the calculator's memory instead of retyping. In long problems, use the scratchpad to keep variables. Lastly, if the screen seems frozen, a quick reset (without losing data) can often resolve the issue – know the reset procedure for your model.
通过将结果存储在计算器内存中而不是重新输入来管理时间。在长问题中，使用草稿本保存变量。最后，如果屏幕似乎冻结，快速重置（而不丢失数据）通常可以解决问题——了解你的型号的重置步骤。
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