📚 Review Set 20B – Calculator | 复习题集20B：计算器技巧全解析
Review Set 20B is designed to stretch your calculator skills across the entire IB Mathematics syllabus. Whether you are working on algebraic equations, calculus, statistics, or financial maths, your graphic display calculator (GDC) can reduce errors and save time – but only if you know how to use it strategically. In this guide we break down the key question types, share pro‑tips for TI‑84, TI‑Nspire and Casio calculators, and offer targeted practice advice so you can walk into the exam hall feeling confident and competent.
复习题集20B旨在全面锤炼你在IB数学各领域的计算器运用能力。无论是代数方程、微积分、统计还是金融数学，图形计算器都能帮你减少失误并节省时间——但前提是你能有策略地使用它。本文拆解了典型考法，分享了TI‑84、TI‑Nspire 和 Casio 等计算器的专业技巧，并提供有针对性的练习建议，助你自信满满地步入考场。
1. Understanding the GDC Requirements | 理解IB计算器使用要求
IB Maths papers come in two flavours: calculator‑active and calculator‑free. For Papers 1 (AA & AI) you must rely on accurate mental arithmetic and algebraic manipulation, but in Papers 2 and 3 your GDC becomes an indispensable tool. You need to know exactly which functions are allowed and how to access them rapidly. Functions like polynomial solvers, numerical integration, statistics wizards, and financial solvers are all permitted and expected to be used.
IB数学试卷分为计算器可用的和不可用的两类。在AA和AI的Paper 1中你需要依靠精准的心算与代数推导，但在Paper 2和Paper 3中，你的图形计算器就变成了不可或缺的工具。你必须清楚哪些功能是允许使用的，并能够快速调用它们。多项式求解器、数值积分、统计向导和金融求解器等都是允许且要求使用的功能。
Most common models (TI‑84 Plus CE, TI‑Nspire CX II, Casio fx‑CG50) all satisfy IB requirements. Make sure your calculator is set to 'Exam Mode' or 'Press‑to‑Test' before entering the hall. Take time to practise with the exact mode that blanks your memory; otherwise you may lose stored shortcuts you rely on at home.
大多数常见机型（TI‑84 Plus CE、TI‑Nspire CX II、Casio fx‑CG50）都满足IB的要求。务必在进入考场前将计算器设置为“考试模式”或“Press‑to‑Test”。花时间在会清空内存的考试模式下练习，否则你可能会丢失居家练习时依赖的快捷键与预设。
2. Solving Equations Graphically and Numerically | 图形与数值方法解方程
When a question asks for solutions to high‑degree polynomials, trigonometric equations, or systems involving unknown parameters, a direct algebraic approach might be messy. The GDC allows you to plot both sides of an equation and use the 'intersect' feature or directly run a polynomial solver. For example, to solve 3x³ – 4x² + x – 6 = 0, you can enter the function and find the zero, or use 'Poly Root Finder' to list all real and complex roots.
当题目要求解高次多项式、三角方程或包含未知参数的方程组时，纯代数方法可能非常繁琐。计算器可以将方程两边分别绘图后使用“交点”功能，或是直接调用多项式求解器。例如，求解 3x³ – 4x² + x – 6 = 0，你可以输入函数并求零点，或使用“多项式求根器”列出所有实根和复根。
Always start with a suitable viewing window. A quick zoom‑fit or adjusting Xmin, Xmax can prevent missed asymptotes or hidden solutions. Remember that graphical solutions are decimal approximations; unless the question requests exact forms, this is perfectly acceptable.
务必先设置一个合适的显示窗口。快速使用 Zoom‑Fit 或调整 Xmin、Xmax 可以避免遗漏渐近线或隐藏的解。请注意，图形解法得到的是小数近似值；除非题目要求精确形式，否则这完全符合答题规范。
3. Function Analysis: Maximums, Minimums, and Intercepts | 函数分析：最大值、最小值与截距
A common Review Set 20B task is to sketch f(x) and label its key features. Your GDC can compute local maximums, minimums, y‑intercepts, and zeros with high precision. Use 'Calculate' > 'Maximum' or 'Minimum' after graphing the curve. The cursor bounds (left bound, right bound) need to be set carefully; a poorly chosen interval can give a wrong extremum.
复习题集20B常常要求画出 f(x) 的草图并标出关键特征。你的计算器可以高精度地计算局部最大值、最小值、y截距和零点。画出曲线后，使用 “Calculate” > “Maximum” 或 “Minimum”。光标的边界（左边界、右边界）需要谨慎设置；如果区间选择不当，可能得到错误的极值点。
When a function involves eˣ, ln x, or trigonometric terms, the GDC handles the transcendental nature without effort. You can also trace along the curve to estimate values, but the numerical derivatives and maximum‑finding routines give much more consistent results for marking purposes.
当函数包含 eˣ、ln x 或三角函数项时，计算器可以毫不费力地处理这些超越特性。你还可以沿着曲线追踪来估算数值，但数值微分和极值查找程序能为评分提供更一致的结果。
4. Calculus Tools: Derivatives and Definite Integrals | 微积分工具：导数和定积分
In a calculator paper you are expected to verify differentiation or integration results, especially when dealing with messy rational functions. The GDC can evaluate a derivative at a point using nDeriv( on TI or d/dx on Casio. For instance, to find the gradient of g(x) = ln(2x+1) at x = 3, type nDeriv(ln(2x+1), x, 3); the output is an accurate decimal.
在计算器试卷中，你需要验证微分或积分结果，特别是处理复杂的有理函数时。计算器可以使用 TI 的 nDeriv( 或 Casio 的 d/dx 命令求某点导数值。例如，求 g(x) = ln(2x+1) 在 x = 3 处的斜率，输入 nDeriv(ln(2x+1), x, 3) 即可得到精确的小数。
Definite integrals are just as straightforward. Use fnInt( or the integral template to compute area under a curve. Remember that area between two curves can be obtained by integrating the difference. If you accidentally integrate with the wrong order, the result will be negative; simply take the absolute value for physical area.
定积分也同样直接。使用 fnInt( 或积分模板可以计算曲线下方面积。请注意，两条曲线间的面积可以通过对差值积分得到。如果积分顺序弄反了，结果为负值；只需取绝对值即为实际面积。
5. Statistics and Data Handling | 统计与数据处理
One of the most error‑prone sections in Review Set 20B involves entering data into lists and performing statistical tests. Always clear old lists (e.g., L1, L2 on TI) before starting. Enter x‑values in one list and frequencies or probabilities in another if needed. Use 1‑Var Stats for mean, standard deviation, and quartiles; 2‑Var Stats for regression lines and correlation coefficient r.
复习题集20B中最容易出错的环节之一就是将数据录入列表并进行统计检验。开始前务必清空旧列表（如TI的 L1, L2）。需要时将 x 值输入一个列表，频数或概率输入另一个列表。使用 1‑Var Stats 可计算均值、标准差和四分位数；2‑Var Stats 则用于回归直线和相关系数 r。
For hypothesis testing, the GDC offers t‑tests, χ² tests, and ANOVA shortcuts. Make sure you understand which test matches the wording. A common mistake is using a 2‑sample t‑test when the data is paired; always check whether the samples are independent or matched. Exact p‑values from the calculator must be compared with the significance level (α) directly.
在假设检验中，计算器提供了 t 检验、χ² 检验和方差分析的快捷方式。务必确保选用的检验与题目措辞吻合。常见错误是在数据配对时错误使用了双样本 t 检验；始终要检查样本是独立还是匹配的。计算器给出的精确 p 值需直接与显著性水平（α）进行比较。
6. Matrices and Vector Operations | 矩阵与向量运算
Matrix manipulations can be tedious by hand, but the GDC transforms them into a rapid entry task. You can store matrices (e.g., [A], [B]) and compute inverses, determinants, and products. To solve a system 2x + 3y – z = 5, x – y + 2z = 6, 3x + y – 4z = 0, store the coefficient matrix and the constant column vector, then multiply the inverse of the coefficient matrix by the constants.
矩阵手算可能非常枯燥，但计算器能将它们变成一项快速输入任务。你可以储存矩阵（如 [A]、[B]）并计算逆矩阵、行列式和乘积。要解方程组 2x + 3y – z = 5, x – y + 2z = 6, 3x + y – 4z = 0，只需存储系数矩阵和常数列向量，然后用系数矩阵的逆乘以常数矩阵即可。
Vector cross products and dot products are also built in. When working in 3D vector geometry, use the built‑in norm function to find magnitudes and check if vectors are perpendicular by verifying that the dot product equals zero. Always interpret angle outputs in degrees or radians as specified by the question.
向量的叉积和点积也是内置功能。在做三维向量几何题时，利用内置范数（模）函数求大小，并通过验证点积是否为零来检查向量是否垂直。一定要根据题目要求的度数或弧度来解读角度输出。
7. Sequences and Series Applications | 数列与级数应用
Arithmetic and geometric sequences appear frequently in IB finance and modelling problems. Your calculator's 'seq' mode can generate terms, and the sum function can total up hundreds of terms instantly. For example, to sum the first 20 terms of uₙ = 5 × 2ⁿ⁻¹, you can either use the formula or directly enter sum(seq(5×2n-1, n, 1, 20)).
等差数列和等比数列在IB金融与建模问题中频繁出现。计算器的序列模式可以生成项，求和函数能立刻累加数百项。例如，要对 uₙ = 5 × 2ⁿ⁻¹ 的前20项求和，你可以使用公式，或者直接输入 sum(seq(5×2n-1, n, 1, 20))。
Be careful with recursive definitions. While a GDC can evaluate a few terms, you may need to write a small program or use the spreadsheet feature for deeply nested recursion. Review Set 20B often includes an 'explore' task where you use the calculator to investigate convergence of a series; always check if the question asks for a limit or a sum to infinity.
处理递推定义时要格外小心。虽然计算器可以计算前几项，但对于深层嵌套的递推，你可能需要编写小程序或使用电子表格功能。复习题集20B往往会设置探究任务，让你用计算器研究级数的收敛性；始终要判断题目要求的是极限还是无穷和。
8. Financial Calculations Made Easy | 金融计算轻松上手
The finance solver (TVM – terest, annuities, and loan repayments. In the TVM solver, N = total number of payments, I% ys ensure the sign convention: money out is negative, money in is positive, or vice versa.
金融求解器（TVM——货币时间价值）是处理复利、年金和贷款还款的救星。在TVM求解器中，N = 总付款次数，I% = 年利率，PV = 现值，PMT = 每期付款额，FV = 终值，P/Y = 每年付款次数，C/Y = 每年复利次数。务必遵循符号约定：支出现金为负，收入现金为正，或者一致反向设置。
When the question asks 'how long will it take to save £50,000?' you solve for N and must interpret a decimal N sensibly – unless stated otherwise. The TVM solver eliminates the need for messy logarithmic algebra.
当题目问“需要多少时间才能存到 £50,000？”时，你求解 N 并需合理解释小数 N——向上取整到下一个完整还款期。类似地，计算贷款月供时，若无特别说明，应设 P/Y = 12 和 C/Y = 12。TVM求解器让你彻底告别繁琐的对数代数。
9. Probability Distributions and Simulations | 概率分布与模拟
The GDC’s distribution menu offers PDF, CDF, and inverse functions for Normal, Binomial, Poisson, and t‑distributions. Instead of consulting printed tables, you input parameters and get precise probabilities. For X ~ B(20, 0.4), to find P(X = 8), use Binomial PDF with n=20, p=0.4, x=8. For cumulative P(X ≤ 10), use Binomial CDF.
计算器的分布菜单为正态、二项、泊松和t分布提供了概率密度函数、累积分布函数与逆函数。你再也不用翻查纸质表格，只需输入参数便能得到精确的概率值。对于 X ~ B(20, 0.4)，求 P(X = 8) 时使用二项PDF，设 n=20, p=0.4, x=8；累积概率 P(X ≤ 10) 则用二项CDF。
A common trap in Review Set 20B is confusing 'at least' with 'less than'. The CDF gives left‑tail probability, so for 'at least 12' you calculate 1 – P(X ≤ 11). Also remember that when the question asks you to 'find the value of μ' or 'standard deviation', you may need the inverse Normal function, specifying the area to the left.
复习题集20B中一个常见陷阱是混淆“至少”与“小于”。CDF给出的是左尾概率，因此对于“至少12”应计算 1 – P(X ≤ 11)。还要记住，当题目要求“求 μ 的值”或“标准差”时，你可能需要使用逆正态功能，并指定左侧面积。
10. Avoiding Common GDC Errors | 规避高频计算器错误
Many students lose marks not because they cannot do the maths but because of avoidable GDC blunders. The most frequent mistake is forgetting to change angle mode between degrees and radians. A sine curve that looks completely wrong is often a degree‑vs‑radian issue. Always check the mode indicator before any trigonometric calculation.
许多学生丢分不是因为不会做数学，而是因为可避免的计算器操作失误。最频繁的错误是忘记在角度模式（度/弧度）之间切换。正弦曲线画出来完全不对，往往是度与弧度混淆所致。进行任何三角运算前，务必检查模式指示器。
Another pitfall is misreading the display: 3.4E‑5 is 0.000034, not 3.4⁻⁵. Learn to interpret scientific notation instantly. Also, when using stored values (like Ans or variables), be aware that rounding can propagate if you cut the displayed value too early. Store full‑precision values in memory and recall them when needed.
另一个陷阱是误读显示：3.4E‑5 是 0.000034，而不是 3.4⁻⁵。要学会即时解读科学计数法。同时，使用存储值（如 Ans 或变量）时，要注意如果你过早地对显示值进行截断，舍入误差会累积传播。应将全精度值存入存储器，需要时再调出。
11. Efficient Navigation: Shortcuts You Must Know | 高效操作：必备快捷键
Every second counts in the exam. Familiarise yourself with copy‑paste functions: on the TI‑84, use 2ND then ENTRY to recall previous calculations. On the TI‑Nspire, swipe or press ctrl + C and ctrl + V. Fraction templates, square root symbols, and quick‑graph buttons should be muscle memory. Set up a custom menu or quick‑plot favourites if your model allows it.
考试中每秒都很宝贵。熟悉复制粘贴功能：在 TI‑84 上，使用 2ND 然后按 ENTRY 调出之前的计算式。在 TI‑Nspire 上，滑动或按 ctrl + C 和 ctrl + V。分数模板、根号符号和快速绘图按钮应该成为肌肉记忆。如果你的机型支持，建立自定义菜单或快速绘图收藏夹。
When working on A4 papers, you do not need to redraw the graphs on your screen; you just need to sketch important features and quote the calculator‑obtained coordinates. Use the 'Table' function to generate coordinate pairs efficiently. Practice producing a neat, labelled sketch within two minutes.
在 A4 试卷上作答时，你无需重绘屏幕上的图形；只需勾画出重要特征并引用计算器得出的坐标即可。利用“表格”功能高效地生成坐标对。练习在两分钟内画出一幅整洁、标注清晰的草图。
12. Preparing for the Exam: A Structured Review | 备考计划：结构化复习
Work through Review Set 20B systematically: allocate 30 minutes per section and simulate exam conditions. After each question, write down the exact GDC function used, the inputs, and the output. This log will become a personalised quick‑reference sheet that you can mentally rehearse the night before the exam. Identify any 'pain points' – tasks where the calculator hangs or gives unexpected syntax errors – and practise them until they become smooth.
系统地过一遍复习题集20B：为每个单元分配30分钟并模拟考试环境。每做完一题，记录下所使用的精确计算器功能、输入值和输出。这份日志将形成一份个性化的快速参考清单，你可以在考前晚上脑内预演。找出所有“痛点”——那些计算器会卡死或给出意外句法错误的任务——反复练习直到驾轻就熟。
On exam day, check that your GDC is fully charged or has fresh batteries. Bring a backup calculator if permitted. Most importantly, trust the tool but also your own reasoning; if a GDC output looks nonsensical, cross‑check with a rough estimate. That final blend of technical fluency and critical thinking is what earns a grade 7.
考试当天，检查计算器已充满电或装有新电池。如允许，可携带备用计算器。最重要的是，既要信任工具也要相信自己的推理；如果计算器输出看起来不合理，用粗略估算加以核对。技术熟练与批判性思维的最终融合，正是赢得7分的秘诀。
Published by TutorHao | IB Mathematics Revision Series | aleveler.com
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