📚 IB Math Review Set 25B: Mastering Calculator Skills | IB数学复习集25B：精通计算器技巧
Review Set 25B in the IB Mathematics curriculum is designed for calculator‑active problems. It tests your ability to use a graphing display calculator (GDC) efficiently, whether for solving equations, analysing functions, or performing statistical tests. This article walks you through the essential calculator skills you need, with paired examples and tips to help you speed through Paper 2 and Paper 3 questions with confidence.
IB数学课程中的复习集25B专为计算器题目设计。它检验你是否能高效使用图形计算器，无论是解方程、分析函数还是进行统计检验。本文将通过中英对照的方式，带你掌握必备的计算器技能，并提供配对示例和技巧，帮助你在试卷二和试卷三中自信快速地完成题目。
1. Calculator Setup and Mode Selection | 计算器设置与模式选择
Before tackling any problem, ensure your GDC is in the correct mode. For most IB questions, you will need radian mode for calculus and trigonometry, standard number format (not scientific), and sequential graphing rather than simultaneous. Check the angle setting under the mode menu; radian errors are among the most common mistakes in Paper 2.
在解决任何问题之前，请确保你的图形计算器处于正确的模式。对于大多数IB题目，微积分和三角函数需要使用弧度模式，数字格式应设为标准而非科学记数法，图形绘制应使用顺序模式而非同时模式。在模式菜单中检查角度设置；弧度错误是试卷二中最常见的失误之一。
2. Solving Equations and Systems | 解方程与方程组
Use the numeric solver or the polynomial root finder for single equations. For a system of linear equations, you can enter a matrix and use the reduced row‑echelon form (rref) function, or use the simultaneous equation solver. Always store the solutions as variables if you need them later. For non‑linear systems, graphing both sides and finding intersections is often faster and less error prone.
对于单个方程，可使用数值求解器或多项式求根功能。对于线性方程组，可以输入矩阵并使用简化行阶梯形（rref）函数，或使用联立方程求解器。如果需要后续使用，务必将解存为变量。对于非线性方程组，将两边分别作图并求交点通常更快且更不易出错。
3. Graphing Functions and Analysis | 函数图像与分析
Learn to adjust the viewing window quickly. Use Zoom‑Fit or set Xmin, Xmax, Ymin, Ymax manually. To find zeros, maximum or minimum points, and points of intersection, use the CALC menu (often 2nd TRACE). When the question asks for a range or domain, trace along the graph and read off coordinates, then confirm with an analytical check where possible.
学会快速调整显示窗口。使用自动缩放或手动设置Xmin、Xmax、Ymin、Ymax。要寻找零点、最大值或最小值以及交点，请使用计算菜单（通常按2nd TRACE）。当题目要求求范围或定义域时，沿图像追踪并读取坐标，然后尽可能通过解析方法加以确认。
4. Statistics and Probability Distributions | 统计与概率分布
Enter data into lists (L1, L2) and use the 1‑Var Stats or 2‑Var Stats commands to obtain mean, standard deviation, and quartiles. Remember: the IB expects the sample standard deviation Sx, not σx. For normal, binomial, and Poisson distributions, use the DISTR menu: normalcdf for probabilities, invNorm for critical values; binompdf/binomcdf for binomial; poissonpdf/poissoncdf for Poisson. Always sketch a quick diagram to check your entries.
将数据录入列表（L1，L2），使用单变量统计或双变量统计命令来获取均值、标准差和四分位数。请记住：IB要求样本标准差Sx，而非σx。对于正态分布、二项分布和泊松分布，使用分布菜单：正态累积函数normalcdf求概率，invNorm求临界值；二项分布用binompdf/binomcdf；泊松分布用poissonpdf/poissoncdf。始终快速画一个示意图以检查输入是否正确。
5. Matrix Operations | 矩阵运算
he augmented matrix. Check the order of multiplication carefully; the GDC follows standard matrix algebra rules.
矩阵出现在变换、方程组和图论中。使用矩阵编辑器定义矩阵A、B等。可直接进行加法、乘法、行列式（det）和求逆（⁻¹）运算。对于求解AX = B，可计算A⁻¹B或对增广矩阵使用rref。仔细检查乘法顺序；图形计算器遵循标准的矩阵代数规则。
6. Complex Number Calculations | 复数计算
Switch to a+bi mode to work with complex numbers. You can add, subtract, multiply, divide, find conjugates, modulus (abs), and argument (angle). For De Moivre’s theorem or roots of complex numbers, the GDC can verify results quickly. When converting between rectangular and polar forms, use the built‑in functions rather than manual conversion to save time and avoid mistakes.
切换到a+bi模式来处理复数。你可以进行加、减、乘、除，求共轭、模（abs）和辐角（angle）。对于棣莫弗定理或复数根，图形计算器可以快速验证结果。在直角坐标和极坐标形式之间转换时，使用内置函数而非手动转换，以节省时间并避免错误。
7. Calculus: Derivatives and Definite Integrals | 微积分：导数与定积分
π ∫ [f(x)]² dx and let the GDC handle the arithmetic, but be careful with squared terms inside the integral.
你的图形计算器可以用nDeriv(或d/dx)求某一点的导数值，用fnInt(或∫)求定积分。这完美适用于检验解析计算结果。要求曲线下方面积，设置带有正确上下限的积分。计算旋转体体积时，使用公式V = π ∫ [f(x)]² dx，让计算器处理运算，但要注意积分号内部的平方项。
8. Sequences and Series | 数列与级数
sequences, you can use the sequence mode to generate terms and the sum function (sum(seq(… of a convergent geometric series, simply apply the formula S∞ = a/(1 − r) after verifying |r| ber of terms to approximate the limit. This is also useful for checking explicit formulas.
对于等差数列和等比数列，可使用数列模式生成项，使用求和函数（sum(seq(…))）求级数和。求收敛等比级数的无穷和时，在验证|r| < 1后直接用公式S∞ = a/(1 − r) 即可，但图形计算器也可以对大量项求和来逼近极限值。这同样有助于检验通项公式。
9. Vectors and Geometry | 向量与几何
Store vectors as lists or matrices. Compute dot product by multiplying and summing elements, and cross product using the crossP( command. Use the norm( function to find the magnitude of a vector. When finding the angle between two vectors, apply the dot product formula and use cos⁻¹ on the GDC. These tools are especially helpful when verifying line and plane intersection points in Paper 2.
将向量存为列表或矩阵。点积可通过元素相乘并求和来计算，叉积使用crossP(命令。使用norm(函数求向量的模。求两向量的夹角时，应用点积公式并在计算器上使用cos⁻¹。在试卷二中，这些工具对于验证直线与平面的交点尤其有用。
10. Financial Mathematics | 金融数学
The TVM (Time‑Value‑of‑Money) solver is a huge time‑saver. Enter N, I%, PV, PMT, FV, P/Y, and C/Y carefully, and set the payment timing to END or BEGIN as appropriate. Solve for the unknown by placing the cursor on that field and pressing SOLVE. Remember the sign convention: money paid out is negative, money received is positive. Double‑check that your I% matches the compounding period.
TVM（资金时间价值）求解器能节省大量时间。小心输入N、I%、PV、PMT、FV、P/Y和C/Y，并将付款时间设置为期末（END）或期初（BEGIN）。将光标置于未知字段上按SOLVE求解。请记住符号惯例：支出为负，收入为正。仔细核对你输入的I%是否与复利周期一致。
11. Probability and Combinatorics | 概率与组合数学
nd probabilities of the form P(X > x), use 1 − binomcdf(n, p, x). The factorial function (!) is also readily available for counting problems.
使用概率菜单下的nCr和nPr命令计算组合与排列。对于二项概率，binompdf(n, p, x)精确给出P(X = x)，而binomcdf(n, p, x)给出累积概率P(X ≤ x)。求P(X > x)形式的概率，使用1 − binomcdf(n, p, x)。阶乘函数(!)也可直接用于计数问题。
12. Common GDC Mistakes and Checking Techniques | 常见计算器错误与检查技巧
Always clear all lists and variables before starting a new problem to avoid memory conflicts. When copying answers, write them to at least three significant figures or exact form if the question requires. Use the 2nd ENTRY feature to re‑evaluate an expression after a small change. If a result looks unreasonable, graph the situation; the visual check often reveals entry errors. Finally, never erase your working—the IB awards method marks even if the final answer is wrong.
开始新题目之前，务必清除所有列表和变量，避免内存冲突。抄写答案时，至少保留三位有效数字，若题目要求则使用精确值形式。使用2nd ENTRY功能在细微修改后重新计算表达式。如果结果看起来不合理，画出图像；视觉检查往往能发现输入错误。最后，切勿擦除你的推理步骤——即使最终答案错误，IB仍会给方法分。
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