📚 Review Set 9B: Mastering Calculator Skills for IB Mathematics | 复习题集9B：掌握IB数学计算器技巧
Review Set 9B is designed to sharpen your graphical display calculator (GDC) techniques for the calculator-allowed papers in IB Mathematics – Paper 2 and the HL Paper 3. Whether you are working through the Analysis & Approaches or Applications & Interpretation syllabus, the ability to efficiently use your GDC for graphing, equation solving, calculus, statistics, matrices, and financial mathematics can save valuable time and reduce simple errors. This article walks you through the essential calculator operations covered in a typical 9B review, pairing each skill with exam-style reasoning and common pitfalls.
复习题集9B旨在加强你在IB数学允许使用计算器的试卷（试卷二和HL试卷三）中的图形计算器（GDC）技能。无论你学习的是分析与方法课程还是应用与解释课程，能高效地运用GDC进行绘图、方程求解、微积分、统计、矩阵和金融数学运算，都可以为你节省宝贵的时间并减少低级错误。本文带你顺一遍典型的9B复习所涵盖的核心计算器操作，每一项技能都配有考试风格的解题思路和常见陷阱。
1. Getting Started with Your GDC | 熟悉你的图形计算器
Before tackling any question, confirm that your calculator is in the correct angle mode – degrees or radians. Look for a small DEG or RAD symbol on the screen; trigonometric calculations in the wrong mode will produce completely wrong answers, especially in questions involving sine and cosine rules, differentiation of trig functions, or periodic modelling.
在解答任何题目之前，先确认你的计算器处于正确的角度模式：角度制或弧度制。屏幕上往往有DEG或RAD的小标识；在涉及正弦定理、余弦定理、三角函数的导数或周期建模的题目中，模式错误会导致完全错误的答案。
Set your GDC to display exact values wherever possible. Most calculators offer an 'Exact/Approx' or 'Math Print' π instead of decimal approximations. This is invaluable when an exact answer is required, such as giving sin(π/3) as √3/2, not 0.8660.
将你的GDC设置为尽可能显示精确值。多数计算器都有“精确/近似”或“数学打印”设置，可让结果保留为分数、平方根(√)或π的倍数，而非小数近似值。这在要求给出精确答案时非常有用，例如将sin(π/3)表示为√3/2，而不是0.8660。
tor and clear all functions, check the STAT lists and empty them, and reset any graphical formats that might hide part of your graph. Lingering plots or equations from an earlier question can interfere with your current work and waste precious exam time.
开始新题目之前，清除先前的所有输入。进入Y=编辑器清空所有函数，检查STAT列表并清空，重置任何可能遮挡部分图像的图形格式。前一问残留的图像或方程会干扰你当前的解答，浪费宝贵的考试时间。
2. Graphing Functions and Finding Intersections | 绘制函数图像与求交点
then press GRAPH. If the shape of the graph is not visible, adjust the viewing window by changing Xmin, Xmax, Ymin, Ymax. A good initial window for many IB problems is X from −10 to 10 and Y from −10 to 10; you can then zoom in on regions of interest using 'Zoom Box' or 'Zoom In'.
利用Y=编辑器输入函数，然后按GRAPH键。如果看不到图形形状，可调整视图窗口，修改Xmin、Xmax、Ymin、Ymax。许多IB题目适宜的初始窗口是X从−10到10，Y从−10到10；之后你可以用“选框放大”或“放大”功能深入感兴趣的区域。
s often represent the solution to an equation f(x) = g(x). Access the CALC menu and select 'intersect' y-coordinates of the intersection, which you can record to a suitable degree of accuracy.
两个函数图像的交点常常代表方程f(x) = g(x)的解。进入CALC菜单选择“intersect”（交点）。计算机会要求你确认两条曲线，并在交点附近提供一个猜测值。之后，它会给出交点的x坐标和y坐标，你可以记录到合适的精度。
For single functions, use 'zero' to find x-intercepts (roots), 'minimum' and 'maximum' to locate turning points. These commands also require a left bound, right bound, and a guess; always check that your bounds bracket the feature you are trying to find. These tools are heavily tested in optimisation and graph-sketching questions.
对于单个函数，使用“zero”求x轴截距（根），使用“minimum”和“maximum”寻找极值点。这些指令也需要左边界、右边界和一个猜测值；要始终确保边界囊括了你想要寻找的特征。这些工具在优化和图像描绘题中是重点考查内容。
3. Solving Equations Numerically | 数值求解方程
Most GDCs have a numerical solver that can handle equations directly. On a TI‑Nspire, use nsolve(equation, variable). On a Casio fx‑CG50, the solver is in the EQUA menu. Enter the equation exactly as it appears, but be aware that the solver only returns one solution at a time, usually the one closest to your initial guess.
多数GDC都有能够直接处理方程的数值求解器。在TI‑Nspire上，使用nsolve(方程, 变量)。在Casio fx‑CG50上，求解器位于EQUA菜单中。照原样输入方程，但要注意求解器每次只返回一个解，通常是距离你的初始猜测最近的那个。
When an equation has multiple solutions – such as a cubic with three real roots – supply different initial guesses to capture all of them. Recording each root with appropriate justification is essential for full marks on a ‘find all solutions’ question. Always check the domain given in the problem; you may need to restrict the solver range or supply boundaries.
当方程有多个解时——例如有三个实根的三次方程——需要提供不同的初始猜测来捕获全部解。把每个根记录下来并给出合适的理由，是在“求出所有解”类题目中获得满分的关键。一定要检查题目中给出的定义域；你可能需要限制求解器的范围或提供边界。
For systems of linear equations, use the simultaneous equation solver (often under the same EQUA or Algebra menu). Input coefficients for two or three equations, and the calculator produces the solution vector. More complex systems can be solved with matrices, which we will cover later.
对于线性方程组，使用联立方程求解器（通常位于同一个EQUA或代数菜单下）。输入两个或三个方程的系数，计算器就会输出解向量。更复杂的方程组可以用矩阵求解，我们稍后会讲到。
4. Calculus Operations: Derivatives and Integrals | 微积分运算：导数和积分
While in the graphing screen, you can find the numerical derivative at a point using the 'dy/dx' option in the CALC menu. Simply enter the x-coordinate, and the calculator displays the derivative value. This is useful for verifying tangent slopes or rates of change in context-based problems.
在图形界面中，你可以在CALC菜单中利用“dy/dx”选项求出某一点处的数值导数。只需输入x坐标，计算器就会显示导数值。这在验证切线斜率或上下文问题中的变化率时非常有用。
To compute a definite integral, select the '∫f(x)dx' s the signed area; areas below the x-axis will be negative, so you must interpret results carefully in questions about total enclosed area.
要计算定积分，在CALC菜单中选择“∫f(x)dx”函数。计算器会提示输入下限和上限，接着给区域涂色并显示数值。请记住这给出的是带符号的面积；x轴下方的面积为负值，因此在有关总封闭面积的题目中必须仔细解读结果。
r example, you can approximate ∫₀ ² x³ dx and compare it with your analytical answer of 4.
你的计算器无法给出符号化的原函数，因此当题目要求精确表达式时，你仍需手动进行积分。不过，数值积分是一种强大的检验工具；例如，你可以近似计算∫₀² x³ dx，并与你得到的解析答案4进行对比。
5. Statistical Analysis and Regression | 统计分析与回归
Enter bivariate data into two list columns, such as L1 for x-values and L2 for y-values. From the STAT CALC menu, choose 1‑Var Stats for single-variable statistics (mean, standard deviation, quartiles) or 2‑Var Stats when you need correlation and summary statistics for two variables. Always check which standard deviation your calculator reports – sample (sₓ) or population (σₓ) – and use the one that matches the problem context.
将双变量数据输入两个列表列，例如L1放x值，L2放y值。从STAT CALC菜单中，单变量统计选择1‑Var Stats（均值、标准差、四分位数），双变量统计需要相关性和汇总数据时选择2‑Var Stats。一定要核对计算器报告的是样本标准差(sₓ)还是总体标准差(σₓ)，并使用与题目情境匹配的那一个。
g. The calculator provides the coefficients and often the correlation coefficient r or coefficient of determination r²; these indicate the strength of the model.
回归模型帮助你找到最贴合数据集的方程。常见的选项有LinReg（y = ax + b）、QuadReg（y = ax² + bx + c）、ExpReg和SinReg。计算器会给出系数，通常还有相关系数r或决定系数r²，它们反映了模型的拟合强度。
pattern in the residuals suggests that another model might be more appropriate, so never skip this visual step when a data set looks suspiciously non‑linear.
在散点图上叠绘回归曲线可进行视觉检验。将原始数据绘制为散点图，把回归方程存储在Y=中，然后一起显示。若残差呈现明显模式，则说明另一个模型可能更合适，因此当数据集看上去明显地非线性时，永远不要跳过这个可视步骤。
6. Probability Distributions | 概率分布
The distribution menu, typically accessed via DISTR (or 2nd VARS on TI‑84), contains functions for the Normal, Binomial, Poisson and other distributions. For a normal distribution with mean μ and standard deviation σ, normalcdf(lower, upper, μ, σ) computes the probability that the variable falls between the two bounds. Leave the lower bound as −10⁹⁹ or a very negative number for left‑tail probabilities.
分布菜单，通常通过DISTR（或在TI‑84上按2nd VARS）访问，包含正态分布、二项分布、泊松分布等函数。对于均值为μ、标准差为σ的正态分布，normalcdf(下限, 上限, μ, σ) 可计算变量落在两个边界之间的概率。计算左尾概率时，把下限设为−10⁹⁹或一个很大的负数。
Inverse normal calculations are used when you know the area to the left and need to find the boundary value. invNorm(area to left, μ, σ) returns the corresponding X. This is particularly common in questions about confidence intervals or when you are given a percentile and asked to find the measurement that corresponds to it.
当你已知左侧面积而需要求边界值时，使用逆正态计算。invNorm(左侧面积, μ, σ)会返回相应的X值。这在置信区间类问题中尤其常见，或者在给出百分位数求对应测量值时出现。
For discrete distributions: binompdf(n, p, x) gives P(X = x) for a binomial distribution with n trials and success probability p; binomcdf(n, p, x) nctions are listed as poissonpdf and poissoncdf. Always read the question to decide whether you need an exact probability or a cumulative one.
对于离散分布：binompdf(n, p, x) 给出试验次数为n、成功概率为p的二项分布中P(X = x)；binomcdf(n, p, x) 给出P(X ≤ x)。类似地，泊松函数列为poissonpdf和poissoncdf。务必审题以确定是需要确切概率还是累积概率。
7. Matrix Calculations (HL Only) | 矩阵计算（仅HL）
Navigate to the Matrix editor (often named MAT or accessed via a button like 2ND x⁻¹ on TI‑84). Define matrices with appropriate dimensions, enter their entries, and then use them in calculations. You can add, subtract, multiply matrices, raise a square matrix to a power, and compute the determinant (det) and inverse (⁻¹).
进入矩阵编辑器（通常称为MAT，或通过TI‑84上的2ND x⁻¹键访问）。定义维度合适的矩阵，输入它们的元素，然后在计算中使用它们。你可以对矩阵进行加、减、乘运算，将方阵进行幂运算，并计算行列式(det)和逆矩阵(⁻¹)。
To solve a system of linear equations using matrices, create an augmented matrix that combines the coefficient matrix and the constant vector, then apply the rref iciently, but you should be ready to interpret infinite solutions or no-solution cases when the rref displays a row of zeros.
要用矩阵解线性方程组，创建一个由系数矩阵和常数向量构成的增广矩阵，然后使用rref指令（简化行阶梯形式）。结果矩阵的最后一列即为解。该方法能够高效地处理2×2、3×3以及更大规模的方程组，但当你看到rref出现一整行零时，要准备好解读无穷多解或无解的情形。
Analysis & Approaches, eigenvalues and eigenvectors may appear. Some GDCs (like the TI‑Nspire CX II) offer built‑in functions for these; check your calculator' (A − λI) = 0 manually, then use the calculator to compute eigenvectors via matrix methods.
对于HL分析与方法课程，可能会出现特征值与特征向量。部分GDC（如TI‑Nspire CX II）提供了这些功能的内置函数；请查阅计算器文档。如果没有，你需要通过手解特征方程det(A − λI) = 0求特征值，再用计算器通过矩阵方法计算特征向量。
8. Complex Numbers (HL Only) | 复数（仅HL）
Set the calculator to a+bi mode (often in the MODE menu) so that complex results are displayed in rectangular form. Enter complex numbers using the imaginary unit i (2ND . on TI‑84). Operations like addition, subtraction, multiplication and division are then performed just as with real numbers.
将计算器设为a+bi模式（通常在MODE菜单中），这样复数结果将以直角坐标形式显示。使用虚数单位i（TI‑84上按2ND .）输入复数。然后像处理实数一样执行加减乘除等运算。
Key functions include abs for modulus |z|, angle for argument θ, and conj for the complex conjugate. To convert between rectangular (a + bi) and polar (r cis θ) forms, use the built‑in commands >Rect and >Polar. This is particularly useful when answering questions about the polar form of complex numbers or when finding powers and roots using De Moivre's theorem.
关键函数包括用于求模|z|的abs，用于求幅角θ的angle，以及用于求共轭的conj。要在直角坐标式(a + bi)与极坐标式(r cis θ)之间转换，可使用内置指令>Rect和>Polar。这在回答关于复数极形式的问题，或运用棣莫弗定理求幂与根时尤其有用。
Remember that the calculator's angle function returns the principal argument, usually between −π and π. If the question asks for the argument in the interval [0, 2π), you will need to add 2π to any negative results. Always verify that your answer matches the required interval specified in the syllabus.
请记住，计算器的angle函数返回的是主幅角，通常在−π到π之间。
Published by TutorHao | IB Mathematics Revision Series | aleveler.com
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