📚 Review set 13B - CALCULATOR | 复习集 13B - 计算器专项
In IB Mathematics, the graphing display calculator (GDC) is not just an accessory — it is an integral part of assessment. Review Set 13B is designed to sharpen your calculator skills across multiple syllabus topics, from solving equations and evaluating integrals to performing statistical tests and handling financial models. This article walks you through the key question types and GDC techniques you must master for the IB exams.
在 IB 数学中，图形计算器 (GDC) 不仅是辅助工具，而是考试评估的核心组成部分。复习集 13B 旨在强化您在多个课程主题中的计算器应用能力，涵盖解方程、计算积分、统计测试以及金融模型等问题。本文将带您逐一攻克考试中必须掌握的关键题型和 GDC 操作技巧。
1. Solving Polynomial Equations Efficiently | 高效求解多项式方程
fficients 1, −5, 2, 8. The calculator immediately returns roots: x = −1, x = 2, and x = 4.
复习集 13B 中的常见任务是找出三次或四次方程的所有实根。例如，求解 x³ − 5x² + 2x + 8 = 0。无需手动因式分解，您可以使用 GDC 多项式求解器（通常在 菜单 > 代数 > 多项式工具）。输入次数 3 和系数 1、−5、2、8，计算器会立即给出根：x = −1、x = 2、x = 4。
When an equation is not presented in polynomial form, like eˣ The GDC yields x ≈ 0.619. Always check the validity of the solution by substituting back.
当方程不是标准多项式形式时，例如 eˣ = 3 − x，您可以使用数值求解器（菜单 > 代数 > 数值求解）。在计算器中输入方程并提供一个初始猜测值，GDC 会得出 x ≈ 0.619。务必通过回代检查解的有效性。
2. Solving Simultaneous Equations with Multiple Variables | 求解多变量联立方程组
3/7 (or decimal forms). The GDC displays the exact fractional output if set to Exact mode.
IB 试题经常要求求解二元或三元一次方程组。您可以在 GDC 上通过 菜单 > 代数 > 求解线性方程组（适用于 2×2 或 3×3）完成。输入方程系数。例如，方程组 2x + 3y = 7、4x − y = 1 会得到 x = 5/7，y = 13/7（或小数形式）。如果设为精确模式，GDC 会给出分数形式。
Non‑ a the graphical method: draw both functions, then use the intersection tool (Menu > Analyze Graph > Intersection). The intersection coordinates give the solution pairs. Alternatively, you can use the numerical solver to satisfy both conditions.
非线性方程组，如 y = x² + 2 与 y = 3x，可以通过图形法求解：绘制两个函数，然后使用交点工具（菜单 > 图形分析 > 交点）。交点坐标即为解对。也可以使用数值求解器同时满足两个条件。
3. Numerical Differentiation at a Point | 某点的数值微分
Review Set 13B tests your ability to find the derivative at a specific x‑ e graph screen, then select Menu > Analyze Graph > dy/dx. Move the cursor to the desired x‑coordinate and press Enter. For f(x) = ln(x) at x = 2, the calculator gives f '(2) ≈ 0.5.
复习集 13B 考查您在不进行符号求导的情况下找出某一点导数的能力。在 GDC 中，先在图形界面输入函数，然后选择 菜单 > 图形分析 > dy/dx。将光标移到目标 x 坐标并按回车。对于 f(x) = ln(x) 在 x = 2 处，计算器给出 f '(2) ≈ 0.5。
When a function is defined parametrically or in polar form, you can still compute the gradient by switching to the appropriate mode and following the same dy/dx command. This is particularly handy for verifying tangents and normal lines in Paper 2, where calculator use is allowed.
当函数以参数方程或极坐标形式定义时，您仍然可以通过切换到相应模式并使用相同的 dy/dx 命令来计算梯度。这个方法对于试卷二（允许使用计算器）中验证切线和法线方程尤为方便。
4. Definite Integration and Area Under a Curve | 定积分与曲线下方面积
In calculator‑ or directly using the Calculus menu). Set the lower and upper bounds, and the GDC produces the numerical result, 2.000. It can also shade the region, helping you visualise the area.
在基于计算器的问题中，计算定积分如 ∫(0 到 π) sin(x) dx 可通过 菜单 > 图形分析 > ∫dx（或直接使用微积分菜单）完成。设定下限和上限，GDC 会给出数值结果 2.000。它还能对区域进行阴影填充，帮助您直观理解面积。
When the integrand involves absolute values or piecewise functions, you can split the integral into sections and use the GDC to find each partial area. For area between two curves, graph both, then use the bounded area tool; the calculator automatically subtracts one function from the other. Always confirm the intersection points first — errors occur if intervals are set incorrectly.
当被积函数涉及绝对值或分段函数时，您可以将积分拆分为若干部分，再用 GDC 分别求出各区间面积。对于两条曲线间的面积，先绘制两者，然后使用包围面积工具；计算器会自动将一个函数减去另一个。务必先确认交点——若区间设置不当，会引发错误。
5. Statistical Data Entry and One‑Variable Analysis | 统计数据录入与单变量分析
Many tasks in Review Set 13B involve importing a data set and computing summary statistics. Press Menu > Statistics > List Editor to enter values in L1. Then use the One‑Variable Statistics tool to obtain mean (x̄), median, standard deviation (σ or s), and quartiles. For IB, you must know whether to use the sample standard deviation (sₓ) or population standard deviation (σₓ).
复习集 13B 中的许多任务涉及导入数据集并计算汇总统计量。按 菜单 > 统计 > 列表编辑器，在 L1 中输入数值。然后使用单变量统计工具获得均值 (x̄)、中位数、标准差（σ 或 s）以及四分位数。在 IB 中，您必须分清使用样本标准差 (sₓ) 还是总体标准差 (σₓ)。
The calculator also creates box‑plots and histograms automatically from the list. In exam situations, you can copy the statistical output directly onto your answer sheet, but you still need to show interpretation — for instance, stating that the interquartile range is Q3 − Q1.
计算器还能自动根据列表生成箱形图和直方图。在考试中，您可以直接将统计输出抄写到答题纸上，但依然需要展示解读——例如，说明四分位距为 Q3 − Q1。
6. Linear Regression and Bivariate Analysis | 线性回归与双变量分析
When given paired data (x, y), the GDC can calculate the least‑squares regression line. Enter x‑values in L1 and y‑values in L2. Run the Linear Regression (mx+b) command. The output includes slope m, y‑ n coefficient r. For example, if r = 0.96, you can describe a strong positive correlation.
给定成对数据 (x, y) 时，GDC 可以计算最小二乘回归直线。在 L1 中输入 x 值，在 L2 中输入 y 值。执行线性回归 (mx+b) 命令。输出包括斜率 m、y 截距 b 以及相关系数 r。例如，若 r = 0.96，您就可以描述强正相关性。
function (e.g., Y1 = regEQ(x)) and evaluate it at a given x. Be careful with extrapolation — orts quadratic, cubic, exponential, and logistic regressions, accessible in the same menu.
使用计算器中存储的回归方程进行预测：选择函数（例如 Y1 = regEQ(x)）并在指定 x 处求值。注意外推的可靠性——IB 常要求您评论数据范围外的预测可信度。GDC 还支持二次、三次、指数和逻辑回归，均在同一菜单中操作。
7. Normal Distribution Calculations | 正态分布计算
he calculator returns 0.9332. For inverse problems, enter the probability and obtain the z‑score.
正态分布问题在复习集 13B 中频繁出现。要求标准正态的 P(Z < 1.5)，使用正态累积分布函数：设下限 = −∞（或 −1E99），上限 = 1.5，μ = 0，σ = 1。计算器返回 0.9332。对于逆问题，输入概率即可得到 z 分数。
For a variable X with mean 50 and standard deviation 8, find P(45 < X < 55). Use Normal Cdf with those parameters. The GDC gives approximately 0.4678. When the distribution is binomial and approximated by normal, remember to apply continuity correction; the calculator can handle both exact binomial Cdf and normal approximation, but IB expects you to know the difference.
对于均值 50、标准差 8 的变量 X，求 P(45 < X < 55)。使用带这些参数的正态 Cdf，GDC 得出约 0.4678。当二项分布近似于正态分布时，切记要应用连续性校正；计算器既可处理精确的二项 Cdf 也可进行正态近似，但 IB 要求您理解两者区别。
8. Matrices, Determinants and Inverses | 矩阵、行列式与逆矩阵
he calculator displays exact fractions where possible, which is essential for IB notation.
矩阵运算是 GDC 的强项。按 菜单 > 矩阵与向量 > 创建 来定义矩阵，例如 A = [[1,2],[3,4]]。随后即可计算行列式 det(A)、逆矩阵 A⁻¹，或求解矩阵方程 AX = B。计算器尽可能显示精确分数，这对 IB 答题格式至关重要。
When dealing with transformations, you can multiply matrices to find the image of a point. For instance, the transformation matrix [[0,−1],[1,0]] represents a rotation of 90° anticlockwise. Apply it to a column vector and verify coordinates. The GDC also helps with eigenvalues and eigenvectors in Further Mathematics topics.
在处理变换时，您可以通过矩阵乘法求出点的像。例如，变换矩阵 [[0,−1],[1,0]] 表示逆时针旋转 90°。将其应用于列向量并验证坐标。对于高等数学主题，GDC 还可帮助计算特征值和特征向量。
9. Complex Number Arithmetic and Polar Conversion | 复数运算与极坐标转换
IB students must be fluent in complex number operations. Switch the GDC to complex mode (often a+i or r∠θ setting). To evaluate (3+4i)(1−2i), simply type the expression; the calculator returns 11−2i. For division, use the fraction template or parentheses. Improper entry often leads to unexpected errors — always enclose complex numbers in brackets when raising to powers.
IB 学生必须熟练进行复数运算。将 GDC 切换到复数模式（通常为 a+i 或 r∠θ 形式）。要计算 (3+4i)(1−2i)，直接输入表达式；计算器返回 11−2i。除法使用分数模板或括号。输入不当常导致意外错误——进行幂运算时切记用括号将复数括起来。
The GDC can convert rectangular form to polar form (r∠θ) and vice versa. Use the built‑in conversion commands or change the output format. When solving polynomial equations, the calculator also lists complex roots without extra effort, which is invaluable for Paper 2 questions on complex numbers.
GDC 能将直角形式转换为极坐标形式 (r∠θ)，反之亦然。使用内置转换命令或更改输出格式即可。在求解多项式方程时，计算器还能直接列出复数根，这对试卷二中复数问题的解答极为有用。
10. Sequences, Series and Sigma Notation | 数列、级数与求和符号
) is straightforward with the GDC. Use the Catalog (or Menu > Calculus > Summation Σ). Enter the expression, variable, lower and upper limits. The calculator returns 120. This can verify your manual work for arithmetic and geometric series.
使用 GDC 计算 Σ(k=1 到 10) (2k+1) 非常简单。利用目录（或 菜单 > 微积分 > 求和 Σ），输入表达式、变量、下限和上限，计算器即返回 120。这可以用来验证您对等差和等比级数的手工计算。
For sequences defined recursively, you can use the sequence mode or build a quick table. Enter the recurrence formula and view term values in a list. This is especially useful for checking convergence in infinite geometric series or solutions to difference equations. Always note that the calculator works with approximate decimal values unless exact mode produces rational outputs.
对于递归定义的数列，您可以使用数列模式或建立快速表格。输入递推公式并在列表中查看项值。这对检查无穷等比级数的收敛性或差分方程的解特别有帮助。请注意，除非精确模式能输出有理数，否则计算器会以近似小数值运行。
11. Financial Mathematics and TVM Solver | 金融数学与 TVM 求解器
ue of Money (TVM) solver is hidden in the Finance menu. You input N (number of periods), I% P/Y (payments per year). For example, to find the monthly payment on a loan of 10,000 at 6% p.a. over 5 years, set N=60, I%=6, PV=10000, FV=0, P/Y=12. The solver gives PMT ≈ −193.33.
货币时间价值 (TVM) 求解器隐藏在金融菜单中。您需输入 N（期数）、I%（年利率）、PV（现值）、PMT（每期付款）、FV（终值）和 P/Y（每年付款次数）。例如，求一笔 10,000 元、年利率 6%、5 年期贷款的月还款额，可设 N=60，I%=6，PV=10000，FV=0，P/Y=12，求解器会给出 PMT ≈ −193.33。
TVM problems often require careful sign convention: money received is positive, money paid out is negative. GDC follows this rule strictly. You can also solve for the interest rate or number of periods by leaving that field blank and placing the cursor on it before pressing solve. Always interpret the result in the context of the problem — IB examiners look for accurate units and explanations.
TVM 问题通常要求注意符号惯例：收入为正，支出为负。GDC 严格遵循这一规则。您还可以通过将某个字段留空并在按下求解前将光标移至该位置，来求解利率或期数。务必结合题意解释结果——IB 阅卷人看重正确的单位与说明。
12. Exam Mode, Memory Restrictions and Troubleshooting | 考试模式、内存限制与排错
All IB calculator exams require the GDC to be in Press‑to‑Test mode, which disables stored programs and user files. Practice using your model's exam light indicator to avoid disqualification. Additionally, learn to reset the memory or clear all definitions (such as stored functions and variables) before starting a new problem.
所有 IB 计算器考试均要求 GDC 处于“按压测试”模式，该模式会禁用存储的程序和用户文件。请练习使用您机型上的考试指示灯，以免被取消资格。此外，要学习在开始新题目之前重置内存或清除所有定义（如存储的函数和变量）。
Common troubleshooting includes error messages like 'domain error' when executing an inverse normal with probability outside (0,1), or 'no sign change' in numerical solve due to a poor initial guess. Always check your window settings when graphs seem empty. Using Zoom Fit or adjusting Xmin/Xmax quickly resolves these issues.
常见排错包括：当逆正态分布的概率超出 (0,1) 时出现“定义域错误”；数值求解时由于初始猜测不佳出现“无符号变化”。当图形显示为空时，请检查窗口设置。使用“缩放适应”或调整 Xmin/Xmax 即可快速解决这些问题。
Finally, never rely on the calculator alone. Use it to verify algebraic steps and explore patterns, but always transcribe your reasoning onto the paper. IB grading values method marks even if the final answer is slightly off due to rounding. Ensure your GDC is fully charged and set to radian or degree mode as appropriate.
最后，切勿单纯依赖计算器。将它用于验证代数步骤与探索规律，但务必将推理过程写在答题纸上。IB 评卷重视方法分，即使最终答案因四舍五入稍有偏差也不例外。确保您的 GDC 电量充足，并根据需要将角度单位设为弧度或度。
Published by TutorHao | IB Mathematics Revision Series | aleveler.com
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