📚 Calculator Skills Sheets | 计算器技巧附录
Mastering your graphing calculator is essential for success in IB and Cambridge mathematics exams. These skill sheets provide step-by-step guidance for key calculator functions, helping you work efficiently and accurately. Whether you are using a TI-Nspire, TI-84 Plus, or Casio fx-CG50, the principles remain similar.
熟练掌握图形计算器对于在IB和剑桥数学考试中取得成功至关重要。这些技能表提供了关键计算器功能的分步指导，帮助您高效准确地工作。无论您使用的是TI-Nspire、TI-84 Plus还是Casio fx-CG50，原理都是相似的。
1. Getting to Know Your Calculator | 认识您的计算器
Before starting a calculation, ensure your calculator is in the correct mode. For most IB and Cambridge problems, use DEGREE mode for trigonometry unless radians are specified. Also set the number display to FLOAT or a suitable decimal place.
在开始计算之前，请确保计算器处于正确的模式。对于大多数IB和剑桥问题，除非指定弧度，否则使用角度（DEGREE）模式进行三角计算。还要将数字显示设置为浮点（FLOAT）或合适的小数位数。
Use the home screen for basic arithmetic and the MODE or SETTINGS menu to configure these options. Familiarise yourself with the catalogue of commands available under CATALOG or by pressing [menu].
使用主屏幕进行基本算术运算，并使用MODE或SETTINGS菜单配置这些选项。熟悉在CATALOG下或按[menu]键可用的命令目录。
2. Graphing Functions | 绘制函数图像
Graphing helps visualise behaviour of functions. Enter the function in the graphing app (e.g., Y= editor on TI or Graph mode on Casio). Adjust the viewing window using Xmin, Xmax, Ymin, Ymax to capture important features.
绘图有助于直观地了解函数的行为。在图形应用程序中输入函数（例如，TI上的Y=编辑器或Casio上的Graph模式）。使用Xmin、Xmax、Ymin、Ymax调整查看窗口，以捕捉重要特征。
After graphing, use ZOOM options such as ‘ZoomFit’ or ‘ZoomBox’ to refine the view. You can also trace points on the curve by pressing TRACE and using arrow keys.
绘制图形后，使用缩放选项，如’ZoomFit’或’ZoomBox’来细化视图。您还可以通过按TRACE并使用箭头键在曲线上追踪点。
3. Finding Roots and Intersections | 求根与交点
To find where a graph crosses the x-axis (roots/zeros), use the analyse graph feature. On TI-84, press [2nd] [CALC] and choose ‘zero’. Set left bound, right bound, and guess. On TI-Nspire, go to ‘Analyse Graph’ -> ‘Zero’. For Casio, use G-Solve -> ROOT.
要找到图形与x轴相交的位置（根/零点），请使用图形分析功能。在TI-84上，按[2nd] [CALC]并选择’zero’。设置左界、右界和猜测值。在TI-Nspire上，转到’Analyze Graph’->’Zero’。对于Casio，使用G-Solve -> ROOT。
Intersection of two curves F(x) and G(x) is found similarly: select ‘intersect’ then choose first curve, second curve, and provide a guess. The calculator displays the coordinates.
两条曲线F(x)和G(x)的交点查找方法类似：选择’intersect’，然后选择第一条曲线、第二条曲线，并提供一个猜测值。计算器会显示坐标。
4. Solving Equations Numerically | 数值解方程
Use the numerical solver to solve equations like x³ – 2x + 1 = 0. On TI-Nspire, open a Calculator page and type solve(x³ – 2x + 1 = 0, x). On TI-84, use the Equation Solver under [MATH] -> Solver. Enter the equation and an initial guess.
使用数值求解器求解诸如x³ – 2x + 1 = 0这样的方程。在TI-Nspire上，打开计算器页面并输入solve(x³ – 2x + 1 = 0, x)。在TI-84上，使用[MATH] -> Solver下的方程求解器。输入方程和一个初始猜测值。
Many models also allow solving systems of equations and inequalities. Always check that the solution is realistic within the domain of the problem.
许多型号还允许求解方程组和不等式。务必检查解在问题定义域内是否合理。
5. Calculating Derivatives at a Point | 计算某一点的导数
For numerical differentiation, use the derivative command. On TI-Nspire, type derivative(expression, x, value) e.g., derivative(x²+3x, x, 2) gives 7. On TI-84, use [MATH] -> nDeriv(expression, variable, value). Casio: use d/dx in RUN-MAT mode.
对于数值微分，可使用导数命令。在TI-Nspire上，输入derivative(表达式, x, 值)，例如derivative(x²+3x, x, 2)得出7。在TI-84上，使用[MATH] -> nDeriv(表达式, 变量, 值)。Casio：在RUN-MAT模式下使用d/dx。
This is useful for checking gradient of a curve at a point without differentiating by hand. Be aware of the tolerance of the numerical method.
这对于检查曲线上某一点的梯度而无需手动求导非常有用。请注意数值方法的容差。
6. Evaluating Definite Integrals | 计算定积分
Use the integrate command to find area under a curve. TI-Nspire: integral(expression, x, lower, upper). TI-84: [MATH] -> fnInt(expression, variable, lower, upper). Casio: use ∫dx from G-Solve in Graph mode or the integration template in RUN-MAT.
使用积分命令求曲线下的面积。TI-Nspire：integral(表达式, x, 下限, 上限)。TI-84：[MATH] -> fnInt(表达式, 变量, 下限, 上限)。Casio：在图形模式下使用G-Solve中的∫dx，或在RUN-MAT中使用积分模板。
Always sketch the graph first to check for sign changes, as the calculator gives signed area. For total area, split the integral into parts where the function is above or below the x-axis.
务必先画出草图检查符号变化，因为计算器给出的是带符号面积。对于总面积，将积分分割成函数在x轴上方和下方的部分。
7. Matrix Operations | 矩阵运算
Matrices can be defined via the Matrix Editor. Enter the dimensions and fill in entries. Operations such as addition (+), multiplication (×), determinant (det), inverse (⁻¹) are available. On TI-Nspire, use the matrix template; on Casio, use the Matrix mode.
矩阵可以通过矩阵编辑器定义。输入维数并填写条目。可进行加法（+）、乘法（×）、行列式（det）、逆矩阵（⁻¹）等运算。在TI-Nspire上使用矩阵模板；在Casio上使用矩阵模式。
For example, to solve AX = B, compute A⁻¹ × B provided A is square and non-singular. Notes: matrix multiplication order matters.
例如，要求解AX = B，可计算A⁻¹ × B，前提是A为方阵且非奇异。注意：矩阵乘法顺序很重要。
8. Descriptive Statistics | 描述性统计
Enter data lists in the Statistics app. One-variable statistics produce mean (x̄), sample standard deviation (s), quartiles, etc. Use two-list option for paired data. Ensure you understand the difference between population and sample standard deviation (σ vs s).
在统计应用程序中输入数据列表。单变量统计可得出平均值（x̄）、样本标准差（s）、四分位数等。对配对数据使用双列表选项。确保您理解总体标准差与样本标准差（σ与s）之间的区别。
Generate a box plot or histogram to visualise distribution. The calculator can also find the regression equation after setting up a scatter plot.
生成盒须图或直方图以可视化分布。在设置散点图后，计算器还可以找到回归方程。
9. Regression and Curve Fitting | 回归与曲线拟合
Fit models to data: linear (LinReg), quadratic (QuadReg), exponential, logarithmic, etc. Store the regression equation in a Y= variable to graph it alongside the data points. Check the correlation coefficient r and coefficient of determination r².
将模型拟合到数据：线性（LinReg）、二次（QuadReg）、指数、对数等。将回归方程存储到Y=变量中，以将其与数据点一起绘制。检查相关系数r和决定系数r²。
For non-linear data, the calculator can perform transformations, e.g., logarithmic transformation for power models. Use the residual plot to assess goodness of fit.
对于非线性数据，计算器可以执行变换，例如幂模型的对数变换。使用残差图来评估拟合优度。
10. Probability Distributions | 概率分布
Calculate probabilities for binomial, normal, Poisson, and other distributions. On TI, use the distr menu: normalcdf(lower, upper, μ, σ) for normal cumulative probabilities. For inverse normal, invNorm(area, μ, σ). On Casio, use the Stat menu’s distribution tools.
计算二项分布、正态分布、泊松分布等概率。在TI上，使用distr菜单：normalcdf(下限, 上限, μ, σ) 计算正态累积概率。对于逆正态，使用invNorm(面积, μ, σ)。在Casio上，使用统计菜单中的分布工具。
For binomial probabilities, binompdf(n, p, x) gives P(X = x) and binomcdf(n, p, x) for P(X ≤ x).
对于二项概率，binompdf(n, p, x)给出P(X = x)，binomcdf(n, p, x)给出P(X ≤ x)。
11. Financial Mathematics | 金融数学
IB and Cambridge syllabi include TVM (Time Value of Money) problems. Use the finance solver (APPS -> Finance on TI, or Financial app on Casio). Enter N (number of periods), I% (interest rate), PV, PMT, FV, P/Y, C/Y. Solve for the unknown.
IB和剑桥教学大纲包括货币时间价值（TVM）问题。使用财务求解器（TI上APPS -> Finance，或Casio上的Financial应用程序）。输入N（期数）、I%（利率）、PV、PMT、FV、P/Y、C/Y。求解未知量。
Common pitfalls: ensure positive/negative cash flow signs correct; use the correct compounding frequency. The solver works for loans, annuities, and investments.
常见陷阱：确保正负现金流符号正确；使用正确的复利频率。该求解器适用于贷款、年金和投资。
12. Exam Tips and Checks | 考试技巧与检查
Always reset your calculator or clear variables before starting an exam to avoid memory interference. Use the ‘Answer’ key (Ans) to carry forward results. Check that your mode is RADIAN or DEGREE as required.
考试开始前务必重置计算器或清除变量，以避免内存干扰。使用’Ans’键传递结果。根据需要检查模式是RADIAN还是DEGREE。
Verify numeric answers by plugging back into the original equation. Use graph analysis to confirm that your algebraic solutions make sense. Don’t forget to document calculator steps on paper where required.
通过代回原方程来验证数值答案。使用图形分析确认代数解是否合理。在需要时，不要忘记在纸上记录计算器步骤。
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