📚 TI-Nspire Essentials for IB Applications and Interpretation SL | IB 应用与解释 SL 的 TI-Nspire 核心技巧
Your TI-Nspire is not just a calculator; it is a laboratory for exploring the numerical, graphical and statistical ideas in IB Applications and Interpretation SL. This guide collects the exact tools and workflows you need for Paper 1 and Paper 2, from graphing functions and solving equations to producing regression models and using the Finance Solver. It also highlights common mistakes so you can use the GDC confidently under exam pressure.
你的 TI-Nspire 不只是计算器，更是探索 IB 应用与解释 SL 中数值、图像与统计思想的实验室。本文整理了 Paper 1 和 Paper 2 所需的精确工具与操作流程，包括绘制函数图像、解方程、建立回归模型以及使用财务求解器。文章还指出常见错误，帮助你在考试压力下自信地使用 GDC。
1. Knowing Your GDC: Document Settings and Modes | 认识你的 GDC：文档设置与模式
Before any question, press ctrl + doc to open Document Settings. Set Angle to Degree for bearings, triangle trigonometry and navigation problems; switch to Radian only when the question explicitly uses radians, such as arc length or trigonometric calculus. Set Display Digits to Float 6 or Float 3 so answers are easy to round to 3 significant figures. Keep Calculation Mode on Approximate for most AI SL work, but choose Exact when a question asks for a simplified radical or fraction. Confirm that Real or Complex format matches the question; AI SL normally uses Real.
做任何题目前，按 ctrl + doc 打开“文档设置”。将角度单位设为“度”来处理方位角、三角形与航海问题；只有题目明确使用弧度时（例如弧长或三角函数的微积分），才切换到“弧度”。将显示位数设为 Float 6 或 Float 3，这样答案容易保留 3 位有效数字。大多数 AI SL 题目把计算模式设为“近似”，但当题目要求化简根式或分数时，应选择“精确”。确认实数/复数格式与题目一致，AI SL 通常使用“实数”。
- Degree mode for bearings; Radian mode for arc length and calculus.
- Float 3 or Float 6 for 3-s.f. rounding.
- Approximate for final checks; Exact for surds and fractions.
中文要点：角度用“度”处理方位角；弧度用于弧长与微积分。显示位数用 Float 3 或 Float 6 便于保留 3 位有效数字。一般计算用近似；根式或分数化简用精确。
2. Graphing Functions and Finding Key Points | 绘制函数图像与求关键点
ss enter. Use menu > Analyze Graph > Zero to find x-intercepts; the GDC asks for a lower and upper bound around the zero. Use menu > Analyze Graph > Intersection to find where two graphs meet, and menu > Analyze Graph > Maximum or Minimum to locate turning points. For a quick view, use menu > Trace > Graph Trace and move along the curve with the touchpad.
打开 Graphs 页面或按 ctrl + G 插入图像页。在输入行中键入函数，例如 f1(x)=x²−3x+2，按 enter。使用 menu > Analyze Graph > Zero 求 x 轴交点；GDC 会要求你在零点附近选择下界和上界。使用 menu > Analyze Graph > Intersection 求两条图像的交点，使用 menu > Analyze Graph > Maximum 或 Minimum 找极值点。需要快速查看时，用 menu > Trace > Graph Trace 沿曲线移动。
Always write down the window settings if you sketch from the screen. A sensible starting window is x from −10 to 10 and y from −10 to 10, but adjust it after seeing the shape. For functions with vertical asymptotes, use dot mode or a narrower y-range to avoid misleading lines.
如果根据屏幕画草图，务必记录窗口设置。合理的初始窗口是 x 从 −10 到 10，y 从 −10 到 10，但要根据图像形状调整。对于有垂直渐近线的函数，使用点模式或缩小 y 范围，避免出现误导性连线。
3. Solving Equations Numerically with nSolve and PolyRoots | 使用 nSolve 与 PolyRoots 数值解方程
On a Calculator page, press menu > Algebra > Numerical Solve to enter the nSolve command. The syntax is nSolve(equation, variable). For example, nSolve(2x f the equation has multiple solutions: nSolve(cos(x)=0.2,x,1) finds the solution near x=1.
在 Calculator 页面，按 menu > Algebra > Numerical Solve 输入 nSolve 命令。语法为 nSolve(equation, variable)。例如，nSolve(2x=10,x) 返回 x≈3.32193。这是求解无法用简单代数解出的方程的主要工具，包括指数、对数与三角方程。你也可以写成 nSolve(f(x)=g(x),x)。如果方程有多个解，可以加入初值或区间：nSolve(cos(x)=0.2,x,1) 会求出 x=1 附近的解。
For polynomial equations, menu > Algebra > Polynomial Tools > Find Roots of Polynomial is often faster. Enter the degree and coefficients, and the GDC returns all real or complex roots. However, if the polynomial is not factorable, the result is approximate unless you have specified Exact mode. Do not use PolyRoots for non-polynomial equations; nSolve is the correct tool.
对于多项式方程，menu > Algebra > Polynomial Tools > Find Roots of Polynomial 通常更快。输入次数和系数，GDC 会返回所有实数或复数根。但如果多项式不可因式分解，除非设置为精确模式，结果将是近似的。不要对非多项式方程使用 PolyRoots；nSolve 才是正确工具。
nSolve(2x = 10, x) → x ≈ 3.32193
4. Working with Data: Lists, Spreadsheets and One-Variable Statistics | 处理数据：列表、电子表格与单变量统计
Insert a Lists & Spreadsheet page. Type your data into column A, and name the list by typing a name in the top cell, such as a. Then press menu > Statistics > Stat Calculations > One-Variable Statistics. Set Number of Lists to 1, X1 List to a[], and Frequency List to 1 if each value appears once. The output includes the mean x̄, sample standard deviation sx, population standard deviation σx, median, quartiles and range.
插入 Lists & Spreadsheet 页面。把数据输入 A 列，并在顶部单元格输入名称，例如 a。然后按 menu > Statistics > Stat Calculations > One-Variable Statistics。将 Number of Lists 设为 1，X1 List 设为 a[]，如果每个值只出现一次，Frequency List 设为 1。输出包括平均值 x̄、样本标准差 sx、总体标准差 σx、中位数、四分位数和极差。
In AI SL, if the data is a sample from a larger population, use sx; if the data is the whole population, use σx. Read the question wording carefully: 'a group of students' often implies a sample, while 'all employees in a company' implies a population. For grouped data, enter midpoints in one column and frequencies in another, then set Frequency List to the frequency column.
在 AI SL 中，如果数据是来自较大总体的样本，使用 sx；如果数据就是总体，则使用 σx。仔细阅读题目措辞：“一组学生”通常表示样本，而“公司所有员工”表示总体。对于分组数据，把组中值输入一列，频数输入另一列，然后把 Frequency List 设为频数列。
5. Bivariate Statistics and Regression Lines | 双变量统计与回归直线
For bivariate data, enter x-values in column A and y-values in column B. Use menu > Statistics > Stat Calculations > Linear Regression (mx+b) or Linear Regression (a+bx). The GDC displays the equation, r and r². IB questions usually require the line of best fit and the correlation coefficient r. If r is not shown, press menu > Statistics > Stat Diagnostics and ensure 'Show r' is selected.
对于双变量数据，把 x 值输入 A 列，y 值输入 B 列。使用 menu > Statistics > Stat Calculations > Linear Regression (mx+b) 或 Linear Regression (a+bx)。GDC 会显示方程、r 和 r²。IB 题目通常要求最佳拟合直线和相关系数 r。如果没有显示 r，按 menu > Statistics > Stat Diagnostics，确保选中“Show r”。
Use the regression equation to make predictions, but be careful with extrapolation. For non-linear trends, TI-Nspire offers Exponential Regression, Quadratic Regression, Sinusoidal Regression and Logistic Regression. Choose the model that matches the scatter plot and gives the most sensible R². In IA work, compare models and justify your choice with R² and residual plots.
使用回归方程进行预测，但要注意外推的合理性。对于非线性趋势，TI-Nspire 提供指数回归、二次回归、正弦回归和逻辑回归。选择与散点图匹配且 R² 最合理的模型。在 IA 作业中，应比较模型，并用 R² 和残差图证明你的选择。
6. Probability Distributions: Binomial and Normal | 概率分布：二项分布与正态分布
. The syntax is binomPdf(n,p,x) and binomCdf(n,p,lowerBound,upperBound). For example, if X ~ ) is binomPdf(12,0.3,4) and P(X ≥ 4) is 1 − binomCdf(12,0.3,0,3) or binomCdf(12,0.3,4,12).
使用 menu > Statistics > Distributions 进入概率工具。二项分布使用 Binomial Pdf 求 P(X = x)，使用 Binomial Cdf 求 P(a ≤ X ≤ b)。语法为 binomPdf(n,p,x) 和 binomCdf(n,p,lowerBound,upperBound)。例如，若 X ~ B(12, 0.3)，则 P(X = 4) 为 binomPdf(12,0.3,4)，P(X ≥ 4) 为 1 − binomCdf(12,0.3,0,3) 或 binomCdf(12,0.3,4,12)。
find a value corresponding to a given left-tail probability, use Inverse Normal: invNorm(area,μ,σ). Always sketch the normal curve and shade the region before entering bounds into the GDC.
正态分布使用 Normal Cdf。语法为 normCdf(lowerBound,upperBound,μ,σ)。如果省略 μ 和 σ，GDC 默认使用 μ=0 和 σ=1。要求给定左侧概率对应的取值时，使用 Inverse Normal：invNorm(area,μ,σ)。输入边界前，务必画出正态曲线并标出阴影区域。
7. Finance Solver for Loans, Annuities and Compound Interest | 财务求解器：贷款、年金与复利
Open the Finance Solver from a Calculator page via menu > Finance > Finance Solver. The fields are N (number of payments), I(%) (annual interest rate), PV (present value), PMT (payment per period), FV (future value), PpY (payments per year) and CpY (compounding periods per year). Enter all known values and move the cursor to the unknown field, then press enter to solve.
在 Calculator 页面通过 menu > Finance > Finance Solver 打开财务求解器。字段包括 N（付款次数）、I(%)（年利率）、PV（现值）、PMT（每期付款额）、FV（终值）、PpY（每年付款次数）和 CpY（每年计息次数）。输入所有已知值，将光标移至未知字段，按 enter 求解。
ney you pay out is negative. For a loan of 10000 with monthly repayments over 5 years at 6% esult should be negative, representing an outflow. If your PMT appears positive, check the sign of PV or FV.
正负号规则至关重要：收到的钱为正，支付的钱为负。例如一笔 10000 的贷款，年利率 6%，5 年内每月还款，应设 N=60，I=6，PV=10000，FV=0，PpY=12，CpY=12，然后求解 PMT。结果应为负值，表示资金流出。如果 PMT 出现正值，请检查 PV 或 FV 的符号。
N = 60, I% = 6, PV = 10000, FV = 0, PpY = 12, CpY = 12 → PMT ≈ −193.33
8. Calculus Tools: Numerical Derivative, Definite Integral and Graphs | 微积分工具：数值导数、定积分与图像
seful for checking your analytical derivative or for finding the slope of a function that is difficult to differentiate.
求某点的数值导数，按 menu > Calculus > Numerical Derivative at a Point。语法为 nDeriv(f(x),x,a)。例如，nDeriv(x²+3x−1,x,2) 返回曲线在 x=2 处的斜率。这可用于检查解析导数，或求难以求导函数的斜率。
For definite integrals, use menu > Calculus > Integral or select the integral template. Type the function, lower limit and upper limit. Alternatively, in a Graphs page, use menu > Analyze Graph > Integral and select the lower and upper bounds. The GDC shades the signed area. Remember that areas below the x-axis contribute negative values to a definite integral, so split the region if you need total area.
求定积分，使用 menu > Calculus > Integral 或选择积分模板。输入函数、下限和上限。也可以在 Graphs 页面使用 menu > Analyze Graph > Integral 并选择上下界。GDC 会为有向面积填充阴影。请记住，x 轴以下的区域在定积分中贡献负值，因此如果需要总面积，应把区域分开计算。
9. Modelling Tasks: Using Sliders and Transformations | 建模任务：使用滑杆与函数变换
a, then type f1(x)=a·x²+b·x+c. Move the slider to adjust a, b and c until the curve fits a
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