📚 TI-Nspire for IB Math Analysis and Approaches SL | IB数学分析与方法SL的TI-Nspire使用指南
The TI-Nspire CX (non-CAS) is the standard graphing calculator for IB Mathematics: Analysis and Approaches SL. It is a powerful tool for checking algebra, visualising functions, and performing numerical calculations, but it must be used alongside clear mathematical reasoning. This guide covers the most exam-relevant Nspire skills for AA SL.
TI-Nspire CX（非CAS版）是IB数学：分析与方法SL的标准图形计算器。它是检查代数、可视化函数和进行数值计算的强大工具，但必须与清晰的数学推理一起使用。本指南涵盖AA SL考试中最相关的Nspire技能。
1. The Role of TI-Nspire in IB Math AA SL | TI-Nspire在IB数学AA SL中的作用
The TI-Nspire CX (non-CAS) is the standard graphing calculator permitted in IB Mathematics: Analysis and Approaches SL. It is a tool for checking algebra, visualising functions, and performing numerical work, but it does not replace exact reasoning. The IB marks method and communication, so calculator screenshots or rounded decimals must be supported by written working.
TI-Nspire CX（非CAS版）是IB数学：分析与方法SL允许使用的标准图形计算器。它用于检查代数、可视化函数和完成数值计算，但不能替代精确推理。IB评分重视方法与表达，因此计算器截图或四舍五入的小数必须有书面步骤支撑。
You should treat the Nspire as a verification device: use it to graph a function before sketching, to confirm a root, or to evaluate an integral numerically after showing the antiderivative. Over-reliance on calculator syntax without mathematical explanation loses marks.
应把Nspire当作验证工具：在画图前先绘制函数、确认零点，或在展示原函数后再用数值积分。只写计算器语法而不作数学解释会失分。
2. Essential Settings: Angle Mode, Exact Mode, Display Digits | 基本设置：角度模式、精确模式与显示位数
Press c then Settings then Document Settings. Set Angle to Radian unless the question uses degrees. Set Calculation Mode to Exact if you want fractions and radicals, or Approximate if the question says ‘give your answer correct to 3 s.f.’. Display Digits can be Float, Fix 3, or Scientific.
按 c 然后 设置 然后 文档设置。角度单位设为弧度，除非题目使用度数。计算模式若需要分数和根式可选精确，若题目要求“保留3位有效数字”可选近似。显示位数可选浮点、定点3位或科学计数法。
In exams, a common mistake is leaving Angle in Degree mode when evaluating sin(π/6). In Radian mode sin(π/6) = 1/2; in Degree mode sin(π/6) treats π/6 as a small degree value and gives a wrong decimal. Always check the status bar.
考试中常见错误是计算 sin(π/6) 时角度仍为度数模式。弧度模式下 sin(π/6)=1/2；度数模式会把 π/6 当成很小的角度，得到错误小数。务必检查状态栏。
| Setting | Recommended for AA SL |
| Angle | Radian |
| Calculation Mode | Exact or Approximate depending on question |
| Display Digits | Float 6 or Fix 3 as requested |
3. Graphing and Analysing Functions | 函数绘图与图像分析
To graph f(x)=x³−3x+1, press c then New Document then Add Graphs. Type f1(x)=x^3-3x+1 and press Enter. Use menu then Window/Zoom then Zoom Standard or Zoom Fit. Use menu then Analyze Graph then Zero to find x-intercepts, and Minimum/Maximum for turning points.
要绘制 f(x)=x³−3x+1，按 c 然后 新文档 然后 添加图形。输入 f1(x)=x^3-3x+1 后回车。使用 menu 然后 窗口/缩放 然后 标准窗口或缩放适配。使用 menu 然后 分析图形 然后 零点找 x 轴截距，用最小值/最大值找极值点。
For intersection of two graphs, graph both f1 and f2, then menu then Analyze Graph then Intersection. Choose a lower and upper bound near the point. The Nspire gives a numerical coordinate, but you should record the exact equation you are solving first.
求两条曲线交点时，画出 f1 和 f2，然后 menu 然后 分析图形 然后 交点。在交点附近选择下界和上界。计算器给出数值坐标，但你应先写出要求解的方程。
4. Solving Equations and Systems Efficiently | 高效求解方程与方程组
In a Calculator page, use menu then Algebra then Solve or type solve(equation,x). For example solve(x^2-5x+3=0,x) returns exact solutions if in Exact mode. Use nSolve for numerical solutions: nSolve(2^x=10,x) gives x ≈ 3.32193.
在计算页面，使用 menu 然后 代数 然后 求解 或输入 solve(方程,x)。例如 solve(x^2-5x+3=0,x) 在精确模式下返回精确解。使用 nSolve 求数值解：nSolve(2^x=10,x) 给出 x ≈ 3.32193。
For systems, menu then Algebra then Solve System of Linear Equations lets you enter equations such as 2x+y=5 and x−3y=4. You can also write solve(2x+y=5 and x−3y=4,{x,y}). Always check whether the system is consistent before relying on the output.
线性方程组使用 menu 然后 代数 然后 求解线性方程组，输入例如 2x+y=5、x−3y=4。也可输入 solve(2x+y=5 and x−3y=4,{x,y})。依赖输出前先判断方程组是否相容。
5. Numerical Differentiation at a Point | 某点处的数值求导
The TI-Nspire can find a numerical derivative at a point. In a Calculator page type d/dx(f(x),x)|x=a, or use menu then Calculus then Numerical Derivative at a Point. For f(x)=√x, evaluating at x=4 gives 0.25. This is useful for checking gradient of a tangent.
TI-Nspire可求某点的数值导数。在计算页面输入 d/dx(f(x),x)|x=a 或使用 menu 然后 微积分 然后 在某点数值求导。对 f(x)=√x，在 x=4 求值得 0.25。这可用于检验切线斜率。
However, AA SL exam questions often ask for the derivative function f'(x) from first principles or differentiation rules. You must show the derivative algebraically; use Nspire only to verify your value or sketch the tangent line.
但AA SL考题常要求用第一原理或求导法则求导函数 f'(x)。必须展示代数求导过程，Nspire只用于验证数值或画切线。
6. Definite Integration and Area Problems | 定积分与面积问题
Use menu then Calculus then Numerical Integral or type ∫(f(x),x,a,b) to evaluate a definite integral. For example ∫(3x²−2,x,1,4) returns 35. In Exact mode, ∫(1/x,x,1,e) may return 1 if e is defined; otherwise use approximate.
使用 menu 然后 微积分 然后 数值积分 或输入 ∫(f(x),x,a,b) 计算定积分。例如 ∫(3x²−2,x,1,4) 得 35。精确模式下 ∫(1/x,x,1,e) 若 e 已定义可能返回1；否则用近似。
Area between two curves y=f(x) and y=g(x) can be found by ∫(|f(x)−g(x)|,x,a,b) or by subtracting after finding intersection points. The absolute value is essential if curves cross inside the interval.
两曲线 y=f(x) 与 y=g(x) 之间的面积可用 ∫(|f(x)−g(x)|,x,a,b) 或先求交点再相减。若曲线在区间内相交，绝对值必不可少。
7. Statistics: One-Variable and Two-Variable Data | 统计：单变量与双变量数据
For one-variable data, open Lists & Spreadsheet. Enter data in column A. Press menu then Statistics then Stat Calculations then One-Variable Statistics. Choose one list (a) and frequency list if needed. The output gives mean x̄, sample standard deviation sx, population standard deviation σx, median, Q1, Q3.
单变量数据：打开列表与电子表格，在A列输入数据。按 menu 然后 统计 然后 统计计算 然后 单变量统计。选择一个列表（a），如有频数列也选择。输出给出均值 x̄、样本标准差 sx、总体标准差 σx、中位数、Q1、Q3。
For bivariate data, enter x-values in column A and y-values in column B. Use menu then Statistics then Stat Calculations then Linear Regression (mx+b). The Nspire gives r, r², and the line equation y=mx+b. Use it to predict y for a given x.
双变量数据：x值输入A列，y值输入B列。使用 menu 然后 统计 然后 统计计算 然后 线性回归 (mx+b)。计算器给出 r、r² 和直线方程 y=mx+b。可用其预测给定 x 的 y 值。
8. Probability Distributions: Binomial and Normal | 概率分布：二项分布与正态分布
For binomial distribution, use menu then Probability then Distributions then Binomial Pdf/Cdf. Binomial Pdf gives P(X=k) for specified n,p,k. Binomial Cdf gives P(a≤X≤b). For example, n=10, p=0.3, P(X≤4) = binomCdf(10,0.3,0,4).
二项分布使用 menu 然后 概率 然后 分布 然后 二项概率密度/累积分布。二项 Pdf 给出指定 n,p,k 时的 P(X=k)。二项 Cdf 给出 P(a≤X≤b)。例如 n=10, p=0.3, P(X≤4) = binomCdf(10,0.3,0,4)。
For normal distribution, use Normal Cdf with lower, upper, μ, σ. For inverse normal, use Inverse Normal with area, μ, σ. Always standardise or draw a diagram before using the calculator.
正态分布使用 Normal Cdf 输入下限、上限、μ、σ。逆正态使用 Inverse Normal 输入面积、μ、σ。使用计算器前先标准化或画图。
9. Sequences, Series and Summation | 数列、级数与求和
In a Calculator page, use menu then Algebra then Sequence or define a function for the nth term. For example u(n)=3n−2. To sum ∑(3n−2,n,1,20), use menu then Calculus then Sum or type ∑(3n−2,n,1,20). The result is 610.
在计算页面，使用 menu 然后 代数 然后 序列 或定义通项函数，如 u(n)=3n−2。求和 ∑(3n−2,n,1,20) 可使用 menu 然后 微积分 然后 求和 或输入 ∑(3n−2
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