📚 TI-Nspire for IB Maths AA HL: GDC Skills and Exam Tips | IB数学AA HL中的TI-Nspire：图形计算器技能与考试技巧
The TI-Nspire CX II is one of the most widely used graphing calculators (GDC) in IB Mathematics: Analysis and Approaches HL. It is not a replacement for proof or clear working, but it is an essential tool for testing conjectures, handling large data sets, and checking exact answers in Paper 2 and Paper 3.
TI-Nspire CX II 是 IB 数学：分析与方法（AA HL）最常用的图形计算器（GDC）之一。它不能替代证明或清晰的解题步骤，但在试卷二和试卷三中，它是检验猜想、处理大量数据以及核对精确答案的重要工具。
This guide covers the exam rules, the core calculator skills, and the habits that turn a powerful machine into reliable marks.
本文将梳理考试规则、核心计算器技能，以及能把一台强大的机器转化为稳定分数的答题习惯。
1. Why the TI-Nspire Matters in AA HL | 为什么TI-Nspire在AA HL中重要
In AA HL, the syllabus places heavy emphasis on conceptual understanding, proof, and analytical methods. The GDC works best when it is used to explore a function before proving a result, or to verify an answer after completing algebraic manipulation by hand.
在 AA HL 中，课程大纲高度重视概念理解、证明和分析方法。GDC 的最佳用途是在证明结果之前探索函数，或在手动完成代数运算之后核对答案。
The TI-Nspire is particularly strong because it combines a computer algebra system in the CAS model, dynamic graphing, and data analysis in one device. Learning to use it efficiently can save valuable time in exam conditions.
TI-Nspire 特别强大之处在于它将计算机代数系统（CAS 型号）、动态绘图和数据分析集成在一个设备中。学会高效使用它，可以在考试环境中节省大量宝贵时间。
ead off the minimum and maximum, then confirm the answer by hand with f′(x) = 3x² − 3 ≥ 0.
一个简单的例子：要研究曲线 y = x³ − 3x + 1 在何处递增，你可以先画图读出极小值与极大值，再用手算 f′(x) = 3x² − 3 ≥ 0 加以确认。
2. IB Calculator Rules for Paper 1, Paper 2 and Paper 3 | IB试卷一、试卷二与试卷三的计算器规则
Assessment in AA HL consists of Paper 1, where no calculator is allowed, and Papers 2 and 3, where a GDC is allowed. For Paper 1, you must be able to work through derivatives, integrals, and equations entirely by hand.
IB AA HL 的评估包括试卷一（不允许使用计算器）以及试卷二、试卷三（允许使用 GDC）。在试卷一中，你必须能够完全手算导数、积分和方程。
IB permits both CAS and non-CAS graphing calculators, but most AA HL students use the TI-Nspire CX II CAS. However, exam questions often ask for exact values or detailed reasoning, so a CAS result alone may not earn full marks.
IB 允许 CAS 和非 CAS 图形计算器，但大多数 AA HL 学生使用 TI-Nspire CX II CAS。然而，考试题目经常要求精确值或详细推理，因此仅凭 CAS 结果可能拿不到满分。
| Paper | 试卷 | GDC Allowed? | 是否允许GDC | Focus | 考查重点 |
| Paper 1 | No | 不允许 | Proof, algebra, calculus by hand | 证明、代数、手算微积分 |
| Paper 2 | Yes | 允许 | Long structured questions | 长结构化题目 |
| Paper 3 | Yes | 允许 | Two extended investigations | 两道拓展探究题 |
The key principle is that the GDC supports reasoning, it does not replace it. Markschemes award method marks for a correct algebraic route, and only the final accuracy mark may be earned from a correctly interpreted calculator output.
核心原则是：GDC 支持推理，而不能取代推理。评分标准给正确的代数路径以方法分，只有最终的准确分才可能来自对计算器输出的正确解读。
3. Setting Up Your TI-Nspire Before the Exam | 考前设置好你的TI-Nspire
Open File > Settings > General and set the calculation mode to Auto or Exact so that algebraic answers stay exact, and make sure the angle mode matches the question - Radian for calculus, Degree only when a problem states degrees.
打开 File > Settings > General，将计算模式设为 Auto 或 Exact，使代数答案保持精确；同时确保角度模式与题目一致——微积分用弧度（Radian），只有题目明确说角度时才用度（Degree）。
In the same menu, set the real or complex format to Real unless complex numbers are being tested, choose Display Digits, and decide between Float and Fix. Float 6 is a sensible default because it keeps enough precision without hiding the structure of numbers.
在同一菜单中，除非正在考查复数，否则将实数／复数格式设为 Real；选择显示位数，并在 Float 与 Fix 之间做出选择。Float 6 是合理的默认值，既能保留足够精度，又不会掩盖数字结构。
You must also clear any stored notes and programs before the exam. IB rules do not allow a GDC that contains stored notes, so delete documents in the My Documents folder rather than simply closing them.
你还必须在考试前清空任何存储的笔记和程序。IB 规则不允许携带存有笔记的 GDC，因此要在 My Documents 文件夹里删除文档，而不是仅仅关闭它们。
4. Core Graphing Skills in the Graphs Application | 图形应用中的核心绘图技能
Type functions into the Graphs application, adjust the window with Menu > Window / Zoom, and use Menu > Analyze Graph to find zeros, minima, maxima and intersections. Each of these is a single command that answers a question you would otherwise solve by hand.
在图形应用中输入函数，用 Menu > Window / Zoom 调整窗口，再用 Menu > Analyze Graph 求零点、极小值、极大值和交点。每一个都只是一条命令，却能回答本来需要手算的问题。
For a quick numerical derivative or definite integral, use Menu > Analyze Graph > dy/dx or Integral directly on the curve, then enter the lower and upper limits. The value appears on the graph and can be pasted into your working.
若要快速求某点的导数值或定积分，直接在曲线上使用 Menu > Analyze Graph > dy/dx 或 Integral，然后输入下限与上限。数值会显示在图上，可以抄录到你的解题过程中。
Always sanity-check a graph before trusting it. If the window is too small, you may miss a root; if it is too large, two distinct roots may merge visually. Support the picture with an algebraic argument such as a sign table or a factorised expression.
信任图形之前一定要做合理性检查。窗口太小可能漏掉根；窗口太大则两个不同的根在视觉上会合并。要用符号表或因式分解等代数论证来支撑图像。
5. Calculus with the GDC: Derivatives and Integrals | 使用GDC做微积分：导数与积分
n a CAS model you can differentiate an expression symbolically and compare it with your handwritten answer.
在计算器应用中，Menu > Calculus 提供 Derivative（d/dx）、Integral（∫）、Limit 和 Sum。在 CAS 型号上，你可以符号化地对表达式求导，并与手写答案对照。
For areas, remember the fundamental relationship between the definite integral and signed area:
求面积时，要记住定积分与代数面积之间的关系：
Area = ∫ₐᵇ f(x) dx
If f(x) changes sign on [a, b], split the interval at the root so that each piece has a constant sign, then add the absolute values. A single integral will cancel positive and negative regions and give the wrong answer.
如果 f(x) 在 [a, b] 上变号，就要在根处分割区间，使每一段符号不变，再把绝对值相加。只算一个积分会把正负区域相互抵消，得到错误答案。
ing about the x-axis. The GDC handles the arithmetic quickly, but the marks are usually for setting up the correct integral.
旋转体体积遵循同样的逻辑：绕 x 轴旋转时 V = π ∫ₐᵇ y² dx。GDC 能快速完成运算，但分数通常给的是正确积分的建立过程。
6. Solving Equations and Systems of Equations | 解方程与方程组
Menu > Algebra > Solve handles equations, inequalities and systems directly on a CAS model, while nsolve gives a numerical solution when no exact form exists. Polynomial Root Finder is faster when the equation is already in polynomial form.
在 CAS 型号上，Menu > Algebra > Solve 可以直接处理方程、不等式和方程组；当不存在精确形式时，用 nsolve 求数值解。若方程本身就是多项式形式，用 Polynomial Root Finder 更快。
erval such as 0 ≤ x ≤ 2π. Add or subtract the period 2πk to generate every valid solution.
三角方程需要格外小心。GDC 通常只返回主值，而题目可能要求在 0 ≤ x ≤ 2π 这样的给定区间内给出全部解。要加上或减去周期 2πk，以生成所有有效解。
For linear systems and matrices, use Menu > Matrix & Vector for determinants, inverses and rref(), or solve the system directly. Writing the augmented matrix in your answer booklet still earns method marks even when the GDC produces the final values.
对于线性方程组与矩阵，可用 Menu > Matrix & Vector 求行列式、逆矩阵和 rref()，或直接求解方程组。即使 GDC 给出最终数值，在答题本上写出增广矩阵仍然能获得方法分。
7. Sequences, Series and Financial Contexts | 数列、级数与金融情境
The seq() function generates a list of terms, for example seq(1/n², n, 1, 20), and the Σ command in Menu > Calculus evaluates partial sums. These are ideal for testing whether a series appears to converge before you prove it.
seq() 函数可以生成一串项，例如 seq(1/n², n, 1, 20)，而 Menu > Calculus 中的 Σ 命令可以计算部分和。在证明之前，它们是检验级数是否看似收敛的理想工具。
e GDC is best used to verify a value or to tabulate terms when the pattern is not obvious.
等差数列与等比数列的考查围绕 uₙ = u₁ + (n − 1)d 与 Sₙ = n/2 (2u₁ + (n − 1)d) 等公式展开。GDC 最适合用来核对数值，或在规律不明显时列出各项。
Compound interest problems link directly to geometric sequences, and the Finance Solver in Menu > Finance can check a value of n, an interest rate or a payment. Even so, write the geometric model explicitly, because that is what the markscheme rewards.
复利问题与等比数列直接相关，Menu > Finance 中的 Finance Solver 可以核对 n、利率或付款额。即便如此，也要明确写出等比模型，因为那才是评分标准所奖励的内容。
8. Statistics and Probability in AA HL | AA HL中的统计与概率
Menu > Statistics > Distributions provides Normal Cdf, Inverse Normal, Binomial Pdf and Binomial Cdf. These turn long probability calculations into a single command, but you should still state the distribution and its parameters, for example X ~ B(n, p).
Menu > Statistics > Distributions 提供 Normal Cdf、Inverse Normal、Binomial Pdf 和 Binomial Cdf。它们能把冗长的概率计算变成一条命令，但你仍应写出分布及其参数，例如 X ~ B(n, p)。
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图