Graphics Calculator Instructions for IB Mathematics | IB数学图形计算器使用指南

📚 Graphics Calculator Instructions for IB Mathematics | IB数学图形计算器使用指南

Graphing calculators are an essential tool for IB Mathematics examinations, especially in Paper 2 where a GDC (Graphic Display Calculator) is required. Mastering the key functions for graphing, solving, statistics, and calculus can save time and boost accuracy. This guide covers the most tested operations on models like the TI‑84 Plus and TI‑Nspire, using step‑by‑step explanations aligned with the IB syllabus.

图形计算器是IB数学考试的重要工具，尤其是在必须使用GDC的试卷二中。掌握图形绘制、方程求解、统计和微积分等关键功能可以节省时间并提高准确性。本指南以TI‑84 Plus和TI‑Nspire等型号为例，按照IB教学大纲逐步说明考试中最常考的操作。

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1. Getting Started: Mode and Settings | 入门：模式与设置

Before any calculation, confirm that your calculator is in the correct mode. Press MODE and check that the angle unit is set to RADIAN for calculus and trigonometric work, unless the question specifically requires degrees. Set the number format to FLOAT to display decimals automatically and keep the calculator in FUNC (function) mode for graphing.

在进行任何计算之前，请确认计算器处于正确的模式。按下MODE键，确保角度单位设置为RADIAN（弧度）以用于微积分与三角运算，除非题目明确要求使用度数。数字格式设为FLOAT以便自动显示小数，并保持FUNC（函数）模式来绘图。

It is also wise to clear any previous entries. Press Y= and use CLEAR to delete old functions. For the home screen, press CLEAR several times or use 2nd + QUIT to return cleanly. For TI‑Nspire users, navigate to a new document or clear the current page to avoid overlapping plots.

最好清除之前的输入。按Y=并用CLEAR删除旧函数。在主屏幕上，多按几次CLEAR或使用2nd + QUIT彻底回到干净状态。TI‑Nspire用户可新建文档或清空当前页面，避免图形重叠。

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2. Graphing Functions | 绘制函数图像

To graph a function, press the Y= key and enter the expression next to (Y₁). Use the button X,T,θ,n for the independent variable. For example, to graph (f(x)=2x²-5x+3), type 2 X,T,θ,n ^ 2 – 5 X,T,θ,n + 3. Press GRAPH to see the plot.

要绘制函数图像，按Y=键，在(Y₁)后面输入表达式。用X,T,θ,n键输入自变量。例如，要绘制(f(x)=2x²-5x+3)，键入2 X,T,θ,n ^ 2 – 5 X,T,θ,n + 3，然后按GRAPH查看图像。

If the graph is not visible, the window settings likely need adjustment. You can use ZOOM 6:ZStandard for a standard –10 to 10 range on both axes. Remember that rational functions may show false vertical asymptotes as near‑vertical lines; these are just the calculator joining disconnected points.

如果图像不可见，很可能需要调整窗口设置。可以用ZOOM 6:ZStandard将两轴范围均设为–10到10。注意，有理函数的图像可能会把渐近线显示为近乎垂直的连线，这只是计算器连接了不连续的点，并非真正的渐近线。

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3. Adjusting the Viewing Window | 调整观察窗口

A well‑chosen window reveals all important features. Press WINDOW and set Xmin, Xmax, Ymin, Ymax manually. The Xscl and Yscl values control the tick marks. After examining the general shape, use ZOOM 2:Zoom In or ZOOM 3:Zoom Out to refine the view. For trigonometric functions, try ZOOM 7:ZTrig, which sets the x‑axis in multiples of π/2.

选择合适的窗口可以展示所有重要特征。按WINDOW手动设置Xmin、Xmax、Ymin和Ymax。Xscl和Yscl控制刻度间距。观察大致形状后，使用ZOOM 2:Zoom In或ZOOM 3:Zoom Out精细调整。对于三角函数，可以尝试ZOOM 7:ZTrig，它将x轴设为π/2的倍数。

When an IB question asks you to “sketch on the axes provided”, use the window values to label intercepts and turning points accurately. Always write down the window used in your working if the calculator display is part of the reasoning.

当IB考题要求“在所提供的坐标轴上画草图”时，利用窗口数值准确标出截距和转向点。如果计算器图像是推理的一部分，记得在工作过程中记下所用的窗口设置。

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4. Finding Roots, Intersections, and Extremes | 求零点、交点与极值

The CALC menu (press 2nd + TRACE) is your primary route to analyze a graph. Select 2:zero to find a root. The calculator asks for a left bound, right bound, and a guess. Move the cursor to the left of the desired root, press ENTER, then move to the right and press ENTER again, and finally place the cursor near the root and press ENTER. The x‑intercept appears on screen.

CALC菜单（按2nd + TRACE）是分析图像的主要途径。选择2:zero求零点。计算器会要求提供左边界、右边界和猜测值。将光标移到零点左侧按ENTER，再移到右侧按ENTER，然后把光标放在零点附近按ENTER，屏幕上便会显示x轴截距。

Use 5:intersect to find the intersection of two curves. Choose the first curve, second curve, then move the cursor close to the intersection and press ENTER. For maximum or minimum points, select 3:minimum or 4:maximum and follow the same bound‑and‑guess procedure. These tools are often needed in paper 2 for optimization and area between curves.

使用5:intersect求两条曲线的交点。依次选择第一条曲线、第二条曲线，然后将光标移动到交点附近并按ENTER。求最大值或最小值时，选择3:minimum或4:maximum，并遵循相同的边界与猜测操作。试卷二中常需这些工具来解决优化问题和曲线间面积问题。

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5. Using Tables of Values | 使用数值表格

Tables are useful for plotting points accurately and detecting asymptotic behavior. After entering a function in Y=, press 2nd + GRAPH to display the table. The default x‑values start at 0 and increase by 1. You can customise the starting value and step by pressing 2nd + WINDOW (TBLSET) and entering TblStart and ΔTbl.

数值表格有助于精确描点和发现渐近特性。在Y=中输入函数后，按2nd + GRAPH显示表格。默认x值从0开始，步长为1。您可以通过按2nd + WINDOW（TBLSET）并输入TblStart和ΔTbl来自定义起始值和步长。

If you need to see specific x‑values, set TblStart to a required number and ΔTbl to a small step like 0.1 or 0.01. Use the arrow keys to scroll through the table. This is particularly handy for limit investigations and for checking sign changes around a suspected root.

如果需要查看特定的x值，将TblStart设为所需数值，并将ΔTbl设为较小的步长，如0.1或0.01。使用方向键滚动表格。这对研究极限和检查可疑零点附近的符号变化特别方便。

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6. Solving Equations Numerically | 数值解方程

To solve a single equation, such as (2e^{0.3x}=10), graph both sides as Y₁ and Y₂ and use the intersect command. Alternatively, bring all terms to one side, graph the resulting expression, and find its zero. Both methods are acceptable in the IB exam, though the zero method is often faster for equations that are easy to rearrange.

要解单个方程，例如(2e^{0.3x}=10)，可将两边分别设为Y₁和Y₂，再使用交点命令。另一种方法是将所有项移到一边，绘制合并后的表达式，并求其零点。两种方法在IB考试中都接受，但零点法通常对容易重排的方程更快捷。

TI‑84 Plus also has a dedicated equation solver in the MATH menu: choose B:Solver… (or 0:Solver on newer OS). Enter the equation as (0=) expression and set a guess. Press ALPHA + ENTER to solve. For systems of linear equations, use matrices (see section 10) or the Apps – PlySmlt2 polynomial root finder.

TI‑84 Plus在MATH菜单中还有专用方程求解器：选择B:Solver…（或新版系统的0:Solver）。将方程输入为 (0=) 表达式并设置猜测值，按ALPHA + ENTER求解。对于线性方程组，可使用矩阵（见第10节）或Apps中的PlySmlt2多项式求根工具。

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7. Numerical Differentiation and Integration | 数值微分与积分

The GDC can evaluate derivatives at a point without symbolic differentiation. In the MATH menu, choose 8:nDeriv(. The syntax is nDeriv(expression, variable, value). For example, to find (f'(2)) where (f(x)=x³-4x), enter nDeriv(X³-4X, X, 2). The calculator uses a symmetric difference quotient and gives a high‑precision result.

GDC可以在不进行符号求导的情况下计算某点处的导数值。在MATH菜单中选择8:nDeriv(。语法为nDeriv(表达式, 变量, 值)。例如，求(f(x)=x³-4x)在(x=2)处的导数，输入nDeriv(X³-4X, X, 2)。计算器采用对称差商，给出高精度结果。

For definite integrals, use 9:fnInt( from the same menu. The syntax is fnInt(expression, variable, lower, upper). To compute (int_1^3 (2x+1),dx), type fnInt(2X+1, X, 1, 3). Alternatively, from the graph screen, press CALC 7:∫f(x)dx and visually select the lower and upper limits. Both give the signed area under the curve.

对于定积分，使用同一菜单中的9:fnInt(。语法为fnInt(表达式, 变量, 下界, 上界)。要计算(int_1^3 (2x+1),dx)，键入fnInt(2X+1, X, 1, 3)。也可以从图形界面按CALC 7:∫f(x)dx，可视地选择下限和上限。两种方法都给出曲线下的带符号面积。

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8. Statistics and Regression | 统计与回归分析

Statistical analysis begins with entering data. Press STAT then 1:Edit to open the list editor. Enter x‑values in L₁ and corresponding y‑values in L₂ (and frequencies in L₃ if needed). After data entry, press STAT → CALC → 1:1‑Var Stats to get mean, standard deviation, and other one‑variable summaries. For two‑variable statistics, choose 2:2‑Var Stats.

统计分析从输入数据开始。按STAT再按1:Edit打开列表编辑器。在L₁中输入x值，L₂中输入对应的y值（如有需要，在L₃中输入频数）。数据输入后，按STAT → CALC → 1:1‑Var Stats获得均值、标准差等单变量统计量。对于双变量统计，选择2:2‑Var Stats。

Regression models are a core IB AI requirement. From STAT → CALC, select an appropriate model: 4:LinReg(ax+b) for linear, 5:QuadReg for quadratic, 9:LnReg for logarithmic, 0:ExpReg for exponential, or B:Logistic for logistic growth. After running the regression, the equation coefficients are stored and can be pasted into Y= for graphing. Always check the correlation coefficient r or R² to judge model fit.

回归模型是IB AI部分的核心要求。通过STAT → CALC选择合适的模型：4:LinReg(ax+b)线性回归、5:QuadReg二次回归、9:LnReg对数回归、0:ExpReg指数回归或B:Logistic逻辑增长模型。回归运行后，方程系数被存储并可粘贴到Y=中绘图。务必检查相关系数r或R²以判断模型拟合度。

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9. Probability Distributions | 概率分布

Binomial and normal probabilities are tested frequently. For binomial distributions, press 2nd + VARS (DISTR). Use A:binompdf( for exact probability P(X=k) and B:binomcdf( for cumulative probability P(X ≤ k). The syntax is binompdf(n, p, k) or binomcdf(n, p, k). For example, binomcdf(10, 0.3, 4) gives P(X ≤ 4) for n=10, p=0.3.

二项分布和正态分布是常考内容。对于二项分布，按2nd + VARS（DISTR）。A:binompdf(求单点概率P(X=k)，B:binomcdf(求累积概率P(X ≤ k)。语法为binompdf(n, p, k)或binomcdf(n, p, k)。例如，binomcdf(10, 0.3, 4) 给出n=10, p=0.3时P(X ≤ 4)。

For the normal distribution, 2:normalcdf( gives the area between two values: normalcdf(lower, upper, μ, σ). Enter a very small number like –1E99 for the left tail. The inverse normal, 3:invNorm(, finds the z‑score or x‑value corresponding to a left‑tail area: invNorm(area, μ, σ). Always sketch a diagram first to ensure you are using the correct tail area.

对于正态分布，2:normalcdf(计算两个值之间的面积：normalcdf(下限, 上限, μ, σ)。左尾可用极小数如–1E99。逆正态函数3:invNorm(根据左尾面积求对应的z值或x值：invNorm(面积, μ, σ)。始终先画简图，确保使用正确的尾部面积。

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10. Financial Mathematics (TVM Solver) | 金融数学（TVM求解器）

IB AI and Applications syllabi include compound interest, loans, and annuities. The TVM (Time Value of Money) Solver is accessed by pressing APPS → 1:Finance… → 1:TVM Solver…. It requires seven input fields: N (total number of payments), I% (annual interest rate), PV (present value), PMT (payment amount), FV (future value), P/Y (payments per year), and C/Y (compounding periods per year). Leave one variable unknown; move the cursor to it and press ALPHA + ENTER to solve.

IB AI及应用课程涵盖复利、贷款和年金。TVM（资金时间价值）求解器通过APPS → 1:Finance… → 1:TVM Solver…进入。需填写七个字段：N（总付款次数）、I%（年利率）、PV（现值）、PMT（每期付款额）、FV（终值）、P/Y（每年付款次数）和C/Y（每年复利次数）。将未知变量留空，光标移至其上并按ALPHA + ENTER求解。

Key conventions: PV is negative if you pay money out (e.g. a deposit), PMT is negative for regular payments made, and FV is positive for money received. Always set P/Y and C/Y to match the problem (often 12 for monthly, 4 for quarterly). A common error is forgetting to set PMT to 0 for lump‑sum problems.

关键符号惯例：如果支付资金（如存款），PV为负；定期付款的PMT为负；收到的资金FV为正。始终将P/Y和C/Y设为与题目一致（通常月付为12，季度为4）。常见错误是处理一次性整笔问题时忘记将PMT设为0。

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11. Matrix Operations and Solving Linear Systems | 矩阵运算与解线性方程组

For IB AA HL and AI HL, matrix algebra is required. Access the matrix editor via 2nd + MATRIX (or x⁻¹). Select EDIT and choose a matrix, e.g. [A]. Define its dimensions and enter the entries. Basic operations like addition, multiplication, determinant (1:det(), and inverse (x⁻¹ key after matrix name) are done from the home screen.

IB AA HL和AI HL要求掌握矩阵代数。通过2nd + MATRIX（或x⁻¹键）进入矩阵编辑器。选择EDIT并指定矩阵，例如[A]，定义维度后输入元素。加法、乘法、行列式（1:det(）和逆矩阵（在矩阵名后按x⁻¹键）等基本运算可在主屏幕执行。

To solve a system like ( begin{cases} 2x + y = 5 \ x – 3y = -1 end{cases} ), store the coefficient matrix as [A] and the constants as a column matrix [B]. Then from the home screen, compute [A]⁻¹ * [B]. Alternatively, use the rref( command under MATRIX → MATH to row‑reduce the augmented matrix [A|B] directly, which is often clearer for larger systems.

要解方程组如 ( begin{cases} 2x + y = 5 \ x – 3y = -1 end{cases} )，将系数矩阵存为[A]，常数存为列矩阵[B]。然后在主屏幕计算[A]⁻¹ * [B]。也可使用MATRIX → MATH下的rref(命令直接对增广矩阵[A|B]进行行化简，这对于较大方程组通常更清晰。

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12. Exam Mode and Common Pitfalls | 考试模式与常见陷阱

Before the IB exam, clear your calculator’s memory as required by the regulations. On TI‑84 Plus, press 2nd + MEM → 7:Reset… → 1:All RAM…. On TI‑Nspire, enter the Press‑to‑Test mode or clear the scratchpad. This ensures no stored programs or documents give unfair advantage. Remember that IB exams do not permit CAS functionality unless the calculator is approved for it (usually only TI‑Nspire CX II CAS is allowed in certain papers).

IB考前，按规定清空计算器内存。TI‑84 Plus上按2nd + MEM → 7:Reset… → 1:All RAM…。TI‑Nspire需进入Press‑to‑Test模式或清空便签本，确保没有存储的程序或文档带来不当优势。请记住，IB考试通常不允许使用CAS功能，除非该计算器得到批准（通常只有TI‑Nspire CX II CAS在某些试卷中允许）。

Watch out for common syntax errors: missing closing parentheses, using minus instead of the negative sign (–) for subtraction, and forgetting to set the angle mode can ruin a question. Always store intermediate results in variables like A or X to avoid re‑typing. During graphs, check that the calculator isn’t plotting something left over from a previous Y=. Finally, never round intermediate values excessively; use the full precision from the GDC and only round the final answer as instructed.

注意常见语法错误：缺少右括号、在减法中误用减号而非负号(–)、忘记设置角度模式，都可能毁掉一道题。始终将中间结果存入A或X等变量，避免重复输入。绘图时检查计算器是否仍显示之前Y=中残留的函数。最后，切勿过度四舍五入中间值；使用计算器提供的全精度，仅按题目要求对最终答案进行舍入。

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