📚 IB Math: Casio fx-CG20 Question Type Analysis | IB 数学：卡西欧 fx-CG20 题型解析
The Casio fx-CG20 graphing calculator is a powerful tool permitted in IB Mathematics exams. Mastering its functions for equation solving, graphing, calculus, statistics, and matrices can save valuable time and reduce errors. This article analyses key question types and shows you exactly how to use the CG20 to answer them efficiently.
卡西欧 fx-CG20 图形计算器是 IB 数学考试允许使用的强大工具。掌握它在方程求解、图形绘制、微积分、统计和矩阵等方面的功能，可以节省宝贵时间并减少失误。本文分析关键题型，并展示如何利用 CG20 高效作答。
1. Getting Started: Menus and Basic Operations | 入门：菜单与基本操作
Press the MENU button to access the main menu. Icons represent different modes: RUN-MAT for general calculations, STAT for statistics, GRAPH for graphing, EQUA for equations, RECUR for sequences, and CONICS for conic sections.
按 MENU 键进入主菜单。图标代表不同模式：RUN-MAT 用于通用计算，STAT 用于统计，GRAPH 用于绘图，EQUA 用于方程，RECUR 用于数列，CONICS 用于圆锥曲线。
Always check the SET UP (SHIFT + MENU) to confirm angle units (degrees/radians), number format, and derivative/integral settings. For IB, radian mode is essential in calculus and trig questions unless stated otherwise.
务必检查 SET UP（SHIFT + MENU）以确认角度单位（度/弧度）、数字格式以及导数/积分设置。对于 IB，除非另有说明，微积分和三角问题中必须使用弧度制。
2. Solving Polynomial Equations | 求解多项式方程
To solve a polynomial equation like 2x³ − 5x² + 3x − 7 = 0, go to EQUA mode, select F2 (Polynomial), then F1 for degree 3. Enter coefficients 2, -5, 3, -7 and press SOLVE (F1). All roots (real and complex) are displayed.
要求解多项式方程如 2x³ − 5x² + 3x − 7 = 0，进入 EQUA 模式，选择 F2（多项式），然后按 F1 选择三次。输入系数 2, -5, 3, -7 并按 SOLVE (F1)，所有根（实数和复数）都会显示。
For a quadratic ax² + bx + c = 0, the CG20 shows the discriminant Δ = b² − 4ac and the vertex coordinates. This is extremely helpful when sketching quadratics in Paper 2.
对于二次方程 ax² + bx + c = 0，CG20 会显示判别式 Δ = b² − 4ac 和顶点坐标。这在 Paper 2 绘制二次函数草图时非常有帮助。
Example: Solve x² − 4x + 1 = 0. You obtain x = 2 + √3 and x = 2 − √3, exactly, not just decimals.
例如：求解 x² − 4x + 1 = 0，会得到精确解 x = 2 + √3 和 x = 2 − √3，而不仅仅是小数。
3. Solving Simultaneous Equations | 求解联立方程组
In EQUA mode, press F1 (Simultaneous). Choose the number of unknowns. For 2 equations in x and y, enter coefficients carefully. The CG20 solves linear systems instantly and also handles up to 6 unknowns.
在 EQUA 模式中，按 F1（联立方程）。选择未知数个数。对于 x 和 y 的二元方程组，仔细输入系数。CG20 立即求解线性方程组，并且最多能处理六个未知数。
Non‑linear systems require the Graph mode. Graph both equations and use G‑Solv (F5) → ISCT to find intersection points. This is common in IB questions involving a line and a curve.
非线性方程组需要使用图形模式。绘制两个方程，然后使用 G‑Solv (F5) → ISCT 求交点。这在涉及直线与曲线的 IB 题目中很常见。
4. Graphing and Analysing Functions | 函数图形与分析
From the main menu, enter GRAPH. Type the function, e.g. Y1 = eˣ − 3x, then press DRAW. To find roots, maximums, minimums, and y‑intercepts, use G‑Solv: ROOT, MAX, MIN, Y‑ICEPT.
在主菜单中，进入 GRAPH。输入函数，例如 Y1 = eˣ − 3x，然后按 DRAW。要寻找零点、最大值、最小值和 y 截距，使用 G‑Solv：ROOT、MAX、MIN、Y‑ICEPT。
For an IB Paper 2 question asking “find the coordinates of the local minimum”, after graphing press F5 (G‑Solv) then F3 (MIN). The cursor jumps to the minimum and displays the coordinates.
对于 IB 试卷二要求“求局部最小值坐标”的问题，绘图后按 F5 (G‑Solv) 再按 F3 (MIN)，光标会跳至最小值并显示坐标。
Use the V‑Window (SHIFT + F3) to set appropriate x‑range and y‑range; otherwise important features may be off‑screen.
使用 V‑Window (SHIFT + F3) 设置合适的 x 范围和 y 范围；否则重要特征可能显示在屏幕之外。
5. Evaluating Derivatives and Definite Integrals | 计算导数与定积分
In RUN‑MAT mode, the derivative is computed via OPTN → CALC → d/dx( ). The syntax is d/dx( expression, value ). For example, to find f ′(2) for f(x) = ln(x) + x², enter d/dx( ln X + X², 2 ).
在 RUN‑MAT 模式中，通过 OPTN → CALC → d/dx( ) 计算导数。语法是 d/dx(表达式, 值)。例如，求 f(x) = ln(x) + x² 在 x=2 的导数，输入 d/dx( ln X + X², 2 )。
Definite integrals use the ∫dx command. To evaluate ∫₀¹ 3x² dx, type ∫( 3X², 0, 1 ) and press EXE. The result is 1. Always check that the integrand uses X as the variable.
定积分使用 ∫dx 命令。计算 ∫₀¹ 3x² dx，输入 ∫( 3X², 0, 1 ) 并按 EXE，结果为 1。务必确保被积函数使用 X 作为变量。
On the GRAPH screen, you can also find the numeric derivative at a point and the area under a curve via G‑Solv → F4 (d/dx) and F7 (∫dx). This visual approach is excellent for checking answers.
在图形界面上，也可以经由 G‑Solv → F4 (d/dx) 和 F7 (∫dx) 求某点的数值导数和曲线下方面积。这种可视化方法非常适合检查答案。
6. One‑Variable Statistical Analysis | 单变量统计分析
Enter STAT mode and input data in List 1. Press CALC (F2) and F1 (1VAR). The calculator displays mean (x̄), sum (Σx), sum of squares (Σx²), standard deviation (σx and sx), median, Q1, Q3, and more.
进入 STAT 模式，在 List 1 中输入数据。按 CALC (F2) 再按 F1 (1VAR)。计算器会显示平均值 (x̄)、总和 (Σx)、平方和 (Σx²)、标准差 (σx 和 sx)、中位数、Q1、Q3 等等。
IB questions often ask for the unbiased estimate of the population standard deviation. The CG20 provides σx (population) and sx (sample). Use sx unless the question specifies population data.
IB 题目经常要求总体标准差的无偏估计。CG20 提供 σx（总体）和 sx（样本）。除非题目指定是总体数据，否则使用 sx。
Box‑plots and histograms can be drawn by pressing GRPH (F1) and selecting the appropriate graph type. Use SET to assign List 1 to the appropriate graph.
箱线图和直方图可以通过按 GRPH (F1) 并选择适当的图形类型来绘制。使用 SET 将 List 1 分配给对应图形。
7. Bivariate Statistics and Regression | 双变量统计与回归
For two‑variable data, store x‑values in List 1 and y‑values in List 2. Press CALC (F2), then REG (F3). Choose the model: linear (X, a+bX), quadratic (X²), exponential (a·e^(bX)), and others.
对于双变量数据，将 x 值储存在 List 1，y 值储存在 List 2。按 CALC (F2)，再按 REG (F3)。选择模型：线性 (X, a+bX)、二次 (X²)、指数 (a·e^(bX)) 等。
The CG20 outputs the regression equation, correlation coefficient r, and coefficient of determination r². It also allows you to copy the equation to the GRAPH mode to plot the regression line together with the scatter plot.
CG20 输出回归方程、相关系数 r 和决定系数 r²。它还允许你将方程复制到 GRAPH 模式，以便将回归线与散点图一起绘制。
Common IB tasks: “Find the equation of the regression line of y on x” → use linear regression, copy formula to Y1, and then predict values. Remember to interpret the gradient and y‑intercept in context.
常见 IB 任务：“求 y 对 x 的回归线方程” → 使用线性回归，将公式复制到 Y1，然后预测数值。记得结合上下文解释斜率和 y 截距。
8. Probability Distributions | 概率分布
In STAT mode, press DIST (F5). Normal, Binomial, and Poisson distributions are available. For a normal probability like P(Z < 1.5), select NORM, then Ncd. Set Lower: -∞ (use -10⁹⁹), Upper: 1.5, σ=1, μ=0.
在 STAT 模式中，按 DIST (F5)。可选用正态、二项和泊松分布。计算正态概率如 P(Z < 1.5)，选择 NORM，然后 Ncd。设 Lower: -∞（用 -10⁹⁹），Upper: 1.5，σ=1，μ=0。
Inverse normal calculations are done with InvN. For a binomial distribution B(n, p), use BINOMIAL, and choose Bpd for P(X = k) or Bcd for P(X ≤ k). These functions will directly give the probability, saving you from using complex formulas.
逆正态计算使用 InvN。对于二项分布 B(n, p)，选择 BINOMIAL，Bpd 求 P(X = k)，Bcd 求 P(X ≤ k)。这些函数直接给出概率，免去使用复杂公式。
Be aware that the IB may ask for probability statements to be written explicitly. The calculator finds the values, but you must show an understanding of the notation and method.
注意 IB 可能要求明确写出概率表达式。计算器可以求出数值，但你仍需展示对符号和方法的理解。
9. Working with Matrices | 矩阵运算
Go to RUN‑MAT mode and press F3 (MAT). Define matrices A and B under the appropriate dimensions. You can add, subtract, multiply, find determinant (det), inverse (A⁻¹), transpose, and solve linear systems via matrix inversion.
进入 RUN‑MAT 模式并按 F3 (MAT)。在适当维度下定义矩阵 A 和 B。你可以执行加、减、乘法，求行列式 (det)、逆矩阵 (A⁻¹)、转置，以及通过矩阵求逆解线性方程组。
To compute A⁻¹, simply type Mat A ^ (-1). To solve AX = B, where X is the variable column vector, compute Mat A⁻¹ * Mat B. The CG20 handles complex and decimal entries perfectly.
计算 A⁻¹ 只需输入 Mat A ^ (-1)。要求解 AX = B（X 为变数列向量），计算 Mat A⁻¹ * Mat B。CG20 对复数和小数项都能完美处理。
Eigenvalues and eigenvectors can also be obtained through the EIGEN function, which appears in the advanced options. This is relevant for Further Mathematics HL but less common in standard IB Math.
特征值和特征向量也可通过 EIGEN 函数获得，这出现在高级选项中。这与进阶数学 HL 相关，但在普通 IB 数学中较少见。
10. Sequences, Series and Financial Calculations | 数列、级数与金融计算
The RECUR mode handles arithmetic and geometric sequences. Define the recursion formula, for example aₙ₊₁ = aₙ + d or aₙ₊₁ = r × aₙ, and then generate a table of terms. You can also find the sum of the first n terms using the Sum function.
RECUR 模式处理等差和等比数列。定义递推公式，例如 aₙ₊₁ = aₙ + d 或 aₙ₊₁ = r × aₙ，然后生成项的表格。你也可用 Sum 函数求前 n 项和。
Financial mathematics problems (compound interest, loans, annuities) are best tackled using the FINANCE icon. Enter N, I%, PV, PMT, FV, and P/Y, then press the specific key to solve for the unknown. This is a syllabus requirement for AI HL, and it dramatically speeds up calculations.
金融数学问题（复利、贷款、年金）最好使用 FINANCE 图标解决。输入 N, I%, PV, PMT, FV 和 P/Y，然后按特定键求解未知数。这是 AI HL 的课程要求，能大幅加快计算速度。
11. Exam‑Taking Strategies with CG20 | CG20 考试应试策略
Always clear the screen and memory before a new question to avoid conflicting definitions. Use the RESET function only if instructed, but for routine purposes, simply clear the graph and list.
开始新题目之前，务必清除屏幕和内存以避免定义冲突。仅当指示时才使用 RESET 功能，日常只需清除图形和列表即可。
When a graphical solution is required, sketch what you see on the screen, label axes, and clearly state the coordinates of key points. The examiner expects a hand‑drawn sketch, not a screenshot.
当要求图形解法时，绘制屏幕所见草图，标注坐标轴，并清晰指出关键点的坐标。考官期望手绘草图，而非截图。
Use the CG20 to verify algebraic working: after solving an integral by hand, check with the ∫dx function; after completing the square, graph the expression. But never rely on the calculator as your sole method when the question demands an analytical approach.
用 CG20 验证代数运算：手算积分后，用 ∫dx 函数检查；配平方后，绘制表达式图像。但切勿在题目要求解析方法时完全依赖计算器。
Finally, manage your battery and keep a spare set. A dead calculator in Paper 2 can be disastrous. Also, turn off ‘Dual Screen’ mode to save power.
最后，管理好电池并准备备用电池。Paper 2 中计算器没电可能是灾难性的。同时，关闭双屏模式以节省电量。
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