📚 IB Math: High-Scoring Techniques with Casio fx-CG20 | IB 数学：Casio fx-CG20 高分技巧
Mastering your graphing calculator is one of the smartest ways to boost your IB Mathematics score. The Casio fx-CG20, allowed in all IB exam papers that permit calculator use, is a powerful tool that can save time, reduce careless errors, and help you visualize complex concepts. This guide reveals targeted techniques that go beyond basic button-pressing, helping you unlock the full potential of the fx-CG20 for both Analysis & Approaches and Applications & Interpretation.
掌握图形计算器是提高 IB 数学成绩最明智的方法之一。所有允许使用计算器的 IB 试卷均允许携带 Casio fx-CG20，这款功能强大的工具能帮你节省时间、减少粗心错误，并将复杂概念可视化。本指南将揭示超越基本按键操作的高分技巧，助你充分挖掘 fx-CG20 在分析与方法和应用与解释两门课程中的全部潜力。
1. Getting to Know the fx-CG20 | 了解 fx-CG20
The fx-CG20 features a high-resolution colour screen, a user-friendly icon-based menu, and a wide range of applications including Graph, Run-Matrix, Statistics, Spreadsheet, and Equation. Before diving into advanced techniques, familiarize yourself with the quick-access keys: MENU, SHIFT, ALPHA, and the cursor pad. Pressing MENU brings up the main application icons – you can jump directly to any app by pressing its two-digit code shown beside the icon.
fx-CG20 拥有高分辨率彩色显示屏、直观的图标菜单，以及图形、运行–矩阵、统计、电子表格和方程等多种应用程序。在深入学习高级技巧之前，请先熟悉快捷功能键：MENU、SHIFT、ALPHA 以及方向键。按 MENU 即可调出主程序图标 – 你可以直接按下图标旁显示的两位代码跳转到任意应用程序。
2. Essential Setup for IB Exams | IB 考试基本设置
Score loss often happens because of incorrect calculator settings. Before any exam, go to the SET UP menu (SHIFT then MENU) and verify: Angle is set to Radian unless a question explicitly uses degrees; Display is Normal 1 or Normal 2 to avoid scientific notation confusion; Complex Mode is Real unless you need complex numbers; and Derivative/Integral applies the correct default values. For IB, it’s wise to set Input/Output to Math mode, which displays fractions, radicals, and integrals in textbook format.
由于计算器设置错误而失分的情况屡见不鲜。每次考试前，请进入设置菜单（SHIFT 再按 MENU），确认：除题目明确要求角度制外，Angle 设为 Radian（弧度）；Display 设为 Normal 1 或 Normal 2 以避免科学计数法混淆；除非处理复数，否则 Complex Mode 设为 Real；导数/积分的默认设置正确。对于 IB，宜将 Input/Output 设为 Math 模式，以便以课本格式显示分数、根号和积分。
3. Graphing Functions Efficiently | 高效绘制函数图形
The Graph app is where you can unpack functions and their intersections in seconds. Enter up to 20 functions as Y1, Y2, etc. Use V-Window (View Window) to set x‑min, x‑max, y‑min, y‑max. For trigonometric graphs, set the x‑axis in terms of π using the radian setting: for example, x‑min = −2π, x‑max = 2π gives a clean view. To find roots or intersections, use G‑Solv (Graph Solve) – press G‑Solv then ROOT for x‑intercepts, or ISCT for intersection points. The calculator marks the point and displays coordinates, cutting minutes off manual solving.
Graph 应用程序能让你在几秒钟内展开函数图像并寻找交点。你最多可输入 20 个函数，如 Y1、Y2 等。使用 V-Window（视图窗口）设置 x‑min、x‑max、y‑min、y‑max。绘制三角函数图像时，可利用弧度设置让 x 轴以 π 表示：例如设定 x‑min = −2π, x‑max = 2π 可获得清晰视图。要寻找零点或交点，使用 G‑Solv（图形求解）—— 按 G‑Solv 后选 ROOT 获取 x 轴截距，或选 ISCT 获取交点。计算器会标出该点并显示坐标，比你手动求解节省好几分钟。
4. Solving Equations with the Solver | 使用求解器解方程
For equations that are tricky to rearrange, the Equation app is your best friend. Choose Simultaneous for linear systems, Polynomial for quadratic/cubic/quartic equations, or Solver for any equation involving sin, ln, eˣ, etc. In Solver mode, type the equation exactly as written, then enter an initial guess for the variable. The fx-CG20 uses Newton’s method and will quickly converge to the nearest root. Always check by trying a second initial guess to see if there are multiple solutions in the given domain, which is vital for trig equations where the solver returns only the closest root to your guess.
对于难以移项整理的方程，Equation 应用程序是你最好的帮手。选择 Simultaneous 求解线性方程组，选择 Polynomial 求解二次/三次/四次方程，或选择 Solver 求解包含 sin、ln、eˣ 等的任意方程。在 Solver 模式下，原样输入方程，然后为变量输入一个初始猜测值。fx-CG20 采用牛顿法，会迅速收敛到最接近的根。务必再尝试另一个初始猜测值，检查给定区间内是否存在多个解，这一点对三角方程尤其重要，因为求解器只返回最接近你猜测值的根。
5. Calculus Tools: Derivatives and Integrals | 微积分工具：导数与积分
You can evaluate derivatives and definite integrals numerically without using the Graph screen. In Run-Matrix mode, press OPTN, then CALC to access d/dx( and ∫dx( . For a derivative at a point, use syntax d/dx( expression , x , point ). For example, d/dx(x²+sin x, x, 0) returns 1. For a definite integral, type ∫( expression , x , lower , upper ). The answer comes in decimal form unless the result is an exact rational. This is ideal for checking your analytic work or solving questions where the emphasis is on interpreting the result, not on symbolic manipulation.
你可以不必打开 Graph 屏幕，直接数值计算导数和定积分。在 Run-Matrix 模式下，按 OPTN 然后选 CALC，即可找到 d/dx( 和 ∫dx( 。求某点导数值的语法为 d/dx(表达式, x, 点)。例如 d/dx(x²+sin x, x, 0) 返回 1。求定积分时，输入 ∫(表达式, x, 下限, 上限)。除非结果为精确有理数，否则答案将以小数形式显示。这种方法非常适合检查你的解析计算，或者解决那些重在解读结果而非符号运算的题目。
6. Statistics Made Simple | 简化统计分析
For one‑variable statistics or bivariate data, use the Statistics app. Enter data in List 1 and List 2. Once entered, press CALC, then 1VAR for mean, standard deviation, median, quartiles, and more. IB often asks for the unbiased estimate of population standard deviation (sₓ), so note that the calculator shows both σₓ and sₓ – the one marked with italic sₙ₋₁ is the sample standard deviation you need. For linear regression, choose REG and select the model; the a, b, and r values appear instantly, along with residuals if needed.
处理单变量统计或双变量数据时，使用 Statistics 应用程序。将数据输入 List 1 和 List 2。输入完毕后，按 CALC，再选 1VAR 即可得到平均值、标准差、中位数、四分位数等。IB 常要求总体标准差的无偏估计量 (sₓ)，因此请注意计算器会同时显示 σₓ 和 sₓ – 标为斜体 sₙ₋₁ 的即为所需的样本标准差。进行线性回归时，选择 REG 并指定模型；a、b 和 r 值会立即显示，如有需要还会输出残差。
7. Probability Distributions at Your Fingertips | 随手可用的概率分布
The fx-CG20 handles normal, binomial, Poisson, t, χ², and F distributions directly. In Run-Matrix mode, press OPTN, then STAT, then DIST to access calculators for P( ), inverse, and random number generation. For a binomial probability P(X = k) with n = 10, p = 0.3, k = 4, select BINOMIAL, then Bpd, fill in x, Numtrial:10, p:0.3. For P(X ≤ k), use Bcd. The same logic applies to normal CDF. The inverse normal function is essential for finding z‑values or calculating confidence intervals – enter the tail area, σ, μ, and the calculator returns the boundary.
fx-CG20 可直接处理正态、二项、泊松、t、χ² 和 F 分布。在 Run-Matrix 模式下，按 OPTN，再按 STAT，然后按 DIST 即可访问概率计算、逆运算和随机数生成。若要求 n = 10, p = 0.3, k = 4 的二项分布概率 P(X = k)，选择 BINOMIAL，然后选 Bpd，填入 x、Numtrial:10、p:0.3。要求 P(X ≤ k) 则使用 Bcd。同样的逻辑适用于正态 CDF。逆正态函数对于确定 z 值或计算置信区间至关重要——输入尾部面积、σ、μ，计算器就会返回界值。
8. Matrix and Vector Operations | 矩阵与向量运算
For solving systems of equations, transformations, or vector cross products, use the Run-Matrix app. Press OPTN, then MAT to define matrices (Mat A, Mat B, etc.) and input their dimensions. Once stored, operations like Mat A × Mat B, Mat A⁻¹, and determinant (Det Mat A) are straightforward. For vectors, input them as single‑row or single‑column matrices. The cross product is not built in, but you can compute it by storing vectors as 1×3 matrices and then forming the determinant of a 3×3 matrix with unit vectors i, j, k, or by using the pre‑programmed program that some teachers distribute.
求解方程组、变换或向量叉积时，可使用 Run-Matrix 应用程序。按 OPTN 再按 MAT 可定义矩阵（Mat A、Mat B 等）并输入其维度。存储后，像 Mat A × Mat B、Mat A⁻¹ 以及行列式 (Det Mat A) 等运算便十分简单。处理向量时，将其输入为单行或单列矩阵。叉积并非内置功能，但你可通过将向量存为 1×3 矩阵，再与单位向量 i, j, k 组成 3×3 矩阵的行列式来计算，或使用部分教师分发的预编程序。
9. Financial Math and Sequences | 金融数学与数列
The Financial app (TVM) simplifies compound interest, annuities, and loan repayments. Enter N, I%, PV, PMT, FV, and P/Y, C/Y as needed. The calculator uses the sign convention: money paid out is negative, money received is positive, so check signs carefully. The Sequence app or the Recursion mode inside Run-Matrix can verify arithmetic and geometric sequence sums. Use the Σ( expression, variable, start, end ) syntax to sum a series directly, for instance Σ(2n+1, n, 1, 10) evaluates the sum of the first 10 odd numbers.
Financial 应用程序（TVM）可简化复利、年金和贷款还款计算。根据需要输入 N、I%、PV、PMT、FV 以及 P/Y、C/Y。计算器遵循符号约定：支出款为负，收入款为正，因此务必仔细核对符号。Sequence 应用程序或 Run-Matrix 中的 Recursion 模式可以验证等差和等比数列求和。直接使用 Σ(表达式, 变量, 起点, 终点) 语法计算级数和，例如 Σ(2n+1, n, 1, 10) 可求出前 10 个奇数的和。
10. Time-Saving Tips for Paper 2 | 试卷二省时技巧
Paper 2 demands speed and accuracy. Program your own shortcut macros: in Program mode, you can create small scripts to automate repetitive tasks like applying the quadratic formula, performing M⁻¹ × N, or generating a normal probability with given parameters. During the exam, running a program takes seconds and eliminates arithmetic mistakes. Also, store constants such as √π, e, or frequently used conversion factors in List or in Alpha memory (A–Z) so you can recall them instantly instead of retyping.
试卷二考验速度与准确性。你可以编写自己的快捷键宏：在 Program 模式下创建小型脚本，自动执行重复性任务，例如应用二次公式、计算 M⁻¹ × N 或生成指定参数的正态概率。考试时运行程序只需数秒，还能杜绝算术错误。此外，将 √π、e 等常数或常用换算因子存入 List 或 Alpha 存储器（A–Z），以便随时调取，无需反复输入。
11. Common Pitfalls and How to Avoid Them | 常见陷阱与避免方法
One major pitfall is forgetting to clear variables or stat lists from a previous question. Always press OPTN, then CLR, then All to reset memory before starting a new problem. Another error: misreading angle mode – if you see unexpected results with sin or cos, immediately check if Radian or Degree is active. When using G‑Solv, the calculator finds only what is visible; extend the viewing window to ensure you don’t miss roots outside the default screen. Finally, never use the solver without a rough sketch or guess range; the solution returned may be mathematically correct but out of the IB-mandated domain.
一大陷阱是忘记清除前一题的变量或统计列表。开做新题前，务必按 OPTN，然后 CLR，再选 All 重置内存。另一种错误：误读角度模式——若 sin 或 cos 的结果出乎意料，请立即检查当前是弧度制还是角度制。使用 G‑Solv 时，计算器只能找到视野范围内解；请扩展视窗，确保不会遗漏默认屏幕外的根。最后，切勿在没有大致草图或猜测范围的情况下使用求解器；返回的解在数学上可能正确，但已超出 IB 要求的定义域。
12. Exam Day Checklist | 考试日检查清单
On exam day, ensure your calculator is fully charged or has fresh batteries. Set the screen brightness to medium to conserve power. Have the backup reset procedure memorized: if the calculator freezes, a small pin on the back restarts it without losing memory. Bring the protective slide case; leaving the screen exposed in a bag can cause pressure damage. In the minutes before the exam, switch to Run-Matrix mode, clear all memories, set Radian mode, and briefly confirm connectivity with the teacher if the examination requires clearing all programs. With these checks done, you can focus entirely on the mathematics.
考试当天，确保计算器电量充足或已更换新电池。将屏幕亮度调至中等以节省电量。熟记备用的重置步骤：若计算器死机，机身背面的小孔可用针复位而不丢失内存。携带保护滑盖；将裸露的屏幕放入包内可能因受压而损坏。开考前的几分钟内，切换到 Run-Matrix 模式，清除所有存储器，设置为弧度制，如果考试要求清除全部程序则与监考老师简短确认连接情况。完成这些检查后，你便可全神贯注于数学答题。
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