📚 Review Set 23B - Calculator | 复习题集 23B - 计算器应用
Review Set 23B is designed to sharpen your calculator skills for IB Mathematics, covering functions, equations, calculus, statistics, and more. Mastering these problems with your graphing calculator will boost your speed and accuracy in both Paper 2 and Paper 3 examinations.
复习题集 23B 旨在提升你在 IB 数学中的计算器使用技巧，涵盖函数、方程、微积分、统计等内容。掌握这些题目并在图形计算器上熟练操作，将大幅提高你在试卷二和试卷三中的解题速度与准确性。
1. Introduction to Calculator Use in IB Mathematics | IB 数学中计算器使用简介
A graphing calculator is an essential tool for IB Mathematics Analysis and Approaches as well as Applications and Interpretation. It is permitted in all Paper 2 and Paper 3 exams, allowing you to solve equations numerically, graph complex functions, analyse statistical data, and perform matrix operations efficiently.
图形计算器是 IB 数学分析与方法以及应用与解释课程的核心工具。在所有试卷二和试卷三考试中均允许使用，它可以帮助你高效地数值求解方程、绘制复杂函数图像、分析统计数据并进行矩阵运算。
In this review set, you will practise typical calculator-based questions that appear frequently in exams. You will learn which functions to use and how to interpret the outputs correctly. Always remember that the calculator gives approximate answers unless you work in exact mode.
在本复习题集中，你将练习考试中常见的基于计算器的题型，学会应使用哪些功能以及如何正确解读输出结果。请始终记住，除非使用精确模式，否则计算器给出的答案通常是近似值。
2. Solving Equations with Polynomial Tools | 多项式工具解方程
the algebra menu. For a cubic equation x³ − 6x² + 11x − 6 = 0, the roots are 1, 2, and 3.
二次及更高次的多项式方程经常出现在 IB 考题中。计算器可以立即求出实根和复根。使用代数菜单中的方程求解器或多项式求根功能。对于三次方程 x³ − 6x² + 11x − 6 = 0，其根为 1、2 和 3。
Be careful to enter the coefficients correctly and to interpret repeated roots. When the equation is not in standard form, rearrange it before solving. Also, if the question asks for exact values, toggle between decimal and fraction views to check if the root is rational.
务必正确输入系数，并正确理解重根。当方程不是标准形式时，先进行整理再求解。此外，如果题目要求精确值，可在小数和分数视图之间切换，以检查根是否为有理数。
Example: Solve 2x² − 5x − 3 = 0 → x = 3 or x = −½
示例：解 2x² − 5x − 3 = 0 → x = 3 或 x = −½
3. Graphing Functions and Finding Intersections | 绘制函数图像并求交点
Graphing is the most visual way to understand a function' see key features: intercepts, turning points, and asymptotes. Use the trace and zoom functions to explore interesting regions.
图像绘制是理解函数性质最直观的方式。将函数输入 Y= 编辑器，并调整窗口以观察关键特征：截距、拐点和渐近线。使用追踪和缩放功能来探索感兴趣的区域。
Finding intersections of two graphs is a common requirement. Use the 'intersect' option after graphing both curves. The calculator will prompt you for first curve, second curve, and a guess. It then displays the coordinates of the intersection point.
求两个图像的交点是常见要求。绘制两条曲线后，使用“交点”选项。计算器会依次提示你选择第一条曲线、第二条曲线以及一个猜测值，随后显示交点坐标。
Remember that the calculator finds only one intersection near your guess. If there are multiple intersections, you must repeat the process with different initial guesses or use a systematic approach.
请记住，计算器只能找到你猜测值附近的一个交点。如果有多个交点，你必须用不同的初始猜测重复该过程，或采用系统性的方法进行查找。
4. Numerical Integration on Your Device | 设备上的数值积分
Numerical integration evaluates definite integrals that may not have elementary antiderivatives. Use the integral function, typing in the integrand, the variable, and the limits. The calculator uses an adaptive algorithm to return an approximation.
数值积分可计算那些可能没有初等不定积分的定积分。使用积分功能，输入被积函数、变量和积分上下限。计算器采用自适应算法返回近似值。
For the area between curves, integrate the absolute difference or use the integral of the upper minus lower function. Be precise with limits obtained from intersection points. Often you must store intersection coordinates in memory for accuracy.
对于曲线之间的面积，可以对上函数减下函数的差进行积分。利用求得的交点作为积分限时务必精确。通常你需要将交点坐标存储在内存中以确保精度。
Example: ∫₀¹ e−x² dx ≈ 0.746824
示例：∫₀¹ e−x² dx ≈ 0.746824
5. Differential Calculus and Derivative at a Point | 微分学与某点导数值
Graphing calculators can evaluate the derivative of a function at a specific point without finding the derivative function explicitly. Use the numerical derivative command, usually labelled nDeriv or d/dx, specifying the variable and the value.
图形计算器可以直接求出函数在某点的导数值，而无需显式求出导函数。使用数值微分命令（通常标记为 nDeriv 或 d/dx），指定变量和点的值。
This is particularly useful in problems about rates of change, slope of a tangent, or optimisation. However, for an exact derivative expression, you may need to use the CAS feature if available, or perform analytic differentiation.
这在关于变化率、切线的斜率或优化问题中尤为有用。然而，若要求精确的导数表达式，可能需要使用 CAS 功能（如果可用），或者进行解析微分。
in x) at x = π, and then write the calculator output rounded to three significant figures.
始终注意精度：小的步长能给出更好的精度。在 IB 考试中，你必须写出设置过程，例如 d/dx (x³ sin x) 在 x = π 处的值，然后给出四舍五入到三位有效数字的计算器输出结果。
6. Statistics: One-Variable and Two-Variable Analysis | 统计学：单变量与双变量分析
Entering data lists is straightforward: use the statistics editor to input values and frequencies. For one-variable statistics, you can quickly obtain mean, median, standard deviation, and quartiles. Know the difference between sx (sample) and σx (population) standard deviation.
输入数据列表非常简单：使用统计编辑器输入变量值和频数。对于单变量统计，你可以快速获得均值、中位数、标准差和四分位数。要清楚 sx（样本标准差）和 σx（总体标准差）的区别。
For two-variable statistics, enter x-values and y-values in separate lists. The calculator can then perform linear regression, quadratic regression, exponential regression, and more. It also provides the correlation coefficient r and the coefficient of determination r².
对于双变量统计，将 x 值和 y 值分别输入不同列表。计算器随后可进行线性回归、二次回归、指数回归等，并给出相关系数 r 和决定系数 r²。
Use the regression equation to make predictions, but be cautious about extrapolation. Always set the diagnostic mode on so that r and r² are displayed with the regression output.
利用回归方程进行预测，但要谨慎对待外推。务必开启诊断模式，以便在回归输出结果中显示 r 和 r²。
7. Probability Distributions and Their Inverses | 概率分布及其反函数
y between two bounds. For continuous distributions, cumulative probabilities are standard.
分布菜单提供正态分布、二项分布、t 分布、卡方分布和泊松分布。你可以直接计算概率：P(X = k)、P(X ≤ k) 或两边界之间的概率。对于连续分布，通常计算累积概率。
The inverse function is vital for confidence intervals and critical values. Input the area to the left and the parameters, and the calculator returns the boundary value. For example, invNorm(0.975, 0, 1) gives approximately 1.96.
反函数对于置信区间和临界值至关重要。输入左侧面积和相关参数，计算器即返回边界值。例如，invNorm(0.975, 0, 1) 的结果约为 1.96。
When dealing with binomial probability, note that the calculator can sum a range quickly using the binomial cumulative function. For a fair coin tossed 20 times, the probability of at most 8 heads is binomcdf(20, 0.5, 8).
处理二项式概率时，注意计算器使用二项累积函数可以快速求出一个范围内的概率和。对于抛掷一枚均匀硬币 20 次，至多出现 8 次正面的概率为 binomcdf(20, 0.5, 8)。
8. Matrices and Systems of Linear Equations | 矩阵与线性方程组
tem of equations, write it as an augmented matrix and use reduced row echelon form (rref).
通过矩阵编辑器输入矩阵，先设定维度然后依次输入各元素。计算器可以计算行列式、逆矩阵、转置矩阵以及特征值（部分型号）。对于 3×3 方程组，将其写为增广矩阵并利用简化的行阶梯形（rref）求解。
Be systematic when using rref: the rightmost column gives the solution for the variables. If a row becomes all zeros, the system may have infinitely many solutions or none; analyse the echelon form to distinguish.
使用 rref 时要有条理：最右侧的一列就是变量的解。如果某一行全为零，则方程组可能有无穷多解或无解；分析阶梯形式以进行区分。
| Operation | Key sequence | 操作 | 按键顺序 |
| Determinant | det([A]) | 行列式 | det([A]) |
| Inverse | [A]⁻¹ | 逆矩阵 | [A]⁻¹ |
| rref | rref([A]) | 简化行阶梯形 | rref([A]) |
9. Complex Numbers and Polar Conversion | 复数与极坐标转换
Complex number calculations are built into the calculator. You can perform addition, multiplication, division, and exponentiation in Cartesian form a + bi. The device can also convert between rectangular and polar forms using dedicated commands.
复数计算内置在计算器中。你可以进行笛卡尔形式 a + bi 的加法、乘法、除法和乘方运算。计算器还可以使用专用命令在直角坐标和极坐标形式之间进行转换。
When solving polynomial equations with complex roots, ensure the calculator is in complex mode. It will display roots as a + bi. For converting (√3 + i) to polar form, the modulus is 2 and the argument is π/6 (30°).
当求解具有复数根的多项式方程时，要确保计算器处于复数模式，它将显示 a + bi 形式的根。将 (√3 + i) 转换为极坐标形式，模长为 2，辐角为 π/6（30°）。
Use the angle and magnitude functions to extract components. In exam questions, you must interpret the results correctly, especially when arguments must be expressed within a specific interval such as (−π, π].
使用角度和模长函数来提取分量。在考试问题中，你必须正确解释结果，特别是当辐角必须在某个特定区间（如 (−π, π]）内表示时。
10. Sequences, Series and Financial Calculations | 数列、级数与金融计算
Arithmetic and geometric sequences can be analysed by defining the explicit formula and using the table feature. Summation of series is done using the sum and sequence commands. For Σ (k², k, 1, 10), the calculator directly gives 385.
等差数列和等比数列可以通过定义通项公式并使用表格功能进行分析。级数求和通过 sum 和 sequence 命令实现。对于 Σ (k², k, 1, 10)，计算器可直接给出结果 385。
Financial mathematics is an important application. Functions like TVM Solver handle loans, investments, and annuities. You input the present value, payment, future value, interest rate, and number of periods, then solve for the unknown.
金融数学是一项重要应用。TVM 求解器等功能可处理贷款、投资和年金问题。你输入现值、付款额、未来值、利率和期数，然后求解未知量。
Be mindful of the sign convention: money received is usually taken as positive, money paid out as negative. Setting the correct compound frequency (annually, monthly) is crucial to obtaining accurate results.
注意符号约定：通常将收到的钱计为正，付出的钱计为负。设置正确的复利频率（每年、每月）对获得准确结果至关重要。
11. Tips for Efficient Calculator Use in Exams | 考试中高效使用计算器的技巧
Before the exam, reset your calculator to default settings to avoid unwelcome restrictions. Configure angle measure to degrees or radians as required, set the number format to 'Normal' or 'Sci', and turn on diagnostics for statistics.
考试前，将计算器恢复为出厂默认设置以避免不必要的限制。按需设置角度单位为度或弧度，将数字格式设为“Normal”或“Sci”，并开启统计功能的诊断模式。
During the exam, store intermediate values in memory variables (A, B, C...) to maintain precision and save time. Use the 'ans' key to chain calculations. For repetition, explore the programmable features if allowed by the exam regulations.
考试期间，将中间值存入记忆变量（A、B、C……）以保持精度并节省时间。使用 'ans' 键进行链式计算。如果考试规定允许，可探索可编程功能来进行重复操作。
Avoid over-reliance on the calculator: you still need to show correct mathematical reasoning. Sketch graphs where required, write the derivatives or integrals you are evaluating, and round the final answer as instructed.
避免过度依赖计算器：你仍需要展示正确的数学推理。按要求绘制图像草图，写出你要计算的导数或积分，并按指令对最终答案进行四舍五入。
12. Summary of Review Set 23B | 复习题集 23B 总结
This review set has covered the core calculator skills for IB Mathematics: solving equations, graphing, numerical calculus, statistics, probability distributions, matrices, complex numbers, sequences, and financial maths. Regular practice with these tools will make them second nature.
本复习题集涵盖了 IB 数学的核心计算器技能：解方程、绘制图像、数值微积分、统计、概率分布、矩阵、复数、数列和金融数学。经常练习这些工具将使它们成为你的第二天性。
Always combine calculator proficiency with a solid conceptual understanding. Read the question carefully to decide what the calculator can do and what must be done analytically. With systematic revision, you will approach Paper 2 and Paper 3 with confidence.
始终将计算器操作熟练度与扎实的概念理解相结合。仔细阅读题目，判断哪些部分可由计算器完成，哪些必须通过解析方法解决。通过系统复习，你将充满信心地应对试卷二和试卷三。
Published by TutorHao | IB Mathematics Revision Series | aleveler.com
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