第五章 · Section 5
Mathematical Ability (M) · 数学能力
Mathematical Ability (M): The depth and breadth of mathematical knowledge and skills.
数学能力（M）：数学知识与技能的深度与广度。
The manipulation of numbers using basic operations and solving word problems.
Sample task: Janet had 22 green pens and 10 yellow pens. She bought 6 bags of 9 blue pens and 2 bags of 6 red pens. How many pens does she have now?
用基本运算操作数字并解应用题。
样例问题：Janet 有 22 支绿笔和 10 支黄笔。她买了 6 袋蓝笔（每袋 9 支）和 2 袋红笔（每袋 6 支）。她现在有多少支笔？
The study of symbols and the rules for combining them to express general relationships and solve equations.
研究符号及其组合规则，以表达一般关系并解方程。
The study of shapes, space, size, position, and distance.
Sample task: An orange shaded rectangle is inscribed in a quarter-circle. Two sides of the rectangle lie along the two perpendicular radii of the quarter-circle, and the rectangle's edge touches the quarter-circle arc. Two segments are 2 and 4 units. What is the area of the orange shaded rectangle?
研究形状、空间、大小、位置与距离。
样例问题：一个橙色阴影矩形内接于四分之一圆。矩形的两条边沿四分之一圆的两条垂直半径，矩形边缘与四分之一圆弧相切。两条线段分别为 2 和 4 单位。橙色阴影矩形的面积是多少？
The quantification of uncertainty by assigning numbers from 0 to 1 to events.
Sample task: Suppose n dice are rolled, where n ≥ 2. Given that no two of the n dice show the same face, what is the probability that one of the dice shows a six? Give a formula in terms of n.
通过给事件赋 0 到 1 之间的数来量化不确定性。
样例问题：假设掷 n 个骰子（n ≥ 2）。已知这 n 个骰子没有两个显示相同面，那么其中一个骰子显示 6 的概率是多少？用 n 给出公式。
The mathematics of change and accumulation.
Sample task: The first three terms of a geometric sequence are the integers a, b, c, where a < b < c. What is the sum of the digits of the least possible value of a?
关于变化与累积的数学。
样例问题：一个几何序列的前三项是整数 a、b、c，其中 a < b < c。a 的最小可能值的各位数字之和是多少？
评估细节与 AI 表现
Assessment Details & AI Performance
Assessment Details. See Appendix C for further details on how to assess mathematical capabilities concretely.
AI System Performance. The table summarizes current AI system performance on Mathematical Ability (M) tasks. GPT-4 has limited mathematical capabilities, while GPT-5 has exceptional mathematical capabilities.
Model | Arithmetic (2%) | Algebra (2%) | Geometry (2%) | Probability (2%) | Calculus (2%) | Total
GPT-4 | 2% | 1% | 0% | 1% | 0% | 4%
GPT-5 | 2% | 2% | 2% | 2% | 2% | 10%
评估细节：如何在具体层面评估数学能力，参见附录 C。
AI 系统表现：下表汇总当前 AI 系统在数学（M）任务上的表现。GPT-4 数学能力有限，而 GPT-5 数学能力出色。
模型 | 算术(2%) | 代数(2%) | 几何(2%) | 概率(2%) | 微积分(2%) | 合计
GPT-4 | 2% | 1% | 0% | 1% | 0% | 4%
GPT-5 | 2% | 2% | 2% | 2% | 2% | 10%