TMUA Mathematical Reasoning Paper: How to Tackle Elementary Logic and Proof Questions | TMUA 数学推理卷：初等逻辑与证明题怎么考

2026-10-15 07:50 · 本文部分内容由AI辅助创作

📚 TMUA Mathematical Reasoning Paper: How to Tackle Elementary Logic and Proof Questions | TMUA 数学推理卷：初等逻辑与证明题怎么考

The TMUA (Test of Mathematics for University Admission) is a two-paper admissions test used by Cambridge, Imperial, LSE, Warwick, Durham and several other universities for competitive mathematics-related courses. Paper 1 tests applications of mathematical knowledge; Paper 2, Mathematical Reasoning, is the paper that catches candidates off guard, because it looks short and harmless but demands precise logical thinking rather than routine calculation. This article explains exactly how elementary logic and proof questions are set, gives worked examples in the TMUA style, and sets out a revision strategy.

TMUA（大学入学数学考试）是剑桥、帝国理工、LSE、华威、杜伦等多所大学用于数学相关热门专业的入学考试，共两卷。卷一考数学知识的应用，卷二"数学推理"则是真正让考生措手不及的一卷：题目看起来短小无害，但考的不是套路计算，而是严密的逻辑判断。本文将系统讲清"初等逻辑与证明"类题目到底怎么考，给出贴近真题的例题精讲，并附上可执行的复习策略。

1. What Paper 2 Really Tests | 数学推理卷到底考什么

The TMUA consists of two papers, each lasting 75 minutes and containing 20 multiple-choice questions. Paper 1 is titled Applications of Mathematical Knowledge; Paper 2 is titled Mathematical Reasoning. Calculators are not permitted in either paper, and no formula sheet is provided.

TMUA 共两卷，每卷 75 分钟、20 道选择题。卷一叫"数学知识的应用"，卷二叫"数学推理"。两卷都不允许使用计算器，也不提供公式表。

Paper 2 deliberately avoids heavy content. Almost every question can be answered with GCSE and early A-level material: basic algebra, indices, surds, inequalities, primes and divisibility, functions and graphs, plus a small amount of probability. The difficulty comes from the logic, not the mathematics.

卷二刻意回避高深内容。几乎所有题目用 GCSE 和 A-level 前期知识就能解决：基础代数、指数、根式、不等式、质数与整除、函数与图像，外加少量概率。难点在逻辑，而不是数学本身。

The recurring question families are: choosing the correct negation of a statement; deciding whether a condition is necessary, sufficient, both or neither; finding a counterexample; identifying the contrapositive; locating the single flawed step in a chain of reasoning; and deciding which conclusion must follow from given information.

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反复出现的题型有六类：选出命题的正确否定；判断条件是必要、充分、充要还是都不是；举出反例；识别逆否命题；找出推理链中唯一出错的一步；判断哪些结论必然成立。

Every question carries the same weight, and there is no negative marking. Your raw score across the two papers is converted to a scale running from 1.0 to 9.0. Because there is no penalty for a wrong answer, an unanswered question is always a wasted mark.

每题分值相同，

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