经济学申请 TMUA 40题150分钟 逻辑与论证
申请英国的经济学，很多人第一反应是补经济学知识点，真正卡住申请的却常常是一场数学笔试。UAT-UK 官网对 TMUA 的定位写得很清楚，面向 Mathematics 以及 Economics、Computer Science 这类数学相关专业，考的是 Higher Level GCSE 到 AS 数学范围里的数学思维与推理，不考经济学概念。2027 入学的周期里，剑桥、LSE、帝国理工与 UCL 的部分经济学专业把这项笔试写成必修，华威写成建议，牛津的经济与管理、PPE 走的却是 TARA。这篇文章把两卷的结构、官方考纲的边界、一月场的报名时间与剑桥的十月限制逐条拆开，也把容易报错的地方标出来。
For a UK economics application, the maths test often decides the outcome rather than the economics reading. According to the UAT-UK website, the TMUA targets mathematics and mathematics-related degrees such as Economics, and it draws on Higher Level GCSE and AS level mathematics instead of economic theory. In the 2027 entry cycle Cambridge, LSE, Imperial and UCL list it as compulsory for some economics courses, Warwick lists it as recommended, and Oxford uses the TARA for Economics and Management and for PPE; the pages below work through the paper structure, the specification boundaries, the January booking dates and the October rule for Cambridge.
TMUA 不考经济学知识 考的是数学与推理
UAT-UK 官网在 Who should sit the test 一段写明，申请 Mathematics 或 Economics、Computer Science 这类数学相关学位的人可能需要参加 TMUA。它把内容限定在 Higher Level GCSE 与 AS 数学，数学知识加上初等逻辑，经济学里的供需、弹性、边际效用一个都不考。很多学生以为申经济学就要在笔试里展示经济学阅读量，翻开样题才发现全是代数、三角与图形推理。真正要练的是把学过的方法用到陌生情境里的速度，以及读懂一个论证结构的能力。官方样题与练习卷都按这个思路设计，题干短、条件藏在文字里，选项之间只差一步推导。数学基础扎实的申请人在这项笔试里通常更容易进入高分段，原因不在知识量，而在运算熟练度。
The test is deliberately narrow in subject matter. UAT-UK states that candidates for mathematics-related degrees such as Economics may need the TMUA, and the specification confines itself to Higher Level GCSE and AS level mathematics plus elementary logic; nothing in the paper asks about supply and demand, elasticity or utility, because every question is algebra, trigonometry, graphs or reasoning. That is why strong mathematicians often find it more comfortable than students who have read widely in economics but have not practised timed algebra without a calculator, and the official specimen papers show the pattern clearly with short stems, conditions embedded in prose, and options separated by a single step of working.
2027 入学把 TMUA 列为必修的六条课程代码
UAT-UK 的 Course List 2027 Entry 文档在 2026 年 4 月更新过，按学校逐条列出课程与笔试要求。剑桥的 BA Economics（L100）要求 TMUA，LSE 的 BSc Economics（L101）与 BSc Econometrics and Mathematical Economics（L140）是强制，帝国理工的 BSc Economics, Finance and Data Science（L1N3）也是强制。UCL 的 BSc Economics（L100）与带海外学习的 L101 同样要求 TMUA。这六条课程代码是经济学申请人最该先核对的部分。文档自己提醒，课程页面才是最终口径，报名之前要回到各校官网确认一遍。常见的错误是只看二手总结不看课程代码，结果把必修当成可选，或者把可选当成必修白花一笔考试费。
The UAT-UK Course List for 2027 entry, updated in April 2026, sets out each requirement course by course. Cambridge lists BA Economics (L100) with the TMUA, LSE makes it compulsory for BSc Economics (L101) and for BSc Econometrics and Mathematical Economics (L140), and Imperial requires it for BSc Economics, Finance and Data Science (L1N3); UCL requires it for BSc Economics (L100) and for the study abroad variant L101. UAT-UK stresses that course pages remain the final authority, and that failing to register for a required test may invalidate the application, so the six codes above are worth checking against the university websites before any booking is made.
沃里克只是建议 杜伦清单里没有经济学
同一份文档里，华威把 TMUA 只写成 recommended，覆盖 BSc Economics（L100）、Economics and Management（LN12）、Economics, Politics and International Studies（LLD2）以及 MORSE 的两个代码 GLN0 与 G0L0。华威真正写 compulsory 的是计算机与数学那几门课，经济学不在其中，细节上还留了 contextual offer 的例外。杜伦的清单只有四门数学课，经济学根本没有出现在这份文档里。牛津的情况更值得注意，经济与管理（LN12）与 PPE（L0V0）用的是 TARA，不是 TMUA，题型与时长都不一样。同样是经济学申请，有人考 TMUA，有人考 TARA，取决于专业代码而不是专业名称。核对时先看代码，再看要求，顺序反了最容易报错。
Warwick lists the TMUA as recommended rather than compulsory for BSc Economics (L100), Economics and Management (LN12), Economics, Politics and International Studies (LLD2) and both MORSE codes GLN0 and G0L0, while its compulsory list covers computer science and mathematics instead, with a contextual offer exception written into the same table. Durham's entry contains only four mathematics courses, so economics does not appear at all. Oxford is the case most often misread, because Economics and Management (LN12) and PPE (L0V0) require the TARA rather than the TMUA, which means the same subject label can lead to a completely different paper and the UCAS code is what settles it.
两卷各 20 题 75 分钟 平均 225 秒一题
TMUA 一共两卷，每卷 20 道选择题、75 分钟，两卷连续作答，总时长 2 小时 30 分钟。把 9000 秒摊到 40 道题上，平均每题 225 秒，也就是 3 分 45 秒。Paper 1 考 Applications of Mathematical Knowledge，Paper 2 考 Mathematical Reasoning。两卷权重相同，都不倒扣分，官方 specification 写明答错没有惩罚，建议全部作答。很多学生以为两卷难度递增，其实 Paper 2 的难点不在计算量，而在读懂逻辑关系。常见的错误是把时间平均分配，最后十分钟才发现有几道题根本没看过。官方建议按计时条件做完整练习卷，练的就是这种分配节奏。
The paper has two sections of 20 multiple-choice questions and 75 minutes each, taken one after the other, for a total of 2 hours 30 minutes. Spread across 40 questions the 9000 seconds work out at 225 seconds per question, or 3 minutes 45 seconds, and the two papers carry equal weight with no penalty for wrong answers. Paper 1 tests Applications of Mathematical Knowledge while Paper 2 tests Mathematical Reasoning, and the second paper is harder because of the reading rather than the arithmetic, which is why UAT-UK recommends completing the practice test under timed conditions rather than dipping into questions at random.
Paper 1 把学过的方法搬进没见过的情境
官方 specification 对 Paper 1 的描述是，考查考生把数学知识应用到各种情境里的能力。题目用到的知识都在 Section 1，情境是新的，比如把线性关系放进定价与销量的场景，或者用图形判断两个方案哪个更省。这一卷不要求额外的方法，要的是识别哪条公式能用。做题顺序上，先扫一遍全卷，把能直接算出答案的题挑出来，再回头处理需要设未知数的题。常见的错误是每道题都从头推，结果最难的题花掉两倍时间。官方不给公式册，常用公式必须能默写出来，这一步在考场里没有替代方案。
Paper 1 is described in the specification as a test of the candidate's ability to apply mathematical knowledge in a variety of contexts. The knowledge required sits inside Section 1, yet the settings are unfamiliar, so the work is recognising which formula fits rather than learning new methods; a typical stem might embed a linear model in a pricing scenario or ask which of two plans costs less. A sensible order is to sweep the paper for questions that can be finished immediately and return to the ones that need an unknown to be set up, since treating every question as a full derivation is how candidates run out of time, and with no formulae booklet provided the common results have to be recalled rather than looked up.
Paper 2 的逻辑清单 逆否命题与必要条件
Section 2 是 Paper 2 独有的部分，官方分成 The Logic of Arguments、Mathematical Proof 与 Identifying Errors in Proofs 三块。逻辑部分要理解 if A then B、A only if B、A if and only if B 这几种说法，还要分清 converse 与 contrapositive。necessary 与 sufficient 的区别、for all 与 there exists 的否定写法都在清单上。证明部分要求能跟住直接证明、分类讨论、反证法与举反例四种形式，也要能把打乱的步骤重新排序。官方明确不考符号化写法，也不考真值表，考的是普通语言里的精确。常见的错误是凭语感判断逆否命题，其实只要把条件与结论同时取反，再交换位置就对了。
Section 2 belongs to Paper 2 alone and is divided into the logic of arguments, mathematical proof, and identifying errors in proofs. Candidates are expected to handle statements of the form if A then B, A only if B and A if and only if B, to separate the converse from the contrapositive, and to know what necessary and sufficient mean, while negation of for all and there exists also appears in the same list. Proof questions ask for direct deduction, proof by cases, proof by contradiction and disproof by counterexample, including reordering scrambled steps, and because symbolic notation and truth tables are explicitly excluded the precision of ordinary language carries the marks.
MM1 代数与函数 根式 判别式 余数定理
Section 1 的第一块是 Algebra and functions，编号从 MM1.1 到 MM1.7。细则要求掌握有理指数的运算法则、根式化简与分母有理化，判别式、配方法与二次方程求解也在其中。多项式部分包含展开、因式分解、用一次式或二次式做除法，以及 Factor Theorem 与 Remainder Theorem。二次不等式与线性不等式要会解，一次与二次联立的方程组要会代入消元。官方还要求理解函数是多对一或一一的映射，并且知道根号符号默认指正平方根。这一块的题量在 Paper 1 里最稳定，练熟能稳住基础分。真正拉开差距的是化简速度，化简到位以后后面的步骤通常很短。
The first block of Section 1 is algebra and functions, running from MM1.1 to MM1.7. The detail covers laws of indices for rational exponents, simplification of surds with rationalising the denominator, and quadratic work including the discriminant, completing the square and solving quadratic equations; polynomial manipulation adds expansion, factorisation, division by a linear or quadratic expression, and the factor and remainder theorems. Inequalities, simultaneous equations with one linear and one quadratic, and the mapping language around functions complete the block, and questions from it are the most predictable source of marks in Paper 1 once the simplification steps are fluent.
数列 二项式与圆的方程
MM2 的 Sequences and series 要求会由通项公式或递推关系生成数列，也要掌握等差数列求和与自然数前 n 项和的公式。等比数列除了有限项求和，还要会用公比绝对值小于 1 求无穷和。二项式展开限定在 (1 + x)^n 与 (a + f(x))^n 这类正整数次幂，n! 与组合数记号要认得会用。MM3 的坐标几何从直线方程写到圆的两种形式，(x - a)² + (y - b)² = r² 与展开后的 x² + y² + cx + dy + e = 0 都要会互化。圆的定理一共列了七条，垂径平分弦、切线垂直于半径、圆周角是圆心角的一半都在内。很多学生以为圆的题只考配方，实际上相切条件与弦长经常出现在同一道题里。求出圆心与半径之后，还要回到题目给的位置关系上判断。
The sequences block requires terms from a formula for the nth term or from a recurrence, the sum of an arithmetic series, and the standard sum of the first n natural numbers. Geometric series cover finite sums and the sum to infinity when the common ratio is smaller than 1 in modulus, while binomial expansion is limited to positive integer powers of (1 + x) and of expressions such as (a + f(x)), together with factorial and combination notation. Coordinate geometry then runs from straight lines to the two forms of a circle equation and the seven circle theorems, and circle questions rarely stop at completing the square because tangency and chord conditions usually arrive in the same stem.
三角 对数 与微分的边界
MM4 的三角部分要求掌握正弦定理与余弦定理，还要理解角边边这种情形下可能有两个解。三角形面积写成两边乘积乘以夹角正弦的一半，弧度制要会算弧长、扇形与弓形面积。特殊角的三角函数值要能直接写出，常用恒等式与给定区间内的方程求解都在考纲里。MM5 的对数部分列了运算法则，换底公式明确不考。MM6 的微分从切线斜率讲起，要求会写二阶导数与一阶导数记号，但明确排除用定义求导。驻点只考极大与极小，拐点不在考试范围，只要求对简单多项式有定性认识。三角方程的多解写法最容易漏解，区间端点也算一种情况。
Trigonometry covers the sine and cosine rules, including the ambiguous angle-side-side case where two triangles can satisfy the data, and the area formula written as half the product of two sides times the sine of the included angle. Radian measure brings arc length and the areas of sectors and segments, while exact values for the standard angles, the common identities and solutions of trigonometric equations within a stated interval are all listed. Differentiation starts from the gradient of a tangent and requires second derivatives and the usual notation, but differentiation from first principles is excluded, stationary points are limited to maxima and minima, and points of inflexion are examined only through a qualitative reading of simple polynomial graphs.
积分 梯形法则与图形变换
MM7 的积分要求分清定积分与曲线下面积的区别，理解微积分基本定理并会用上下限代入相减。x 的 n 次幂在 n 不等于负一时可以直接积分，先化简再积分的题更常见。梯形法则要求会用，还要能判断结果是高估还是低估。MM8 的图形部分要求能画出直线、二次、三次、三角、对数、指数、根号与绝对值函数的草图。变换只看 y = af(x)、y = f(x) + a、y = f(x + a) 与 y = f(ax) 四种，复合函数 f(g(x)) 也要会。图表交点与方程解的对应关系是另一条常考线索。这一步最容易丢分的地方，是把左右平移的方向写反。
Integration requires the distinction between a definite integral and the area between a curve and an axis, together with the fundamental theorem of calculus applied by substituting the limits. Powers of x can be integrated directly except when the index is minus one, and expressions that need simplifying first are more common than straightforward ones; the trapezium rule has to be used and its result judged as an overestimate or an underestimate. The graphs section asks for sketches of lines, quadratics, cubics, trigonometric, logarithmic, exponential, square root and modulus functions, the four simple transformations and compositions, and the link between intersections and the solutions of equations.
没有公式册 也不能带计算器
TMUA 的 specification 写明这项考试不提供公式册，考生要自己记住并调用所有相关公式，也不能使用计算器。官网的 Good to know 一段同样写明不得使用计算器与词典。这条规定直接抬高了精确计算的分量，根式、分数与 π 的倍数都要能手算，分母有理化是常规动作。M2.11 要求能精确计算根式与 π 的倍数，M2.14 要求用近似估算检验结果，上下界问题在 M2.12 里单独列出。很多学生以为机考能用内置计算器，进考场才发现只有可擦写草稿册和一支笔。平时练习就把计算器收起来，用估算先判断数量级，再动笔算精确值。
The TMUA specification states that no formulae booklet is provided and that candidates must understand and recall all relevant formulae, and it also rules out calculators. The Good to know section of the UAT-UK website adds that neither a calculator nor a dictionary may be used, which raises the value of exact arithmetic: surds, fractions and multiples of pi have to be handled by hand, and rationalising a denominator becomes routine. The number content asks for exact work with surds and multiples of pi, for approximation as a check on a result, and for upper and lower bounds in context, so practising without a calculator is part of preparation rather than a detail.
答错不扣分 但中位数只有 4.5
TMUA 只给一个总分，刻度是 1 到 9，保留一位小数，没有及格线，也不设通过与不通过的判定。Prepare 页面写明分数刻度按当年考生的能力分布确定，中位数固定为 4.5，第 90 百分位固定为 7.0。这两组数字的用途是给出参照，不是一条分数线。官方样题与练习卷只反馈对错，不显示分数，因为分数要等同场考生的分布才能算出来。答错不扣分，40 道题都值得作答，空着等于放弃一次可能的机会。成绩按课程自动送达 UCAS 上的院校，考生不能选择送给谁，也不能撤回。十月场出分是 2026 年 11 月 16 日，一月场出分是 2027 年 2 月 8 日。
The TMUA produces one overall score on a scale from 1 to 9, reported to one decimal place, with no pass mark and no threshold that decides anything on its own. The UAT-UK Prepare page explains that the scale is set against the ability distribution of the cohort each year, with the median fixed at 4.5 and the 90th percentile fixed at 7.0, so those two numbers are reference points rather than targets; the specimen and practice tests mark answers right or wrong but award no score, precisely because a score needs a cohort behind it. Results reach the universities named on the UCAS application automatically, candidates cannot choose or withdraw the recipients, and the two dates to remember are 16 November 2026 for the October sitting and 8 February 2027 for the January sitting.
一月场 10 月 28 日开放报名 剑桥只能考十月
2027 入学的一月场报名在 2026 年 10 月 28 日下午 3 点（英国时间）开放，报名截止是 12 月 21 日下午 6 点。特殊安排申请截止 12 月 7 日，助学金申请截止 12 月 14 日，两项都要先批准才能报名，审核分别要十个与五个工作日。考试窗口是 2027 年 1 月 4 日到 8 日，出分日是 2027 年 2 月 8 日。十月场的报名早在 2026 年 9 月 28 日截止，考试窗口 10 月 12 日到 16 日已经过去，出分日是 11 月 16 日。剑桥与牛津的申请人必须在十月场应考，例外只有剑桥一月截止的成熟学院与牛津的 Astrophoria 预科年。中国内地、香港与澳门考区的 TMUA 只开 10 月 15 日、16 日与 1 月 8 日，官网写明不做例外。费用按考点所在地计算，英国与爱尔兰 78 英镑，其他地区 133 英镑，助学金覆盖全额但要先申请。
Booking for the January 2027 sitting opens on Wednesday 28 October 2026 at 3pm UK time and closes on 21 December 2026 at 6pm, with access arrangement requests due by 7 December and bursary requests by 14 December, both of which must be approved before a booking can be made. The test window runs from 4 to 8 January 2027 with results on 8 February 2027, while the October sitting closed for booking on 28 September 2026 and ran from 12 to 16 October with results on 16 November. Cambridge and Oxford applicants must sit in October, apart from mature applicants to a Cambridge college with a January deadline and applicants to the Oxford Astrophoria Foundation Year; candidates in mainland China, Hong Kong and Macau can only sit the TMUA on 15 or 16 October and on 8 January, a restriction UAT-UK says it cannot vary, and the fee is 78 pounds in the UK and Ireland and 133 pounds elsewhere, with bursaries covering the full amount if claimed first.
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