📚 UAT-UK Written Tests: Why Calculators and Dictionaries Are Banned | UAT-UK 笔试禁止使用计算器与字典
Every year thousands of applicants sit the UAT-UK admissions tests - TMUA, ESAT and TARA - at Pearson VUE centres around the world. Almost every candidate meets the same surprise in their first mock paper: no calculator, and no dictionary of any kind. This guide explains where the rule comes from, what arithmetic and language skills it forces you to build, and how to train for an exam in which the machine in your pocket cannot help you.
每年都有成千上万的申请者在全球各地的 Pearson VUE 考试中心参加 UAT-UK 系列笔试——TMUA、ESAT 与 TARA。几乎所有考生在第一次模考时都会撞上同一条意外规则：不许用计算器，也不许用任何字典。本文将说明这条规则的由来、它迫使你建立的运算与语言能力，以及如何为一场"手机里的机器帮不上忙"的考试做准备。
1. What UAT-UK Is and Which Papers Are Affected | UAT-UK 是什么，哪些试卷受影响
UAT-UK stands for University Admissions Tests UK, a shared admissions testing service used by several leading UK universities. It currently covers three test families: TMUA for mathematics-heavy degrees, ESAT for engineering and science degrees, and TARA for courses that emphasise general academic reasoning. All three are delivered on computer at Pearson VUE test centres.
UAT-UK 全称 University Admissions Tests UK，是由多所英国顶尖大学共同采用的入学笔试服务。目前涵盖三大类考试：面向数学类专业的 TMUA、面向工程与理科专业的 ESAT，以及侧重综合学术推理能力的 TARA。三类考试全部在 Pearson VUE 考试中心以机考形式进行。
TMUA has two papers of 75 minutes each with 20 multiple-choice questions per paper. ESAT has three 40-minute modules of 27 multiple-choice questions each, beginning with the compulsory Mathematics 1 module. TARA combines multiple-choice critical-thinking and problem-solving sections with a written task.
TMUA 共两卷，每卷 75 分钟、20 道选择题；ESAT 共三个模块，每模块 40 分钟、27 道选择题，其中数学 1 是必考模块；TARA 则由批判性思维、问题解决两个选择题部分与一项写作任务构成。
The no-calculator rule applies to every one of these papers, including the physics and chemistry modules of ESAT where you might reasonably expect to be allowed one. Most sittings also provide no formula booklet, so recall matters as much as method.
"禁用计算器"适用于上述所有试卷，包括你可能以为允许带计算器的 ESAT 物理与化学模块。大多数场次同样不提供公式表，因此"记得住"与"会推导"同等重要。
2. The Official Rule in Plain Terms | 官方规定的直白解读
Published test-day rules state that calculators, smart watches, phones and any electronic device with computational or storage capability are prohibited. Candidates may not bring their own paper, notes, formula rulers or dictionaries into the test room.
官方公布的考试当天规则明确规定：计算器、智能手表、手机以及任何具备计算或存储功能的电子设备一律禁止携带；考生不得自带纸张、笔记、公式尺或字典进入考场。
The word "dictionary" covers bilingual and monolingual printed dictionaries, electronic dictionaries, translation apps and handwritten glossaries. This is a common disappointment for candidates who use English as an additional language and had planned to bring an English-Chinese dictionary.
"字典"一词涵盖双语与单语纸质词典、电子词典、翻译软件以及手写词汇表。对以英语为附加语言的考生来说，这常常令人失望——他们原本打算带一本英汉词典进场。
An erasable note board or paper and pen is supplied by the test centre, and must be handed back at the end of the session. Bringing your own stationery, apart from acceptable identification, is not permitted.
考试中心会提供可擦写记事板或纸张与笔，考试结束后必须交回。除可接受的身份证明文件外，考生不得自带文具。
| Item | 物品 | Allowed? | 是否允许 | Notes | 说明 |
| Passport or photo ID | 护照或带照片证件 | Yes | 可以 | Must match your registration name | 须与报名姓名一致 |
| Calculator (any type) | 计算器（任何类型） | No | 不可以 | Includes on-screen calculator tools | 含屏幕内置计算器功能 |
| Smart watch or phone | 智能手表或手机 | No | 不可以 | Stored in a locker | 须锁入储物柜 |
| Printed or electronic dictionary | 纸质或电子词典 | No | 不可以 | Includes translation apps | 含翻译软件 |
| Own pen and paper | 自备笔和纸 | No | 不可以 | Centre provides a note board | 由考点提供记事板 |
3. Why the Ban Exists | 禁令背后的三个理由
The first reason is construct validity. These tests claim to measure mathematical reasoning, scientific reasoning and academic literacy. If a calculator performed the arithmetic, the score would partly reflect the device rather than the candidate's thinking.
第一个原因是"构念效度"。这些考试声称测量的是数学推理、科学推理与学术读写能力。如果运算交给计算器，分数就会部分反映设备性能，而不是考生的思维水平。
The second reason is comparability. Thousands of candidates sit comparable papers at hundreds of centres on different days. Banning calculators removes a major source of variation in speed and accuracy between candidates.
第二个原因是可比性。成千上万的考生在不同日期、于数百个考点参加可比的试卷。禁用计算器可以消除考生之间在运算速度与准确度上的一大差异来源。
The third reason is predictive validity. University tutors consistently report that students who can estimate, sanity-check and manipulate expressions by hand cope better with first-year physics, engineering and economics, where a wrong button press is invisible but a wrong order of magnitude is not.
第三个原因是预测效度。大学导师普遍反映：能估算、能检验、能手算处理表达式的学生，更能适应大一物理、工程与经济学课程——按错键不易察觉，但数量级错了却一目了然。
4. Number Facts You Must Own Cold | 必须烂熟于心的数字事实
Without a calculator, speed comes from memory rather than computation. You should be able to recall squares from 1 to 20, cubes from 1 to 10, powers of 2 up to 2¹⁰, and the multiplication tables up to 15 without hesitation.
没有计算器时，速度来自记忆而非计算。你应当能够不假思索地回忆 1 到 20 的平方、1 到 10 的立方、2 的幂直到 2¹⁰，以及 15 以内的乘法表。
Fraction-to-decimal conversions appear constantly in TMUA and ESAT. Learn the eighths, sixteenths, thirds and sixths as automatic reflexes.
分数与小数的互换在 TMUA 与 ESAT 中反复出现。八分之一、十六分之一、三分之一与六分之一这一组，要练成条件反射。
1/16 = 0.0625 1/3 ≈ 0.333 2/3 ≈ 0.667 1/6 ≈ 0.167 5/8 = 0.625
Useful irrational approximations are worth memorising to three decimal places, because multiple-choice options are usually far enough apart that this precision is sufficient.
常用无理数的近似值记到小数点后三位即可，因为选择题的选项之间通常间隔足够大，这样的精度完全够用。
√2 ≈ 1.414 √3 ≈ 1.732 √5 ≈ 2.236 √7 ≈ 2.646 π ≈ 3.142 e ≈ 2.718
.693. From these you can rebuild log₁₀ 4, log₁₀ 6, log₁₀ 8 and log₁₀ 9 by simple addition.
对数方面，三个数值就能解锁大部分估算：log₁₀ 2 ≈ 0.301、log₁₀ 3 ≈ 0.477、ln 2 ≈ 0.693。由此通过简单相加即可推出 log₁₀ 4、log₁₀ 6、log₁₀ 8 与 log₁₀ 9。
5. Mental Maths Techniques That Save Minutes | 能省下几分钟的心算技巧
Multiplication shortcuts are the fastest wins. Multiplying by 5 is multiplying by 10 then halving; multiplying by 25 is multiplying by 100 then dividing by 4; multiplying by 9 is multiplying by 10 then subtracting the original number.
乘法捷径是见效最快的部分。乘以 5 等于乘以 10 再折半；乘以 25 等于乘以 100 再除以 4；乘以 9 等于乘以 10 再减去原数。
The difference of two squares identity turns awkward products into easy ones. This single trick removes a great deal of long multiplication from your exam.
平方差公式能把难算的乘积变成好算的乘积。仅这一招就能在考场上替你省掉大量竖式乘法。
a² − b² = (a + b)(a − b) → 47 × 53 = 50² − 3² = 2500 − 9 = 2491
Squaring a number ending in 5 is even quicker: multiply the leading digits by the next integer, then append 25.
个位是 5 的数平方更快：把前面的数字乘以它加 1，后面直接写上 25。
85² → 8 × 9 = 72 → 7225 35² → 3 × 4 = 12 → 1225
g by 3, and dividing by 0.25 is multiplying by 4. Percentage work is easiest split into 10% and 5% building blocks, so 15% of 240 is 24 + 12 = 36.
除法捷径同样重要：除以 0.5 就是乘以 2，除以 1.5 就是乘以 2 再除以 3，除以 0.25 就是乘以 4。百分数最省力的做法是拆成 10% 与 5% 的积木，因此 240 的 15% 就是 24 + 12 = 36。
6. Estimation, Bounds and Sanity Checking | 估算、界值与合理性检验
Estimation is not a fallback; it is the main strategy for calculator-free multiple choice. Round every number to one or two significant figures, compute the approximate answer, and check which option lies in that neighbourhood.
估算不是退而求其次，而是无计算器选择题的主策略。把每个数四舍五入到一到两位有效数字，算出近似答案，再看哪个选项落在这个范围附近。
Square roots can be estimated by linear interpolation between the nearest perfect squares. The correction term is small enough that two decimal places come out reliably.
平方根可以在最接近的两个完全平方数之间做线性插值来估算。修正项足够小，结果通常准到小数点后两位。
√50: since 7² = 49, √50 ≈ 7 + 1/(2 × 7) ≈ 7 + 0.071 ≈ 7.07
a very different claim from 9 kJ, and only estimation catches that class of error quickly.
在 ESAT 物理与化学中，务必先估计数量级。动能 0.5 × 2 × 3² = 9 J 与 9 kJ 是完全不同的结论，而只有估算才能迅速抓住这类错误。
Finally, keep a rough upper and lower bound in your head. If an exact answer must lie between 3.0 and 3.5 and only one option does, you have answered the question without finishing the arithmetic.
最后，脑中保留一个粗略的上下界。如果精确答案必然落在 3.0 到 3.5 之间，而只有一个选项落在这个区间，那么你其实没算完就已经答对了。
7. Algebra and Surds Without a Calculator | 无计算器的代数与根式
Surd manipulation is examined directly and rewards fluency. Simplifying, multiplying and rationalising denominators should all be automatic by the week before the test.
根式运算是直接考点，熟练度越高越占优势。化简、相乘与分母有理化，都应在考前一周成为自动动作。
√8 = 2√2 √12 = 2√3 √18 = 3√2 1/√2 = √2/2 √a × √b = √ab
Quadratics appear in several disguises: factorising, completing the square, using the discriminant, and applying the quadratic formula without a calculator. Discriminant questions are especially common because they need no arithmetic at all.
二次式会以多种面貌出现：因式分解、配方、用判别式判断根的个数，以及无计算器地套用求根公式。判别式题尤其常见，因为
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