Engineering Admissions Assessment 2018 Section 1 Answer Key | 2018年工程入学评估第一部分答案详解

📚 Engineering Admissions Assessment 2018 Section 1 Answer Key | 2018年工程入学评估第一部分答案详解

The Engineering Admissions Assessment (EAA) is used by leading UK universities to evaluate candidates’ mathematical and physical intuition under timed conditions. Section 1 consists of 40 multiple-choice questions spanning pure mathematics and physics, often requiring quick, insightful approaches. This article presents the answer key for the 2018 Section 1 paper, with detailed worked solutions for key questions. By studying these explanations, students can sharpen their problem-solving techniques, recognise common traps, and build the confidence needed to excel in such competitive assessments.

工程入学评估（EAA）是英国顶尖大学用来在限时条件下评估考生数学与物理直觉的测试。第一部分包含40道多项选择题，涵盖纯数学和物理，通常需要快速且富有洞察力的解题方法。本文提供2018年第一部分试卷的答案，并对重点题目给出了详尽的解答。通过学习这些解析，同学们可以提升解题技巧、识别常见陷阱，并建立在竞争性评估中脱颖而出所需的信心。

1. How to Use This Answer Key | 如何使用本答案解析

The answer key is designed as a learning resource, not just a list of letters. For each selected question, we first state the correct option, then break down the reasoning step by step. The questions chosen represent the range of topics in the 2018 paper. We recommend attempting each problem yourself before reading the solution, and then comparing your method with the one provided. Focus on efficiency — many EAA questions can be solved much faster with a clever substitution or an energy argument rather than a brute-force calculation.

本答案解析旨在作为学习资源，而不仅是一串字母。对于每一道入选的题目，我们首先给出正确选项，然后逐步拆解推理过程。所选题目覆盖了2018年试卷中的各类主题。建议你在阅读解答前先自己尝试每道题，然后比较你的方法与所提供的方法。重点关注效率——许多EAA题目通过巧妙的代换或能量分析，往往比蛮力计算快得多。

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2. Algebra and Functions | 代数与函数

Question 1 (Algebraic fractions). Simplify (x² – 4)/(x² – 5x + 6) for x ≠ 2, 3. Factorising numerator and denominator gives (x-2)(x+2) / (x-2)(x-3) = (x+2)/(x-3). The correct answer is D.

题1（代数分式）。 化简 (x² – 4)/(x² – 5x + 6)，x ≠ 2, 3。对分子分母因式分解得 (x-2)(x+2) / (x-2)(x-3) = (x+2)/(x-3)。正确答案是 D。

Question 3 (Logarithms). Solve log₂ x + log₂ (x – 2) = 3. Combine the logs: log₂[x(x-2)] = 3 ⇒ x(x-2) = 2³ = 8. Solve x² – 2x – 8 = 0 ⇒ (x-4)(x+2)=0. The domain requires x>2, so x=4. Answer: B.

题3（对数）。 解 log₂ x + log₂ (x – 2) = 3。合并对数：log₂[x(x-2)] = 3 ⇒ x(x-2) = 2³ = 8。解方程 x² – 2x – 8 = 0 ⇒ (x-4)(x+2)=0。定义域要求 x>2，所以 x=4。答案：B。

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3. Geometry and Trigonometry | 几何与三角

Question 7 (Trigonometric identities). If sin θ = 3/5 and θ is acute, find cos(90° – θ). Using the co-function identity, cos(90° – θ) = sin θ = 3/5. Straightforward recognition saves time. Answer: A.

题7（三角恒等式）。 已知 sin θ = 3/5 且 θ 为锐角，求 cos(90° – θ)。利用余角恒等式，cos(90° – θ) = sin θ = 3/5。直接识别能节约时间。答案：A。

Question 12 (Trigonometric equation). Solve 2cos²θ – cosθ – 1 = 0 for 0° ≤ θ ≤ 360°. Let y = cosθ, then 2y² – y – 1 = 0 ⇒ (2y+1)(y-1)=0. cosθ = -1/2 → θ = 120°, 240°; cosθ = 1 → θ = 0°, 360°. Four distinct solutions. Answer: C.

题12（三角方程）。 在 0° ≤ θ ≤ 360° 内解 2cos²θ – cosθ – 1 = 0。令 y = cosθ，则 2y² – y – 1 = 0 ⇒ (2y+1)(y-1)=0。cosθ = -1/2 → θ = 120°, 240°；cosθ = 1 → θ = 0°, 360°。共四个不同的解。答案：C。

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4. Calculus | 微积分

Question 15 (Differentiation). Differentiate y = 3x² + 1/x with respect to x. Write 1/x as x⁻¹, then y’ = 6x – x⁻² = 6x – 1/x². Answer: B.

题15（微分）。 对 y = 3x² + 1/x 关于 x 求导。将 1/x 写成 x⁻¹，得 y’ = 6x – x⁻² = 6x – 1/x²。答案：B。

Question 18 (Definite integral). Evaluate ∫₀² (2x + 3) dx. The antiderivative is x² + 3x. Evaluating from 0 to 2 gives (4 + 6) – 0 = 10. Answer: E.

题18（定积分）。 计算 ∫₀² (2x + 3) dx。原函数为 x² + 3x。从 0 到 2 求值得 (4+6) – 0 = 10。答案：E。

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5. Mechanics | 力学

Question 21 (Kinematics). A car accelerates uniformly from rest at 2 m s⁻² for 5 seconds. Distance travelled: s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m. Answer: D.

题21（运动学）。 一辆汽车从静止以 2 m s⁻² 匀加速 5 秒。行驶距离：s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m。答案：D。

Question 25 (Inclined plane). A 2 kg block slides frictionlessly down a 30° incline. Acceleration down the slope: a = g sin30° = 9.8 × 0.5 = 4.9 m s⁻². Mass does not affect the acceleration in the absence of friction. Answer: A.

题25（斜面）。 一个 2 kg 的滑块沿 30° 光滑斜面下滑。沿斜面的加速度：a = g sin30° = 9.8 × 0.5 = 4.9 m s⁻²。在没有摩擦的情况下，质量不影响加速度。答案：A。

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6. Electricity and Circuits | 电学与电路

Question 29 (Resistors in parallel). Three resistors 2 Ω, 3 Ω, and 6 Ω are connected in parallel. Total resistance: 1/R = 1/2 + 1/3 + 1/6 = (3+2+1)/6 = 1 ⇒ R = 1 Ω. Answer: C.

题29（并联电阻）。 三个电阻 2 Ω、3 Ω 和 6 Ω 并联。总电阻：1/R = 1/2 + 1/3 + 1/6 = (3+2+1)/6 = 1 ⇒ R = 1 Ω。答案：C。

Question 32 (Internal resistance). A battery of emf 12 V and internal resistance 0.5 Ω is connected to a 3.5 Ω load. Current I = 12/(0.5+3.5) = 3 A. Power delivered to the load is I²R = 9 × 3.5 = 31.5 W. The question asks for current; answer: 3 A, option B.

题32（内阻）。 一个电动势为 12 V、内阻为 0.5 Ω 的电池连接到一个 3.5 Ω 的负载。电流 I = 12/(0.5+3.5) = 3 A。负载功率为 I²R = 9 × 3.5 = 31.5 W。题目询问电流；答案：3 A，选项 B。

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7. Waves and Optics | 波动与光学

Question 35 (Wave speed). A sound wave has frequency 500 Hz and speed 340 m s⁻¹. Wavelength λ = v/f = 340/500 = 0.68 m. Recognise the inverse relationship. Answer: E.

题35（波速）。 一个声波频率为 500 Hz，波速为 340 m s⁻¹。波长 λ = v/f = 340/500 = 0.68 m。识别反比关系。答案：E。

Question 38 (Snell’s law). Light enters glass (refractive index n₂=1.5) from air (n₁=1) at incidence angle 30°. Snell’s law: 1×sin30° = 1.5×sinθ₂ ⇒ sinθ₂ = 0.5/1.5 = 1/3. Hence θ₂ ≈ 19.5°. Answer: D.

题38（斯涅尔定律）。 光从空气（折射率 n₁=1）以 30° 入射角进入玻璃（n₂=1.5）。斯涅尔定律：1×sin30° = 1.5×sinθ₂ ⇒ sinθ₂ = 0.5/1.5 = 1/3。因此 θ₂ ≈ 19.5°。答案：D。

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8. Thermodynamics | 热力学

Question 39 (First law). An ideal gas expands isothermally, doing 200 J of work on the surroundings. For an isothermal process, internal energy change ΔU = 0. By the first law, Q = ΔU + W = 0 + 200 = 200 J of heat must be supplied. Answer: C.

题39（热力学第一定律）。 理想气体等温膨胀，对外做功 200 J。对于等温过程，内能变化 ΔU = 0。根据第一定律，Q = ΔU + W = 0 + 200 = 200 J，必须供给 200 J 的热量。答案：C。

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9. Estimation and Data Interpretation | 估算与数据解读

Question 40 (Order-of-magnitude estimation). Estimate the number of heartbeats in a typical human lifetime. Assume 70 beats per minute, 60 × 24 = 1440 beats per day, ×365 ≈ 525 600 per year, ×80 years ≈ 42 000 000, or 4 × 10⁷. The closest order of magnitude is 10⁷. Answer: B.

题40（数量级估算）。 估算普通人一生中的心跳次数。假设每分钟 70 次，每天 60×24 = 1440 次，每年 ×365 ≈ 525 600 次，乘以 80 年 ≈ 42 000 000，即 4×10⁷。最接近的数量级是 10⁷。答案：B。

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10. Common Mistakes and Final Tips | 常见错误与最终建议

A recurring error in the 2018 Section 1 was misapplying sign conventions, especially in mechanics and thermodynamics. Always define a positive direction clearly. In algebra, many candidates lost marks by forgetting domain restrictions, such as excluding values that make denominators zero. For estimation questions, practise rounding numbers to one significant figure and using standard form fluently. Finally, time management is critical — if a question takes more than two minutes, mark your best guess, circle it, and move on; you can return if time permits. Use this answer key as a diagnostic: for any wrong answer, reattempt the problem from scratch before reading the solution.

2018年第一部分考试中一个常见的错误是符号约定使用不当，特别是在力学和热力学中。一定要清晰地定义正方向。在代数题中，许多考生因忘记定义域限制（例如排除使分母为零的值）而失分。对于估算题，要练习将数值四舍五入到一位有效数字并熟练使用标准形式。最后，时间管理至关重要——如果某道题花费超过两分钟，就选出你最好的猜测，圈出来然后继续；时间允许的话可以回头再做。将本答案解析用作诊断工具：对于任何错误的答案，在阅读解答之前，从头重新尝试这道题。

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