📚 AS AQA Maths Unit 2 January 2020 Mark Scheme Breakdown | AS AQA数学第2单元2020年1月评分方案解析
The January 2020 AQA AS Mathematics Unit 2 mark scheme gives a clear picture of how examiners award marks for method, accuracy, and final answers. This revision guide breaks down the key features of the mark scheme, topic by topic, to help you understand exactly what earns marks and where students commonly lose them.
2020年1月AQA AS数学第2单元评分方案清楚地展示了考官如何对方法、准确性和最终答案给分。本复习指南逐项拆分评分方案的关键特点，帮助你准确理解哪些步骤能得分，以及学生常在哪些地方失分。
1. Overview of the Paper and Mark Scheme | 试卷与评分方案概览
The AQA AS Maths Unit 2 paper is designed to test pure mathematics and applied content covered in the first year of A-level. The January 2020 mark scheme follows a consistent pattern: method marks (M1), accuracy marks (A1), and independent marks (B1).
AQA AS数学第2单元试卷旨在考查A-level第一年所学的纯数学与应用内容。2020年1月评分方案遵循固定模式：方法分（M1）、准确性分（A1）和独立分（B1）。
Each question is marked using a three-letter code system. For example, M1 means one method mark for a correct process, A1 means one accuracy mark for a correct final or intermediate result, and B1 means one independent mark that does not require a method.
每道题都使用三字母代码系统评分。例如，M1表示正确步骤得到的一分方法分，A1表示正确最终结果或中间结果得到的一分准确性分，B1表示不需要方法步骤的一分独立分。
You will also see abbreviations such as ‘ft’ for follow-through, ‘oe’ for or equivalent, and ‘cao’ for correct answer only. These tell you whether a wrong earlier answer can still earn later marks if your method is correct.
你还会看到诸如“ft”表示后续给分、“oe”表示或等价答案、“cao”表示仅正确答案等缩写。这些缩写告诉你如果前面答案有误但方法正确，后面的分数是否仍可获得。
| Mark Code | Meaning | 中文含义 |
|---|---|---|
| M1 | Method mark for a correct process | 正确步骤的方法分 |
| A1 | Accuracy mark for correct answer | 正确答案的准确性分 |
| B1 | Independent mark for statement or answer | 陈述或答案的独立分 |
| ft | Follow-through from previous error | 由前面错误延续给分 |
| oe | Or equivalent | 或等价答案 |
2. Command Words and What They Mean | 指令词及其含义
Understanding command words is essential because the mark scheme allocates marks based on what the question asks you to do. Common command words in the January 2020 Unit 2 paper include ‘Find’, ‘Show that’, ‘Solve’, and ‘Prove’.
理解指令词至关重要，因为评分方案根据题目要求的内容分配分数。2020年1月第2单元试卷中常见的指令词包括“Find（求）”、“Show that（证明）”、“Solve（解）”和“Prove（证明）”。
‘Find’ usually means you need to show working and obtain a specific value or expression. ‘Show that’ means the answer is given in the question, so you must provide a complete method that leads to that given result without skipping steps.
“Find”通常意味着你需要展示过程并得到具体数值或表达式。“Show that”意味着答案已在题目中给出，因此你必须提供完整步骤，得出该给定结果，不能跳步。
‘Solve’ requires you to find all possible values that satisfy an equation or inequality. ‘Prove’ is more formal and expects a logical argument, often using algebra or identities, rather than a simple calculation.
“Solve”要求你找出满足方程或不等式的所有可能值。“Prove”更正式，要求逻辑论证，通常使用代数或恒等式，而不是简单计算。
- Find: obtain a result, show working.
- Show that: derive a given result fully.
- Solve: find all values satisfying a condition.
- Prove: give a logical algebraic or geometric argument.
- Find：得到结果，展示过程。
- Show that：完整推导给定结果。
- Solve：找出满足条件的所有值。
- Prove：给出逻辑代数或几何论证。
3. Algebra and Functions: Marking Focus | 代数与函数：评分重点
Algebraic manipulation attracts many M1 and A1 marks in Unit 2. In January 2020, candidates needed to simplify rational expressions, solve quadratic inequalities, and use the discriminant efficiently.
代数运算在第2单元中获得大量M1和A1分。2020年1月考试中，考生需要化简有理式、解二次不等式，并高效使用判别式。
For a quadratic inequality such as x² – 5x + 6 ≤ 0, the mark scheme often gives M1 for factorising into (x – 2)(x – 3), M1 for identifying critical values 2 and 3, and A1 for writing the correct interval 2 ≤ x ≤ 3.
对于二次不等式如x² – 5x + 6 ≤ 0，评分方案通常给M1分用于因式分解为(x – 2)(x – 3)，再给M1分用于识别临界值2和3，最后给A1分用于写出正确区间2 ≤ x ≤ 3。
The discriminant Δ = b² – 4ac is a common source of method marks. If a question asks you to show that a quadratic has no real roots, you must set Δ < 0, substitute correctly, and simplify to the required form.
判别式Δ = b² – 4ac是方法分的常见来源。如果题目要求证明二次函数没有实数根，你必须令Δ < 0，正确代入并化简到所需形式。
When completing the square, examiners look for the correct format (x + p)² + q. A sign error in p or q can lose the A1 accuracy mark even if the method is correct.
配方时，考官会检查正确格式(x + p)² + q。p或q的符号错误即使方法正确也会丢失A1准确性分。
4. Coordinate Geometry and Circles | 坐标几何与圆
Questions on straight lines and circles are frequent in AS Unit 2. The mark scheme rewards finding the midpoint, gradient, perpendicular gradient, and equation of a line in a structured way.
直线与圆的题目在AS第2单元中经常出现。评分方案对求中点、斜率、垂直斜率以及直线方程的过程有结构化给分。
For a circle equation given as x² + y² – 6x + 4y – 12 = 0, you might be asked to find its centre and radius. The mark scheme gives M1 for completing the square on x and y, and A1 for stating the centre (3, -2) and radius 5.
对于圆方程x² + y² – 6x + 4y – 12 = 0，你可能需要求圆心和半径。评分方案给M1分用于对x和y配方，给A1分用于写出圆心(3, -2)和半径5。
When finding the equation of a tangent to a circle, the key step is using the fact that the tangent is perpendicular to the radius. You must identify the gradient of the radius, then use the negative reciprocal for the tangent gradient.
求圆的切线方程时，关键步骤是利用切线与半径垂直这一事实。你必须找出半径的斜率，然后取其负倒数作为切线斜率。
Marks are often lost when candidates use the wrong sign for the perpendicular gradient or substitute into the line equation incorrectly. Write y – y₁ = m(x – x₁) clearly, and check your arithmetic.
考生常因垂直斜率符号错误或代入直线方程时出错而丢分。清晰写出y – y₁ = m(x – x₁)并检查计算。
5. Trigonometry: Exact Values and Graphs | 三角函数：精确值与图像
Trigonometry in Unit 2 requires fluency with exact values for angles such as 30°, 45°, and 60°, as well as the ability to solve simple trigonometric equations in a given interval.
第2单元的三角函数要求熟练掌握30°、45°、60°等角度的精确值，以及能在给定区间内解简单三角方程。
The mark scheme typically awards B1 for stating sin 45° = √2/2 or cos 60° = 1/2 without working. For equation solving, M1 is given for rearranging to sinθ = k, M1 for finding one correct value, and A1 for all values in the interval.
评分方案通常给B1分用于直接写出sin 45° = √2/2或cos 60° = 1/2。解方程时，M1分用于变形为sinθ = k，再给M1分用于求出一个正确值，最后给A1分用于写出区间内所有值。
When solving 2sinθ – 1 = 0 for 0° ≤ θ ≤ 360°, the steps are: sinθ = 1/2, θ = 30° and θ = 150°. The mark scheme often expects both values; giving only 30° loses the final A1.
解方程2sinθ – 1 = 0（0° ≤ θ ≤ 360°）时，步骤为：sinθ = 1/2，θ = 30°和θ = 150°。评分方案通常要求两个值；只写30°会丢失最后A1分。
Sketching trigonometric graphs may also appear. You must label key points such as maximum, minimum, and intercepts accurately because these are often independent B1 marks.
画三角图像也可能出现。你必须准确标出最大值、最小值与截距等关键点，因为这些通常是独立B1分。
6. Exponentials and Logarithms | 指数与对数
Exponential and logarithmic questions often combine algebraic manipulation with graph interpretation. In January 2020, candidates needed to convert between exponential and logarithmic form and solve equations involving eˣ and ln x.
指数与对数题目通常将代数运算与图像解读相结合。2020年1月考试中，考生需要在指数形式与对数形式之间转换，并解涉及eˣ和ln x的方程。
The mark scheme gives M1 for taking logarithms of both sides correctly, M1 for using the power rule log(aᵇ) = b log a, and A1 for solving to a specified number of significant figures.
评分方案给M1分用于正确对两边取对数，再给M1分用于使用幂法则log(aᵇ) = b log a，最后给A1分用于按指定有效数字求解。
A typical question is: Solve 3e²ˣ = 15. The method is to divide by 3, take natural logs, and then divide by 2. Each step carries a mark, so show your working clearly.
典型题目如：解方程3e²ˣ = 15。方法是先除以3，取自然对数，再除以2。每一步都有分，因此要清楚展示过程。
When using ln and e as inverse operations, remember that ln(eʸ) = y. This identity is often the key to releasing both method and accuracy marks.
使用ln与e互为逆运算时，记住ln(eʸ) = y。这一恒等式通常是获得方法分和准确性分的关键。
7. Differentiation and Integration | 微分与积分
Calculus is a large part of Unit 2, and the mark scheme rewards systematic application of rules. For differentiation, you must bring down the power and reduce the exponent: d/dx (xⁿ) = n xⁿ⁻¹.
微积分是第2单元的重要内容，评分方案奖励系统应用规则。求导时，必须降幂并减少指数：d/dx (xⁿ) = n xⁿ⁻¹。
For example, differentiating y = 4x³ – 3x² + 2x – 7 gives dy/dx = 12x² – 6x + 2. The mark scheme often gives M1 for each power differentiated correctly and A1 for a fully correct derivative.
例如，对y = 4x³ – 3x² + 2x – 7求导得到dy/dx = 12x² – 6x + 2。评分方案通常对每个正确求导的幂给M1分，对完全正确的导数给A1分。
Integration is marked similarly: ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + c. Do not forget the constant of integration, as omitting ‘+ c’ usually loses the A1 mark for indefinite integrals.
积分评分类似：∫ xⁿ dx = xⁿ⁺¹/(n + 1) + c。不要忘记积分常数，因为省略“+ c”通常会丢失不定积分的A1分。
Applied calculus questions may ask for the gradient of a curve at a point or the area under a curve. You must substitute correctly and simplify fully to earn the final accuracy marks.
应用微积分题目可能要求求曲线在某点的斜率或曲线下的面积。你必须正确代入并完全化简才能获得最终准确性分。
d/dx (xⁿ) = n xⁿ⁻¹ and ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + c
8. Vectors and Kinematics in Applied Questions | 应用题的向量与运动学
If Unit 2 includes mechanics, vector and kinematics questions appear with a focus on correct substitution into suvat equations. The mark scheme rewards identifying known values, choosing the correct equation, and solving for the unknown.
如果第2单元包含力学，向量和运动学题目会出现，重点在于正确代入suvat方程。评分方案奖励识别已知量、选择正确方程并求解未知量。
For example, with initial velocity u = 2 m s⁻¹, acceleration a = 3 m s⁻², and time t = 4 s, the displacement s is found using s = ut + ½at². M1 is given for substituting, M1 for simplifying, and A1 for s = 32 m.
例如，初速度u = 2 m s⁻¹，加速度a = 3 m s⁻²，时间t = 4 s，位移s使用s = ut + ½at²求得。M1分用于代入，M1分用于化简，A1分用于s = 32 m。
Vector questions often ask for magnitude or direction. The magnitude of vector a = 3i + 4j is √(3² + 4²) = 5. The mark scheme gives B1 for the correct magnitude and may give M1 for use of Pythagoras.
向量题常要求大小或方向。向量a = 3i + 4j的大小为√(3² + 4²) = 5。评分方案给B1分用于正确大小，也可给M1分用于使用勾股定理。
Always include units where applicable, as A1 marks in applied questions often require correct units such as m, s, or m s⁻¹.
在适用处始终写明单位，因为应用题的A1分通常要求正确单位，如m、s或m s⁻¹。
9. Common Errors and Mark Loss | 常见错误与失分点
The mark scheme reveals the most common places where candidates lose marks. These include sign errors, missing constants of integration, premature rounding, and incomplete final answers.
评分方案揭示了考生最常失分的地方。这些包括符号错误、遗漏积分常数、过早四舍五入以及最终答案不完整。
Premature rounding is especially costly in trigonometry and exponential questions. If you round sinθ = 0.7 to 0.7 too early, your final angle may be outside the accepted range and lose A1.
过早四舍五入在三角函数和指数题中代价尤其大。如果你过早将sinθ = 0.7取为0.7，最终角度可能超出可接受范围而丢失A1。
Another common error is not reading the question carefully. If the question asks for exact values, decimal approximations are not acceptable. Similarly, if it asks for answers to 3 significant figures, extra rounding loses marks.
另一个常见错误是没有仔细审题。如果题目要求精确值，小数近似是不可接受的。同样，如果要求保留3位有效数字，多余舍入会丢分。
In ‘Show that’ questions, candidates sometimes start from the given result and work backwards. This rarely earns method marks; you must derive the given result from first principles.
在“Show that”题目中，考生有时从给定结果出发反向推导。这很少能获得方法分；你必须从基本原理推导出给定结果。
10. How to Use the Mark Scheme for Revision | 如何利用评分方案复习
The January 2020 Unit 2 mark scheme is not just for teachers; it is a powerful revision tool for students. Use it to check your working against the exact steps that earn marks.
2020年1月第2单元评分方案不仅是给老师用的，也是学生强大的复习工具。用它来对照你的过程与得分的确切步骤。
After attempting a past paper, mark your answers with the scheme. Identify whether you lost method marks due to missing working or accuracy marks due to arithmetic slips.
做完真题后，用评分方案给自己判分。判断你是因为缺少过程而丢失方法分，还是因为算术失误丢失准确性分。
Create a personal error log from the mark scheme. Write down the type of mark you lost, the topic, and a corrected version of the solution. Review this log before your next practice paper.
根据评分方案制作个人错题记录。写下丢失的分数类型、所属主题以及修正后的解题过程。在下一次练习前复习该记录。
Remember that mark schemes show one accepted method, but alternative valid methods can also earn full marks. Focus on communicating your method clearly so the examiner can award M1 even if the final answer is wrong.
记住评分方案只展示一种可接受方法，但其他有效方法也能得满分。重点在于清楚地表达你的方法，以便即使最终答案错误，考官也能给M1分。
11. Example Question with Mark Breakdown | 例题与分数分配
Consider this typical Unit 2 style question: Find the coordinates of the turning point of the curve y = x² – 6x + 5, and determine whether it is a maximum or minimum.
考虑这道典型的第2单元风格题目：求曲线y = x² – 6x + 5的驻点坐标，并判断它是极大值还是极小值。
The mark scheme might allocate marks as follows: M1 for differentiating to get dy/dx = 2x – 6, M1 for setting dy/dx = 0, A1 for x = 3, A1 for y = -4, and B1 for stating minimum because the second derivative is positive.
评分方案可能如下分配分数：M1分用于求导得到dy/dx = 2x – 6，M1分用于令dy/dx = 0，A1分用于x = 3，A1分用于y = -4，以及B1分用于根据二阶导数为正判断为极小值。
Notice that the method marks are separate from the accuracy marks. Even if you make an arithmetic error in finding y, you can still earn M1 marks for the correct differentiation and setting dy/dx = 0.
注意方法分与准确性分是分开的。即使你在求y时出现算术错误，你仍可因正确求导和令dy/dx = 0而获得M1分。
| Step | Mark | Reason |
|---|---|---|
| dy/dx = 2x – 6 | M1 | Correct differentiation |
| 2x – 6 = 0 | M1 | Setting derivative to zero |
| x = 3 | A1 | Correct x-coordinate |
| y = -4 | A1 | Correct y-coordinate |
| Minimum | B1 | Second derivative positive |
12. Final Exam-Day Tips | 考试日最终提示
On exam day, read each question twice and underline command words. This helps you understand whether the examiner wants a full method, a final answer, or a proof.
考试当天，每道题读两遍并划出指令词。这有助于你理解考官是要求完整方法、最终答案还是证明。
Show all your working, even for simple calculations. The January 2020 mark scheme makes clear that method marks are only awarded when the examiner can see your process.
展示所有过程，即使是简单计算。2020年1月评分方案明确说明，只有考官能看到你的过程时才会给方法分。
Manage your time by attempting every question. Even if you cannot complete a problem, writing a correct first step can earn M1 marks and build your total.
合理分配时间，尝试每道题。即使不能完整解出，写下一个正确的第一步也能获得M1分并增加总分。
Finally, check your answers against the mark scheme language. If the question says ‘exact value’, leave your answer in surd or π form; if it says ‘3 significant figures’, round only at the final step.
最后，根据评分方案语言检查答案。如果题目说“精确值”，请保留根号或π形式；如果说“3位有效数字”，只在最后一步舍入。
Published by TutorHao | AS AQA Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导