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AS AQA Further Mathematics Unit 2 Mark Scheme (June 2022): An Examiner's Guide | AS AQA 进阶数学第二卷评分标准解析（2022年6月）

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📚 AS AQA Further Mathematics Unit 2 Mark Scheme (June 2022): An Examiner's Guide | AS AQA 进阶数学第二卷评分标准解析（2022年6月）

The June 2022 AS AQA Further Mathematics Paper 2 (7366/2) carries 80 marks and lasts 1 hour 30 minutes. It tests the applied content of the AS specification: Mechanics, Statistics or Discrete, depending on your option route. This article unpacks the mark scheme: how examiners award method, accuracy and interpretation marks, and how you can convert that knowledge into higher scores in future sittings.

2022年6月AS AQA进阶数学第二卷（7366/2）满分80分，时长1小时30分钟，考查AS大纲中的应用数学内容，具体为力学、统计或离散数学，取决于你选择的模块路线。本文将深入解析评分标准：考官如何分配方法分、准确分与解释分，以及你如何利用这些规则在未来的考试中提高得分。

1. The Structure of the Unit 2 Mark Scheme | 第二卷评分标准的整体结构

The published mark scheme for 7366/2 is organised as a table. Each row contains the question part, the marking instruction (for example "M1 for ...", "A1 for ..."), the number of marks, and a comment column. Read the comment column carefully: it tells you which errors are condoned and which are fatal.

7366/2的官方评分标准以表格形式呈现。每一行包含题目序号、评分说明（例如"M1用于……"、"A1用于……"）、分值以及备注栏。务必仔细阅读备注栏，它会说明哪些错误可以容忍，哪些错误会导致整题丢分。

Marks are grouped by Assessment Objective. AO1 rewards correct use of techniques, AO2 rewards reasoning and problem-solving, and AO3 rewards mathematical communication and interpretation. In the June 2022 series, roughly 60% of Paper 2 marks targeted AO1 and 40% targeted AO2/AO3.

分数按评估目标分组：AO1考查技巧的正确运用，AO2考查推理与问题解决能力，AO3考查数学表达与解释。在2022年6月考试中，第二卷约60%的分数属于AO1，40%属于AO2/AO3。

A key skill is learning to read a mark scheme like an examiner. When an answer is wrong but the method is visible, method marks are still awarded. A bare answer with no working receives zero unless the row says "CAO" (correct answer only). Show every substitution and every solved equation.

一项关键技能是学会像考官一样阅读评分标准。当答案错误但方法可见时，方法分仍然有效。如果只有孤零零的答案而没有过程，除非该行标注"CAO"（仅限正确答案），否则只能得0分。务必展示每一步代入和每一步解方程的过程。

2. M, A, B and E Marks: What Each Symbol Means | M、A、B、E各类分数符号的含义

AQA uses a small set of symbols in the mark scheme. Knowing them prevents confusion when you self-mark. The table below summarises the convention used throughout the June 2022 paper.

AQA在评分标准中使用少量固定符号。弄清这些符号可以避免自评时的混乱。下表总结了2022年6月试卷中通篇使用的标记约定。

Symbol Meaning Typical example
M1 Method mark: correct method, even with a numerical slip Writing m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for a collision
A1 Accuracy mark: correct result following correct method Solving to v₁ = 2.5 m⁻¹
B1 Independent mark: given for a correct statement or value Stating X ~ Po(2.5) correctly
E1 Explanation / conclusion mark, usually in context "There is sufficient evidence to reject H₀"
ft Follow through: use the candidate's previous value Using a wrong λ but testing correctly

In the June 2022 scheme, many Mechanics rows combined an M1 with an A1: one for building the correct momentum equation and one for the correct velocity. If you wrote the equation with a sign error, you lost the A1 immediately, and often lost subsequent A1 marks as well.

在2022年6月的评分标准中，许多力学题将M1与A1搭配使用：一个用于列出正确的动量方程，另一个用于得到正确的速度。如果你的方程出现符号错误，会立刻失去A1，通常会连带丢失后续所有A1。

The abbreviation "oe" means "or equivalent" — the mark scheme does not demand one fixed method. "awrt" means "answer which rounds to", giving you leeway of a few units in the last digit. Both appear frequently on the June 2022 applied paper.

"oe"表示"或等价表述"，即评分标准不要求唯一固定的解法。"awrt"表示"四舍五入后接近的答案"，在末位上留有一定容差。两者在2022年6月的应用数学试卷中频繁出现。

3. Mechanics Option: Momentum and Collisions | 力学模块：动量与碰撞

Collision questions were the backbone of the Mechanics option in June 2022. The typical set-up is two spheres of masses m and 2m moving along the same line. The mark scheme rewards a disciplined order of working: define positive direction, write the momentum equation, write Newton's Experimental Law, then solve simultaneously.

碰撞问题是2022年6月力学模块的主干。典型情境是两个质量分别为m和2m的球体沿同一直线运动。评分标准鼓励有条理的解题顺序：定义正方向、写出动量方程、写出牛顿碰撞实验定律，再联立求解。

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

e = (speed of separation) ÷ (speed of approach)

Candidates who wrote NEL with a missing minus sign or a wrong order of velocities lost the A1 on that row, even if their substitution was otherwise faultless. The mark scheme for June 2022 awarded a full method chain only when both principles were stated in symbolic form before numbers were substituted.

如果考生在写牛顿实验定律时漏掉负号或颠倒了速度的顺序，即使代入计算完全正确，该行A1也会失去。2022年6月的评分标准要求先在符号层面完整写出两个原理，然后才代入数值，否则无法获得完整方法链。

A typical mark breakdown for a two-sphere collision, worth 6–7 marks, is shown below. Notice that the final speed each sphere is worth its own A1, because a sign error on one does not necessarily imply a sign error on the other.

一道典型的双球碰撞题通常占6–7分，典型分值分布如下表。注意：每个球体的最终速度各自独立占一个A1，因为其中一个符号错误并不必然意味着另一个也错。

Working step Mark
Conservation of momentum equation M1 A1
Newton's Experimental Law equation M1 A1
Solving to v₁ A1
Solving to v₂ A1
Stating both final directions E1 (context)

e final E1 was often missed. After computing v₁ = 1.2 m⁻¹ and v₂ = 0.8 m⁻¹, you must state "in the original direction of motion of A" or "in the opposite direction" interpretation mark. In June 2022, many otherwise correct solutions lost this single mark.

最后的E1常常被忽略。算出v₁ = 1.2 m⁻¹和v₂ = 0.8 m⁻¹之后，还必须注明"沿A原运动方向"或"沿相反方向"，否则考官无法给出解释分。2022年6月，许多本来正确的解答就栽在这1分上。

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4. Mechanics Option: Work, Energy and Power | 力学模块：功、能与功率

Energy questions on the June 2022 paper required the work–energy principle. The mark scheme always looked first for a correct energy statement: the total initial energy plus work done equals the total final energy. Writing this as one symbolic equation before substituting numbers is the single most reliable way to secure the method marks.

2022年6月试卷中的能量问题要求使用功能原理。评分标准首先寻找正确的能量表达式：初始总能量加上外力做功等于末态总能量。在代入数值前，先用符号写出这个单一方程，是锁定方法分最可靠的做法。

Work done = F × s

Kinetic energy = ½mv²

Gravitational potential energy = mgh

resent; the scheme therefore required an explicit statement that the vehicle was moving at constant speed before awarding the power method mark.

功率题占比不大但反复出现。关键公式是恒定驱动力下的P = Fv，评分标准的第一行就是要求正确写出这一关系。2022年6月一个常见错误是：物体仍有加速度时却使用P = W/t。因此评分标准要求先明确说明车辆匀速运动，才给出功率方法分。

hod mark survived but the accuracy mark fell. Write all conversions in the working column: "30 km/h = 30 × 1000 ÷ 3600 = 8.33 m/s" earns reassurance to the examiner and protects your argument.

单位换算错误通常在A1阶段受罚而不是M1阶段。如果你把以km/h为单位的速度当作m/s代入，方法分得以保留，准确分却会丢失。请在解题区写出换算过程："30 km/h = 30 × 1000 ÷ 3600 = 8.33 m/s"，这既能取信于考官，也能保护你的得分链。

5. Statistics Option: Discrete Random Variables | 统计模块：离散随机变量

In the Statistics route, discrete random variables earned high marks in June 2022. The mark scheme commonly started with a B1 for writing down the probability distribution in table form with all probabilities between 0 and 1 summing to 1. This single table unlocks every subsequent calculation.

在统计路线中，离散随机变量在2022年6月占了很大分值。评分标准通常以B1开始，要求以表格形式写出概率分布，所有概率在0与1之间且总和为1。这一张表会解锁后续所有计算。

E(X) = Σ xⱼ P(X = xⱼ)

Var(X) = E(X²) − (E(X))²

olumn, simply squaring the x-values, lost the method mark. Always display the column for xⱼ, then the column for xⱼP(X = xⱼ), then the column for xⱼ²P(X = xⱼ).

2022年6月的评分标准分别给E(X)和E(X²)设置方法分。如果只对x值取平方而没有乘概率列，就会丢失方法分。务必展示xⱼ列、xⱼP(X = xⱼ)列以及xⱼ²P(X = xⱼ)列。

The mark scheme also awarded an E1 for commenting on the variance: for example, stating that Var(X) cannot be negative, used as a check on a computed value. Showing the check demonstrates AO3 communication and is nearly always worth a small independent mark.

评分标准还会给方差相关评论一个E1：例如说明Var(X)不可能为负，以此检验计算结果。展示这样的检验体现了AO3的数学交流能力，几乎总能拿到一个独立的分数。

6. Statistics Option: Poisson Model and Hypothesis Testing | 统计模块：泊松模型与假设检验

Poisson questions appeared both as probability calculations and as the basis for a hypothesis test. The June 2022 mark scheme required the distribution to be stated explicitly in the form X ~ Po(λ), earning a B1 before any probability was computed.

泊松问题既出现在概率计算中，也作为假设检验的基础。2022年6月的评分标准要求先明确写出分布形式X ~ Po(λ)，这本身就是B1，之后才开始计算概率。

P(X = r) = e⁻λ × λʳ ÷ r!

For hypothesis tests, the mark scheme followed a fixed five-part template, and each part was separately marked:

对于假设检验，评分标准遵循固定的五步模板，每一步单独计分：

The final conclusion mark was an E1 in June 2022 and required the context word (for example "the rate of arrivals"). A conclusion that said only "reject H₀" without mentioning the real-world situation lost this mark entirely.

2022年6月中的最后结论分属于E1，必须包含情境关键词（例如"到达率"）。如果结论只写"拒绝H₀"而不联系实际背景，会整分丢失。

7. Discrete Option: Algorithms and Critical Paths | 离散模块：算法与关键路径

For the Discrete route, the June 2022 paper included shortest-path and scheduling questions. The mark scheme here is strictly procedural: each correctly selected edge in Kruskal's algorithm or each correctly completed Dijkstra label box earns a distinct B1. There are no method marks "in general", only marks for observed correct actions.

对于离散路线，2022年6月的试卷包含最短路与排程调度问题。这里的评分标准是严格程序性的：在Kruskal算法中每正确选取一条边，或在Dijkstra算法中每正确完成一个标签框，都单独获得一个B1。这里没有笼统的方法分，只有针对具体正确操作的分数。

In Dijkstra's algorithm, the June 2022 scheme showed the complete labelling table: each vertex rows with temporary labels, and the final permanent label circled. If you only wrote the final distances without the temporary workings, you earned the answer mark but lost all the working marks — often three or four marks in one question.

在Dijkstra算法中，2022年6月的评分标准展示了完整的标注表：每个顶点的多行临时标号，以及最终圈出的永久标号。如果只写出最终距离而不展示临时标号过程，你只能拿到答案分，却会失去所有过程分——一道题往往因此损失3到4分。

For critical path analysis, the mark scheme distinguished between the forward pass and the backward pass. The earliest start times and latest finish times formed two separate B-groups. A single arithmetic error in the forward pass usually cost only the A1 for that box, while follow-through marks protected your backward pass if you used your own forward values consistently.

对于关键路径分析，评分标准区分正向遍历与反向遍历：最早开始时间与最迟完成时间分别构成两组B分。正向遍历中的单个计算错误通常只损失该格的A1；只要你前后一致地使用自己的正向数值，后续的反向遍历仍受follow-through分数保护。

8. Common Errors Exposed by the June 2022 Mark Scheme | 2022年6月评分标准揭示的常见错误

Studying the examiner's report alongside the mark scheme reveals a short list of recurring errors. Each one maps directly onto lost rows in the scheme.

将考官报告与评分标准对照阅读，会发现一份反复出现的错误清单。每一条都直接对应评分标准中丢失的行。