AS AQA Mathematics Unit 5 Mark Scheme Jun19 | AS AQA 数学 Unit 5 2019年6月评分方案解析

📚 AS AQA Mathematics Unit 5 Mark Scheme Jun19 | AS AQA 数学 Unit 5 2019年6月评分方案解析

The June 2019 Unit 5 mark scheme from AQA AS Mathematics is more than a set of answers. It is a map of how marks are awarded, showing where method credit begins, where accuracy is essential, and where a correct final answer without supporting working may still gain a mark. Understanding this map helps students answer exam questions in the way that examiners expect.

2019年6月AQA AS数学Unit 5评分方案不仅仅是一份答案，更是一幅得分地图，标明了方法分从哪里开始、准确分在何处至关重要，以及仅有正确最终答案而无过程时能否得分。理解这张地图，可以帮助考生按照考官期望的方式作答。

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1. Understanding the Structure of the Mark Scheme | 理解评分方案的结构

AQA mark schemes are organised into a grid of statements. Each statement corresponds to a visible step in a model solution. Marks are usually labelled M for method, A for accuracy, B for a mark given independently of a method, and sometimes R for a reason required in a proof. The June 2019 Unit 5 scheme follows this pattern, so the first step is to identify which label applies to the step you have written.

AQA评分方案以表格形式组织，每个陈述对应模型解题中的一个可见步骤。分数通常用M表示方法分，A表示准确分，B表示不依赖方法而独立给予的分，有时R表示证明中需要给出的理由。2019年6月Unit 5评分方案遵循这一模式，因此第一步就是判断你所写步骤对应哪个标签。

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2. Method Marks: How to Earn the M | 方法分：如何拿到M分

A method mark is awarded for attempting an appropriate procedure, even if the arithmetic is wrong. For example, when asked to solve a quadratic equation, writing x = (-b ± √(b² – 4ac)) / (2a) and substituting the coefficients correctly would earn the M mark before any simplification. In the mark scheme, M marks are often described by phrases such as “correct method seen” rather than “correct answer obtained”.

方法分奖励的是尝试了正确步骤，即使计算有误。例如，解一元二次方程时，写出求根公式 x = (-b ± √(b² – 4ac)) / (2a) 并正确代入系数，在化简之前就可以获得M分。评分方案中的M分通常用“已看到正确方法”而不是“已得出正确答案”来描述。

To protect your M marks, always show the algebraic step that indicates the method. A silent calculator result is much less safe than a written substitution. In the 2019 scheme, several M marks require an explicit line of working before the final answer, so do not skip that line.

要保住M分，务必写出能表明方法的代数步骤。只写计算器结果远不如写出代入过程安全。在2019年的评分方案中，多项M分都要求最终答案之前有明确的工作步骤，因此切勿省略这一步。

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3. Accuracy Marks: The Value of the A | 准确分：A分的价值

An accuracy mark is awarded only when a correct result or expression follows from the previous method mark. For example, after correctly differentiating y = x³ + sin x, the derivative dy/dx = 3x² + cos x may carry an A mark. If you write the correct derivative of one term but make an error on the second, the A mark is lost, though the M mark for applying the differentiation rules may remain.

准确分仅在前一个方法分成立后，得到正确结果或表达式时授予。例如，正确求导 y = x³ + sin x 后，导数 dy/dx = 3x² + cos x 可以拿A分。如果你写对了一项的导数，但第二项出错，则A分丢失，但应用求导规则的M分可能保留。

Mark schemes also use “DM” for a mark that depends on a preceding method mark. In Unit 5, a follow-through error can still allow a DM mark if the later work is consistent with your earlier wrong result. The 2019 scheme clearly states where FT (follow-through) is allowed.

评分方案还使用“DM”表示依赖前一个方法分的分数。在Unit 5中，只要后续步骤与前面错误结果保持一致，仍然可以获得DM分。2019年的方案明确注明了哪些地方允许FT（跟进给分）。

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4. Correct Answer with Working: B marks | 无过程正确答：B分

Some questions give a mark for the correct answer even when no method is shown. These are B marks. In AQA schemes, B marks typically appear on short factual questions or where a value can be read directly from a graph or table. However, do not assume every correct answer will earn all marks; in longer questions, method marks dominate and a bare answer may gain only one mark.

有些题目只要答案正确，即使没有过程也给分，这就是B分。在AQA方案中，B分通常出现在简短的纯事实题，或可以直接从图表读出的数值上。但不要认为每个正确答案都会拿到全部分数；在较长的题目中，方法分占主导，只写答案可能只能得1分。

For example, if a question asks for the value of P(X < 2) and you simply state 0.841, you may receive a B mark. But if the question asks you to show that the mean of a distribution is 4.2, the B mark alone will not be enough; you must provide the calculation that the scheme expects.

例如，如果题目要求 P(X < 2) 的值，你直接写出0.841可能获得一个B分。但如果题目要求证明分布的均值为4.2，仅靠B分远远不够，你必须写出评分方案所要求的计算。

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5. Common Pitfalls in Algebraic Manipulation | 代数运算中的常见失分点

The June 2019 Unit 5 scheme highlights several algebraic errors that caused lost marks. A common one is solving 3x – 2 = 7 incorrectly: some candidates wrote 3x = 7 – 2, losing the M mark for an incorrect rearrangement. The correct line is 3x = 7 + 2, then x = 3. The mark scheme expects the sign change to be shown explicitly.

2019年6月Unit 5评分方案重点指出了几个导致失分的代数错误。常见的错误是解 3x – 2 = 7 时写成 3x = 7 – 2，由于移项错误而丢失M分。正确步骤是 3x = 7 + 2，然后 x = 3。评分方案期望符号变化被明确写出。

3x – 2 = 7 → 3x = 7 + 2 → x = 3

Another pitfall is forgetting to simplify surds or cancelling incorrectly. For example, √(4 + 9) is sometimes written as √4 + √9 = 5, which is mathematically false. The correct value is √13. Examiners award no method mark for a false algebraic law, so always check that your manipulation preserves equality.

另一个错误是忘记化简根式或错误约分。例如，√(4 + 9) 有时被写成 √4 + √9 = 5，这在数学上是错误的，正确值是 √13。考官不会为错误的代数法则提供方法分，因此请检查你的变形是否保持等式。

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6. Function Transformations and Coordinates | 函数变换与坐标

Transforming graphs is a core AS topic. In the 2019 Unit 5 scheme, a typical question might ask for the image of the point (3, -2) after applying y = f(x) + 4. The mark scheme awards one method mark for adding 4 to the y-coordinate and one accuracy mark for writing (3, 2). Some candidates incorrectly add to the x-coordinate and lose both marks.

图形变换是AS核心主题。在2019年Unit 5评分方案中，典型题目可能是求点 (3, -2) 在 y = f(x) + 4 变换后的像。评分方案给一个方法分用于将y坐标加4，给一个准确分用于写出 (3, 2)。有些考生错误地加在x坐标上，导致两个分都丢失。

y = f(x) + a → translation vector (0, a); y = f(x + a) → translation vector (-a, 0)

For the same reason, a question on y = f(2x) requires you to divide the x-coordinate by 2. The mark scheme often contains a note that a correct transformation without a written or drawn original graph is still credited, but any incorrect coordinate after a correct operation is penalised.

同样，关于 y = f(2x) 的问题需要你将x坐标除以2。评分方案经常注明，即使没有写出或画出原图，只要变换正确仍给分，但在正确操作后出现错误坐标会被扣分。

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7. Differentiation: Following the Chain of Marks | 微分：顺着分数链取分

In a differentiation question, the mark scheme usually splits the process into separate M and A marks. For example, find dy/dx for y = (2x – 1)⁴. The first M is for applying the chain rule, the second M for multiplying by the derivative of the inner function, and the A is for the final simplified expression.

在微分题中，评分方案通常将过程分成独立的M和A分。例如，求 y = (2x – 1)⁴ 的 dy/dx。第一个M分是应用链式法则，第二个M分是乘以内层函数的导数，A分是最终简化表达式。

dy/dx = 4(2x – 1)³ × 2 = 8(2x – 1)³

The 2019 scheme reveals that many candidates forgot the factor 2, so they earned the first M but not the second M or the A. To collect all marks, write each step: “dy/dx = 4(2x – 1)³ × d/dx(2x – 1)” before simplifying. This makes the chain rule visible.

2019年的方案显示许多考生忘记因子2，只得到第一个M分，未得到第二个M分和A分。要拿满分，请在化简前写下每一步：“dy/dx = 4(2x – 1)³ × d/dx(2x – 1)”，让链式法则显式可见。

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8. Integration: Constant of Integration and Limits | 积分：积分常数与上下限

Indefinite integration questions in Unit 5 always require an arbitrary constant, usually written as + c. Omitting the constant loses an A mark even if the integral is otherwise correct. For example, ∫(3x² + 2) dx = x³ + 2x + c. The mark scheme checks for the constant as a separate accuracy mark.

Unit 5中的不定积分题总是需要写上任意常数，通常写成 + c。即使积分本身正确，漏掉常数也会丢失一个A分。例如，∫(3x² + 2) dx = x³ + 2x + c。评分方案将常数作为一个独立的准确分检查。

For definite integrals, the scheme expects substitution of the upper limit minus the lower limit. A common error is forgetting to subtract after substituting. If F(x) is an antiderivative, then the correct working is F(b) – F(a), and the mark scheme gives a method mark for seeing this subtraction explicitly.

对于定积分，评分方案期望用上限代入减下限代入。常见错误是在代入后忘记相减。若 F(x) 是一个原函数，则正确步骤是 F(b) – F(a)，评分方案给出方法分的前提是看到明确的相减步骤。

∫ₐᵇ f(x) dx = [F(x)]ₐᵇ = F(b) – F(a)

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9. Statistics: Probability Distribution Notation | 统计：概率分布符号

Unit 5 may contain statistics content. The mark scheme is strict about notation. For example, if X ~ B(10, 0.3), then P(X ≤ 2) is not the same as P(X < 2). Writing the correct inequality symbol is part of the accuracy mark. The 2019 scheme penalises a missing "≤" because it changes the probability value.

Unit 5可能包含统计内容。评分方案对符号要求严格。例如，若 X ~ B(10, 0.3)，则 P(X ≤ 2) 与 P(X < 2) 不同。写出正确的不等号是准确分的一部分。2019年方案对漏写“≤”进行扣分，因为它会改变概率值。

When using the normal distribution, you should state Z = (X – μ)/σ in your working. Many mark schemes award a method mark for this standardisation step, even if the subsequent table reading is inaccurate. Writing the formula also helps you decide whether to add or subtract 0.5 for continuity correction.

使用正态分布时，你应在过程中写出 Z = (X – μ)/σ。许多评分方案会为这个标准化步骤给方法分，即使后续查表不准确。写出公式也有助于你判断是否需要进行连续性修正，即加上或减去0.5。

Z = (X – μ)/σ

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10. Using the Mark Scheme Effectively for Revision | 高效利用评分方案复习

Do not simply read the mark scheme after a past paper. Instead, try to match every line of your solution to a mark in the scheme. If you missed a mark, ask which label was attached to the part you missed: M, A, B or R. This tells you whether your problem was choosing the wrong method, making a calculation error, or failing to supply a reason.

做完一套真题后，不要只看评分方案。试着把你答案中的每一行与方案中的每个分对应起来。如果你丢了分，就问自己丢的那一分的标签是M、A、B还是R。这能告诉你问题出在选择错误方法、计算失误，还是未能提供理由。

In the countdown to the exam, use mark schemes to build a checklist of common command words: “show”, “hence”, “verify”. The word “show” often requires a full derivation, while “verify” can be satisfied by substitution. The June 2019 scheme explicitly marks a question with “show that” where an unsupported answer cannot receive full credit.

在考前冲刺阶段，利用评分方案建立常见指令词清单：“show”、“hence”、“verify”。“show”通常需要完整推导，而“verify”可通过代入满足。2019年6月方案中有一道“show that”的题目，仅给出答案无法获得满分。

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Published by TutorHao | Mathematics Revision Series | aleveler.com

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