AQA AS Mathematics Unit 2 June 2019 Paper Walkthrough | AQA AS 数学 Unit 2 2019年6月试卷解析

📚 AQA AS Mathematics Unit 2 June 2019 Paper Walkthrough | AQA AS 数学 Unit 2 2019年6月试卷解析

The AQA AS Mathematics Unit 2 paper, formally numbered 7356/2, is the second of two papers in the AS qualification. It covers statistics and mechanics, with a total of 80 marks and a time allowance of 1 hour 30 minutes. In June 2019, candidates were expected to use an approved graphics calculator and the AQA formulae booklet throughout the paper.

AQA AS 数学 Unit 2 试卷（编号 7356/2）是 AS 资格证书中两张试卷中的第二张，涵盖统计与力学两大板块，总分 80 分，考试时间 1 小时 30 分钟。2019 年 6 月的考试中，考生全程可使用认可的图形计算器和 AQA 公式表。

1. Exam Structure and Assessment Objectives | 试卷结构与评估目标

The June 2019 paper was divided into two clear sections. Section A focused on statistics and Section B focused on mechanics. Questions ranged from short single-part items worth 2–3 marks to extended multi-part problems worth 8–10 marks. The paper tested knowledge, application, and problem-solving in equal measure.

2019 年 6 月的试卷清晰地分为两个部分：A 部分考查统计，B 部分考查力学。题目既包括 2–3 分的简短小题，也包括 8–10 分的多步综合大题。试卷均衡地考查了知识理解、应用技巧和问题解决能力。

Section	Topics	Approximate marks
A	Statistics: sampling, data, probability, binomial, hypothesis testing	40
B	Mechanics: kinematics, forces, Newton’s laws	40

2. Statistical Sampling Techniques | 统计抽样方法

The statistics section often opened with a question on sampling. In June 2019, candidates needed to identify the most appropriate sampling method for a given context and justify their choice. Common methods included simple random sampling, systematic sampling, and stratified sampling.

统计部分通常以抽样方法题开头。2019 年 6 月的考试中，考生需要根据给定情境判断最合适的抽样方法，并说明理由。常见方法包括简单随机抽样、系统抽样和分层抽样。

Simple random sampling: every member of the population has an equal chance of selection.
Simple random sampling（简单随机抽样）：总体中每个成员被选中的机会均等。
Stratified sampling: the population is divided into groups, then proportional samples are taken from each group.
Stratified sampling（分层抽样）：将总体分成若干层，然后从各层中按比例抽取样本。

Many students lost marks by writing ‘random’ without specifying that each selection must be independent and equally likely. In a modern exam, a clear definition and a practical example are often required.

许多学生仅仅写出“随机”而丢分，因为他们没有说明每次选择必须独立且概率相等。在现今的考试中，通常需要给出清晰的定义并配以实际例子。

3. Data Presentation and Location Measures | 数据展示与集中趋势量数

Data questions required calculating the mean, median, and standard deviation from raw data or a grouped frequency table. The formula for the standard deviation was printed in the formulae booklet, but candidates still needed to know when to use it correctly.

数据题要求从原始数据或分组频数表中计算均值、中位数和标准差。标准差公式印在公式表中，但考生仍需知道何时正确使用它。

s = √(Σ(x – x̄)² / n)

s = √(Σ(x − x̄)² / n)

For grouped data, the mid-point of each class is used as an estimate of x. In the June 2019 paper, a common error was using the class width instead of the mid-point when calculating the mean.

对于分组数据，通常使用各组中点值作为 x 的估计。2019 年 6 月的试卷中，一个常见错误是计算均值时误用了组距而不是组中点。

4. Bivariate Data and Correlation | 双变量数据与相关性

Bivariate data questions tested the interpretation of scatter diagrams and the product-moment correlation coefficient (PMCC). The PMCC, denoted r, measures the strength of a linear relationship between two variables. In June 2019, candidates were asked to comment on the value of r in context.

双变量数据题考查散点图的解读以及积矩相关系数（PMCC）。PMCC 用字母 r 表示，衡量两个变量之间线性关系的强弱。2019 年 6 月的考试要求考生结合具体情境解释 r 值。

-1 ≤ r ≤ 1

r close to 1: strong positive linear correlation.
r 接近 1：强正线性相关。
r close to -1: strong negative linear correlation.
r 接近 -1：强负线性相关。
r close to 0: weak or no linear correlation.
r 接近 0：线性相关弱或不存在。

Another part of this section involved the linear regression equation y = a + bx. Candidates had to interpret the gradient b as the change in y for each unit increase in x.

该部分还涉及线性回归方程 y = a + bx。考生需要解释斜率 b 表示 x 每增加一个单位时 y 的变化量。

5. Probability and Set Notation | 概率与集合记号

Probability questions in June 2019 required fluency with set notation such as A ∪ B and A ∩ B. The addition rule was essential, especially for overlapping events.

2019 年 6 月的概率题要求熟悉集合记号，如 A ∪ B 和 A ∩ B。加法公式尤其适用于计算有交叠的事件。

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

For conditional probability, the standard formula was tested directly in a two-way table context.

对于条件概率，考试通过双因素表直接考查标准公式的应用。

P(A | B) = P(A ∩ B) / P(B)

A common error in this area was forgetting to divide by P(B) when computing a conditional probability. Always ask: ‘out of which reduced sample space?’

这类题目最常见的错误是计算条件概率时忘记除以 P(B)。始终问自己：“分母使用哪一个缩减后的样本空间？”

6. The Binomial Distribution | 二项分布

The binomial distribution appeared prominently in the statistics section. A typical June 2019 question defined X as the number of successes in n independent trials, with constant probability p. The distribution is written as X ~ B(n, p).

二项分布在统计部分占据重要地位。2019 年 6 月的一道典型题定义 X 为 n 次独立试验中成功的次数，且每次成功的概率 p 恒定。该分布记为 X ~ B(n, p)。

P(X = r) = nCr × pʳ × (1 − p)ⁿ⁻ʳ

Candidates were expected to use the binomial probability function on their calculators for single probabilities, and to use the cumulative distribution function for questions involving ranges such as P(X ≤ 2).

考生应使用计算器的二项概率函数计算单个概率，并使用累积分布函数处理 P(X ≤ 2) 等范围概率。

In June 2019, many candidates confused ‘at most 2’ with ‘fewer than 2’. Remember: ‘at most 2’ means X ≤ 2, while ‘fewer than 2’ means X ≤ 1.

2019 年 6 月的考试中，许多考生混淆“最多 2 个”与“少于 2 个”。请记住：“最多 2 个”表示 X ≤ 2，而“少于 2 个”表示 X ≤ 1。

7. Hypothesis Testing | 假设检验

Hypothesis testing was tested using the binomial distribution. Candidates needed to set up a null hypothesis H₀ and an alternative hypothesis H₁. For a one-tailed test at a 5% significance level, the critical region was found by accumulating probabilities from the tail until the total exceeded 0.05.

假设检验通过二项分布进行考查。考生需要建立原假设 H₀ 和备择假设 H₁。对于 5% 显著水平的单尾检验，临界区域需要从尾部开始逐项累加概率，直到总概率超过 0.05。

P(Test statistic in critical region) ≤ significance level

In the June 2019 paper, a typical scenario involved testing whether a claimed probability p was realistic based on observed data. Students often lost marks by not stating the conclusion in the original context, for example ‘there is insufficient evidence to reject the manufacturer’s claim’.

2019 年 6 月的试题中，一个典型场景是根据观测数据检验某一声称的概率 p 是否合理。学生常因为未结合原题语境下结论而失分，例如应写“没有充分证据拒绝生产商的声称”。

8. Kinematics in Mechanics | 力学中的运动学

The mechanics section of June 2019 opened with kinematics. Candidates used the suvat equations for motion in a straight line under constant acceleration. The key equations are shown below.

2019 年 6 月力学部分以运动学开始。考生使用匀加速直线运动的 suvat 方程。核心方程如下。

v = u + at

s = ut + ½at²

v² = u² + 2as

When using these equations, all quantities must be measured in consistent units. For example, if acceleration is in m s⁻², then time must be in seconds and displacement in metres. A common error in June 2019 was using km/h without first converting to m/s.

使用这些方程时，所有物理量必须使用一致的单位。例如，若加速度以 m s⁻² 为单位，则时间必须用秒，位移必须用米。2019 年 6 月的一个常见错误是直接使用 km/h 而未先转换成 m/s。

For two-particle problems, drawing a clear direction of motion and assigning signs before substituting into suvat is essential.

对于双物体问题，先画出运动方向并确定正负号，再代入 suvat 方程，这一点至关重要。

9. Forces and Resultants | 力与合力

Forces questions tested the ability to form equations from force diagrams. A particle in equilibrium satisfies the condition that the resultant force is zero.

力的题目考查从受力图中列方程的能力。处于平衡状态的质点满足合力为零的条件。

ΣF = 0

For motion on a horizontal plane, Newton’s second law gives F = ma. For motion on an incline, the component of weight parallel to the plane is mg sin θ, and the perpendicular component is mg cos θ.

对于水平面上的运动，牛顿第二定律给出 F = ma。对于斜面上的运动，沿斜面方向的分力为 mg sin θ，垂直于斜面的分力为 mg cos θ。

F = ma

W = mg

In June 2019, many candidates correctly found components but then failed to include friction when forming the net force. Friction always acts to oppose the direction of motion, and its magnitude is often given by μR, where R is the normal reaction.

2019 年 6 月的考试中，许多考生能正确分解力，但在列净力方程时却漏掉了摩擦力。摩擦力总是阻碍物体运动，其大小通常为 μR，其中 R 是支持力（法向反作用力）。

10. Newton’s Third Law and Connected Particles | 牛顿第三定律与连接体

Connected particles, such as two masses joined by a string over a pulley, involve applying Newton’s second law to the whole system and to individual particles. The tension T in the string is internal when considering the whole system, but becomes an external force when considering each particle separately.

连接体问题，例如通过滑轮用细绳连接的两个物体，需要对整体系统和各物体分别应用牛顿第二定律。当考虑整体系统时，绳子中的张力 T 是内力；而当分别考虑每个物体时，T 则变为外力。

Whole system: F = (m₁ + m₂)a

Individual particle: T − f = ma

A standard exam command is ‘find the tension’. Students who solved using the whole system alone cannot find T. They must isolate one of the particles. The June 2019 paper often required exactly this two-stage approach.

考试中常见的指令是“求张力”。如果从整体系统出发，则无法求得 T，必须隔离其中一个物体。2019 年 6 月的试卷经常要求这种两阶段解法。

11. Common Pitfalls and How to Avoid Them | 常见错误与规避方法

Many mark schemes from June 2019 show a repeated pattern of lost marks. These include: using rounded values prematurely, mixing units, misreading ‘after 2 seconds’ as ‘at 2 seconds’, and forgetting to state hypotheses in symbol form.

2019 年 6 月的评分标准反映出一些反复失分模式：过早使用四舍五入的结果、单位混用、把“2 秒后”误读为“在 2 秒时”，以及忘记用符号形式写出假设。

Do not round intermediate answers. Keep at least three significant figures until the final step.
不要在中间步骤四舍五入，最后一步前至少保留三位有效数字。
Always write down the standard deviation with units, e.g. cm.
写标准差时要带上单位，例如 cm。
In mechanics, draw a labelled force diagram before writing any equations.
在力学中，先画带标注的力图，再列方程。

Another frequent issue was leaving answers as fractions instead of decimals when the question requested a specific accuracy. Check the command words carefully: ‘Give your answer to 2 decimal places’ is mandatory.

另一个常见问题是题目要求特定精度时，考生只给出分数而不化为小数。请仔细阅读指令：“答案保留两位小数”是必须遵守的。

12. Final Revision Strategy | 最终复习策略

To prepare for AQA AS Mathematics Unit 2, practice with past papers under timed conditions. Build a checklist of theorems and formulas: the binomial probability formula, the suvat equations, and Newton’s laws. Use the formula booklet in every practice session so that you know exactly where each formula appears.

备考 AQA AS 数学 Unit 2，应使用限时条件练习历年真题。建立一份定理与公式清单：二项概率公式、suvat 方程和牛顿定律。每次练习都使用公式表，以便准确知道每个公式的位置。

Focus on explaining answers in context. The examiner rewards conclusions that mention real people, products, or physical situations, not just abstract numbers. This was especially important in the June 2019 paper.

重点训练结合情境解释答案的能力。评分员更青睐提到实际人物、产品或物理情境的结论，而非抽象的数字。这一点在 2019 年 6 月的试卷中尤为重要。

Finally, revisit your mistakes. For each incorrect question, write a one-sentence note about the error: ‘forgot to subtract P(A ∩ B)’ or ‘used 9.8 instead of taking the component down the slope’. These small reminders are powerful revision tools.

最后，回顾自己的错误。对每道错题写一句错误提醒，例如“忘了减去 P(A ∩ B)”或“用了 9.8，却没有分解沿斜面的分量”。这些小贴士是非常有效的复习工具。

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AQA AS Mathematics Unit 2 June 2019 Paper Walkthrough | AQA AS 数学 Unit 2 2019年6月试卷解析