📚 AS AQA Mathematics Unit 1 (January 2022) | Exam Report and Revision Guide | AS AQA 数学 Unit 1（2022年1月）考情报告与备考指南
The January 2022 AS AQA Mathematics Unit 1 paper tested pure mathematics and statistics in a single sitting. This article summarises the main themes, reviews common errors reported by examiners, and gives a structured revision plan for future candidates.
2022 年 1 月的 AQA AS 数学 Unit 1 考卷在同一份卷子中考查了纯数学与统计。本文总结试卷重点、回顾阅卷报告中的常见错误，并为未来考生提供系统的备考方案。
In the January session, examiners reported that the paper allowed well-prepared students to show what they knew, but the middle questions caused many avoidable mistakes. The main losses appeared in multi-stage “show that” questions, incorrect sign handling, and weak statistical conclusions.
阅卷报告显示，1 月这次考试给准备充分的学生提供了足够的展示机会，但中段题目出现了大量可避免的失分。主要失分点集中在多步骤“证明/说明”题、符号处理和统计结论表述不完整。
1. Exam Overview | 试卷概览
The AS AQA Mathematics Unit 1 paper is usually 80 marks with a time allowance of 1 hour 30 minutes. The paper expects students to use a scientific or graphical calculator, and to present exact values where required.
AQA AS 数学 Unit 1 试卷通常满分 80 分，考试时间为 1 小时 30 分钟。试卷要求使用科学计算器或图形计算器，并在需要时给出精确值。
The table below summarises the main assessment areas that students should review.
下表总结了学生必须复习的主要考查板块。
| Area / 板块 | Key content / 核心内容 |
| Algebra / 代数 | Quadratics, simultaneous equations, inequalities, indices / 二次函数、联立方程、不等式、指数 |
| Coordinate geometry / 坐标几何 | Straight lines, circles, gradients / 直线、圆、斜率 |
| Sequences / 数列 | Arithmetic, geometric, binomial expansion / 等差、等比、二项展开 |
| Trigonometry / 三角学 | Exact values, equations, identities / 精确值、三角方程、恒等式 |
| Calculus / 微积分 | Differentiation, integration, stationary points / 微分、积分、驻点 |
| Statistics / 统计 | Data summary, probability, hypothesis testing / 数据概括、概率、假设检验 |
2. Algebraic Manipulation and Index Laws | 代数变形与指数法则
(x + 5) = 3x² + 15x − 2x − 10 = 3x² + 13x − 10 requires clear attention to negative signs.
2022 年 1 月考试中，很多早期得分的丢失源于展开与因式分解中的符号错误。例如 (3x − 2)(x + 5) = 3x² + 15x − 2x − 10 = 3x² + 13x − 10，必须特别注意负号。
Index laws are central to the AQA AS scheme of work. Students need to handle fractional and negative powers confidently.
指数法则是 AQA AS 数学教学大纲的核心。学生需要熟练处理分数指数和负指数。
aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ
Examiners reported that some candidates confused √x² + 4 with x + 2. The correct view is that √x² + 4 cannot be simplified into a sum. This issue often appeared in later calculus questions.
阅卷报告指出，一些考生错误地把 √x² + 4 写成 x + 2。实际上 √x² + 4 不能化简为两项之和。这个问题在后续
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