Year 10 AQA Maths: Unit Test Mock Paper Walkthrough | AQA十年级数学：单元测试模拟卷解析

📚 Year 10 AQA Maths: Unit Test Mock Paper Walkthrough | AQA十年级数学：单元测试模拟卷解析

This article takes you through a complete Year 10 AQA maths unit test mock paper, breaking down key questions, revealing common pitfalls, and sharing revision strategies to help you master the content. Whether you are preparing for an end‑of‑topic assessment or consolidating your GCSE foundation skills, working through a mock paper with targeted commentary is one of the most effective ways to improve.

本文带你逐题剖析一份十年级 AQA 数学单元测试模拟卷，拆解核心题型，揭示常见错误，并分享复习策略，帮助你扎实掌握知识点。无论你是在准备阶段性测试，还是巩固 GCSE 基础，跟随详细的解析来演练模拟卷都是极为有效的提升方式。

1. Overview of the Mock Paper | 模拟卷概览

The mock paper consists of 30 questions split into two sections: Section A (non‑calculator) and Section B (calculator). The total mark is 80, and the recommended time is 90 minutes. Topics are weighted to reflect the AQA specification: Number (15%), Algebra (25%), Ratio, proportion and rates of change (20%), Geometry and measures (20%), Probability (10%) and Statistics (10%).

模拟卷共 30 道题，分为 A 部分（无计算器）和 B 部分（可使用计算器）。总分 80 分，建议用时 90 分钟。各主题分值权重参考 AQA 考纲：数 (15%)、代数 (25%)、比与比例 (20%)、几何与测量 (20%)、概率 (10%) 及统计 (10%)。

Familiarity with this structure helps you plan time per mark and identify which topics carry the most weight. For a 90‑minute paper, aim for roughly 1 minute per mark, with time built in for checking.

熟悉试卷结构有助于你合理分配时间，并明确哪些主题分值最高。90 分钟的试卷，大致按每分 1 分钟来规划，留出检查时间。

2. Number and Calculations | 数与计算

A classic early question tests fraction arithmetic: Work out 2/5 + 3/8. Many students forget to find a common denominator before adding.

试卷中有一道经典的基础题：计算 2/5 + 3/8。不少同学忘记先通分再相加。

+ 15 = 31, denominator stays 40. The answer is 31/40, which cannot be simplified further.

步骤 1：找到 5 和 8 的最小公倍数 40。步骤 2：通分，2/5 = 16/40，3/8 = 15/40。步骤 3：分子相加 16+15=31，分母不变，结果为 31/40，已是最简分数。

2/5 + 3/8 = 16/40 + 15/40 = 31/40

. A common slip is counting the zeros in the wrong direction and writing a positive power.

另有一题要求将 0.000 056 写成标准形式。数小数点移位：得到 5.6 × 10⁻⁵。常见错误是数错零的方向，写成正指数。

ly powers for a power raised to another power: 3² ³ = 3⁶. Then division: 3⁶ ÷ 3⁴ = 3² = 9.

指数律也有考查：化简 (3²)³ ÷ 3⁴。根据指数运算法则：幂的乘方指数相乘，得到 3⁶。再相除，指数相减：3⁶ ÷ 3⁴ = 3² = 9。

3. Algebra Essentials | 代数基础

Solving linear equations is a core skill. For example: Solve 2x + 5 = 3x – 7. Subtract 2x from both sides to group variable terms: 5 = x – 7. Then add 7: x = 12. Always check: LHS = 2(12)+5 = 29, RHS = 3(12)–7 = 29.

解一元一次方程是核心技能。例如：解 2x + 5 = 3x – 7。两边减去 2x 使变量集中在一边：5 = x – 7，再加 7 得 x = 12。务必检验：左式 = 2×12+5=29，右式 = 3×12–7=29。

Expanding double brackets: (x + 4)(x – 3). Multiply each term: x² – 3x + 4x – 12, then combine like terms: x² + x – 12. The most frequent mistake is mishandling the negative sign, ending up with –3x – 4x instead of –3x + 4x.

展开双括号：(x + 4)(x – 3)。逐项相乘得 x² – 3x + 4x – 12，合并同类项：x² + x – 12。最常见错误是处理负号出错，把中间项错写成 –3x – 4x。

Factorising a difference of squares: x² – 9 = (x + 3)(x – 3). Recognising this pattern saves time and avoids trial‑and‑error.

平方差公式因式分解：x² – 9 = (x + 3)(x – 3)。识别这一模式可节省时间，避免盲目尝试。

4. Ratio and Proportion | 比与比例

One question asks: Share £120 in the ratio 3:5. Find the total parts: 3 + 5 = 8. One part is £120 ÷ 8 = £15. The first share is 3 × £15 = £45, and the second is 5 × £15 = £75.

有一题要求按 3:5 的比例分配 £120。总份数为 3+5=8，一份为 £120÷8=£15。第一份 3×£15=£45，第二份 5×£15=£75。

es 200 g flour, 100 g sugar and 50 g butter for 6 servings. How much flour for 15 servings? ÷ 6 = 2.5. Flour needed: 200 g × 2.5 = 500 g. Use the same multiplier for all ingredients.

一道食谱类比例题：蛋糕配方 6 份用 200 g 面粉、100 g 糖、50 g 黄油。15 份需要多少面粉？先算倍数：15÷6=2.5，面粉用量：200 g×2.5=500 g。所有食材均乘相同倍数。

5. Geometry and Measures | 几何与测量

Pythagoras’ theorem is tested with a right‑ g a² + b² = c²: 6² + 8² = 36 + 64 = 100. Therefore c = √100 = 10 cm. Always include units.

勾股定理的考题：直角三角形的两条直角边为 6 cm 和 8 cm，求斜边。由 a²+b²=c² 得 6²+8²=36+64=100，所以 c=√100=10 cm。不要遗漏单位。

9π cm². A common slip is to use the diameter instead of the radius or to forget to square.

圆的面积与周长也有考查：已知半径为 7 cm，求面积，保留 π。面积 = π×7² = 49π cm²。常见错误是用直径代替半径，或忘记平方。

Angle reasoning: A triangle has angles labelled x, 2x and x – 10. Use the angle sum: x + 2x + (x – 10) = 180 → 4x – 10 = 180 → 4x = 190 → x = 47.5. So angles are 47.5°, 95° and 37.5°.

角度推理：一个三角形的三个角分别为 x、2x 和 x–10。利用内角和：x+2x+(x–10)=180 → 4x–10=180 → 4x=190 → x=47.5。因此三个角为 47.5°、95° 和 37.5°。

6. Probability | 概率

d the probability of getting an even number on the dice and a head on the coin. Even numbers: 2, 4, 6 (3 outcomes). Combined with head: 3 outcomes. Probability = 3/12 = 1/4.

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一道涉及均匀骰子和均匀硬币的题目：列出掷骰子和抛硬币的样本空间。共有 6×2=12 种等可能结果。求骰子偶数且硬币正面的概率。骰子偶数：2、4、6（3 种），与正面组合共 3 种结果，概率 = 3/12 = 1/4。

east one red. First pick: P(R)=3/5, P(B)=2/5. Second pick: branches change. At least one red is 1 – P(both blue) = 1 – (2/5 × 1/4) = 1 – 2/20 = 18/20 = 9/10.

树状图：袋中有 3 红 2 蓝，随机无放回地取两次。画出树状图，求至少一个红色的概率。第一次：P(R)=3/5，P(B)=2/5。第二次概率相应变化。至少一红可用 1 – P(两个均蓝) = 1 – (2/5 × 1/4) = 1 – 2/20 = 18/20 = 9/10。

7. Statistics | 统计

, 12, 20. Calculate the mean, median, mode and range. Mean: sum = 91, divide by 6 = 15.166… 14, 15, 18, 20. Median = average of 3rd and 4th = (14+15)/2 = 14.5. Mode = 12. Range = 20 – 12 = 8.

给出数据 12、15、14、18、12、20。计算平均值、中位数、众数和极差。总和 91，除以 6，平均值为 15.166…，约等于 15.2（保留一位小数）。排序：12, 12, 14, 15, 18, 20。中位数 = (14+15)/2 = 14.5。众数 = 12。极差 = 20–12=8。

A frequency table may look like this:

Score	Frequency
0	3
1	7
2	5
3	2

To find the mean from this table, multiply each score by its frequency, sum those products, then divide by the total frequency. Always check the total frequency matches the number of data points.

通过频率表求平均值时，需将每个分数乘以对应频数，求乘积之和，再除以总频数。务必核对总频数与数据点数量一致。

8. Common Mistakes and How to Avoid Them | 常见错误与避免方法

Error 1: Confusing area and perimeter. When asked for the area of a rectangle, some students add lengths instead of multiplying. Double‑check the command word and write the formula first.

错误 1：混淆面积与周长。题目要求矩形的面积，却有学生用加法而非乘法。务必看清指令词，先写下公式。

Error 2: Mishandling negative numbers when expanding brackets. (x – 3)(x + 2) often yields x² – x – 6 from –3x + 2x correctly, but missing a sign can give x² – 5x – 6. Use a grid method to track signs.

错误 2：展开括号时处理负数不当。(x – 3)(x + 2) 展开时，–3x+2x 正确得 –x，但一旦符号错就可能变成 x²–5x–6。使用网格法可有效追踪符号。

Error 3: Rounding intermediate values too early. In multi‑step calculations, keep full calculator precision until the final answer, then round. Early rounding can cause significant inaccuracies.

错误 3：过早对中间结果四舍五入。在多步计算中，应保持计算器所有精度，最后一步再按要求舍入。过早舍入会产生明显误差。

Error 4: Not showing work. In non‑calculator sections, method marks are awarded even if the final answer is wrong. Always write down the steps you take.

错误 4：不写解题过程。在无计算器部分，即使最终答案错了，过程正确仍可得分。一定要写出推导步骤。

9. Effective Exam Techniques | 有效考试技巧

Before starting, skim the whole paper. Estimate how long you can spend on each section based on marks. Begin with the questions you find easiest to build confidence and secure quick marks.

开考前快速浏览全卷，根据分值估算每题的大致用时。先做最有把握的题目，建立信心并保住基础分。

When you meet a difficult question, mark it and move on. Return later with a fresh mind rather than losing time. Always leave a few minutes at the end to check calculations and reread the question to confirm you answered what was asked.

遇到难题时，先标记并跳过去，完成其他题目后再回头思考，避免浪费时间。最后务必留出几分钟检查计算，并重读题目确认回答无误。

Use the answer spaces as a guide: if a question provides a single line, a one‑word answer is expected. If a whole page is given, detailed working is necessary. Show all reasoning, especially in multi‑step problems.

答题空间也能提示作答量：只给一行意味着只需一个简短答案；若给整页，则需要详细步骤。多步问题尤其要把推理过程写清楚。

10. Revision Tips for Unit Tests | 单元测试复习建议

Active practice beats passive reading. Work through past mock papers and topic tests under timed conditions, then mark your answers with the mark scheme. Identify which topics cost you the most marks and target those weaknesses.

主动练习远胜于被动阅读。在限时条件下完成往年模拟卷和单元测试，然后对照评分方案批改。找出失分最多的主题，集中攻克薄弱环节。

Create a mistake log: write down every error you make, correct it, and note the reason. Revisiting this log before the test prevents repeated mistakes.

建立错题日志：记下每道错题，订正并分析原因。考前翻阅日志能有效避免再犯同类错误。

Use visual aids like formula flashcards and geometry diagrams. For formulae you must memorise, practise writing them out from memory at the start of each revision session.

运用视觉辅助工具，如公式闪卡和几何示意图。需要记忆的公式，在每次复习开始时先默写一遍，强化记忆。

Finally, don't neglect topics that appear straightforward. Simple number and algebra questions often carry hidden trick steps that catch out overconfident students.

最后，不要轻视看似简单的主题。基础的数与代数题中往往隐藏着易错步骤，盲目自信的学生常在此失分。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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