📚 Year 11 Edexcel Maths: Mock Unit Test Walkthrough | Year 11 Edexcel 数学：单元测试模拟卷解析
Welcome to this detailed walkthrough of a Year 11 Edexcel Maths mock unit test. The paper covers algebra, geometry, ratio, probability, trigonometry, graphs, and multi-step problem solving. Each question is explained with step-by-step solutions, common pitfalls, and revision tips so you can improve accuracy and exam confidence.
欢迎来到 Year 11 Edexcel 数学单元测试模拟卷的详细解析。试卷涵盖代数、几何、比率、概率、三角学、图像和多步骤问题解决。每道题都配有逐步解答、常见错误分析和复习提示，帮助你提升准确率和考试信心。
1. Structure and Assessment Objectives | 模拟卷结构与评估目标
This mock unit test contains 10 questions worth 50 marks in total, with a suggested time of 45 minutes. It mirrors Edexcel unit assessment style and targets AO1 (recall and use knowledge), AO2 (select and apply methods), and AO3 (interpret and analyse problems). Some questions are calculator-friendly, while others test non-calculator fluency.
本模拟单元测试包含 10 道题，满分 50 分，建议用时 45 分钟。试卷贴合 Edexcel 单元评估风格，覆盖 AO1（回忆和运用知识）、AO2（选择和应用方法）和 AO3（解释和分析问题）。部分题目适合使用计算器，另一些则考查非计算器运算能力。
| Topic | Marks | Assessment Focus |
| Algebra | 15 | AO1, AO2 |
| Ratio and proportion | 8 | AO2 |
| Probability | 7 | AO2, AO3 |
| Geometry and trigonometry | 15 | AO1, AO3 |
| Graphs and problem solving | 5 | AO3 |
2. Question 1: Solving Linear Equations | 第1题：解线性方程
Question: Solve the equation 4(x − 3) = 2x + 6.
题目：解方程 4(x − 3) = 2x + 6。
4(x − 3) = 2x + 6
Step 1 - Expand the bracket on the left side: 4x − 12 = 2x + 6.
步骤1 - 展开左边括号：4x − 12 = 2x + 6。
Step 2 - Subtract 2x from both sides: 4x − 2x − 12 = 6, so 2x − 12 = 6.
步骤2 - 两边同时减去 2x：4x − 2x − 12 = 6，得到 2x − 12 = 6。
Step 3 - Add 12 to both sides: 2x = 18.
步骤3 - 两边同时加 12：2x = 18。
Step 4 - Divide both sides by 2: x = 9.
步骤4 - 两边同时除以 2：x = 9。
Check: 4(9 − 3) = 4 × 6 = 24, and 2(9) + 6 = 18 + 6 = 24. The solution is correct.
检验：4(9 − 3) = 4 × 6 = 24，2(9) + 6 = 18 + 6 = 24。解正确。
Common pitfall: forgetting to multiply both terms inside the bracket by 4, or making a sign error when subtracting 2x.
常见错误：忘记用 4 乘括号内每一项，或在减去 2x 时出现符号错误。
3. Question 2: Expanding and Factorising Quadratics | 第2题：展开与因式分解二次式
Question: Expand (x + 5)(x − 3), then factorise x² − 7x + 12.
题目：展开 (x + 5)(x − 3)，然后因式分解 x² − 7x + 12。
Expansion: x² − 3x + 5x − 15 = x² + 2x − 15.
展开：x² − 3x + 5x − 15 = x² + 2x − 15。
that multiply to +12 and add to −7. These are −3 and −4. So x² − 7x + 12 = (x − 3)(x − 4).
因式分解：找两个数，乘积为 +12，和为 −7，即 −3 和 −4。因此 x² − 7x + 12 = (x − 3)(x − 4)。
Also remember the difference of two squares: x² − 49 = (x + 7)(x − 7).
还要记住平方差公式：x² − 49 = (x + 7)(x − 7)。
4. Question 3: Simultaneous Equations | 第3题：联立方程
Question: Solve 3x + 2y = 16 and 2x − y = 6.
题目：解 3x + 2y = 16 和 2x − y = 6。
From the second equation, y = 2x − 6. Substitute into the first: 3x + 2(2x − 6) = 16.
由第二个方程得 y = 2x − 6。代入第一个方程：3x + 2(2x − 6) = 16。
Expand: 3x + 4x − 12 = 16, so 7x = 28, giving x = 4.
展开：3x + 4x − 12 = 16，所以 7x = 28，得 x = 4。
e back: y = 2(4) − 6 = 2. Check in the first equation: 3(4) + 2(2) = 12 + 4 = 16. Correct.
回代：y = 2(4) − 6 = 2。代入第一个方程检验：3(4) + 2(2) = 12 + 4 = 16。正确。
Common pitfall: not multiplying the whole expression when substituting, or losing the negative sign.
常见错误：代入时没有乘以整个表达式，或丢失负号。
5. Question 4: Ratio, Proportion and Percentages | 第4题：比率、比例与百分比
Question: Divide £240 in the ratio 3 : 5. Then increase £80 by 15%.
题目：将 240 英镑按 3 : 5 分配。然后将 80 英镑增加 15%。
Total parts: 3 + 5 = 8. One part = 240 ÷ 8 = 30. So the shares are 3 × 30 = £90 and 5 × 30 = £150.
总份数：3 + 5 = 8。一份 = 240 ÷ 8 = 30。因此两份分别为 3 × 30 = 90 英镑和 5 × 30 = 150 英镑。
Percentage increase: 80 × 1.15 = 92, so the new amount is £92.
百分比增加：80 × 1.15 = 92，所以新金额为 92 英镑。
r direct proportion use y = kx. For inverse proportion use y = k ÷ x. Always find k first.
正比例使用 y = kx。反比例使用 y = k ÷ x。始终先求出 k。
6. Question 5: Probability | 第5题：概率
Question: A bag has 5 red, 3 blue, and 2 green counters. One counter is taken without replacement, then a second is taken. Find P(red then blue).
题目：袋中有 5 个红、3 个蓝、2 个绿筹码。不放回地取一个，再取第二个。求 P(先红后蓝)。
Total counters = 5 + 3 + 2 = 10. P(red first) = 5/10 = 1/2.
筹码总数 = 5 + 3 + 2 = 10。P(先红) = 5/10 = 1/2。
After removing a red, 9 counters remain, with 3 blue. P(blue second) = 3/9 = 1/3.
取出红色后剩 9 个筹码，其中蓝色 3 个。P(后蓝) = 3/9 = 1/3。
For AND events, multiply: P(red then blue) = (5/10) × (3/9) = 15/90 = 1/6.
对于“且”事件，相乘：P(先红后蓝) = (5/10) × (3/9) = 15/90 = 1/6。
For OR events that are mutually exclusive, add probabilities. Tree diagrams help organise without-replacement questions.
对于互斥的“或”事件，概率相加。树状图有助于整理不放回问题。
7. Question 6: Angles, Polygons and Circle Theorems | 第6题：角度、多边形与圆定理
Question: Find the interior angle of a regular pentagon. Then state the angle in a semicircle.
题目：求正五边形的内角。然后说出半圆所对的圆周角。
°. For a pentagon, n = 5, so sum = 3 × 180° = 540°. Each interior angle = 540° ÷ 5 = 108°.
n 边形内角和 = (n − 2) × 180°。五边形 n = 5，内角和 = 3 × 180° = 540°。每个内角 = 540° ÷ 5 = 108°。
Circle theorem: the angle in a semicircle is 90°. Also, the angle at the centre is twice the angle at the circumference, and opposite angles in a cyclic quadrilateral sum to 180°.
圆定理：半圆所对的圆周角是 90°。另外，圆心角是圆周角的两倍，圆内接四边形对角和为 180°。
A tangent is perpendicular to the radius at the point of contact. The alternate segment theorem is also commonly tested.
切线与接触点处的半径垂直。切线角定理（交替段定理）也经常考查。
8. Question 7: Pythagoras and Right-Angled Trigonometry | 第7题：勾股定理与直角三角形三角学
Question: A right-angled triangle has legs 6 cm and 8 cm. Find the hypotenuse. Then find the opposite side when the angle is 35° and the hypotenuse is 12 cm.
题目：直角三角形两直角边为 6 cm 和 8 cm。求斜边。然后求角度为 35°、斜边为 12 cm 时的对边。
Pythagoras: a² + b² = c². So c² = 6² + 8² = 36 + 64 = 100, giving c = 10 cm.
勾股定理：a² + b² = c²。所以 c² = 6² + 8² = 36 + 64 = 100，得 c = 10 cm。
= opposite ÷ hypotenuse. Here sin 35° = opposite ÷ 12, so opposite = 12 sin 35° ≈ 6.88 cm.
三角学：sin θ = 对边 ÷ 斜边。这里 sin 35° = 对边 ÷ 12，所以对边 = 12 sin 35° ≈ 6.88 cm。
SOHCAHTOA: sin = O/H, cos = A/H, tan = O/A. Check that your calculator is in degree mode.
记住 SOHCAHTOA：sin = 对/斜，cos = 邻/斜，tan = 对/邻。检查计算器是否处于角度模式。
9. Question 8: Sine Rule and Cosine Rule | 第8题：正弦定理与余弦定理
Question: In triangle ABC, b = 7 cm, c = 9 cm, and angle A = 60°. Find side a.
题目：三角形 ABC 中，b = 7 cm，c = 9 cm，角 A = 60°。求边 a。
Use the cosine rule: a² = b² + c² − 2bc cos A.
使用余弦定理：a² = b² + c² − 2bc cos A。
Substitute: a² = 7² + 9² − 2 × 7 × 9 × cos 60° = 49 + 81 − 126 × 0.5 = 130 − 63 = 67.
代入：a² = 7² + 9² − 2 × 7 × 9 × cos 60° = 49 + 81 − 126 × 0.5 = 130 − 63 = 67。
So a = √67 ≈ 8.19 cm.
所以 a = √67 ≈ 8.19 cm。
rea of a triangle = ½ ab sin C. Watch out for the ambiguous case when using the sine rule.
正弦定理为 a ÷ sin A = b ÷ sin B = c ÷ sin C。三角形面积 = ½ ab sin C。使用正弦定理时注意“ ambiguous case ”（两解情况）。
10. Question 9: Straight-Line Graphs and Gradients | 第9题：直线图像与斜率
Question: Find the equation of the line through (2, 5) and (6, 13).
题目：求经过 (2, 5) 和 (6, 13) 的直线方程。
Gradient m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2.
斜率 m = (y₂ − y₁) ÷ (x₂ − x₁) = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2。
Using y = mx + c and point (2, 5): 5 = 2(2) + c, so c = 1. The equation is y = 2x + 1.
使用 y = mx + c 和点 (2, 5)：5 = 2(2) + c，所以 c = 1。方程为 y = 2x + 1。
t. Perpendicular lines satisfy m₁ × m₂ = −1. The midpoint of (2, 5) and (6, 13) is (4, 9).
平行线斜率相同。垂直线满足 m₁ × m₂ = −1。(2, 5) 和 (6, 13) 的中点是 (4, 9)。
11. Question 10: Multi-Step Problem Solving (AO3) | 第10题：多步骤问题解决（AO3）
Question: A rectangular garden has length 3 m more than its width. Its area is 40 m². Find the dimensions.
题目：一个矩形花园的长比宽多 3 m，面积为 40 m²。求它的尺寸。
Let the width be w. Then length = w + 3. Area: w(w + 3) = 40.
设宽为 w，则长 = w + 3。面积：w(w + 3) = 40。
Expand and rearrange: w² + 3w − 40 = 0. Factorise: (w + 8)(w − 5) = 0. So w = 5 or w = −8.
展开并整理：w² + 3w − 40 = 0。因式分解：(w + 8)(w − 5) = 0。所以 w = 5 或 w = −8。
ce width cannot be negative, w = 5 m and length = 8 m. Check area: 5 × 8 = 40 m². Correct.
宽度不能为负，所以 w = 5 m，长 = 8 m。检验面积：5 × 8 = 40 m²。正确。
AO3 questions often require forming an equation, solving it, and interpreting the answer in context.
AO3 题目通常需要建立方程、求解，并结合情境解释答案。
12. Revision Strategy and Common Pitfalls | 复习策略与常见错误
Use these strategies before the mock: practise with a timer, show every step of working, write units clearly, and check whether answers are reasonable. Keep a formula sheet for area, trigonometry, and circle theorems. Review past-paper questions by topic, then attempt full papers under exam conditions.
模拟考前使用这些策略：计时练习、写出每一步过程、清楚标注单位，并检查答案是否合理。整理面积、三角学和圆定理公式表。先按主题复习历年真题，再在考试条件下完成整套试卷。
Common pitfalls include sign errors in algebra, mixing up sine and cosine rules, forgetting "without replacement" in probability, reversing ratio order, and using radians instead of degrees. Always re-read the question and check what form the answer should take.
常见错误包括代数符号错误、混淆正弦定理和余弦定理、概率中忘记“不放回”、比率顺序颠倒，以及误用弧度而非角度。务必重读题目，检查答案应采用的格式。
Final tip: mark your mock honestly, log every mistake in a revision notebook, and redo those questions three days later. This turns a mock test into a powerful learning tool.
最后提示：诚实批改模拟卷，把每道错题记入复习笔记本，并在三天后重做。这样能把模拟测试变成强大的学习工具。
Published by TutorHao | Year 11 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图