📚 Year 8 AQA Further Maths: Unit Test Mock Paper Walkthrough | Year 8 AQA 进阶数学：单元测试模拟卷解析
Welcome to the walkthrough of a Year 8 AQA Further Maths unit test mock paper. This guide will break down typical question types, step-by-step solutions, and the reasoning behind each answer to help you build confidence and accuracy.
欢迎来到 Year 8 AQA 进阶数学单元测试模拟卷的解析。本指南将逐步拆解典型题型、解题步骤以及每个答案背后的推理，帮助你建立信心并提高准确性。
1. Understanding the Exam Structure | 理解考试结构
The mock paper is divided into two sections: non-calculator and calculator. It tests fluency in algebra, geometry, proportional reasoning, and probability. You are expected to show clear working for each question.
模拟卷分为两部分：不可用计算器部分和可用计算器部分。它考查代数、几何、比例推理和概率方面的熟练程度。你需要对每道题展示清晰的解题步骤。
Time management is crucial. Spend about one minute per mark. Check that answers are in the simplest form.
时间管理至关重要。大约按照每分钟得一分来安排。确保答案是最简形式。
2. Algebraic Simplification | 代数化简
Simplify 3(2x - 5) - 2(x + 4).
化简 3(2x - 5) - 2(x + 4)。
x = -2x, and -2 × 4 = -8, giving -2x - 8. Combine the expressions to get 6x - 15 - 2x - 8.
首先展开括号：3 × 2x = 6x，3 × (-5) = -15，得到 6x - 15。然后 -2 × x = -2x，-2 × 4 = -8，得出 -2x - 8。合并表达式得到 6x - 15 - 2x - 8。
Group like terms: 6x - 2x = 4x, and -15 - 8 = -23. The simplified expression is 4x - 23.
合并同类项：6x - 2x = 4x，-15 - 8 = -23。化简结果为 4x - 23。
3. Solving Linear Equations | 解一元一次方程
Solve (2x)/3 + 4 = 10.
解方程 (2x)/3 + 4 = 10。
Subtract 4 from both sides: (2x)/3 = 6.
两边同时减去 4： (2x)/3 = 6。
Multiply both sides by 3: 2x = 18.
两边同时乘以 3：2x = 18。
Divide by 2: x = 9.
除以 2：x = 9。
Check: (2×9)/3 + 4 = 18/3 + 4 = 6 + 4 = 10. Correct.
检验：(2×9)/3 + 4 = 18/3 + 4 = 6 + 4 = 10。正确。
4. Coordinate Geometry | 坐标几何
Find the equation of the line passing through (1, 3) and (4, 9).
求通过点 (1, 3) 和 (4, 9) 的直线方程。
Calculate the gradient m: m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(4 - 1) = 6/3 = 2.
计算斜率 m：m = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(4 - 1) = 6/3 = 2。
Use point-slope form: y - y₁ = m(x - x₁). Substitute (1, 3): y - 3 = 2(x - 1).
使用点斜式：y - y₁ = m(x - x₁)。代入 (1, 3)：y - 3 = 2(x - 1)。
Simplify: y - 3 = 2x - 2, so y = 2x + 1.
化简：y - 3 = 2x - 2，得到 y = 2x + 1。
The y-intercept is 1.
y 轴截距为 1。
5. Sequences and Patterns | 数列与规律
The nth term of a sequence is given by 3n² - 1. Find the first three terms.
一个数列的第 n 项公式为 3n² - 1。求前三项。
Substitute n = 1: 3×(1)² - 1 = 3 - 1 = 2.
代入 n = 1：3×(1)² - 1 = 3 - 1 = 2。
n = 2: 3×(2)² - 1 = 3×4 - 1 = 12 - 1 = 11.
n = 2：3×(2)² - 1 = 3×4 - 1 = 12 - 1 = 11。
n = 3: 3×(3)² - 1 = 3×9 - 1 = 27 - 1 = 26.
n = 3：3×(3)² - 1 = 3×9 - 1 = 27 - 1 = 26。
The first three terms are 2, 11, 26.
前三项为 2, 11, 26。
6. Fractions, Decimals and Percentages | 分数、小数和百分比
Increase £240 by 15%.
将 £240 增加 15%。
Find 15% of £240: 15% = 0.15, 0.15 × 240 = 36.
求 £240 的 15%：15% = 0.15，0.15 × 240 = 36。
Add to the original amount: £240 + £36 = £276.
加到原金额：£240 + £36 = £276。
Alternatively, use multiplier 1.15: £240 × 1.15 = £276.
或者使用乘数 1.15：£240 × 1.15 = £276。
7. Ratio and Proportion | 比和比例
Divide £300 in the ratio 2:3.
按 2:3 的比例分配 £300。
Total parts = 2 + 3 = 5.
总份数 = 2 + 3 = 5。
One part = £300 ÷ 5 = £60.
一份 = £300 ÷ 5 = £60。
First share = 2 × £60 = £120; second share = 3 × £60 = £180.
第一份 = 2 × £60 = £120；第二份 = 3 × £60 = £180。
8. Geometry: Area and Perimeter | 几何：面积与周长
A trapezium has parallel sides of length 8 cm and 12 cm, and perpendicular height 5 cm. Find its area.
一个梯形的平行边长分别为 8 cm 和 12 cm，垂直高为 5 cm。求其面积。
Area of trapezium = ½ × (a + b) × h, where a and b are parallel sides.
梯形面积 = ½ × (a + b) × h，其中 a 和 b 为平行边。
Substitute: ½ × (8 + 12) × 5 = ½ × 20 × 5 = 10 × 5 = 50.
代入：½ × (8 + 12) × 5 = ½ × 20 × 5 = 10 × 5 = 50。
The area is 50 cm².
面积为 50 cm²。
9. Probability | 概率
A bag contains 3 red, 2 blue and 5 green counters. One counter is taken at random. What is the probability it is not green?
一个袋子里有 3 个红色、2 个蓝色和 5 个绿色计数片。随机取出一个计数片，它不是绿色的概率是多少？
Total counters = 3 + 2 + 5 = 10.
总计数片数量 = 3 + 2 + 5 = 10。
Number of non-green counters = red + blue = 3 + 2 = 5.
非绿色数量 = 红 + 蓝 = 3 + 2 = 5。
Probability = 5/10 = 1/2.
概率 = 5/10 = 1/2。
10. Final Tips and Common Mistakes | 最终提示与常见错误
Always read the question carefully – check if units, rounding, or specific formats are required. In algebra, watch for sign errors when expanding brackets.
仔细读题——确认是否需要单位、舍入或特定格式。在代数中，展开括号时注意符号错误。
When solving equations, perform the same operation on both sides and double-check your answer by substitution. For geometry, remember to include the correct units for area or volume.
解方程时，两边进行相同操作并通过代入检验答案。几何题中，记得为面积或体积加上正确的单位。
Manage your time and don't get stuck on one problem – move on and come back if you have time. Good luck!
管理好时间，不要在一道题上卡住——先做后面的，如果有时间再回来做。祝你好运！
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