📚 Year 9 AQA Further Mathematics: Unit Test Mock Paper Analysis | 九年级 AQA 进阶数学：单元测试模拟卷解析
This article provides a detailed walkthrough of a mock unit test for Year 9 AQA Further Mathematics. We break down each question type, offering step-by-step solutions and key revision notes to strengthen your understanding of core topics.
本文针对九年级 AQA 进阶数学单元测试模拟卷进行详细解析，逐一拆解各类题型，给出分步解答和关键复习笔记，帮助你巩固核心知识点。
1. Simplifying Algebraic Expressions | 代数表达式化简
Example Question: Simplify 5x + 3y – 2x + 7y.
例题：化简表达式 5x + 3y – 2x + 7y。
Identify like terms: the x terms are 5x and –2x; the y terms are 3y and 7y. Combine them.
识别同类项：x 项为 5x 和 –2x；y 项为 3y 和 7y。将它们合并。
5x – 2x = 3x, 3y + 7y = 10y. Therefore, the simplified expression is 3x + 10y.
5x – 2x = 3x，3y + 7y = 10y。因此化简结果为 3x + 10y。
Always reorder terms carefully and watch the signs in front of each term.
务必仔细观察每一项前面的符号，并仔细重新排列项。
2. Expanding and Factorising | 展开与因式分解
Example 1 (Expand): Expand and simplify 3(x + 4) – 2(x – 1).
例题1（展开）：展开并化简 3(x + 4) – 2(x – 1)。
Distribute: 3x + 12 – 2x + 2. Then combine like terms: (3x – 2x) + (12 + 2) = x + 14.
分配：3x + 12 – 2x + 2。然后合并同类项：(3x – 2x) + (12 + 2) = x + 14。
Example 2 (Factorise): Factorise x² + 5x + 6.
例题2（因式分解）：因式分解 x² + 5x + 6。
Find two numbers that multiply to 6 and add to 5: they are 2 and 3. So the factorised form is (x + 2)(x + 3).
找出两个相乘得6、相加得5的数：2和3。因此分解结果为 (x + 2)(x + 3)。
Always check by expanding the brackets to confirm the original expression.
务必通过展开括号检验是否能还原为原表达式。
3. Solving Linear Equations | 解线性方程
Example: Solve 2(3x – 1) = 4x + 10.
例题：解方程 2(3x – 1) = 4x + 10。
Expand the bracket: 6x – 2 = 4x + 10. Subtract 4x from both sides: 2x – 2 = 10. Add 2: 2x = 12. Divide by 2: x = 6.
展开括号：6x – 2 = 4x + 10。两边减去4x：2x – 2 = 10。加2：2x = 12。除以2：x = 6。
Check by substituting x = 6 back into the original equation: left side 2(18–1)=34, right side 24+10=34. Correct.
将 x=6 代入原方程检验：左边 2(18–1)=34，右边 24+10=34。正确。
4. Solving Inequalities | 解不等式
Example: Solve 3x – 7 < 5 and illustrate the solution on a number line.
例题：解不等式 3x – 7 < 5 并在数轴上表示解集。
Add 7 to both sides: 3x < 12. Divide by 3: x < 4.
两边加7：3x < 12。除以3：x < 4。
On a number line, draw an open circle at 4 and shade to the left. Remember: if multiplying or dividing by a negative number, reverse the inequality sign.
在数轴上，在4处画空心圆并向左涂色。记住：乘以或除以负数时，不等号方向要改变。
5. Simultaneous Equations | 联立方程组
Example: Solve the simultaneous equations: 2x + y = 7, x – y = 2.
例题：解联立方程组：2x + y = 7，x – y = 2。
Add the two equations to eliminate y: (2x + y) + (x – y) = 7 + 2 → 3x = 9, so x = 3.
将两式相加消去 y：(2x + y) + (x – y) = 7 + 2 → 3x = 9，所以 x = 3。
Substitute x = 3 into x – y = 2: 3 – y = 2 → y = 1. Thus the solution is x = 3, y = 1.
将 x=3 代入 x – y = 2：3 – y = 2 → y = 1。因此解为 x = 3, y = 1。
6. Sequences and the nth Term | 数列与第n项
Example: Find the nth term of the arithmetic sequence: 4, 9, 14, 19, …
例题：求等差数列 4, 9, 14, 19, … 的第n项公式。
The difference between terms is +5, so the coefficient of n is 5. The nth term is 5n – 1 (since 5(1) – 1 = 4).
项之间的差为 +5，因此 n 的系数为 5。第n项公式为 5n – 1（因为 5×1 – 1 = 4）。
Use the formula to find the 10th term: 5(10) – 1 = 49.
用此公式求第10项：5×10 – 1 = 49。
7. Equation of a Straight Line |
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