A-Level数学不等式高分攻略 | A-Level Maths Inequalities Mastery

不等式是A-Level数学代数模块的核心考点，也是许多同学容易失分的地方。本文结合历年真题与评分标准，系统梳理不等式求解的关键技巧，帮助你稳稳拿下这一考点。

Inequalities are a core topic in A-Level Mathematics Algebra, and a common source of lost marks. This post distills key techniques from real past papers and mark schemes to help you tackle inequality questions with confidence.

📌 核心知识点 / Key Knowledge Points

1. 线性不等式求解 / Solving Linear Inequalities：掌握 ax + b > c 型不等式，注意乘除负数时不等号方向反转。Remember: multiplying or dividing by a negative number flips the inequality sign.
2. 二次不等式 / Quadratic Inequalities：通过因式分解或求根公式找到临界值，画数轴判定区间。例如 4x² - 25 < 0 解得 -2.5 < x < 2.5。Use critical values and a sign diagram — never skip the diagram, examiners look for it.
3. 不等式组 / Inequality Systems：同时满足多个不等式条件，需取交集。如图中 4x² - 25 < 0 与 12 - 5x - 3x² > 0 联立，最终只保留公共解集。Always show the intersection on a number line.
4. 整数解问题 / Integer Solution Problems：给定 2 ≤ n < 5 且 n 为整数，要能准确列出所有可能值。Don’t rush — carefully check whether the endpoint is inclusive (≤) or exclusive (<).
5. 数轴表示法 / Number Line Representation：考试要求你用数轴直观标记不等式范围，空心圈代表不包含、实心圈代表包含。Open circle = strict inequality, closed circle = inclusive. A simple detail that costs marks when wrong.

💡 学习建议 / Study Tips

• 📝 先练后看：每次先独立完成题目，再对照评分标准逐条核对，关注”Method mark”和”Accuracy mark”的区别。
• 📊 画图必备：二次不等式一定画抛物线草图和数轴——即使答案对，缺少图解步骤也可能丢分。
• ⏱️ 计时训练：A-Level不等式题平均分配2-3分钟，速度来自熟练度。
• 🔄 错题本：把符号反转、区间端点判断等高频错误单独记录，考前集中回顾。

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📞 Need 1-on-1 A-Level Maths tutoring? Contact: 16621398022 (WeChat)