Common Mistakes in AS Mathematics Unit 2 June 2019 Paper | AS数学Unit 2 2019年6月真题易错点总结

📚 Common Mistakes in AS Mathematics Unit 2 June 2019 Paper | AS数学Unit 2 2019年6月真题易错点总结

The AS Mathematics Unit 2 paper from June 2019 covered core topics such as algebra, functions, trigonometry, differentiation, and integration. Although the questions followed standard formats, the examiners’ report revealed several areas where students consistently lost marks. This article highlights the most common mistakes and shows you how to avoid them, with clear explanations and corrected examples.

2019年6月的AS数学第二单元试卷涵盖了代数、函数、三角函数、微分和积分等核心主题。尽管题目形式常规，但考官报告指出学生在多个知识点上频繁失分。本文总结了这些常见错误，并提供清晰的解释和正确示例，帮助你避免类似失误。

1. Misreading the Leading Coefficient in Completing the Square | 完成平方时忽视首项系数

When asked to express 2x² + 8x + 5 in the form a(x + p)² + q, many candidates forgot to factor out the leading coefficient 2 from the x terms first. A common error was to write 2(x + 2)² + 1, obtained by adding and subtracting (8/2)² = 16 incorrectly. The correct procedure is to rewrite the expression as 2(x² + 4x) + 5, then complete the square inside the bracket: 2[(x + 2)² − 4] + 5 = 2(x + 2)² − 8 + 5 = 2(x + 2)² − 3.

在将 2x² + 8x + 5 写成 a(x + p)² + q 的形式时，许多考生忘记先提取二次项系数 2。典型的错误是直接写成 2(x + 2)² + 1，这是错误地加上和减去 (8/2)² = 16 导致的。正确做法是先将表达式写成 2(x² + 4x) + 5，然后在括号内配平方：2[(x + 2)² − 4] + 5 = 2(x + 2)² − 8 + 5 = 2(x + 2)² − 3。

2x² + 8x + 5 = 2(x + 2)² − 3

2. Forgetting to Check Roots in Logarithmic Equations | 解对数方程漏验根

In the June 2019 paper, a logarithmic equation such as log₂(x − 1) + log₂(x + 3) = 3 required students to first combine the logs into log₂[(x − 1)(x + 3)] = 3, then solve (x − 1)(x + 3) = 2³ = 8. This gave x = −5 or x = 3. However, many did not check the domain: for log₂(x − 1) to

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