📚 Oxford AQA International AS Mathematics (9660) PSM1 Common Mistakes | Oxford AQA 国际 AS 数学 (9660) 纯数1 易错点总结
The PSM1 paper is the first pure mathematics unit for Oxford AQA International AS Mathematics. It tests a wide range of foundational topics, from algebra and functions to calculus and trigonometry. Even well-prepared students often lose marks due to recurring slip-ups. This article compiles the most frequent mistakes seen in topic tests and exams, helping you spot and avoid them early.
PSM1 是 Oxford AQA 国际 AS 数学的第一份纯数试卷，涵盖代数、函数、微积分和三角学等基础知识。即使准备充分的学生也常因重复出现的小错误而失分。本文整理了专题测试和考试中最常见的错误，帮助你及早发现并避开这些陷阱。
1. Algebraic Missteps and Sign Errors | 代数失误与符号错误
A common slip occurs when expanding brackets with a negative sign in front: a − (b − c) is often wrongly expanded as a − b − c instead of a − b + c. Always apply the distributive property carefully.
在展开括号时，如果前面有负号，常会出错：a − (b − c) 常被错误地展开为 a − b − c，而正确应为 a − b + c。务必仔细运用分配律。
2x − 1, incorrectly writing 3x − 2x = 1 + 5. The correct arrangement is 3x − 2x = −1 − 5.
移项时，学生有时未改变运算符号。例如从 3x + 5 = 2x − 1，错误地写成 3x − 2x = 1 + 5。正确的移项应为 3x − 2x = −1 − 5。
Misinterpreting negative indices is another pitfall. For instance, treating x⁻² as −x² rather than 1/x². Remember that a negative exponent means the reciprocal.
对负指数的误解是另一个陷阱，例如将 x⁻² 当作 −x² 而非 1/x²。记住负指数表示倒数。
2. Solving Quadratic Equations | 解二次方程
e sign on the second root; it should be x = −2. Always use the principle of zero products.
因式分解后，有些学生忘记将每个因式设为零。例如 (x − 3)(x + 2) = 0，他们可能会写出 x = 3 和 x = 2，忽略了第二个根的符号，应为 x = −2。一定要利用零乘积原理。
When using the quadratic formula x = [−b ± √b² − 4ac b² − 4ac = 25 − 4(2)(−3) = 25 + 24 = 49. Misplacing signs leads to the wrong discriminant.
使用求根公式 x = [−b ± √b² − 4ac] / (2a) 时，负号 b 容易出错。对于 2x² − 5x − 3 = 0，a=2, b=−5, c=−3，则 −b=5 而不是 −5。判别式 b² − 4ac = 25 − 4(2)(−3) = 25+24=49。符号放错会导致判别式错误。
Completing the square is often done incorrectly when the coefficient of x² is not 1. For 2x² + 8x + 5, factor out the 2 first: 2[x² + 4x] + 5, then complete the square inside. The same care is needed when the quadratic term has a negative sign.
当 x² 系数不是 1 时，配方法常会出错。例如 2x² + 8x + 5，应先提取 2：2[x² + 4x] + 5，然后在括号内完成配方。当二次项系数为负时同样需小心。
3. Inequalities and Set Notation | 不等式与集合表示
Multiplying or dividing by a negative number without flipping the inequality sign is a classic mistake. For −3x < 9, dividing by −3 gives x > −3, not x < −3.
乘或除以负数时未翻转不等号是一个典型错误。例如 −3x < 9，除以 −3 得 x > −3，而不是 x < −3。
When solving quadratic inequalities such as x² − 4x + 3 < 0, a quick sketch of the parabola helps. The solution is 1 < x < 3. Many write x < 1 and x > 3, confusing the region where the quadratic is below zero.
解二次不等式如 x² − 4x + 3 < 0 时，快速画出抛物线草图会很有帮助。解为 1 < x < 3。很多学生却写成 x < 1 和 x > 3，混淆了二次函数小于零的区域。
Set notation errors: using 'and' when 'or' is required, or mixing up union (∪) and intersection (∩). Also, miswriting an interval like x
Published by TutorHao | 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