Maths Pure Paper 1 Common Mistakes Summary | 纯数试卷1易错点总结

📚 Maths Pure Paper 1 Common Mistakes Summary | 纯数试卷1易错点总结

When tackling Pure Mathematics Paper 1, students often lose marks not because they do not understand the concepts, but because they fall into predictable traps. This article summarises the most frequent mistakes observed in exams, ranging from sign errors in algebra to subtle pitfalls in calculus and trigonometry. By reviewing these, you can sharpen your accuracy and boost your confidence.

在应对纯数试卷1时，学生丢分往往不是因为不理解概念，而是掉进了可以预见的陷阱。本文总结了考试中最常见的错误，从代数中的符号错误到微积分和三角学的细微陷阱。复习这些内容可以帮助你提高解题准确度，增强信心。

1. Algebraic Sign Errors | 代数符号错误

One of the most common mistakes is mishandling negative signs when expanding brackets or simplifying expressions. For example, when simplifying 2 – (x – 3), many students incorrectly write 2 – x – 3, forgetting that the minus sign in front of the bracket changes the sign of every term inside.

最常见的错误之一是在展开括号或化简表达式时错误处理负号。例如，在化简 2 – (x – 3) 时，很多学生错误地写成 2 – x – 3，忘记了括号前的负号会改变括号内每一项的符号。

Correct: 2 – (x – 3) = 2 – x + 3 = 5 – x.

正确：2 – (x – 3) = 2 – x + 3 = 5 – x。

Another frequent slip occurs with the difference of two squares: students sometimes think that (a – b)² = a² – b², which is wrong. The correct expansion is a² – 2ab + b².

另一个常见失误发生在平方差公式上：学生有时认为 (a – b)² = a² – b²，这是错误的。正确的展开是 a² – 2ab + b²。

2. Misapplying Laws of Indices | 指数运算法则误用

Indices rules are fundamental, yet examiners report that students frequently misuse them, especially when dealing with fractional and negative powers. A typical error is writing a³ × a² = a⁶ instead of a⁵. Also, (a³)² = a⁵ instead of a⁶ is a common mistake.

指数法则是最基本的，然而考官报告指出学生经常用错，尤其是在处理分数指数和负指数时。一个典型错误是把 a³ × a² 写成 a⁶ 而不是 a⁵。同样，(a³)² = a⁵ 而不是 a⁶ 也是常见错误。

Another pitfall is confusing a^(1/n) with √a: a^(1/2) is √a, but a^(1/3) is the cube root of a. Many students mistakenly treat a^(1/2) as 1/(a²), which is completely wrong. Remember: a^(–1) = 1/a.

另一个陷阱是混淆 a^(1/n) 与 √a：a^(1/2) 是 √a，但 a^(1/3) 是 a 的立方根。很多学生误将 a^(1/2) 当作 1/(a²)，这完全错误。记住：a^(–1) = 1/a。

3. Quadratic Equation Factorisation Errors | 二次方程因式分解错误

When factorising quadratics like x² – 5x + 6, pupils often write (x – 2)(x – 3) correctly, but may incorrectly set the factors equal to zero: x – 2 = 0 and x – 3 = 0 gives roots 2 and 3. However, errors creep in when the coefficient of x² is not 1. For 2x² – x – 6, a wrong factorisation might be (2x + 3)(x – 2). The signs must multiply to give –6 and add to give –1 (when considering 2x² – x – 6). Practice with systematic approaches.

在因式分解二次方程时，例如 x² – 5x + 6，学生通常正确写出 (x – 2)(x – 3)，但可能会错误地让因子等于零：x – 2 = 0 和 x – 3 = 0 得到根 2 和 3。然而，当 x² 的系数不为 1 时错误就出现了。对于 2x² – x – 6，错误分解可能是 (2x + 3)(x – 2)。符号必须乘积为 –6，并且加起来为 –1（当分解 2x² – x – 6 时）。要用系统方法练习。

Also, forgetting to check the discriminant when solving word problems can lead to claiming real solutions when none exist. Always evaluate b² – 4ac.

此外，在解应用题时忘记检查判别式，会导致声称存在实数解而实际上没有。务必计算 b² – 4ac。

4. Function Notation and Domain/Range | 函数记号与定义域/值域

Common errors include confusing f(x) with f(–x) or misapplying f(x) + c as vertical shift. For instance, f(x + 2) is a horizontal translation to the left by 2, not to the right. Many students shift in the wrong direction. Also, when finding inverse functions, they often forget to swap x and y or to correctly restrict the domain of the original function so that the inverse exists.

常见错误包括混淆 f(x) 与 f(–x)，或误用 f(x) + c 作为垂直平移。例如，f(x + 2) 是向左水平平移 2 个单位，而不是向右。很多学生搞错方向。同时，在求反函数时，他们经常忘记交换 x 和 y，或忘记适当限制原函数的定义域以使反函数存在。

Another mistake is with domain and range of composite functions

Published by TutorHao | Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）