Exact Answers | 精确答案

📚 Exact Answers | 精确答案

In Edexcel A Level Mathematics, many questions ask for an exact answer rather than a decimal approximation. This means you should leave numbers in forms such as fractions, surds, π, e, or logarithms.

在爱德思 A Level 数学中，许多题目要求给出精确答案而不是小数近似值。这意味着你需要把结果保留成分数、根式、π、e 或对数等形式。

1. What Are Exact Answers? | 什么是精确答案？

An exact answer preserves the true mathematical value without rounding. For example, √2 is exact, while 1.414 is a rounded decimal approximation.

精确答案保留真实数学值而不四舍五入。例如，√2 是精确的，而 1.414 是四舍五入后的小数近似值。

Common exact forms include fractions such as 1/3, surds such as √5, multiples of π such as π/6, powers of e such as e², and logarithms such as ln 2.

常见的精确形式包括分数如 1/3、根式如 √5、π 的倍数如 π/6、e 的幂如 e²，以及对数如 ln 2。

On Edexcel papers, the instruction ‘give your answer in exact form’ means a decimal answer will not receive full credit unless the question explicitly allows approximation.

在爱德思试卷中，’以精确形式给出答案’ 这一要求意味着小数答案不会得满分，除非题目明确允许近似值。

2. Surds and Simplifying Radicals | 根式与根式化简

Surds are irrational roots such as √2, √3, and √5. You should simplify them by extracting square factors: √12 = √(4 × 3) = 2√3.

根式是无理根，如 √2、√3 和 √5。你应当通过提取平方因子来化简它们：√12 = √(4 × 3) = 2√3。

When multiplying surds, use √a × √b = √(ab). For example,

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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