📚 9H Homework Book Answers: Prelims | 9H 作业本答案：预备部分
This article explains the key ideas and sample answers from the first two preliminary pages of a typical Year 9 Higher (9H) mathematics homework book. It supports students, parents and tutors who need a clear self-study reference for the skills that reappear throughout the 9H course.
本文讲解典型 9 年级高等（9H）数学作业本前两页预备部分的核心概念与示例答案，适合学生、家长和辅导教师使用，为贯穿整个 9H 课程的必备技能提供清晰的自学参考。
1. How to Use the Prelim Answer Book | 如何使用预备答案册
The prelim pages of a 9H homework book are not a full mark scheme. They show worked answers and key reminders for early topics such as indices, prime factorisation and linear equations. Always attempt each question before checking the answer, and use the notes to diagnose where your method went wrong.
9H 作业本的预备页并不是完整的评分方案。它们展示早期主题（如指数、质因数分解、线性方程）的详细答案和关键提示。请务必先独立完成题目再核对答案，并利用注释诊断解题方法中的错误。
Many 9H prelim answers include two columns: one for the final answer and one for the working or alternative method. Copying the final answer alone will not build exam technique. Focus on the line-by-line working shown, then cover it and reproduce the method from memory.
许多 9H 预备答案包含两栏：一栏是最终答案，另一栏是解题过程或替代方法。仅抄写最终答案并不能培养考试技巧，重点应放在逐步展示的过程上，然后遮住答案，凭记忆复现方法。
Step 1: Attempt the question in your exercise book without looking at the answer.
第一步：在练习本上独立作答，不先看答案。
Step 2: Compare your working line by line with the answer, not just the final value.
第二步：逐行对比解题过程，而不只是核对最终数值。
Step 3: Rewrite any incorrect line in a different colour and note the rule you missed.
第三步：用不同颜色重写错误行，并记下遗漏的规则。
2. Key Symbols and Terminology | 核心符号与术语
multiplication, ÷ for division, and superscripts such as x² and x³ for powers. The symbol ⇒ means 'implies' or 'therefore'.
在完成前两页之前，请确保熟悉 9H 层级使用的符号。常见符号包括 Δ 表示变化量，× 表示乘法，÷ 表示除法，上标如 x² 和 x³ 表示幂。符号 ⇒ 表示 "推出" 或 "因此"。
Terms such as 'integer', 'factor', 'multiple', 'prime', 'coefficient' and 'constant' often appear in prelim instructions. A coefficient is the number multiplying a variable in a term, while a constant is a term without a variable.
"整数"、"因数"、"倍数"、"质数"、"系数" 和 "常数" 等术语常出现在预备页说明中。系数是项中乘以变量的数，常数则是不含变量的项。
| Symbol or term | Meaning | 中文说明 |
|---|---|---|
| Δ | change | 变化量 |
| × ÷ | multiplication and division | 乘法与除法 |
| ⇒ | implies or therefore | 推出或因此 |
| x², x³ | x squared, x cubed | x 的平方、x 的立方 |
3. Indices and Index Laws | 指数与指数定律
d x × x × x × x = x⁴. The index tells you how many times the base is multiplied by itself.
指数是重复乘法的简写形式。例如 2 × 2 × 2 = 2³，x × x × x × x = x⁴。指数表示底数被自身相乘的次数。
The main index laws are used constantly in 9H algebra. Learn them as rules, not as separate tricks.
9H 代数中会不断使用主要指数定律。请把它们当作规则来掌握，而不是零散技巧。
xᵃ × xᵇ = xᵃ⁺ᵇ
同底数相乘，指数相加。
xᵃ ÷ xᵇ = xᵃ⁻ᵇ
同底数相除，指数相减。
(xᵃ)ᵇ = xᵃᵇ
幂的幂，指数相乘。
x⁰ = 1 for x ≠ 0
任何非零数的零次幂等于 1。
x⁻ⁿ = 1 ÷ xⁿ
负指数表示倒数。
x¹ᐟ² = √x and x¹ᐟ³ = ∛x
分数指数对应根号形式。
3x² × 4x⁵ = 12x⁷
This example multiplies the coefficients 3 and 4, then adds the indices 2 and 5. The final index is 7.
这个例子先相乘系数 3 和 4，再把指数 2 和 5 相加，最终指数为 7。
4. Prime Factorisation and HCF/LCM | 质因数分解与 HCF/LCM
Prime factorisation writes a number as a product of prime numbers. Use a factor tree
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