📚 Essential Maths 9H Homework Answers: Topic Review and Worked Solutions | Essential Maths 9H 作业答案：主题复习与详细解答
This article is a topic-by-topic guide to the types of homework questions found in Essential Maths 9H. We do not reproduce complete answer keys, but we show how to solve representative problems and how to check your own work.
本文按主题梳理 Essential Maths 9H 中的常见作业题型。我们不复制完整答案，但会示范如何解答典型题目，以及如何检查自己的作业。
1. Number and Place Value | 数与位值
. A typical homework question asks you to evaluate an expression such as 3² × (4 + 5) ÷ 3.
在 Year 9 高阶课程中，你必须熟练掌握运算顺序（BIDMAS/BODMAS）、幂与方根。常见的作业题目会要求你计算类似 3² × (4 + 5) ÷ 3 的表达式。
Worked answer: 3² = 9, 4 + 5 = 9, so 9 × 9 = 81, then 81 ÷ 3 = 27.
解答：3² = 9，4 + 5 = 9，所以 9 × 9 = 81，然后 81 ÷ 3 = 27。
Also check rounding and significant figures: for example, 0.004738 to 2 significant figures is 0.0047 because the first non-zero digit is 4 and the next digit is 7.
还要检查四舍五入与有效数字：例如 0.004738 保留 2 位有效数字是 0.0047，因为第一个非零数字是 4，下一位是 7。
To multiply numbers in standard form, multiply the front numbers and add the powers of 10.
标准形式也常考：45000 = 4.5 × 10⁴，0.0032 = 3.2 × 10⁻³。计算标准形式乘法时，先乘前部的数，再把 10 的指数相加。
2³ × 2² = 2⁵ = 32 and (3²)³ = 3⁶ = 729
Remember that a negative power means a reciprocal: 10⁻² = 1/100 and 5⁻¹ = 1/5.
请记住，负指数表示倒数：10⁻² = 1/100，5⁻¹ = 1/5。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
1/4, write both over a common denominator: 2/3 = 8/12 and 1/4 = 3/12, so the sum is 11/12.
分数、小数和百分比经常综合考查。计算 2/3 + 1/4 时，先通分：2/3 = 8/12，1/4 = 3/12，所以和为 11/12。
20 = 3/10. To divide, flip the second fraction and multiply: 3/5 ÷ 2/3 = 3/5 × 3/2 = 9/10.
分数乘法：分子乘分子，分母乘分母：2/5 × 3/4 = 6/20 = 3/10。分数除法：把第二个分数取倒数后相乘：3/5 ÷ 2/3 = 3/5 × 3/2 = 9/10。
A common percentage increase question: increase £240 by 15%. Multiply by 1.15: 240 × 1.15 = 276, so the new amount is £276.
常见的百分比增加题：将 240 英镑增加 15%。乘以 1.15：240 × 1.15 = 276，所以新金额为 276 英镑。
To decrease by 20%, multiply by 0.80 because 100% − 20% = 80%. A £60 item after a 20% decrease costs 60 × 0.80 = £48.
减少 20% 时乘以 0.80，因为 100% − 20% = 80%。原价 60 英镑的商品减少 20% 后价格为 60 × 0.80 = 48 英镑。
imal to a fraction when needed: for example, 0.375 = 375/1000 = 3/8 after dividing by 125.
需要时将小数化为分数：例如 0.375 = 375/1000，分子分母同除以 125 得 3/8。
3. Ratio and Proportion | 比与比例
Ratio questions often ask you to share an amount in a given ratio. To share £ 5, first add the parts: 3 + 5 = 8 parts. One part is 56 ÷ 8 = 7, so the shares are 3 × 7 = £21 and 5 × 7 = £35.
比例题常要求按给定比例分配金额。将 56 英镑按 3 : 5 分配，先求总份数：3 + 5 = 8 份。一份是 56 ÷ 8 = 7，所以分配为 3 × 7 = 21 英镑和 5 × 7 = 35 英镑。
Always simplify a ratio like 24 : 36 by dividing both sides by 12: the simplified ratio is 2 : 3.
化简比例 24 : 36 时，两边同时除以 12：化简后为 2 : 3。
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