9C Homework Book Answers: Prelims | 9C 作业本答案：预备篇

📚 9C Homework Book Answers: Prelims | 9C 作业本答案：预备篇

This article works through typical Prelims questions found in a 9C homework book. It focuses on the key skills tested at the start of the course: number work, algebra, ratio, geometry, and problem solving. Each section gives a worked example, the answer, and a short explanation of the method.

本文讲解 9C 作业本预备篇中的常见题目。内容围绕课程开篇考查的核心技能：数字运算、代数、比例、几何和问题解决。每一节提供例题、答案和解题方法说明。

1. Understanding the Prelims Section | 认识预备篇

The Prelims section is designed to check the knowledge you should already have before starting the main 9C topics. It usually contains short questions covering arithmetic, fractions, simple equations, and basic shape facts.

预备篇旨在检查你在进入 9C 主要专题之前应已掌握的知识。它通常包含算术、分数、简单方程和基本图形的短问题。

Do not skip the Prelims. If you can answer these questions quickly and accurately, the main chapters will feel much easier.

不要跳过预备篇。如果你能快速准确地回答这些问题，后续章节会轻松很多。

A common mark scheme awards one mark for method and one for accuracy, so always show your working.

常见评分标准是方法得一分、结果得一分，因此一定要写出过程。

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2. Number Skills: Fractions, Decimals and Percentages | 数字技能：分数、小数与百分比

Question: Write 0.36 as a fraction in its lowest terms.

题目：将 0.36 写为最简分数。

Answer: 0.36 = 36/100 = 9/25.

答案：0.36 = 36/100 = 9/25。

Method: Write two decimal places as hundredths, then cancel the common factor 4 from numerator and denominator.

方法：两位小数写成分母为 100 的分数，再将分子分母同时除以公因数 4。

Question: Increase £80 by 15%.

题目：将 80 英镑增加 15%。

Answer: 15% of 80 = 12, so new amount = 80 + 12 = £92.

答案：80 的 15% 是 12，所以新金额 = 80 + 12 = 92 英镑。

Using a multiplier is faster: 80 × 1.15 = 92.

使用乘数更快：80 × 1.15 = 92。

Question: Convert 3/8 to a decimal and a percentage.

题目：将 3/8 转换为小数和百分数。

Answer: 3/8 = 0.375 = 37.5%.

答案：3/8 = 0.375 = 37.5%。

Method: Divide 3 by 8 to get the decimal, then multiply by 100 to change it to a percentage.

方法：用 3 除以 8 得到小数，再乘以 100 转换为百分数。

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3. Algebraic Simplification | 代数化简

Question: Simplify 5a + 3b − 2a + 7b.

题目：化简 5a + 3b − 2a + 7b。

Answer: 3a + 10b.

答案：3a + 10b。

Method: Collect like terms. 5a − 2a = 3a and 3b + 7b = 10b.

方法：合并同类项。5a − 2a = 3a，3b + 7b = 10b。

Question: Expand 4(2x − 5).

题目：展开 4(2x − 5)。

Answer: 8x − 20.

答案：8x − 20。

Method: Multiply each term inside the bracket by 4. Remember that a negative sign stays with the 5.

方法：将括号内每一项都乘以 4。注意负号跟着 5 一起乘。

Question: Factorise 12x + 18.

题目：因式分解 12x + 18。

Answer: 6(2x + 3).

答案：6(2x + 3)。

Method: Find the highest common factor of 12 and 18, which is 6, then write the bracket with the remaining terms.

方法：找出 12 和 18 的最大公因数 6，再把剩余项写进括号。

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4. Solving Linear Equations | 解一元一次方程

Question: Solve 3x + 7 = 22.

题目：解方程 3x + 7 = 22。

Answer: x = 5.

答案：x = 5。

Method: Subtract 7 from both sides to get 3x = 15, then divide both sides by 3.

方法：两边同时减去 7，得到 3x = 15，再两边同时除以 3。

Always check by substituting the value back into the original equation.

一定要把值代回原方程检验。

Question: Solve 2(x − 4) = 10.

题目：解方程 2(x − 4) = 10。

Answer: x = 9.

答案：x = 9。

Method: Expand first to get 2x − 8 = 10, then add 8 and divide by 2.

方法：先展开得 2x − 8 = 10，再加 8 后除以 2。

Question: Solve 5x − 2 = 3x + 8.

题目：解方程 5x − 2 = 3x + 8。

Answer: x = 5.

答案：x = 5。

Method: Subtract 3x from both sides: 2x − 2 = 8. Then add 2: 2x = 10. Divide by 2: x = 5.

方法：两边同时减去 3x：2x − 2 = 8。再加 2：2x = 10。除以 2：x = 5。

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5. Ratio and Proportion | 比与比例

Question: Divide £60 in the ratio 2:3.

题目：按 2:3 的比例分配 60 英镑。

Answer: £24 and £36.

答案：24 英镑和 36 英镑

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