📚 Year 9 Core Mathematics Homework Answers (Pages 1-27) | 九年级核心数学作业答案（第1-27页）
This revision guide provides worked answers and key methods for the Year 9 Core Mathematics homework set on pages 1 to 27. It covers number, algebra, ratio, geometry, statistics and probability, with each answer paired to a short explanation so you can check your reasoning and fix common mistakes.
本复习指南提供九年级核心数学作业第 1–27 页的详细答案与关键方法。内容涵盖数、代数、比、几何、统计和概率，每个答案都配有简要解释，帮助你检查推理并纠正常见错误。
1. Integers and Order of Operations | 整数与运算顺序
8 − 5). Apply BIDMAS: brackets first, then division and multiplication left to right, and finally addition.
示例：计算 24 ÷ 6 + 3 × (8 − 5)。按 BIDMAS 规则：先算括号，再从左到右算除法和乘法，最后算加法。
Answer: 24 ÷ 6 = 4, 3 × 3 = 9, so 4 + 9 = 13.
答案：24 ÷ 6 = 4，3 × 3 = 9，因此 4 + 9 = 13。
Second worked example: Evaluate (−5)² − 2³. Squaring a negative gives a positive; cubing 2 gives 8.
第二个示例：计算 (−5)² − 2³。负数平方为正；2 的立方为 8。
Answer: (−5)² = 25, 2³ = 8, so 25 − 8 = 17.
答案：(−5)² = 25，2³ = 8，因此 25 − 8 = 17。
Common error: Writing −5² as 25 instead of −25. The index only attaches to 5 unless brackets are used.
常见错误：把 −5² 写成 25 而不是 −25。除非有括号，指数只作用于 5。
2. Fractions, Decimals and Percentages | 分数、小数与百分比
Worked example: Write 7/20 as a decimal and as a percentage. Use an equivalent fraction with denominator 100.
示例：把 7/20 写成小数和百分数。使用分母为 100 的等值分数。
Answer: 7/20 = 35/100 = 0.35 = 35%.
答案：7/20 = 35/100 = 0.35 = 35%。
Worked example: Find 15% of £240. Convert the percentage to a decimal and multiply.
示例：求 £240 的 15%。把百分数转换为小数后相乘。
Answer: 0.15 × 240 = £36.
答案：0.15 × 240 = £36。
Worked example: Express 1/3 as a recurring decimal. Perform short division: 1 ÷ 3.
示例：把 1/3 写成循环小数。进行短除：1 ÷ 3。
Answer: 1/3 = 0.333... = 0.3̇ (use a dot over the 3).
答案：1/3 = 0.333... = 0.3̇（在 3 上加循环点）。
| Fraction | 分数 | Decimal | 小数 | Percentage | 百分数 |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
3. Algebraic Expressions and Substitution | 代数式与代入求值
Worked example: Simplify 4a + 3b − 2a + 5b. Collect like terms: a terms and b terms.
示例：化简 4a + 3b − 2a + 5b。合并同类项：a 项与 b 项。
Answer: 4a − 2a = 2a and 3b + 5b = 8b, so 2a + 8b.
答案：4a − 2a = 2a，3b + 5b = 8b，所以 2a + 8b。
Worked example: Expand 3(x − 4). Multiply each term inside the bracket by 3.
示例：展开 3(x − 4)。将括号内每一项乘以 3。
Answer: 3 × x = 3x, 3 × (−4) = −12, so 3x − 12.
答案：3 × x = 3x，3 × (−4) = −12，所以 3x − 12。
: If a = 3, b = −2 and c = 4, evaluate 2a² + bc. Substitute carefully and use index rules.
示例：若 a = 3，b = −2，c = 4，计算 2a² + bc。仔细代入并运用指数规则。
Answer: 2(3)² + (−2)(4) = 2(9) − 8 = 18 − 8 = 10.
答案：2(3)² + (−2)(4) = 2(9) − 8 = 18 − 8 = 10。
4. Linear Equations | 线性方程
Worked example: Solve 5x + 3 = 23. Subtract 3 from both sides, then divide by 5.
示例：解方程 5x + 3 = 23。两边减 3，再除以 5。
Answer: 5x = 20, so x = 4.
答案：5x = 20，所以 x = 4。
Worked example: Solve 4(x − 2) = 2x + 6. Expand the left side, then
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