📚 AQA GCSE Business: Formula & Theorem Quick Reference Handbook | Year 11 AQA 商务：公式定理速查手册
This handbook is designed to give Year 11 AQA Business students a fast and accurate way to revise every essential formula. From revenue and profit to capacity utilisation, you will find the key calculations grouped by topic, with clear English explanations followed by their Chinese counterparts.
本手册旨在为 Year 11 AQA 商务学生提供快速准确的公式复习方法。从收入与利润到产能利用率，所有关键计算都按主题分组，并配有简洁的英文和对应的中文说明。
1. Revenue, Costs and Profit | 收入、成本与利润
These three building blocks appear in almost every business calculation. Memorising them perfectly gives you a strong foundation for break-even, margins and cash flow.
这三个基本公式几乎出现在每一道商务计算题中。准确记忆它们将为盈亏平衡、利润率和现金流打下坚实基础。
Revenue = Selling price per unit × Quantity sold — The total money coming into the business from selling goods or services before deducting any costs.
收入 = 单价 × 销量 — 扣除任何成本之前，企业通过销售商品或服务获得的总金额。
Total variable costs = Variable cost per unit × Quantity produced — Costs that change directly with the level of output, such as raw materials.
总变动成本 = 单位变动成本 × 产量 — 直接随产量变化的成本，如原材料。
Total costs = Fixed costs + Total variable costs — Fixed costs remain the same regardless of output (e.g. rent), while variable costs rise with production.
总成本 = 固定成本 + 总变动成本 — 固定成本不随产量变化（如租金），变动成本则随产量增加。
Profit = Revenue − Total costs — Profit is the surplus left after all costs have been subtracted from the money earned.
利润 = 收入 − 总成本 — 从赚取的收入中扣除所有成本后剩余的盈余。
2. Gross Profit and Net Profit | 毛利润与净利润
Understanding the difference between gross and net profit helps you analyse how efficiently a business manages its direct production costs and its overheads.
理解毛利与净利的区别，有助于分析企业如何有效管理直接生产成本和间接费用。
Gross profit = Revenue − Cost of sales — Cost of sales refers to the direct expenses of producing goods, e.g. raw materials and direct labour.
毛利润 = 收入 − 销售成本 — 销售成本指生产商品的直接费用，如原材料和直接人工。
Net profit = Gross profit − Other operating expenses — Operating expenses include rent, salaries of office staff, marketing and utilities.
净利润 = 毛利润 − 其他营业费用 — 营业费用包括租金、行政人员工资、营销和水电等。
3. Profit Margins | 利润率
Profit margins tell you what percentage of revenue becomes profit. They are vital for comparing performance over time or with competitors.
利润率告诉你收入中有多大比例转化为利润。这些比率对于跨期比较或与竞争对手的对比至关重要。
Gross profit margin = (Gross profit ÷ Revenue) × 100% — This shows how well a business controls its production costs relative to sales.
毛利率 = (毛利润 ÷ 收入) × 100% — 显示企业相对于销售额控制生产成本的能力。
Net profit margin = (Net profit ÷ Revenue) × 100% — A higher net margin indicates better overall cost management once all expenses are considered.
净利率 = (净利润 ÷ 收入) × 100% — 更高的净利率表明在考虑所有费用后，整体成本管理更出色。
4. Break-even Analysis | 盈亏平衡分析
Break-even helps a business work out how many units it must sell before it starts making a profit and how much of a safety cushion it has.
盈亏平衡帮助企业计算出需要销售多少单位才能开始盈利，以及它拥有多少安全缓冲。
Contribution per unit = Selling price per unit − Variable cost per unit — Contribution is the amount each sale contributes towards fixed costs and profit.
单位贡献毛利 = 单位售价 − 单位变动成本 — 贡献毛利是每笔销售为覆盖固定成本和利润所做的贡献。
Break-even output = Fixed costs ÷ Contribution per unit — At break-even, total revenue exactly equals total costs and the business makes zero profit or loss.
盈亏平衡点产量 = 固定成本 ÷ 单位贡献毛利 — 在盈亏平衡点上，总收入恰好等于总成本，企业既不盈利也不亏损。
Margin of safety = Actual sales (units) − Break-even output (units) — This shows how far sales can fall before the business starts losing money.
安全边际 = 实际销量 − 盈亏平衡产量 — 显示在开始亏损之前，销售量可以下滑多少。
5. Cash Flow | 现金流量
Cash flow formulas predict the movement of money in and out of the business, helping to avoid liquidity problems.
现金流公式用于预测货币的流入和流出，有助于避免流动性问题。
Net cash flow = Total cash inflows − Total cash outflows — A positive net cash flow means more money came in than went out in that period.
净现金流 = 现金流入总额 − 现金流出总额 — 正净现金流意味着该期间流入的现金多于流出。
Closing balance = Opening balance + Net cash flow — The closing balance of one month becomes the opening balance of the next.
期末余额 = 期初余额 + 净现金流 — 当月期末余额成为下月期初余额。
6. Average Rate of Return (ARR) | 平均回报率
ARR measures the average yearly profit of an investment as a percentage of the money spent. It is used to compare different investment options.
平均回报率衡量投资每年平均利润占投入资金的百分比，用于比较不同的投资方案。
Average Rate of Return = (Average annual profit ÷ Cost of investment) × 100% — Average annual profit is calculated by dividing the total expected profit by the number of years.
平均回报率 = (平均年利润 ÷ 投资成本) × 100% — 平均年利润由预期总利润除以年数得出。
7. Percentage Change | 百分比变动
This universal formula appears in many contexts, from sales growth to cost increases. It expresses change relative to the original value.
这个通用公式出现在许多情境中，从销售增长到成本增加，它表达了相对于原始值的变动。
Percentage change = [(New value − Old value) ÷ Old value] × 100% — A positive result indicates growth, while a negative result signals a decline.
百分比变动 = [(新值 − 旧值) ÷ 旧值] × 100% — 正数表示增长，负数表示下降。
8. Market Share and Market Growth | 市场份额与市场增长
Market share shows a business's slice of total sales in its industry, while market growth reveals whether the overall market is expanding or shrinking.
市场份额显示企业在行业总销售中所占的份额，而市场增长揭示整体市场是在扩大还是萎缩。
Market share = (Sales of the business ÷ Total market sales) × 100% — A rising market share often indicates competitive strength.
市场份额 = (企业销售额 ÷ 市场总销售额) × 100% — 市场份额上升通常意味着竞争优势。
Market growth = (Change in market size ÷ Original market size) × 100% — Change in market size is the difference between the new and the old total market size.
市场增长 = (市场规模的变化量 ÷ 原始市场规模) × 100% — 市场规模的变化量是新旧市场总规模之差。
9. Unit Cost | 单位成本
Unit cost shows the average expense of making one item. Managing unit costs is crucial for pricing and profitability.
单位成本显示制造一件产品所需的平均支出。管理单位成本对于定价和盈利能力至关重要。
Average unit cost = Total costs ÷ Number of units produced — Economies of scale often help reduce unit costs as output rises.
平均单位成本 = 总成本 ÷ 生产数量 — 规模经济通常有助于随着产量增加降低单位成本。
10. Labour Productivity and Labour Turnover | 劳动生产率与劳动力流动
These human resource formulas measure workforce efficiency and stability. They help a business assess how well it uses its people.
这些人力资源公式衡量员工效率和稳定性，帮助企业评估用人效果。
Labour productivity = Total output ÷ Number of employees — Higher productivity means each worker produces more on average.
劳动生产率 = 总产出 ÷ 员工人数 — 更高的生产率意味着每位员工平均产出更多。
turnover = (Number of employees leaving during period ÷ Average number of employees) × 100% — A very high turnover rate can signal low morale or poor working conditions.
劳动力流失率 = (期间离职员工人数 ÷ 平均员工人数) × 100% — 过高的流失率可能表明士气低落或工作条件不佳。
11. Capacity Utilisation | 产能利用率
Capacity utilisation measures the percentage of a firm's total possible output that is actually being achieved. It is heavily examined in AQA GCSE Business.
产能利用率衡量企业实际产出占最大可能产出的百分比。这是 AQA GCSE 商务常考的知识点。
Capacity utilisation = (Actual output ÷ Maximum possible output) × 100% — Operating near full capacity can lower unit costs but may strain resources.
产能利用率 = (实际产出 ÷ 最大可能产出) × 100% — 接近满负荷运行可降低单位成本，但可能造成资源紧张。
Published by TutorHao | Business Revision Series | aleveler.com
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