📚 Year 9 AQA Business: Formula & Theorem Quick Reference Handbook | Year 9 AQA 商务：公式定理速查手册
This quick reference handbook brings together all the essential formulas, calculations and key theorems you need to master for the Year 9 AQA Business course. From revenue and costs to break‑even, cash flow and the laws of demand and supply, every topic is presented with clear definitions, step‑by‑step examples and bilingual explanations. Use this guide to reinforce your learning and boost your confidence for class tests, topic assessments and end‑of‑year exams.
这本速查手册汇集了 Year 9 AQA 商务课程中你必须掌握的所有核心公式、计算方法和关键定理。从收入、成本到盈亏平衡、现金流，再到需求与供给定律，每个主题都配有清晰的定义、分步示例和双语解释。利用本手册夯实知识，增强你在课堂测验、主题评估和年终考试中的信心。
1. Revenue Formula | 收入公式
Revenue is the total income a business generates from selling its goods or services before any costs are deducted. It is often called 'sales' or 'turnover'. The basic formula links the selling price of one unit and the quantity sold.
收入是企业在扣除任何成本之前，通过销售商品或服务所产生的总收入，通常被称为“销售额”或“营业额”。基本公式将一个单位的售价与销售数量联系起来。
Revenue = Selling Price per unit × Quantity Sold
If a bicycle retailer sells 45 bikes at £320 each, total revenue = £320 × 45 = £14,400. Remember, revenue is not profit — a business can have high revenue but still make a loss if its costs are even higher.
如果一家自行车零售商以每辆 320 英镑的价格售出 45 辆自行车，总收入 = 320 × 45 = 14,400 英镑。请记住，收入不是利润——企业的收入可能很高，但如果成本更高，仍然会亏损。
Businesses can increase revenue either by raising the selling price (if demand allows) or by selling more units through promotions or market expansion.
企业可以通过提高售价（如果需求允许）或通过促销和市场扩张来销售更多单位，从而增加收入。
2. Total Costs Formula | 总成本公式
Total costs are all the expenses a business incurs to produce its output. They are split into fixed costs, which stay the same regardless of output, and variable costs, which rise as more units are produced.
总成本是企业在生产过程中发生的全部开支。成本分为固定成本（无论产量多少都保持不变）和变动成本（随着产量增加而上升）。
Total Costs = Total Fixed Costs + Total Variable Costs
Examples of fixed costs include rent, insurance and managers' salaries. Variable costs include raw materials, packaging and piece‑rate labour. If a café pays £1,800 monthly rent (fixed) and spends £2.50 on coffee beans per cup (variable), making 1,000 cups gives total costs = £1,800 + (£2.50 × 1,000) = £4,300.
固定成本的例子包括租金、保险费和管理人员工资。变动成本包括原材料、包装材料和计件工资。如果一家咖啡馆每月支付租金 1,800 英镑（固定成本），每杯咖啡的咖啡豆成本为 2.50 英镑（变动成本），制作 1,000 杯的总成本 = 1,800 + (2.50 × 1,000) = 4,300 英镑。
When output is zero, variable costs are zero, but fixed costs still have to be paid. Understanding this distinction is crucial for break‑even analysis.
当产量为零时，变动成本为零，但固定成本仍需支付。理解这一区别对于盈亏平衡分析至关重要。
3. Profit Calculation | 利润计算
Profit measures financial success. It is the reward a business earns for taking risks and can be reinvested to fuel growth or distributed to owners. The calculation is straightforward: subtract total costs from total revenue.
利润衡量财务成功。它是企业因承担风险而获得的回报，可用于再投资以推动增长，或分配给企业主。计算很简单：从总收入中减去总成本。
Profit = Total Revenue − Total Costs
sult means a profit (surplus); a negative result means a loss. For instance, using the café above: revenue from 1,000 cups at £5 each = £5,000, total costs = £4,300, so profit = £5,000 − £4,300 = £700.
正数表示盈利（盈余），负数表示亏损。以前面的咖啡馆为例：1,000 杯咖啡，每杯售价 5 英镑，收入 = 5,000 英镑，总成本 = 4,300 英镑，利润 = 5,000 − 4,300 = 700 英镑。
Profit is vital for survival: without it a business cannot pay its bills, invest in new equipment or attract investors.
利润对生存至关重要：没有利润，企业就无法支付账单、投资新设备或吸引投资者。
4. Break-even Analysis | 盈亏平衡分析
Break-even analysis tells managers how many units they must sell to cover all costs. At the break‑even point, total revenue exactly equals total costs, so the business makes neither a profit nor a loss.
盈亏平衡分析告诉管理者需要销售多少件产品才能覆盖所有成本。在盈亏平衡点，总收入恰好等于总成本，因此企业既不盈利也不亏损。
Break‑even Point (units) = Total Fixed Costs ÷ (Selling Price per unit − Variable Cost per unit)
The bottom part of the formula is called the contribution per unit — sale contributes towards paying fixed costs and then generating profit. If fixed costs are £10,000, selling price is £25, and variable cost per unit is £15, contribution = £10. Break‑even = £10,000 ÷ £10 = 1,000 units.
公式下半部分称为单位贡献——每售出一件产品为支付固定成本并最终产生利润所贡献的金额。如果固定成本为 10,000 英镑，售价为 25 英镑，单位变动成本为 15 英镑，贡献 = 10 英镑。盈亏平衡点 = 10,000 ÷ 10 = 1,000 件。
Margin of Safety: This shows how far actual sales can fall before the business hits the break‑even level.
安全边际：它显示在触及盈亏平衡水平之前，实际销售量可以下降多少。
Margin of Safety = Actual Sales (units) − Break‑even Sales (units)
If the business sells 1,400 units and break‑even is 1,000 units, the margin of safety is 400 units — a comfortable buffer against unexpected drops in demand.
如果企业实际销售 1,400 件，盈亏平衡点为 1,000 件，安全边际就是 400 件——这是一个抵御需求意外下降的舒适缓冲。
5. Profit Margin Ratios | 利润率比率
Profit margins express profit as a percentage of revenue, making it easy to compare performance over time or against competitors. The two key margins are gross profit margin and net profit margin.
利润率将利润表示为收入的百分比，便于比较不同时期或与竞争对手的表现。两个关键比率是毛利率和净利率。
Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100
ss profit = Revenue − Cost of sales (direct production costs). A toy maker with revenue of £80,000 and cost of sales of £50,000 has gross profit of £30,000. Gross margin = (30,000 ÷ 80,000) × 100 = 37.5% This measures how efficiently a business turns raw materials into profit before overheads.
毛利润 = 收入 − 销售成本（直接生产成本）。一家玩具制造商收入 80,000 英镑，销售成本 50,000 英镑，毛利润为 30,000 英镑。毛利率 = (30,000 ÷ 80,000) × 100 = 37.5%。这衡量企业在扣除管理费用之前，将原材料转化为利润的效率。
Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100
xpenses (rent, salaries, interest, tax). If the same business has other expenses totalling £18,000, net profit = £30,000 − £18,000 = £12,000. Net margin = (12,000 ÷ 80
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