KS3 AQA Business: Formulas & Theorems Quick Reference Guide | KS3 AQA 商务：公式定理速查手册

📚 KS3 AQA Business: Formulas & Theorems Quick Reference Guide | KS3 AQA 商务：公式定理速查手册

Welcome to your go-to quick-reference handbook for the essential formulas and theorems in KS3 AQA Business. This guide brings together all the key calculations, principles and frameworks you need to master – from demand and supply to break‑even, profit margins and cash flow. Whether you are preparing for an end‑of‑topic test or building a strong foundation for GCSE, these clear definitions and worked examples will help you learn faster and revise smarter.

欢迎使用这本 KS3 AQA 商务必备公式定理速查手册。本指南汇集了你需要掌握的所有关键计算、原理和框架——从需求与供给到盈亏平衡、利润率和现金流。无论你正在准备单元测验，还是为 GCSE 打下扎实基础，这些清晰的定义和示例都能帮助你学得更快、复习得更有条理。

Each section presents a business concept with its formula or theorem in bold, followed by a concise English explanation and its Chinese translation. Use this handbook to check your understanding, complete homework tasks and build confidence in applying business maths.

每一节都以加粗的形式呈现商务概念及其公式或定理，随后给出简明的英文解释和对应的中文翻译。利用这本手册来检查你的理解、完成家庭作业，并在应用商务数学时建立信心。

1. The Law of Demand | 需求定律

Price Increase → Quantity Demanded Decreases (ceteris paribus)

The law of demand states that when the price of a product rises, the quantity consumers are willing and able to buy falls, assuming all other factors remain unchanged. This inverse relationship is fundamental to understanding how markets work. For example, if a cinema ticket price goes up from £5 to £8, fewer teenagers may go to the movies.

需求定律指出，在其他条件不变的前提下，当产品价格上升时，消费者愿意且能够购买的数量会下降。这种反向关系是理解市场运行的基础。例如，电影票价格从5英镑涨到8英镑，去看电影的青少年的数量就可能减少。

Economists use the term ‘ceteris paribus’ to mean ‘all other things being equal’. Changes in income, tastes or the price of substitutes can shift demand, but the law itself describes a movement along the demand curve rather than a shift of the whole curve.

经济学家用“ceteris paribus”表示“其他条件不变”。收入、喜好或替代品价格的变化会移动需求，但需求定律本身指的是沿需求曲线的移动，而不是整条曲线的平移。

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2. The Law of Supply | 供给定律

Price Increase → Quantity Supplied Increases (ceteris paribus)

According to the law of supply, producers are willing to offer more of a good for sale as its price rises, provided other factors stay the same. Higher prices can mean higher potential profit, which encourages firms to increase output. For instance, a bakery will bake more croissants if the selling price rises from £1 to £1.50.

根据供给定律，在其他条件不变的情况下，当商品价格上升时，生产者愿意提供更多数量的该商品。较高的价格可能带来更高的潜在利润，这会激励企业增加产量。例如，假如牛角包的单价从1英镑涨到1.50英镑，面包房就会烤制更多的牛角包。

A change in production costs, technology or the number of sellers can shift the supply curve. The law of supply explains movements along a given supply curve: at higher prices there is an expansion of supply, and at lower prices a contraction.

生产成本、技术或卖方数量的变化会导致供给曲线的移动。供给定律解释了沿给定供给曲线的移动：在价格更高时，供给量扩张；在价格更低时，供给量收缩。

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3. Revenue, Cost and Profit | 收入、成本与利润

Profit = Total Revenue – Total Costs

Revenue is the income a business earns from selling its goods or services. It is calculated by multiplying the selling price by the quantity sold. Total costs are the sum of all expenses required to produce and deliver those goods. Profit – the reward for taking a business risk – is what remains when costs are subtracted from revenue.

收入是企业通过销售产品或服务而获得的款项，通过售价乘以销售量计算。总成本是生产和交付这些商品所需的所有费用的总和。利润——承担商业风险的回报——就是从收入中减去成本后剩下的部分。

If a business sells 200 phone cases at £8 each, total revenue is £1,600. If the combined costs (materials, rent, wages) equal £1,200, then profit is £400. Understanding this equation helps owners decide whether a product is worth selling.

如果一家企业以每个8英镑的价格卖出200个手机壳，总收入就是1,600英镑。如果总成本（材料、租金、工资）为1,200英镑，那么利润就是400英镑。理解这个等式有助于经营者判断某产品是否值得销售。

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4. Total Cost Formula | 总成本公式

Total Costs = Fixed Costs + (Variable Cost per Unit × Quantity)

Fixed costs, such as rent and insurance, do not change with the level of output in the short run. Variable costs, such as raw materials and direct labour, rise as more units are produced. The total cost at any production level is the sum of fixed costs and total variable costs.

固定成本（如租金和保险）在短期内不随产量变化。可变成本（如原材料和直接人工）会随着产出数量的增加而上升。任何产量水平下的总成本都是固定成本与总可变成本之和。

For a T-shirt printing business, fixed costs might be £500 per month. If each T-shirt requires £3 of materials and £2 of labour, variable cost per unit is £5. Printing 300 shirts would incur total variable costs of £1,500, giving total costs of £2,000.

对一家T恤印花公司而言，固定成本可能为每月500英镑。如果每件T恤需要3英镑材料和2英镑人工，单位可变成本就是5英镑。印制300件T恤会产生1,500英镑的总可变成本，总成本则为2,000英镑。

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5. Break-even Point | 盈亏平衡点

Break-even Point (units) = Fixed Costs ÷ (Selling Price per Unit – Variable Cost per Unit)

The break-even point is the number of units a business must sell to cover all its costs exactly, making neither a profit nor a loss. The difference between selling price and variable cost per unit is called the contribution. Each unit sold contributes towards paying off fixed costs.

盈亏平衡点是指企业必须销售的产品数量，以恰好覆盖所有成本，既不盈利也不亏损。单位售价与单位可变成本之间的差额称为边际贡献。每售出一单位产品都帮助分摊固定成本。

Suppose a smoothie bar has fixed costs of £800 per week, sells each smoothie for £4, and incurs a variable cost of £1.50 per cup. Break-even = 800 ÷ (4 – 1.50) = 800 ÷ 2.50 = 320 smoothies. Selling more than 320 generates profit; selling fewer results in a loss.

假设一家果汁吧每周固定成本为800英镑，每杯果汁售价4英镑，每杯可变成本为1.50英镑。盈亏平衡点 = 800 ÷ (4 – 1.50) = 800 ÷ 2.50 = 320杯果汁。超过320杯就有利润，不足320杯则亏损。

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6. Cash Flow Forecast | 现金流预测

Net Cash Flow = Total Cash Inflows – Total Cash Outflows

A cash flow forecast estimates the money a business expects to receive (inflows) and pay out (outflows) over a period. Net cash flow shows whether the business will have surplus cash or a deficit. Positive cash flow is crucial for paying bills, buying stock and avoiding insolvency.

现金流预测是对企业在一个时期内预计收到（流入）和支付（流出）的资金进行的估算。净现金流显示企业将拥有现金盈余还是赤字。保持正向现金流对于支付账单、采购库存和避免破产至关重要。

If a small shop expects cash inflows of £5,000 from sales and outflows of £4,200 for suppliers and rent in March, net cash flow is +£800. The closing balance would be the opening balance plus this net cash flow. Regular forecasting helps businesses spot periods of potential cash shortage.

如果一家小商店预计三月从销售中获得5,000英镑的现金流入，并向供应商和房租支付4,200英镑的现金流出，那么净现金流为+800英镑。期末余额为起初余额加上净现金流。定期进行预测能帮助企业发现潜在的现金短缺期。

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7. Profit Margin Ratios | 利润率比率

Gross Profit Margin (%) = (Gross Profit ÷ Revenue) × 100

Net Profit Margin (%) = (Net Profit ÷ Revenue) × 100

Gross profit is revenue minus the cost of sales (direct costs). The gross profit margin shows how much of each pound of sales is left after covering the direct costs of production. Net profit further deducts all expenses, including overheads, tax and interest, revealing the final percentage of revenue that the business keeps as profit.

毛利润是收入减去销售成本（直接成本）。毛利率显示每一英镑销售收入在覆盖直接生产成本之后还剩下多少。净利润则进一步扣除了所有费用，包括间接费用、税收和利息，揭示企业最终保留为利润的收入百分比。

A business with £50,000 revenue and £30,000 cost of sales has a gross profit of £20,000. Gross profit margin = (20,000 ÷ 50,000) × 100 = 40%. If total expenses are £12,000, net profit is £8,000, giving a net profit margin of 16%. Higher margins generally indicate better cost control and pricing power.

一家企业收入50,000英镑，销售成本30,000英镑，则毛利润为20,000英镑。毛利率 = (20,000 ÷ 50,000) × 100 = 40%。若总费用为12,000英镑，净利润则为8,000英镑，净利润率为16%。较高的利润率通常意味着更好的成本控制和定价能力。

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8. Simple Interest Formula | 单利公式

Simple Interest = Principal × Rate × Time (years)

When a business borrows money or invests savings, the cost of borrowing or the return on savings is often calculated using simple interest. The principal is the original amount, the rate is the annual interest percentage, and time is the number of years. Total repayment = Principal + Simple Interest.

当企业借款或投资存款时，借款成本或存款回报通常用单利计算。本金是初始金额，利率是年利息百分率，时间是年数。总还款额 = 本金 + 单利。

If a start‑up borrows £4,000 at an annual simple interest rate of 6% for 3 years, the interest = 4,000 × 0.06 × 3 = £720. The total amount owed after 3 years is £4,720. This formula helps entrepreneurs compare loan offers and understand the true cost of finance.

如果一家初创企业以6%的年单利借款4,000英镑，期限3年，利息 = 4,000 × 0.06 × 3 = 720英镑。3年后需偿还总额为4,720英镑。这个公式有助于创业者比较贷款方案并理解融资的实际成本。

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9. The Marketing Mix (4Ps) Framework | 营销组合框架

Marketing Mix = Product + Price + Place + Promotion

The 4Ps are not a mathematical formula but a framework — a theorem for making decisions that satisfy customer needs while achieving business objectives. Product refers to the good or service itself; Price is how much customers pay; Place is where and how the product is sold; Promotion covers advertising, sales offers and public relations.

4P并非数学公式，而是一个框架——帮助企业做出既能满足顾客需要又能达成商业目标的决策的一套“法则”。Product指产品自身；Price是顾客支付的价格；Place指产品销售的地点和渠道；Promotion包括广告、促销和公关活动。

For a successful launch, all four elements must be consistent. A premium perfume (Product) with a high price (Price) should be sold in department stores (Place) and promoted through glossy magazine adverts (Promotion). The marketing mix helps KS3 learners analyse real‑world business strategies.

一项成功的推出，需要四个要素保持一致。一款高端香水（产品）配上高价（价格），应当在百货商场（渠道）销售，并通过精美杂志广告（促销）进行推广。营销组合有助于KS3学生分析现实中的商业战略。

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10. Business Averages (Mean) | 商务平均值

Mean = Sum of All Values ÷ Number of Values

The mean average is widely used in business to analyse sales figures, customer ratings, employee performance scores and many other data sets. It gives a simple central value that helps managers spot trends and make comparisons.

平均值在商务中广泛用于分析销售数据、客户评分、员工绩效得分和许多其他数据集。它提供了一个简洁的中心值，帮助管理者发现趋势并进行比较。

A café records daily coffee sales over a week: 85, 92, 78, 88, 90, 95, 80. The sum is 608 and the number of days is 7, so the mean is 608 ÷ 7 ≈ 86.9 cups. This average helps the café order the right amount of coffee beans for a typical day.

一家咖啡馆记录了一周每日咖啡销量：85、92、78、88、90、95、80 杯。总和为608，天数为7，因此平均值约为608 ÷ 7 ≈ 86.9 杯。这个平均值有助于咖啡馆为普通的一天订购适量的咖啡豆。

Businesses often combine the mean with other measures like the mode and range to get a fuller picture of performance. For KS3, mastering the mean is an essential numeracy skill directly applied in business contexts.

企业常会把平均值与众数、极差等其他指标结合使用，以更全面地了解业绩。对于KS3阶段而言，掌握平均值运算是一项直接应用于商务情境的基本计算技能。

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Published by TutorHao | Business Revision Series | aleveler.com

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