📚 Year 7 CAIE Business: Formula & Theorem Quick Reference Handbook | 商务公式定理速查手册
This handbook collects the essential formulas and core theorems you will meet in the Year 7 CAIE Business Studies course. Understanding each formula helps you analyse a business’s performance, calculate profit, set prices, and predict how markets work. Use this guide to revise key calculations and economic principles before tests and exams.
本手册整理了 Year 7 CAIE 商务课程中你会遇到的基本公式与核心定理。理解每一个公式能帮助你分析企业表现、计算利润、制定价格并预测市场运作方式。在测试与考试前，用这份指南复习关键计算和经济原理。
1. Total Revenue Formula | 总收入公式
Total revenue (or total sales) is the full amount of money a business receives from selling its goods or services before any costs are taken away. It is the top line of a simple income statement.
总收入（或总销售额）是企业在扣除任何成本之前，通过销售商品或服务获得的全额款项。它是简易利润表中的第一行数字。
Total Revenue = Selling Price per Unit × Quantity Sold
总收入 = 单位售价 × 销售数量
If a bakery sells 200 loaves of bread for £1.50 each, total revenue equals 200 × £1.50 = £300. Revenue rises when a firm sells more units or raises its selling price, but higher prices may reduce the quantity customers buy.
如果一家面包店以每条 1.50 英镑的价格卖出 200 条面包，总收入即为 200 × 1.50 = 300 英镑。当企业卖出更多产品或者提高售价时，收入会增加，但更高的价格可能让顾客购买的数量减少。
2. Total Cost Formula | 总成本公式
Total cost is the sum of all expenses a business must pay to produce and deliver its products. It usually splits into fixed costs and variable costs.
总成本是企业为生产和配送产品而必须支付的全部费用之和，通常分为固定成本和可变成本。
Total Cost = Fixed Costs + Variable Costs
总成本 = 固定成本 + 可变成本
Fixed costs stay the same regardless of output, such as monthly rent of £500. Variable costs change with production, e.g. raw materials costing £2 per unit. If a firm produces 100 units, fixed costs are £500 and variable costs are 100 × £2 = £200, so total cost = £700.
固定成本不随产量变化，比如每月租金 500 英镑。可变成本随生产变化，例如每单位原材料成本 2 英镑。若一家企业生产 100 单位产品，固定成本为 500 英镑，可变成本为 100 × 2 = 200 英镑，因此总成本 = 700 英镑。
3. Profit Formula | 利润公式
Profit is the reward a business earns for taking risks. It shows whether a business is financially healthy. Profit can be reinvested in the business or paid to owners.
利润是企业因承担风险而获得的回报。它能显示一家企业的财务是否健康。利润可以被重新投入企业，也可以支付给所有者。
Profit = Total Revenue − Total Cost
利润 = 总收入 − 总成本
A positive profit means the business earns more than it spends. If revenue is £1,000 and total cost is £750, profit is £250. If costs exceed revenue, the business makes a loss, which is shown as a negative figure.
正利润意味着企业的收入大于支出。如果收入为 1,000 英镑，总成本为 750 英镑，利润就是 250 英镑。如果成本超过收入，企业就会亏损，以负数表示。
4. Average Cost (Unit Cost) Formula | 平均成本（单位成本）公式
Average cost tells a business how much it spends on average to make one unit of output. It helps managers set a suitable selling price.
平均成本告诉企业平均每生产一单位产品需要花费多少钱。它有助于管理者制定合理的售价。
Average Cost = Total Cost ÷ Quantity Produced
平均成本 = 总成本 ÷ 生产数量
If total cost for making 500 T‑shirts is £2,500, the average cost is £2,500 ÷ 500 = £5 per T‑shirt. To earn a profit, the selling price must be set higher than £5, unless the business uses a different pricing strategy.
若生产 500 件 T 恤的总成本为 2,500 英镑，平均成本为 2,500 ÷ 500 = 每件 5 英镑。若要盈利，售价必须定得高于 5 英镑，除非企业采用其他定价策略。
5. Break-even Point Formula | 盈亏平衡点公式
The break-even point shows the number of units a business must sell to cover all its costs exactly—profit is zero at this point. It is one of the most important planning tools for start-ups.
盈亏平衡点表示企业必须卖出多少单位产品才能正好覆盖所有成本——此时利润为零。它是初创企业最重要的规划工具之一。
Break-even Point (units) = Fixed Costs ÷ (Selling Price per Unit − Variable Cost per Unit)
盈亏平衡点（单位数量） = 固定成本 ÷ (单位售价 − 单位可变成本)
The bottom part of the fraction, (Selling Price − Variable Cost per Unit), is called the contribution per unit. For example, if fixed costs are £2,000, selling price is £10 and variable cost per unit is £6, the contribution is £4. Break-even point = £2,000 ÷ £4 = 500 units.
分数下方的 (售价 − 单位可变成本) 叫作单位边际贡献。例如，固定成本为 2,000 英镑，售价为 10 英镑，单位可变成本为 6 英镑，边际贡献就是 4 英镑。盈亏平衡点 = 2,000 ÷ 4 = 500 单位。
6. Profit Margin Formula | 利润率公式
Profit margin compares profit to revenue and shows the percentage of each pound of sales that becomes profit. It helps businesses see how efficiently they turn sales into earnings.
利润率将利润与收入进行比较，显示每一英镑销售收入中有多大比例成为利润。它有助于企业看清自己将销售转化为盈利的效率。
Profit Margin (%) = (Profit ÷ Total Revenue) × 100
利润率 (%) = (利润 ÷ 总收入) × 100
A business with a profit of £400 and revenue of £2,000 has a profit margin of (400 ÷ 2,000) × 100 = 20%. This means for every £1 earned, 20 pence is pure profit. Higher margins usually indicate stronger cost control.
一家企业利润为 400 英镑，收入为 2,000 英镑，其利润率为 (400 ÷ 2,000) × 100 = 20%。这意味着每赚取 1 英镑，就有 20 便士是纯利润。利润率越高通常表明成本控制越好。
7. Mark-up Formula | 加成率公式
Mark-up describes how much a business adds to the cost price of a product to set its selling price. It is usually expressed as a percentage of cost.
加成率描述的是一家企业在产品成本价基础上加价多少来制定售价，通常以成本的百分比表示。
Mark-up (%) = ((Selling Price − Cost Price) ÷ Cost Price) × 100
加成率 (%) = ((售价 − 成本价) ÷ 成本价) × 100
If a gift shop buys a candle for £4 and sells it for £6, the mark-up is ((6 − 4) ÷ 4) × 100 = 50%. Retailers often use mark-up to ensure they cover overheads and earn a profit on every item.
如果一家礼品店以 4 英镑购入一支蜡烛，并以 6 英镑售出，加成率为 ((6 − 4) ÷ 4) × 100 = 50%。零售商常用加成率来确保覆盖间接费用并在每件商品上获得利润。
8. Law of Demand | 需求定律
The law of demand is a core economic theorem. It states that, all else being equal, as the price of a good rises, the quantity demanded by consumers falls, and vice versa.
需求定律是核心经济定理。它指出，在其他条件不变的情况下，当商品价格上升时，消费者需求的数量会下降，反之亦然。
There is an inverse (negative) relationship between price and quantity demanded. People tend to buy less of something when it becomes expensive and switch to cheaper alternatives. Demand curves slope downwards from left to right.
价格与需求数量之间存在反向（负相关）关系。商品变贵时人们往往会减少购买，并转向更便宜的替代品。需求曲线从左到右向下倾斜。
9. Law of Supply | 供给定律
The law of supply says that, other things being constant, when the price of a good increases, producers are willing to supply more of it because they can earn higher revenue.
供给定律指在其他因素不变的情况下，当商品价格上升时，生产者愿意提供更多该商品，因为他们可以获得更高的收入。
A direct (positive) relationship exists between price and quantity supplied. If a farmer can sell strawberries at £4 per punnet rather than £2, they will likely grow more strawberries next season. Supply curves therefore slope upwards.
价格与供给数量之间存在直接（正相关）关系。如果一位农民能以每盒 4 英镑的价格出售草莓，而不是 2 英镑，他很可能会在下个季度种植更多草莓。因此供给曲线向上倾斜。
10. Budget Variance Analysis | 预算差异分析
A budget is a financial plan that estimates future income and spending. Budget variance measures the difference between the planned (budgeted) figure and the actual result.
预算是对未来收入和支出的财务规划。预算差异衡量的是计划（预算）数字与实际结果之间的差额。
Variance = Actual Figure − Budgeted Figure
差异 = 实际数字 − 预算数字
A positive variance (actual greater than budget) can be favourable if it relates to revenue, because the business earned more than expected. For costs, a negative variance (actual less than budget) is favourable because spending was kept under control. Managers investigate large variances to improve future planning.
若实际数字大于预算，对于收入来说是正差异（有利差异），因为企业赚得比预期多。对于成本而言，实际小于预算的负差异才是有利的，因为支出得到了控制。管理者会调查较大的差异，以改进未来的规划。
11. Opportunity Cost Principle | 机会成本原理
Opportunity cost is not a formula but a fundamental concept in business decision-making. It is the value of the next best alternative that must be given up when a choice is made.
机会成本不是一个公式，却是商业决策中的基础概念。它指的是做出某种选择时必须放弃的次优替代选项的价值。
When you decide to spend Saturday working on a school business project instead of earning £30 babysitting, the opportunity cost is £30. Businesses face opportunity costs every day: if a factory uses its machinery to produce tables instead of chairs, the opportunity cost is the profit lost from not making chairs.
当你决定在周六做一个学校商业项目，而不是通过照看小孩赚取 30 英镑时，机会成本就是 30 英镑。企业每天都面临着机会成本：如果工厂用机器生产桌子而不是椅子，机会成本就是因未生产椅子而损失的利润。
12. Simple Interest Formula | 简单利息公式
When a business borrows money or keeps savings in a bank, it often deals with simple interest. This formula helps calculate the cost of a loan or the return on savings over a fixed period.
当企业借钱或将存款存入银行时，常会涉及简单利息。这个公式有助于计算在一段固定时期内贷款的成本或储蓄的收益。
Simple Interest = Principal × Interest Rate × Time (years)
简单利息 = 本金 × 利率 × 时间（年）
If a small business borrows £1,000 at an annual interest rate of 5% for 3 years, the simple interest is 1,000 × 0.05 × 3 = £150. The total amount to repay is £1,150. Understanding interest helps a firm decide whether taking a loan is affordable.
如果一家小企业以年利率 5% 借款 1,000 英镑，期限 3 年，简单利息为 1,000 × 0.05 × 3 = 150 英镑。需要偿还的总金额为 1,150 英镑。了解利息有助于企业判断贷款是否承担得起。
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