This worksheet applies percentages and rational numbers to real financial contexts — tax, compound growth, depreciation and profit/loss — through practical, everyday modelling problems. The worksheet is split into warm-up questions, standard questions and then extension questions to test you.
The concepts it covers:
- A mark-up is a percentage added to the cost price to set the selling price; a discount is a percentage subtracted from the original price.
- Progressive income tax applies a rate only to the portion of income within a tax bracket, not the whole income.
- Repeated percentage growth or decline (e.g. year after year) compounds — each year's change applies to the new value, not the original.
- A quantity can be modelled with negative rational numbers in context, e.g. depth below sea level, or a temperature below zero.
- Reviewing a model means checking the answer makes sense in context — e.g. a discounted price should always be lower than the original.
What your child will practise:
- Formulating a real situation (mark-up, discount, tax, population, depreciation) as a percentage calculation.
- Applying a tax bracket rate only to the portion of income that falls within that bracket.
- Applying repeated percentage change year by year (or use a repeated multiplier) for compounding growth or decline.
- Working with percentage change involving negative rational numbers, such as depth or temperature.
- Interpreting and communicate a solution in the context's own units and language, checking it's reasonable.
Every section opens with a worked example, and the download includes a full answer key with step-by-step solutions and teaching notes on the mistakes students most commonly make.
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