GCSE Maths: Interest, Growth and Proportion

Money and growth questions are some of the most practical on a GCSE Mathematics paper, and they reward a clear method: choose the right multiplier, apply it the right number of times, and know when to work backwards. This material trains the growth-and-decay and proportion content of the GCSE subject content for England: simple interest, compound interest, depreciation and population growth, finding how long an investment takes to reach a target, and, on the Higher tier, constructing and using proportion equations with powers and roots.

The quiz has thirteen questions with all money in pounds. You calculate simple interest, compound interest to the nearest penny and the difference between them, the value of a car after three years of depreciation, the size of a growing population, the number of whole years an investment needs to pass a target, and the original amount before two years of compound growth. You also match direct and inverse proportion to their graphs. The Higher-tier questions find a missing value when $y$ is proportional to $x^2$, inversely proportional to $x^2$ or proportional to $\sqrt{h}$, and describe what happens to $y$ when $x$ is doubled. The wrong options come from the usual mistakes: using simple interest where interest compounds, taking 12% off the original value three times, dividing a final amount by the wrong power, and forgetting to square or cube a scale factor.

The flashcards give the simple and compound interest formulae, the multipliers for increases and decreases, depreciation, the equations for proportion with squares, square roots and inverse squares, the shapes of proportion graphs and how to find the constant $k$.

The printable written work has eight problems with full working: comparing simple and compound interest, a depreciating laptop and the year its value first drops below a limit, a reverse compound-interest problem, a town's population growth, an interest rate that changes after the first year, an inverse-square relationship, a square-root relationship, and recognising direct and inverse proportion from a table and a graph.

Interest, growth, decay and simple proportion graphs are content for both tiers; proportion equations with powers and roots and repeated changes with different rates are Higher-tier skills. The material builds on the percentage multipliers practised in the category's fractions, decimals and percentages material and suits Year 10 and Year 11 students.

• Calculate simple interest and compound interest, and compare them
• Solve growth and depreciation problems using multipliers
• Find the time needed to reach a target by repeated calculation
• Work backwards to an original amount after compound growth
• Recognise direct and inverse proportion from graphs and tables
• Form and use equations for proportion with squares, cubes and roots (Higher)

Practice material written by Zestly, based on the DfE GCSE mathematics subject content (DFE-00233-2013), Ratio, proportion and rates of change R9, R10, R13, R16.