Compound growth and decay
Ratio, proportion and rates of change
- Crossover
- Calculator allowed
- 8 questions
- 29 marks
Questions marked Higher are aimed at the Higher tier.
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Increase $200$ by $10\%$.
2 marks
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A price of £$80$ is reduced by $15\%$. Find the new price.
2 marks
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£$500$ increases by $4\%$ per year for $2$ years. Find the value after $2$ years.
3 marks
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A car worth £$12000$ loses $20\%$ of its value each year. Find its value after $2$ years.
3 marks
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A population of $2000$ increases by $5\%$ each year. After how many whole years does it first exceed $2400$?
4 marks
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The value of an investment is $V = 800 \times 1.03^{t}$. Find $V$ when $t = 3$, to the nearest penny. Higher
4 marks
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A sample of $250$ g decreases by $8\%$ each hour. Find the mass after $3$ hours, to $3$ significant figures. Write the single multiplier for the $3$ hours. Higher
5 marks
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Town P has $40000$ people and grows by $2\%$ a year. Town Q has $50000$ people and falls by $3\%$ a year. Find each population after $3$ years, to the nearest person, and say which population changes by more people. Higher
6 marks
Mark scheme
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Answer. $220$
- $10\%$ of $200$ is $20$.
- $220$
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Answer. £$68$
- $80 \times 0.85$
- £$68$
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Answer. £$540.80$
- Multiplier $1.04$.
- $500 \times 1.04^{2} = 500 \times 1.0816 = 540.80$.
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Answer. £$7680$
- Multiplier $0.8$.
- $12000 \times 0.64 = 7680$.
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Answer. $4$ years
- After $1$ year: $2100$. After $2$ years: $2205$.
- After $3$ years: $2315.25$. After $4$ years: $2431.01$.
- It first exceeds $2400$ after $4$ years.
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Answer. £$874.18$
- $1.03^{2} = 1.0609$ and $1.03^{3} = 1.092727$.
- $800 \times 1.092727 = 874.1816$, so £$874.18$.
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Answer. $195$ g, multiplier $0.778688$
- The multiplier for one hour is $0.92$.
- $0.92^{3} = 0.778688$.
- $250 \times 0.778688 = 194.672$, which is $195$ g to $3$ s.f.
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Answer. P is $42448$ and Q is $45634$. Q changes by more people.
- $40000 \times 1.02^{3} = 42448.32$, so $42448$.
- $50000 \times 0.97^{3} = 45633.65$, so $45634$.
- P increases by $2448$ and Q decreases by $4366$.
- Q changes by more people.