Stage 9 - Q1 - 2 marks
Write the growth factor for 9% per year.
Hint
Use a multiplier rather than adding a fixed amount.
Stage 9 - Q2 - 2 marks
A quantity starts at 250 and falls 10% each year. Write its value after 3 years.
Hint
The number of equal multipliers becomes the exponent.
Stage 9 - Q3 - 3 marks
Increase 300 by 12% per year for 2 years.
Hint
Square the multiplier, not the percentage.
Stage 9 - Q4 - 3 marks
Decrease 350 by 4% per year for 3 years. Give 2 d.p.
Hint
Retain calculator precision between years.
Stage 9 - Q5 - 4 marks
A model quantity starts at 400 and grows 6% each year. After how many complete years does it first exceed 600?
Hint
Try consecutive whole-number exponents and show both boundary years.
Stage 9 - Q6 - 4 marks
A model quantity starts at 450 and grows 8% each year. After how many complete years does it first exceed 675?
Hint
Try consecutive whole-number exponents and show both boundary years.
Stage 9 - Q7 - 5 marks
A quantity falls 10% each year. After 2 years it is 405. Find its starting value.
Hint
Reverse the complete multiplier, not just one year.
Stage 9 - Q8 - 5 marks
For a starting value 550, compare 3 years of 12% compound growth with a single 36% increase. Which is larger and by how much? Give 2 d.p.
Hint
Calculate both models from the same starting value.
Stage 9 - Q9 - 5 marks
Does this model lose equal amounts each period? Derive the amount lost during period \(n+1\).
Hint
Subtract the next-period expression and factor out the current value.
Stage 9 - Q10 - 3 marks
A fictional points balance begins at 500. In each two-year cycle it rises 10% in the first year and falls 5% in the second. At the end of how many complete cycles does it first exceed 600 points? State the corresponding number of years.
Hint
Combine the two yearly multipliers before testing powers.