Maximum percentage error

AI HL · Mathematics

Seven worked examples, one to a page, built up a step at a time: areas, a volume and four from finance.

  1. Example 1 · Area of a squareA square floor tile has side length 50 cm, correct to the nearest 10 cm. Find the maximum percentage error in the area of the tile.
  2. Example 2 · Area of a circleA circular pond has radius 20 m, correct to the nearest 10 m. Find the maximum percentage error in the area of the pond.
  3. Example 3 · Volume of a cubeA cube-shaped storage box has edge length 30 cm, correct to the nearest 10 cm. Find the maximum percentage error in the volume of the box.
  4. Example 4 · Finance: a yearly costA gym membership costs CHF 80 per month, correct to the nearest CHF 10. Find the maximum percentage error in the cost for a year.
  5. Example 5 · Finance: a loan repaymentSam borrows CHF 20 000 over 5 years, repaid monthly. The bank quotes 4% per year compounded monthly, rounded to the nearest whole percent. Find the maximum percentage error in the monthly repayment.
  6. Example 6 · Finance: savings with interestLina invests CHF 5000 for 10 years at 3% per year compounded annually. The rate is rounded to the nearest whole percent. Find the maximum percentage error in her estimate of the final balance.
  7. Example 7 · Finance: savings with inflationInflation is 2% per year. Lina finds the real value of her CHF 5000 after 10 years using the real rate 3% − 2% = 1%. The 3% is rounded to the nearest whole percent. Find the maximum percentage error in her estimate.