Percentages, Rate & Ratio, Variations and Estimation

Percentages

• Concept: usually used to express part of a certain value with meaning of "1/whole part" as 100%
  e.g. 23% of 10 = 10 x 23% = 2.3
• Concept of Increase/Decrease: new value ＝ original value (1 ± change %)
• Selling problems: e.g. selling price＝cost (1 ＋ profit %);    selling price＝marked price (1 － discount %)
• Interest:   Simple interest and Compound interest
  　　　 Note the difference between “annual interest rate” and “interest rate per compounding period”

Rate and Ratio

• Concept of Rate:“For each hour, Peter walks 3km ＝ 3km/h”
• Concept of Ratio:
  • Use “a:b” and “b:c” to calculate “a:b:c”
  • Concept of distribution, e.g. Distribute $2000，among 3 people in a ratio of 2:3:5.

Variations

• Direct variation (x=ky), inverse variation (x=k / y), joint variation (x=kyz), partial variation (x=ky+Ky^2)

Estimations

• To know the common ways of expressing an error (e.g. absolute error, relative error, including their definitions).