Page 17 - Grab Me SPM Add Mathematics Form 4,5

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D. Rates of change for related quantities E. Small changes and approximations of
certain quantities
• If y = f(x) and x = g(t), then dy = dy × dx
(Chain rule). dt dx dt • For a function y = f(x),
dy ≈ dy
t dx dx
TIPS dy
Steps to solve problems involving the rates of dy ≈ dx × dx (dx = x new – x initial )
change for related quantities:
1. Interpret the information in the form of where dy is a small change in y and dx is a small
mathematical symbols. change in x.
2. Determine the appropriate chain rule. (a) When dy  0 or dx  0, there is a small
increase in y or x.
(b) When dy  0 or dx  0, there is a small
• Interpretation of rates of change for related decrease in y or x.
quantities:
• The approximation value of y is given by the
(a) When dy  0, y increases when t formula:
dt
increases. y new = y initial + dy
(b) When dy  0, y decreases when t • If y = f(x) and x changes by dx, then
dt
increases. (a) the percentage change in x = dx × 100%
x
(b) the percentage change in y = dy × 100%
y
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Ch 2_Grab Me SPM AddMaths F5.indd 137 13/05/2022 9:09 AM