CAIE IGCSE Additional Math 14.7 rates and approximations

Use this rates-and-approximations page to connect variables with chain rule, find dy/dx and estimate small changes from h.

Exam points

Use chain rule links such as dV/dt=(dV/dr)(dr/dt) in related-rate problems.
Find dy/dx before estimating an approximate change for a small increase h.
Substitute the stated value of x or r after differentiating to calculate the rate or change.

[Maximum number: 3]

In this question, the units are metres and seconds.
A particle P is travelling in a straight line through a fixed point O.
At time t its acceleration, a, is given by $a=(2 t-3)^{2}$ , where $t \geqslant 0$ .
When t=3, P has a velocity of 6.

Use calculus to find the approximate change in v when t increases from $\frac{5}{2}$ by the small amount 0.02.

$\frac{dv}{dt}=(2t-3)^2$ oe, soi, or $\frac{d}{dt}(\text{their }v)=k(2t-3)^2$ , where $k\ne0$
B1 FT their expression for v if necessary.
Correct small changes relationship: $\frac{\delta v}{0.02}=\text{their }(2\times2.5-3)^2$ oe
M1 FT their $\left.\frac{dv}{dt}\right|_{t=2.5}$ .
$\delta v=0.08$
A1

All question bank results loaded

14.7. Apply differentiation to rates and approximations question 1