CAIE IGCSE Additional Math 14.7 Apply Differentiation to Rates and Approximations Questions

Practise using derivatives for connected rates of change, small increments and numerical approximations in Cambridge Additional Mathematics problems.

Exam points

Apply connected rates, small-increment and approximation methods to calculate changes in quantities from derivatives.

[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

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CAIE IGCSE Additional Math 14.7 Apply Differentiation to Rates and Approximations Questions question 1