IB Maths AA SL 5.1 Limits & derivative concept

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise reading limits, instantaneous rates and derivative meaning from functions, motion models, graphs and contextual units.

How this is tested

interpret limits such as lim v(t) as t→∞, then decide whether the limiting value is valid in context
find rates by evaluating derivatives at key events, such as when v=0 or at point A
explain derivative meaning from graphs or formulae, including zero speed or curvature

[Maximum number: 9]

Two athletes, Fiona and Lucy, compete in a 200 metres race along a straight track.
Fiona's velocity, in $\mathrm{m} \mathrm{s}^{-1}$ , during the race can be modelled by $v(t)=\frac{8.14 t}{\sqrt{t^{2}+0.2}}$ , where $t \geq 0$ .
Time, t, is measured in seconds from when the race starts.

(a)

Write down the value of v(1).

[ 3 ]

(b)

Write down the limit of v(t) as t approaches infinity.

[ 3 ]

(c)

State a reason why the value in part (c)(i) is not valid in the context of this question.

Lucy's velocity, in $\mathrm{ms}^{-1}$ , during the race can be modelled by $w(t)=\frac{8 t}{\sqrt{t^{2}+0.3}}$ , where $t \geq 0$ .
Fiona completes the race and crosses the finishing line in front of Lucy.

[ 3 ]

How this is tested

Question 9

Question 9(a)(i)

Question 9(c)(i)

Question 9(c)(ii)