IB Maths AI SL 2.5 Modelling with functions Question Bank

Practise IB Maths AI SL 2.5 by interpreting function models for motion, cycles, growth and measured data.

Exam points

Identify amplitude, period, intercepts or extrema in a function model for a real situation.
Use a model to calculate a time, height, angle or other quantity with appropriate units.
Interpret a parameter and explain what the model predicts within its valid domain.

[Maximum number: 5]

The Scheveningen Ferris wheel's lowest point is 8 m above sea level, and its highest point is 45 m above sea level.

(a)

Find the value of b.

[ 1 ]

$\quad\left(b=\frac{360}{15}=\right) 24$

(b)

Find the value of d.

[ 2 ]

$\frac{\max +\min }{2}$

\begin{aligned} & (d=) \frac{45+8}{2} \text { OR } 45-18.5 \text { OR } 8+18.5 \\ & =26.5 \end{aligned}

(c)

Hence, write down the equation of the sinusoidal model.

[ 2 ]

$h(t)=18.5 \sin (24 t)+26.5$

Note: Award A1 for 18.5 seen as parameter a, A1 for a completely correct equation (including LHS).

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