IB Maths AI HL Sl 2 5 Modelling with Functions Questions

Practise selecting and fitting linear, quadratic, exponential, piecewise or sinusoidal models, interpreting parameters, checking domains and evaluating predictions.

Exam points

Select and use an appropriate linear, piecewise, quadratic, exponential, variation, cubic or sinusoidal model for a real situation.
Interpret model parameters such as roots, vertex, asymptotes, amplitude, period or principal axis and use them to predict a quantity.
Use technology or fitted parameters to calculate a prediction, checking the input/output domain and units.
Evaluate model fit, assumptions, uncertainty and the consequences of using the model beyond its supported range.

[Maximum number: 1]

This question explores models for the height of water in a cylindrical container as water drains out.
The diagram shows a cylindrical water container of height 3.2 metres and base radius 1 metre. At the base of the container is a small circular valve, which enables water to drain out.

Figure for Question IB Maths AI HL Sl 2 5 Modelling with Functions Questions question 1 — IB Maths AI HL

Eva closes the valve and fills the container with water.
At time t=0, Eva opens the valve. She records the height, h metres, of water remaining in the container every 5 minutes.

Table for Question IB Maths AI HL Sl 2 5 Modelling with Functions Questions question 1 — IB Maths AI HL

Eva first tries to model the height using a linear function, h(t)=a t+b, where $a, b \in \mathbb{R}$ .

Interpret the meaning of parameter a in the context of the model.

Eva uses the equation of the regression line of h on t, to predict the time it will take for all the water to drain out of the container.

All question bank results loaded

IB Maths AI HL Sl 2 5 Modelling with Functions Questions question 1