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IB Maths AI HL 2.5 Modelling with functions and parameters Question Bank

Practise IB Maths AI HL 2.5 by constructing and evaluating parameterised function models and regression predictions.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Interpret parameters in a function or regression model and connect them to the physical situation.
  • Use a model to predict a value, then check whether the input and output lie within a valid domain.
  • Evaluate model fit, assumptions and uncertainty when using a function to make a prediction.

SL 2.5—Modelling with functions question 1

[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 SL 2.5—Modelling with functions 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 SL 2.5—Modelling with functions 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∈Ra, 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.

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