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IB Maths AI HL 5.16 Euler's method Question Bank

Practise IB Mathematics HL 5.16 by applying euler's method methods to exam-style questions.

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

Exam points

  • identify the mathematical structure, variable or representation
  • select and apply the correct theorem, formula or algorithm
  • check the result using units, domain, graph or logical reasoning

AHL 5.16 (HL)—Euler's method question 1

[Maximum number: 3]

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 AHL 5.16 (HL)—Euler's method 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 AHL 5.16 (HL)—Euler's method 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}.

Use Euler's method with a step length of 0.5 minutes to estimate the maximum value of H.

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