CourseCourseConceptConceptDocsDocuments

IB Maths AI HL Ahl 5 16 Hl Eulers Method Questions

Practise applying Euler’s method with a stated step size, using technology for iterative systems, and interpreting approximation error, variables and domain.

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

Exam points

  • Apply Euler’s method with a stated step size to approximate a first-order differential equation.
  • Use technology or spreadsheets for iterative numerical solutions and coupled first-order systems such as predator–prey models.
  • Report and interpret the approximation, step-size effects, variables and domain.

Learn this topic

Study AHL 5.16 (HL)—Euler's method conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 5 16 Hl Eulers Method Questions 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 IB Maths AI HL Ahl 5 16 Hl Eulers Method 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 Ahl 5 16 Hl Eulers Method 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∈Ra, b \in \mathbb{R}.

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

All question bank results loaded