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IB Maths AI HL 5.17 Phase portraits Question Bank

Practise IB Mathematics HL 5.17 by applying phase portraits 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 5.17 (HL)—Phase portraits question 1

[Maximum number: 1]

Consider the system given by the coupled differential equations

dx dt=3x−2y dy dt=4x−y\begin{aligned} & \frac{\mathrm{d} x}{\mathrm{~d} t}=3 x-2 y \\ & \frac{\mathrm{~d} y}{\mathrm{~d} t}=4 x-y \end{aligned}

The following phase portrait shows the trajectory that passes through the point (1,0) at time t=5.

Figure for Question AHL 5.17 (HL)—Phase portraits question 1 — IB Maths AI HL

Write down which one of the following could be an eigenvalue for the system.

A

1

B

2 i

C

1+2 i

D

-1+2 i

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