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IB Maths AI HL Ahl 5 17 Hl Phase Portraits Questions

Practise reading phase portraits for coupled differential equations, classifying equilibria and trajectories, and interpreting stability or long-term behaviour in an applied…

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

Exam points

  • Use a phase portrait for dx/dt=ax+by, dy/dt=cx+dy to identify equilibrium and future paths.
  • Classify stable populations, saddle points, spirals, circles or ellipses using eigenvalue information.
  • Interpret the phase trajectory and long-term behaviour in the applied system.

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Study AHL 5.17 (HL)—Phase portraits conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 5 17 Hl Phase Portraits Questions 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 IB Maths AI HL Ahl 5 17 Hl Phase Portraits Questions 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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