AP®︎ Precalculus: Topic 4.14 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 4.14 of AP Precalculus – Matrices Modeling Contexts.
Questions List
Topic 4.14
Question 1 Easy
There are two regions, North and South. Each year, 8% of North's residents move to South and 5% of South's residents move to North. No one enters or leaves the two regions. The model is , where the column state vector lists North first and South second. Which matrix is ?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 4.14: Matrices Modeling Contexts
Learning Objective: 4.14.A
Construct a model of a scenario involving transitions between two states using matrices.
Essential Knowledge: 4.14.A.1
A contextual scenario can indicate the rate of transitions between states as percent changes. A matrix can be constructed based on these rates to model how states change over discrete intervals.
Learning Objective: 4.14.B
Apply matrix models to predict future and past states for \(n\) transition steps.
Essential Knowledge: 4.14.B.1
The product of a matrix that models transitions between states and a corresponding state vector can predict future states.
Essential Knowledge: 4.14.B.2
Repeated multiplication of a matrix that models the transitions between states and corresponding resultant state vectors can predict the steady state, a distribution between states that does not change from one step to the next.
Essential Knowledge: 4.14.B.3
The product of the inverse of a matrix that models transitions between states and a corresponding state vector can predict past states.
