KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 13 · Lesson 01

Defining a Researchable Modelling Question

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Defining a Researchable Modelling Question

U13 · L01
1

Name the response variable in a model predicting height from age.

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: Height
Reasoning: Height is the predicted outcome.
2

What does a positive residual mean?

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: Observed value exceeds predicted value
Reasoning: Residual=observed−predicted.
3

Why document assumptions?

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: They define when the model is defensible
Reasoning: Assumptions limit interpretation and use.
4

What is interpolation?

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: Prediction within the observed data range
Reasoning: It stays inside the fitted domain.
5

What is extrapolation?

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: Prediction beyond the observed data range
Reasoning: It extends the model outside evidence.
6

What should a model defense include?

Modeling visualFormulate, fit, compare, validate, communicate, and defend mathematical models with explicit assumptions and limitations. xy
Answer: Choice, parameters, evidence, residuals, limitations, and conclusion
Reasoning: A defensible model connects method, evidence, and scope.
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