What three things are you asked to do with a model beyond using it?

State its assumptions , offer criticisms of it, and suggest refinements . All three depend on understanding what the model is actually describing.

A model uses a reciprocal function. Why is usually only one of its two branches relevant?

Because the quantity being modelled, such as a time or a length, can only take positive values. The branch sitting in the negative region has no meaning in the context, so it is discarded.

A LevelMathsEdexcelPureFlashcardsAlgebra & FunctionsFurther Modelling with Functions

Further Modelling with Functions (Edexcel A Level Maths: Pure): Flashcards

Exam code: 9MA0

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What three things are you asked to do with a model beyond using it?

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What three things are you asked to do with a model beyond using it?
State its assumptions, offer criticisms of it, and suggest refinements.
All three depend on understanding what the model is actually describing.
A model uses a reciprocal function. Why is usually only one of its two branches relevant?
Because the quantity being modelled, such as a time or a length, can only take positive values.
The branch sitting in the negative region has no meaning in the context, so it is discarded.
What decides the domain of a function used as a model?
The context, not the algebra.
A formula may be defined for every real $x$ , but if $x$ counts items or measures a length then only positive values make any sense.
True or False?
Everyday knowledge is of no use in a mathematical modelling question.
False.
Common sense about the situation is what tells you which answers are plausible and which values a variable can sensibly take.
An answer of $- 3$ people, or a garden fence $2000$ metres long, is caught that way rather than algebraically.
Saying where a model is likely to fail is called a $______$ ; improving it afterwards is called a $______$ .
Saying where a model is likely to fail is called a criticism; improving it afterwards is called a refinement.
The two go together: a criticism identifies the weakness, and a refinement addresses it.

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