Build and Interpret Models
Modeling questions turn a situation into math and then back into a decision. The algebra matters, but the bigger skill is deciding what each quantity means and whether the result actually fits the situation.
核心知识
A useful model keeps the important relationship from the context. On ACT Math, that usually means separating fixed values from changing values, choosing a structure that matches the relationship, and checking that the answer makes sense with the units and limits in the problem.
深入理解
Start by naming the quantities.
- What changes?
- What stays fixed?
- What restriction matters?
That tells you whether you need an equation, an inequality, a function rule, a graph, or a labeled diagram.
In many ACT questions, the structure is the test.
- A constant rate usually leads to a linear model.
- A fixed fee becomes a constant term.
- A limit like "at most" or "no less than" should appear as an inequality, not an equation.
Once the model is built, read it back in context.
- A coefficient should carry units.
- An intercept should mean a starting amount, not just "the number left over."
- If the model predicts a negative count, a half-person, or a value far outside the data range, stop and re-check before choosing an answer.
示例解析
A shuttle service charges a booking fee of $18 plus $2.50 for each mile traveled. Which choice gives a correct model for the total cost
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知识点教程
5Represent a context with equations, inequalities, functions, or diagrams.
Match each part of the context to the right mathematical form: variable, fixed amount, rate, or rest
Interpret parameters (slope, intercept, coefficients) in terms of the context.
Read each parameter with its unit and with its role in the expression.
Use a model to make predictions and evaluate whether results are reasonable.
Substitute carefully, keep the units attached, and check whether the result is realistic.
Compare models and select a better fit based on given evidence/data.
Compare residuals across the same data points to decide which model fits better.
Revise a model when assumptions change or new constraints are introduced.
Revise only the part of the model that the new condition actually changes.