Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.179

Pre CAL.179 Distinguish Interpolation and Extrapolation and Apply Constraints Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.179 Distinguish Interpolation and Extrapolation and Apply Constraints. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.179 Distinguish Interpolation and Extrapolation and Apply Constraints - Distinguish Interpolation and Extrapolation and Apply Constraints

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.179 Distinguish Interpolation and Extrapolation and Apply Constraints skill assessments:

Problem 1Difficulty: Mastery

A freezer’s internal temperature T(t) (°C) after t hours is modeled by T(t)=−1.2·t+5. The model was fit using data for 0 ≤ t ≤ 10 and is intended for that interval. For food safety, the temperature must stay at or below 0°C. For t=2, which choice correctly classifies the prediction and says whether it is reasonable?

AInterpolation; the prediction is reasonable under the stated constraints.

BExtrapolation (outside the data interval); reasonable under the constraints given.

CInterpolation; using the model here is not reasonable.

DExtrapolation; not reasonable because a constraint is violated.

Solution & Explanation:The input 2 is within the data range 0 to 10, so this is **interpolation**. Using the model, the predicted value is 2.6. The prediction is **not reasonable** because the prediction exceeds the constraint (the requirement that temperature stays at or below 0°C).

Problem 2Difficulty: Mastery

A server latency model is L(p)=5+0.4·p+0.02·p², where p is the number of concurrent users. The model was fit using data for 0 ≤ p ≤ 30, and the server is rated for up to 40 users. For p=25, which choice correctly classifies the prediction and says whether it is reasonable?

AExtrapolation; the estimate should not be trusted here.

BInterpolation; but the prediction is not reasonable given the constraints.

CInterpolation (inside the data interval); reasonable.

DExtrapolation; reasonable to use the model here.

Solution & Explanation:The input 25 is within the data range 0 to 30, so this is **interpolation**. Using the model, the predicted value is 27.5. All stated constraints are satisfied, so the prediction is **reasonable**.

Problem 3Difficulty: Mastery

A travel model for average speed v(t) (mph) is v(t)=−2·t²+12·t+5, where t is hours since departure. The model was fit using data for 0 ≤ t ≤ 4. The trip ends after 5 hours, so the model should not be used for t>5. For t=6, which choice correctly classifies the prediction and says whether it is reasonable?

AInterpolation; reasonable to use the model for this input.

BExtrapolation; the estimate should not be trusted here.

CExtrapolation; and it is still reasonable because it fits the stated constraints.

DInterpolation; not reasonable because at least one constraint is violated.

Solution & Explanation:The input 6 is outside the data range 0 to 4, so this is **extrapolation**. Using the model, the predicted value is 5. The prediction is **not reasonable** because the input is outside the allowed range (0 to 5).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.179 (Distinguish Interpolation and Extrapolation and Apply Constraints).