Free Printable WorksheetMathAlgebra IIMath CurriculumS-ID.6

ALG2.122 Comparing Polynomial Models Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.122 Comparing Polynomial Models. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.122 Comparing Polynomial Models - Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Select the correct comparison between linear, quadratic, and higher-degree models for the same data and select the reasoning that justifies selection using residuals and context. Associated standards listed with this skill in this prompt cell: CCSS S-ID.6; S-ID.8; ★ Modeling; CA CCSSM S-ID.6; S-ID.8; ★ Modeling; MA 2017 S-ID.6; S-ID.8; ★ Modeling; NY NGLS S-ID.6; S-ID.8; ★ Modeling; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.

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

Algebra II

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 ALG2.122 Comparing Polynomial Models skill assessments:

Problem 1Difficulty: Mastery

A final comparison chart for the same data shows: linear residuals have a curved pattern, quadratic residuals are random with SSE 11.8, quartic residuals are random with SSE 11.5, and the quartic model creates two unsupported extra turns. Which comparison is best?

AQuadratic is best because it fixes the linear residual pattern and the quartic improvement is tiny with unsupported turns.

BQuartic is best because 11.5 is less than 11.8.

CLinear is best because a curved residual pattern is desirable.

DQuartic is best because extra turns prove the model understands the context.

Solution & Explanation:The quadratic model captures the main pattern with random residuals. The quartic model adds very little fit improvement and creates unsupported complexity.

Problem 2Difficulty: Mastery

A data team compares models for predicted energy output from a solar panel during a partly cloudy morning. Linear residuals miss the midday bend, quadratic residuals are random with SSE 6.4, and a quintic model has SSE 6.2 but creates several wiggles between measurements. The goal is a clear model for the observed morning only. Which comparison is best?

AQuadratic is preferred because it captures the main bend with random residuals and the quintic wiggles are not justified by the tiny SSE gain.

BQuintic is preferred because any decrease from 6.4 to 6.2 must be used.

CLinear is preferred because solar data cannot be curved.

DQuintic is preferred because several wiggles make the context clearer.

Solution & Explanation:The quadratic model removes the main residual pattern and has random residuals. A tiny SSE reduction from a much higher-degree model is not enough to justify unsupported wiggles.

Problem 3Difficulty: Mastery

A medical dosage model is compared on the same data. Linear residuals are random overall but slightly high near the safe upper dose. Quadratic residuals are random overall and smaller near the safe upper dose, but it has slightly larger errors at low doses. The goal is upper-dose accuracy. Which comparison is best?

AQuadratic may be preferred because its residuals are better in the range most important to the context.

BLinear must be preferred because it is simpler regardless of the goal.

CCubic must be preferred because medical contexts always use high degree.

DLinear must be preferred because low-dose residuals are the only ones that matter.

Solution & Explanation:Model choice depends on the prediction goal. For upper-dose decisions, smaller residuals in that range can justify the quadratic model.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard S-ID.6 (Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Select the correct comparison between linear, quadratic, and higher-degree models for the same data and select the reasoning that justifies selection using residuals and context. Associated standards listed with this skill in this prompt cell: CCSS S-ID.6; S-ID.8; ★ Modeling; CA CCSSM S-ID.6; S-ID.8; ★ Modeling; MA 2017 S-ID.6; S-ID.8; ★ Modeling; NY NGLS S-ID.6; S-ID.8; ★ Modeling; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).