Free Printable WorksheetMathAlgebra IIMath CurriculumF-TF.5

ALG2.197 Modeling Periodic Phenomena Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.197 Modeling Periodic Phenomena. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.197 Modeling Periodic Phenomena - Primary standard selected for prompt fields in this prompt cell: CCSS F-TF.5. Skill statement in this prompt cell: Select the best-fitting a sinusoidal select a model to to data (tables or graphs) and select the correct interpretation of parameters such as amplitude, period, and phase in context. Associated standards listed with this skill in this prompt cell: CCSS F-TF.5; ★ Modeling; CA CCSSM F-TF.5; ★ Modeling; MA 2017 F-TF.5; ★ Modeling; NY NGLS F-TF.5; ★ 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 ALG2.197 Modeling Periodic Phenomena skill assessments:

Problem 1Difficulty: Mastery
Use the planned graph of a noisy periodic data set with average value 30, high points near y = 45 at x = 6 and x = 30, and a low point near y = 15 at x = 18. Which model and interpretation best fit?
Ay = 45 + 15cos((pi/12)(x - 6)); the amplitude means the average is 15.
By = 30 + 30sin((pi/24)(x - 6)); the period is 12 units.
Cy = 30 - 15cos((pi/12)(x - 6)); the maximum occurs at x = 6.
Dy = 30 + 15cos((pi/12)(x - 6)); the amplitude means the data varies about 15 units from its average.
Solution & Explanation:The average is 30 and the amplitude is about 15. The high points are 24 units apart, so the coefficient is pi/12. Positive cosine shifted to x = 6 starts at a maximum.
Problem 2Difficulty: Mastery
Which explanation best supports choosing a sinusoidal model instead of a linear model for a data set?
AThe values are all positive numbers.
BThe data table has more than four points.
CThe values repeat with regular maximums and minimums rather than changing at a constant rate.
DThe average of the data values is easy to compute.
Solution & Explanation:Sinusoidal models are appropriate for repeating periodic behavior. Linear models describe constant rate of change, not regular cycles.
Problem 3Difficulty: Mastery
A table is x: 0, 5, 10, 15, 20; y: 60, 74, 60, 46, 60. Which conclusion about phase is correct?
AA cosine model with no horizontal shift starts at a maximum, so it matches the table.
BA sine model with no horizontal shift starts at the midline and increases, so it matches the table.
CA sine model shifted right 5 units is required because the maximum is at x = 5.
DA negative cosine model is required because the graph has a minimum.
Solution & Explanation:At x = 0 the value is the midline 60 and the next value is higher, so an unshifted positive sine model matches the phase.

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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 F-TF.5 (Primary standard selected for prompt fields in this prompt cell: CCSS F-TF.5. Skill statement in this prompt cell: Select the best-fitting a sinusoidal select a model to to data (tables or graphs) and select the correct interpretation of parameters such as amplitude, period, and phase in context. Associated standards listed with this skill in this prompt cell: CCSS F-TF.5; ★ Modeling; CA CCSSM F-TF.5; ★ Modeling; MA 2017 F-TF.5; ★ Modeling; NY NGLS F-TF.5; ★ Modeling; TX TEKS Algebra II: §111.40. Use this prompt-provided wording as the supporting standard description for this workflow.).

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