Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-TF.1-9(+)

Pre CAL.94 Determine Key Features of a Sinusoid from Context or Graph 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.94 Determine Key Features of a Sinusoid from Context or Graph. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.94 Determine Key Features of a Sinusoid from Context or Graph - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given a sinusoidal graph or situation, determine amplitude, period, midline, and phase shift and select the interpretation that matches the context. Associated standards listed with this skill in this prompt cell: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3. 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

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.94 Determine Key Features of a Sinusoid from Context or Graph skill assessments:

Problem 1Difficulty: Mastery
A sinusoidal force F(t) has a maximum of 28 at t = 3, a minimum of 4 at t = 9, and the next maximum at t = 15. Which interpretation is correct?
Aamplitude = 12; midline = 16; period = 12; a positive cosine model is shifted right 3
Bamplitude = 24; midline = 12; period = 6; a positive cosine model is shifted right 3
Camplitude = 12; midline = 16; period = 6; a negative cosine model is shifted right 9
Damplitude = 16; midline = 12; period = 15; a sine model has no phase shift
Solution & Explanation:The amplitude is (28 - 4)/2 = 12 and the midline is (28 + 4)/2 = 16. Maxima at t = 3 and t = 15 are 12 units apart, and positive cosine shifted right 3 starts at that maximum.
Problem 2Difficulty: Mastery
The first maximum of a sinusoid occurs at x = 1.2 and the third maximum occurs at x = 16.8. What is the period?
Solution & Explanation:The third maximum is two full periods after the first. The distance is 16.8 - 1.2 = 15.6, so one period is 15.6/2 = 7.8.
Problem 3Difficulty: Mastery
For y = 9 + 4 sin((4pi/7)(x - 1)), which correction best identifies the period and phase shift?
Aperiod = 3.5; phase shift right 1
Bperiod = 7; phase shift left 1
Cperiod = 4pi/7; phase shift right 1
Dperiod = 3.5; phase shift right 7
Solution & Explanation:Here b = 4pi/7, so period = 2pi/(4pi/7) = 7/2 = 3.5. The factor (x - 1) shifts right 1.

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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 Pre-Calculus Math students. It aligns with educational standard HSF-TF.1-9(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-TF.1-9(+). Skill statement in this prompt cell: Given a sinusoidal graph or situation, determine amplitude, period, midline, and phase shift and select the interpretation that matches the context. Associated standards listed with this skill in this prompt cell: CCSS HSF-TF.1-9(+); CCSS HSF-IF.7e; CCSS HSG-SRT.C.6-8; SMP 1,2,3,5,7,8; AP Precalculus CED Unit 3; TX §111.42(c)(4)(A-D), (c)(5)(I); FL MA.912.T.1.3-1.8, MA.912.T.2.1-2.5, MA.912.T.3.1-3.3, MA.912.T.4.1-4.7; VA T.CT.1-2, T.GT.1-2, T.IE.1-3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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