Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.1-6,9

Pre CAL.20 Identify Symmetry and Periodicity Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.20 Identify Symmetry and Periodicity. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

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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.20 Identify Symmetry and Periodicity. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.20 Identify Symmetry and Periodicity - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function equation or graph, determine whether it is even, odd, or neither and identify whether the function is periodic (and, if so, its period). Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. 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.20 Identify Symmetry and Periodicity skill assessments:

Problem 1Difficulty: Mastery
For f(x)=2cos((pi/3)x)+sin((pi/2)x)+4, identify the symmetry and least positive period.
AEven; periodic with period 6
BOdd; periodic with period 12
CNeither; periodic with period 12
DNeither; not periodic
Solution & Explanation:The cosine term and constant are even, while the sine term is odd, so the sum is neither. The component periods 6 and 4 first align at 12.
Problem 2Difficulty: Mastery
A tide-height model is p(t)=3+2sin((pi/6)t). Classify p as a function of t and give the least positive period.
AOdd; periodic with period 12
BEven; periodic with period 12
CNeither; periodic with period 12
DNeither; not periodic
Solution & Explanation:The vertical shift 3 breaks odd symmetry, and the sine term is not even. The period is 2pi divided by pi/6, which equals 12.
Problem 3Difficulty: Mastery
A temperature model is h(t)=70+10cos((pi/12)t). Classify h as a function of t and give the least positive period.
AEven; periodic with period 24
BOdd; periodic with period 24
CNeither; periodic with period 12
DEven; not periodic
Solution & Explanation:The cosine term and the constant are both even in t. The period is 2pi divided by pi/12, which equals 24.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.20 Identify Symmetry and Periodicity worksheet?

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QIs this Pre CAL.20 Identify Symmetry and Periodicity worksheet free for teachers and homeschoolers?

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Yes! In addition to this printable worksheet, students can practice Pre CAL.20 Identify Symmetry and Periodicity interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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-IF.1-6,9 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given a function equation or graph, determine whether it is even, odd, or neither and identify whether the function is periodic (and, if so, its period). Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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