Free Printable WorksheetMathPre-CalculusMath CurriculumHSG-GPE.A.1-3(+)

Pre CAL.114 Conic Sections in Polar Form 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.114 Conic Sections in Polar Form. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.114 Conic Sections in Polar Form - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a polar conic equation, determine the conic type and select key features such as eccentricity and orientation. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. 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.114 Conic Sections in Polar Form skill assessments:

Problem 1Difficulty: Mastery
Which equation has eccentricity 0.4 and directrix x = -15?
Ar = 6/(1 + 0.4cos(theta))
Br = 6/(1 - 0.4cos(theta))
Cr = 15/(1 - 0.4sin(theta))
Dr = 6/(1 - 2.5cos(theta))
Solution & Explanation:The numerator should be ed = 0.4(15) = 6. A left directrix uses 1 - e cos(theta), so the correct equation is r = 6/(1 - 0.4cos(theta)).
Problem 2Difficulty: Mastery
In r = 18/(6 - c sin(theta)), what positive value of c gives directrix y = -3?
Solution & Explanation:For A/(B - Csin(theta)), the directrix is y = -A/C. Set A/C = 3: 18/c = 3, so c = 6.
Problem 3Difficulty: Mastery
For r = (9/2)/(1 - (3/2)cos(theta)), which description is correct?
Aellipse, e = 2/3, horizontal axis, directrix x = -3
Bhyperbola, e = 3/2, vertical axis, directrix y = -3
Cparabola, e = 1, horizontal axis, directrix x = 3
Dhyperbola, e = 3/2, horizontal axis, directrix x = -3
Solution & Explanation:The equation is already normalized with e = 3/2, so it is a hyperbola. Cos(theta) gives a horizontal axis, and d = (9/2)/(3/2) = 3; the minus sign gives x = -3.

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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 HSG-GPE.A.1-3(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a polar conic equation, determine the conic type and select key features such as eccentricity and orientation. Associated standards listed with this skill in this prompt cell: CCSS HSG-GPE.A.1-3(+); CCSS HS-Modeling; SMP 1,2,4,5,7,8; AP Precalculus CED Units 3-4; TX §111.42(c)(3)(D-H); FL MA.912.GR.7.1-7.9, MA.912.T.4.5-4.7; VA MA.AG.1-2. Use this prompt-provided wording as the supporting standard description for this workflow.).

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