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

Pre CAL.109 Key Features and Eccentricity of Conic Sections 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.109 Key Features and Eccentricity of Conic Sections. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.109 Key Features and Eccentricity of Conic Sections - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a conic section representation, determine key features (including eccentricity when applicable) and select the statement that correctly describes the conic's shape and properties. 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.109 Key Features and Eccentricity of Conic Sections skill assessments:

Problem 1Difficulty: Mastery
A conic has center (-1, 2), foci (-1, 8) and (-1, -4), and eccentricity 3/4. Which statement is correct?
AIt is a parabola because its foci are listed vertically.
BIt is a hyperbola with vertical transverse axis, semi-major axis 8, and vertices (-1, 10) and (-1, -6).
CIt is an ellipse with horizontal major axis, semi-major axis 8, and vertices (7, 2) and (-9, 2).
DIt is an ellipse with vertical major axis, semi-major axis 8, and vertices (-1, 10) and (-1, -6).
Solution & Explanation:The foci are vertical and 6 units from the center, so c = 6. Since e = c/a = 3/4, a = 8. Because e < 1, the conic is an ellipse, and its vertices are vertical.
Problem 2Difficulty: Mastery
Rewrite y2 - 10y + 20x + 5 = 0 in standard form. Which statement is correct?
AIt is a parabola opening upward with vertex (1, 5), focus (1, 10), directrix y = 0, and eccentricity 1.
BIt is a parabola opening right with vertex (1, 5), focus (6, 5), directrix x = -4, and eccentricity 1.
CIt is a parabola opening left with vertex (1, 5), focus (-4, 5), directrix x = 6, and eccentricity 1.
DIt is a hyperbola centered at (1, 5), with horizontal transverse axis.
Solution & Explanation:Complete the square: (y - 5)2 = -20(x - 1). Thus 4p = -20, so p = -5; the focus is (1 - 5, 5) and the directrix is x = 1 - (-5) = 6.
Problem 3Difficulty: Mastery
Rewrite x2 + 4x + 12y - 20 = 0 in standard form. Which statement is correct?
AIt is a parabola opening upward with vertex (-2, 2), focus (-2, 5), directrix y = -1, and eccentricity 1.
BIt is a parabola opening downward with vertex (-2, 2), focus (-2, -1), directrix y = 5, and eccentricity 1.
CIt is a parabola opening right with vertex (-2, 2), focus (1, 2), directrix x = -5, and eccentricity 1.
DIt is an ellipse centered at (-2, 2) with eccentricity 1/3.
Solution & Explanation:Complete the square: (x + 2)2 = -12(y - 2). Thus 4p = -12, so p = -3; the focus is (-2, -1) and the directrix is y = 5.

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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 conic section representation, determine key features (including eccentricity when applicable) and select the statement that correctly describes the conic's shape and properties. 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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