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

Pre CAL.119 Graph Conics Using Key Features and Technology 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.119 Graph Conics Using Key Features and Technology. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.119 Graph Conics Using Key Features and Technology - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given conic features or an equation, select the graph that matches and identify the key feature values that support the match. 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.119 Graph Conics Using Key Features and Technology skill assessments:

Problem 1Difficulty: Mastery
A conic has center (-2, 3), vertices (-2, -2) and (-2, 8), foci (-2, -4) and (-2, 10), and a vertical transverse axis. Which equation and graph type match?
A(y - 3)2/25 - (x + 2)2/24 = 1; vertical hyperbola
B(x + 2)2/25 - (y - 3)2/24 = 1; horizontal hyperbola
C(y - 3)2/24 + (x + 2)2/25 = 1; vertical ellipse
D(y + 3)2/25 - (x - 2)2/24 = 1; vertical hyperbola
Solution & Explanation:The conic is a vertical hyperbola. The distance to a vertex is a = 5, and the distance to a focus is c = 7, so b2 = c2 - a2 = 49 - 25 = 24.
Problem 2Difficulty: Mastery
Which feature comparison most efficiently distinguishes x2/36 + y2/16 = 1 from x2/36 - y2/16 = 1 on a graphing utility?
AThe ellipse is bounded, while the hyperbola has two branches with asymptotes y = +/- (2/3)x.
BBoth graphs have the same asymptotes, so use the center only.
CThe hyperbola is bounded, while the ellipse has asymptotes y = +/- (2/3)x.
DThe equations have the same graph because the denominators match.
Solution & Explanation:The plus sign gives a bounded ellipse. The minus sign gives a horizontal hyperbola with asymptotes y = +/- (b/a)x = +/- (4/6)x = +/- (2/3)x.
Problem 3Difficulty: Mastery
Error analysis: A student graphs (y - 4)2 = -20(x + 2) opening right because of the x-term. What correction is correct?
AIt opens left; vertex (-2, 4); focus (-7, 4); directrix x = 3.
BIt opens right; vertex (-2, 4); focus (3, 4); directrix x = -7.
CIt opens down; vertex (-2, 4); focus (-2, -1); directrix y = 9.
DIt opens left; vertex (2, -4); focus (-3, -4); directrix x = 7.
Solution & Explanation:For (y - k)2 = 4p(x - h), the sign of p gives the horizontal opening. Since 4p = -20, p = -5, so the graph opens left from vertex (-2, 4).

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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 conic features or an equation, select the graph that matches and identify the key feature values that support the match. 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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