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

Pre CAL.118 Determine Asymptotes and Key Features for Hyperbolas 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.118 Determine Asymptotes and Key Features for Hyperbolas. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.118 Determine Asymptotes and Key Features for Hyperbolas - Primary standard selected for prompt fields in this prompt cell: CCSS HSG-GPE.A.1-3(+). Skill statement in this prompt cell: Given a hyperbola equation, determine asymptote equations and key features and select the correct graph that matches. 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.118 Determine Asymptotes and Key Features for Hyperbolas skill assessments:

Problem 1Difficulty: Mastery

Use the planned graph choices to select the graph that matches 49x² + 490x - 36y² - 360y - 1439 = 0.

AGraph A: center (5, 5), opens left and right, vertices (-1, 5) and (11, 5), asymptotes through (5, 5)

BGraph B: center (-5, -5), opens up and down, vertices (-5, -11) and (-5, 1)

CGraph C: center (-5, -5), opens left and right, swapped asymptote slopes 6/7 and -6/7

DGraph D: center (-5, -5), opens left and right, vertices (-11, -5) and (1, -5), asymptotes y + 5 = (7/6)(x + 5) and y + 5 = -(7/6)(x + 5)

Solution & Explanation:The equation shows center (-5, -5), a = 6, b = 7, opens left and right, and has asymptotes y + 5 = (7/6)(x + 5) and y + 5 = -(7/6)(x + 5). The matching graph is D.

Problem 2Difficulty: Mastery

Which feature package matches the hyperbola 100(y - 6)² - 9(x - 2)² = 900?

Acenter (2, 6); opens up and down; vertices (2, 3) and (2, 9); asymptotes y - 6 = (3/10)(x - 2) and y - 6 = -(3/10)(x - 2)

Bcenter (2, 6); opens left and right; vertices (-1, 6) and (5, 6); asymptotes y - 6 = (10/3)(x - 2) and y - 6 = -(10/3)(x - 2)

Ccenter (-2, -6); opens up and down; vertices (-2, -9) and (-2, -3); asymptotes y + 6 = (3/10)(x + 2) and y + 6 = -(3/10)(x + 2)

Dcenter (2, 6); opens up and down; vertices (2, -4) and (2, 16); asymptotes y - 6 = (10/3)(x - 2) and y - 6 = -(10/3)(x - 2)

Solution & Explanation:Rewrite or read the equation in standard form. The center is (2, 6), a = 3, b = 10, and the positive term makes it open up and down; this gives vertices (2, 3) and (2, 9) and asymptotes y - 6 = (3/10)(x - 2) and y - 6 = -(3/10)(x - 2).

Problem 3Difficulty: Mastery

Decide whether the statement is true or false: The asymptotes of (x + 3)²/81 - (y - 6)²/16 = 1 are y - 6 = (4/9)(x + 3) and y - 6 = -(4/9)(x + 3).

ATrue

BFalse

Solution & Explanation:The center is (-3, 6), and the correct asymptote slopes are 4/9 and -4/9; compare that with the statement.

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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 hyperbola equation, determine asymptote equations and key features and select the correct graph that matches. 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.).