Free Printable WorksheetMathGeometryMath CurriculumG-MG.A.2-3

GEO.191 Analyze How Changing Inputs Affects a Model Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.191 Analyze How Changing Inputs Affects a Model. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.191 Analyze how changing inputs affects a model - Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the correct statement describing how an output changes when an input parameter increases or decreases in a geometric model. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3; CCSS SMP.8; G-GPE.B; G-GMD.A; NY HS MP. 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

Geometry

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 GEO.191 Analyze How Changing Inputs Affects a Model skill assessments:

Problem 1Difficulty: Mastery
A rounded-corner walkway area model is A(t) = 50 + 12t + pi t2, where t is the walkway width. Which statement best describes the output as t increases by 1?
AThe area increases by a larger amount each time because the model includes pi t2.
BThe area increases by exactly 12 each time.
CThe area decreases because t appears in a squared term.
DThe area stays 50 because 50 is constant.
Solution & Explanation:The linear term adds 12 per unit, but the pi t2 term has increments pi(2t + 1), which grow as t grows. Therefore each 1-unit increase in t adds more area than the previous one.
Problem 2Difficulty: Mastery
An open box is made by cutting squares of side x from a 20 by 12 sheet, so V = x(20 - 2x)(12 - 2x). Which statement is correct for x = 1, 2, and 3?
AThe volume increases from 180 to 256, then decreases to 252.
BThe volume decreases from 180 to 256, then increases to 252.
CThe volume increases by the same amount each time.
DThe volume is zero for all three values.
Solution & Explanation:V(1) = 1(18)(10) = 180, V(2) = 2(16)(8) = 256, and V(3) = 3(14)(6) = 252. Increasing x does not always increase the output.
Problem 3Difficulty: Mastery
A closed cylinder with fixed height 5 has surface area S(r) = 2 pi r(r + 5). Compare r increasing from 2 to 3 and from 3 to 4. Which statement is correct?
AThe first increase adds 20 pi and the second adds 24 pi, so the output increases at an increasing rate.
BBoth increases add 20 pi because r increases by 1.
CThe first increase adds 24 pi and the second adds 20 pi.
DSurface area decreases because height is fixed.
Solution & Explanation:S(2) = 28 pi, S(3) = 48 pi, and S(4) = 72 pi. The increases are 20 pi and 24 pi, so the output increase gets larger.

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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 Geometry Math students. It aligns with educational standard G-MG.A.2-3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the correct statement describing how an output changes when an input parameter increases or decreases in a geometric model. Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3; CCSS SMP.8; G-GPE.B; G-GMD.A; NY HS MP. Use this prompt-provided wording as the supporting standard description for this workflow.).

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