Free Printable WorksheetMathAlgebra IMath CurriculumN-Q.1–3

ALG1.104 Use Radicals to Model Distance and Geometry Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.104 Use Radicals to Model Distance and Geometry. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.104 Use Radicals to Model Distance and Geometry - Select the option that shows how to model distance and other measurement situations with radicals (such as distance between points); Select the statement that correctly interprets solutions with correct units and precision. (CCSS: N-Q.1–3; TEKS: §111.39(b),(c)(1) Process Standards; VA SOL (2023): A.EO.1a; FL B.E.S.T.: MA.912.F.1.3, MA.912.AR.2.* (modeling contexts); NY-NGLS: AI-N.Q.1, AI-N.Q.3; CA CCSSM: N-Q; MA 2017: HS.N-Q (Model Algebra I); DoDEA CCRSM (Algebra I); NAEP: Algebra—using symbols/expressions; NCTM P2A: Practices 1, 2, 6.)

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

Algebra I

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 ALG1.104 Use Radicals to Model Distance and Geometry skill assessments:

Problem 1Difficulty: Mastery
Point P(x, 1) is 10 units from point A(3, 5). Which statement correctly interprets the horizontal distance from A to P?
A∣x - 3∣ = sqrt(102 + 42) = sqrt(116), so P is about 10.8 units horizontally from x = 3.
Bx - 3 = 10 + 4, so P is 14 units horizontally from x = 3.
C∣x - 3∣ = sqrt(10 - 4), so P is about 2.4 units horizontally from x = 3.
D∣x - 3∣ = sqrt(102 - 42) = sqrt(84), so P is about 9.2 units horizontally from x = 3.
Solution & Explanation:The vertical change from y = 5 to y = 1 is -4. The horizontal distance satisfies horizontal2 + 42 = 102, so horizontal = sqrt(84), about 9.2 units.
Problem 2Difficulty: Mastery
For the distance between (-5, 2) and (4, -10), a student writes sqrt((-5 - 4)2 + (2 - (-10))2) = 15. Which evaluation is correct?
AThe student is wrong because the first point must always be subtracted from the second point.
BThe student is wrong because the distance should be -15 units.
CThe student is correct because the squared differences are 81 and 144, and sqrt(225) = 15.
DThe student is correct only if the answer is labeled square units.
Solution & Explanation:The differences -9 and 12 are valid because each is squared. The distance is sqrt(81 + 144) = sqrt(225) = 15 units.
Problem 3Difficulty: Mastery
A triangular support has perpendicular legs x feet and x + 7 feet, and hypotenuse 17 feet. Which equation correctly models the support?
Asqrt(x + (x + 7)) = 17
Bsqrt(x2 + (x + 7)2) = 17
Cx + (x + 7) = 17
Dsqrt(172 + x2) = x + 7
Solution & Explanation:The two legs are perpendicular, so the hypotenuse is modeled by sqrt(x2 + (x + 7)2). Setting this equal to 17 gives the correct equation.

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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 Algebra I Math students. It aligns with educational standard N-Q.1–3 (Primary standard selected for prompt fields in this prompt cell: CCSS N-Q.1–3. Skill statement in this prompt cell: Select the option that shows how to model distance and other measurement situations with radicals (such as distance between points); Select the statement that correctly interprets solutions with correct units and precision. Associated standards listed with this skill in the curriculum source: CCSS: N-Q.1–3; TEKS: §111.39(b),(c)(1) Process Standards; VA SOL (2023): A.EO.1a; FL B.E.S.T.: MA.912.F.1.3, MA.912.AR.2.* (modeling contexts); NY-NGLS: AI-N.Q.1, AI-N.Q.3; CA CCSSM: N-Q; MA 2017: HS.N-Q (Model Algebra I); DoDEA CCRSM (Algebra I); NAEP: Algebra—using symbols/expressions; NCTM P2A: Practices 1, 2, 6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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