Free Printable WorksheetMathAlgebra IIMath CurriculumALG2.151

ALG2.151 Comparing Radical and Polynomial Growth Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.151 Comparing Radical and Polynomial Growth. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.151 Comparing Radical and Polynomial Growth - Practice questions for Comparing Radical and Polynomial Growth.

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 II

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 ALG2.151 Comparing Radical and Polynomial Growth skill assessments:

Problem 1Difficulty: Mastery

Compute the limit as x → ∞ of (x² − ∛(x⁵)) divided by x² (x > 0).

Solution & Explanation:Rewrite as 1 − (∛(x⁵) ÷ x²). Since ∛(x⁵)=x to the 5⁄3 power, the ratio is x to the 5⁄3−2 power=x to the −1⁄3 power→0. So the limit is 1.

Problem 2Difficulty: Mastery

Which statement about growth and rates of change is true for x > 0 and very large?

AThey have the same slope for all x because both are power functions.

B√(x⁷) grows faster because it is a radical.

Cx⁵ has both larger values and a larger slope than √(x⁷).

D√(x⁷) has larger values than x⁵ for large x.

Solution & Explanation:√(x⁷)=x to the 7⁄2 power=x to the 3 power.5 while x⁵ is exponent 5. Larger exponent means faster growth and a derivative that also grows faster for large x.

Problem 3Difficulty: Mastery

Let f(x)=x²√x and g(x)=√(x⁷) (x > 0). Solve f′(x)=g′(x). Round x to the nearest thousandth.

Solution & Explanation:f(x)=x to the 5⁄2 power so f′(x)=(5⁄2)x to the 3⁄2 power. g(x)=x to the 7⁄2 power so g′(x)=(7⁄2)x to the 5⁄2 power. Set equal: 5x to the 3⁄2 power=7x to the 5⁄2 power. For x>0, divide by x to the 3⁄2 power: 5=7x, so x=5⁄7≈0.714285…, which rounds to 0.714.

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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 II Math students. It aligns with educational standard ALG2.151 (Practice questions for Comparing Radical and Polynomial Growth.).