Free Printable WorksheetMathPre-CalculusMath CurriculumHSA-SSE.1-3

Pre CAL.41 Partial Fraction Decomposition 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.41 Partial Fraction Decomposition. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.41 Partial Fraction Decomposition - Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a rational expression, select the correct partial fraction decomposition and determine how the decomposition supports solving or graph interpretation. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. 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.41 Partial Fraction Decomposition skill assessments:

Problem 1Difficulty: Mastery
When (2x + 14)/((x - 2)(x + 4)) is written as 3/(x - 2) - 1/(x + 4), what domain statement must still be kept?
AThe decomposition is valid for x not equal to 2 or -4, the same restrictions as the original denominator.
BThe decomposition is valid for every real x because the terms are simpler.
CThe decomposition is invalid only at x = 0.
DThe decomposition changes the excluded values to x = 3 and x = -1.
Solution & Explanation:Partial fraction decomposition rewrites the expression but does not remove restrictions from the original denominator. The excluded values remain x = 2 and x = -4.
Problem 2Difficulty: Mastery
A classmate decomposes (5x - 1)/((x - 1)(x + 2)) as 2/(x - 1) + 3/(x + 2). What error check reveals the mistake?
AThe expression is improper and needs division first.
BCombining gives 2(x + 2) + 3(x - 1) = 5x + 1, not 5x - 1.
CThe denominators have different signs, so no decomposition is possible.
DThe coefficients must add to -1, not 5.
Solution & Explanation:Combine the proposed decomposition. The numerator becomes 5x + 1, which does not match 5x - 1.
Problem 3Difficulty: Mastery
For f(x) = 1 + 2/(x - 2) + 3/(x + 1), which numerator equation finds the x-intercepts?
A1 + 2 + 3 = 0
B2(x - 2) + 3(x + 1) = 0
C(x - 2)(x + 1) = 0
D1(x - 2)(x + 1) + 2(x + 1) + 3(x - 2) = 0
Solution & Explanation:The constant 1 also must be written over the common denominator, so it contributes (x - 2)(x + 1) to the numerator.

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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 HSA-SSE.1-3 (Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a rational expression, select the correct partial fraction decomposition and determine how the decomposition supports solving or graph interpretation. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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