Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55

CAL2.40 Solving Partial Fraction Coefficients Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.40 Solving Partial Fraction Coefficients. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.40 Solving Partial-Fraction Coefficients - Choose the correct coefficient values using substitution, comparison, or a system of equations. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55.

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

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related CAL2.40 Solving Partial Fraction Coefficients skill assessments:

Problem 1Difficulty: Mastery
Determine A, B, C, and D in \(\frac{11x2 - 75x + 66}{(x - 5)2(x2 - 2x + 2)} = \frac{A}{(x - 5)} + \frac{B}{(x - 5)2} + \frac{Cx + D}{(x2 - 2x + 2)}\).
AA=-2, B=3, C=-3, D=4
BA=-3, B=2, C=3, D=-4
CA=-3, B=-2, C=-3, D=4
DA=3, B=-2, C=-3, D=4
Solution & Explanation:Clear the denominator: 11x2 - 75x + 66 = A(x - 5)(x2 - 2x + 2) + B(x2 - 2x + 2) + (Cx + D)(x - 5)2. The squared linear factor requires the B/(x - 5)2 term; solving gives A=3, B=-2, C=-3, D=4.
Problem 2Difficulty: Mastery
Determine A, B, C, and D in \(\frac{-x3 - 13x2 - 51x - 61}{(x + 2)2(x2 + 3x + 5)} = \frac{A}{(x + 2)} + \frac{B}{(x + 2)2} + \frac{Cx + D}{(x2 + 3x + 5)}\).
AA=-1, B=-4, C=3, D=-4
BA=4, B=1, C=-3, D=4
CA=-4, B=-1, C=3, D=-4
DA=4, B=-1, C=3, D=-4
Solution & Explanation:Clear the denominator: -x3 - 13x2 - 51x - 61 = A(x + 2)(x2 + 3x + 5) + B(x2 + 3x + 5) + (Cx + D)(x + 2)2. The squared linear factor requires the B/(x + 2)2 term; solving gives A=-4, B=-1, C=3, D=-4.
Problem 3Difficulty: Mastery
Determine A, B, C, and D in \(\frac{4x3 - 27x2 + 80x - 114}{(x - 5)2(x2 + 2x + 2)} = \frac{A}{(x - 5)} + \frac{B}{(x - 5)2} + \frac{Cx + D}{(x2 + 2x + 2)}\).
AA=3, B=2, C=2, D=-4
BA=2, B=3, C=2, D=-4
CA=-2, B=-3, C=-2, D=4
DA=-2, B=3, C=2, D=-4
Solution & Explanation:Clear the denominator: 4x3 - 27x2 + 80x - 114 = A(x - 5)(x2 + 2x + 2) + B(x2 + 2x + 2) + (Cx + D)(x - 5)2. The squared linear factor requires the B/(x - 5)2 term; solving gives A=2, B=3, C=2, D=-4.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55 (Choose the correct coefficient values using substitution, comparison, or a system of equations. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55.).

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