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

CAL2.38 Partial Fractions with Irreducible Quadratics Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.38 Partial Fractions with Irreducible Quadratics. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.38 Partial Fractions with Irreducible Quadratics - Choose the correct linear numerator form and integration strategy for irreducible quadratic factors. 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 CAL2.38 Partial Fractions with Irreducible Quadratics skill assessments:

Problem 1Difficulty: Mastery
For integral (11x - 7)/(x2 + 10x + 29) dx, which antiderivative is correct?
A(11/2) ln(x2 + 10x + 29) - 13 arctan((x + 5)/2) + C
B11 ln(x2 + 10x + 29) - 31 arctan((x + 5)/2) + C
C(11/2) ln(x2 + 10x + 29) - 31 arctan((x + 5)/2) + C
D(11/2) ln(x2 + 10x + 29) + 31 arctan((x + 5)/2) + C
Solution & Explanation:The derivative is 2x+10. Since 11x-7 = (11/2)(2x+10) - 62 and the denominator is (x+5)2+4, the constant part gives -62 times (1/2)arctan((x+5)/2), which is -31 arctan((x+5)/2).
Problem 2Difficulty: Mastery
Which check proves that (Ax+B)/(x2+4) is necessary in the general setup for a single irreducible quadratic factor?
AThe numerator must have the same degree as the denominator.
BThe numerator degree must be less than 2, so the most general real numerator is degree at most 1.
CThe quadratic should be split into x - 2 and x + 2 first.
DA constant numerator is always enough because the denominator is quadratic.
Solution & Explanation:Partial fractions use numerators of lower degree than their denominator factors. For a quadratic factor, lower degree means linear or constant, captured by Ax+B.
Problem 3Difficulty: Mastery
Evaluate integral 1/((x2+1)(x2+4)) dx.
A(1/3) arctan(x) - (1/6) arctan(x/2) + C
B(1/3) arctan(x) - (1/3) arctan(x/2) + C
Carctan(x) - (1/2) arctan(x/2) + C
D(1/3) arctan(x) + (1/6) arctan(x/2) + C
Solution & Explanation:Use 1/3 over x2+1 minus 1/3 over x2+4. The second integral includes the scale factor 1/2, producing -(1/6)arctan(x/2).

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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 linear numerator form and integration strategy for irreducible quadratic factors. 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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