Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55

CAL2.118 p Series Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.118 p Series. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.118 p-Series - Choose the convergence conclusion for a p-series based on the value of p. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; 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 CAL2.118 p Series skill assessments:

Problem 1Difficulty: Mastery
A planned comparison chart shows p = -2, p = 0, p = 1, and p = 2. Which row has the only convergent p-series?
Ap = -2
Bp = 2
Cp = 0
Dp = 1
Solution & Explanation:Among the listed values, only p = 2 is greater than 1. The values p = -2, 0, and 1 are all in the divergent range; for p <= 0, the terms do not even approach 0.
Problem 2Difficulty: Mastery
For the p-series sum_{n=1}infty 1/n^(1 + 10^(-6)), what is the convergence conclusion?
ADiverges, because the exponent is too close to 1.
BDiverges, because 10^(-6) is very small.
CCannot be determined without estimating many terms.
DConverges, because the exponent is strictly greater than 1.
Solution & Explanation:The p-series rule uses a strict cutoff, not a speed cutoff. Since 1 + 10^(-6) is greater than 1, the series converges, even if slowly.
Problem 3Difficulty: Mastery
For the p-series sum_{n=1}infty 1/n^((x - 1)/(x + 1)), with x not equal to -1, what values of x make the series converge?
Ax < -1
Bx > -1
Cx > 1
D-1 < x < 1
Solution & Explanation:Convergence requires (x - 1)/(x + 1) > 1. Subtracting 1 gives -2/(x + 1) > 0, so x + 1 must be negative and x < -1.

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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 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55 (Choose the convergence conclusion for a p-series based on the value of p. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55.).

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