Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55

CAL2.135 Power Series Form and Center Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.135 Power Series Form and Center. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.135 Power Series Form and Center - Select the center, coefficient pattern, or term form for a given power series. Standards tags: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; 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 CAL2.135 Power Series Form and Center skill assessments:

Problem 1Difficulty: Mastery
A planned number-line diagram marks the center at \(c=\frac32\). Which series has coefficient pattern \(a_n=\frac{(2n)!}{n!}\) and that center?
A\(\sum_{n=0}\infty\frac{(2n)!}{n!}(x+\tfrac32)n\)
B\(\sum_{n=0}\infty\frac{n!}{(2n)!}(x-\tfrac32)n\)
C\(\sum_{n=1}\infty\frac{(2n)!}{n!}(x-\tfrac23)n\)
D\(\sum_{n=0}\infty\frac{(2n)!}{n!}(x-\tfrac32)n\)
Solution & Explanation:The center c=3/2 requires powers of (x-3/2)n, and the coefficient must remain (2n)!/n!.
Problem 2Difficulty: Mastery
Which term form matches \(4-8(x+1)2+16(x+1)4-32(x+1)6+\cdots\)?
A\(\sum_{n=0}\infty4(-2)n(x-1)2n\)
B\(\sum_{n=1}\infty4(-2)n(x+1)2n\)
C\(\sum_{n=0}\infty4(-2)n(x+1)2n\)
D\(\sum_{n=0}\infty(-8)n(x+1)n\)
Solution & Explanation:The coefficients are 4, -8, 16, -32, which are 4(-2)n, and only even powers of x+1 appear. The center is -1.
Problem 3Difficulty: Mastery
If \(p(x)=\sum_{n=0}\inftya_n(x-2)n\) and \(q(t)=p(2+t)\), which form describes q(t)?
A\(\sum_{n=0}\inftya_n(t-2)n\), centered at t=2
B\(\sum_{n=0}\inftya_n tn\), centered at t=0
C\(\sum_{n=0}\infty2n a_n tn\), centered at t=0
D\(\sum_{n=0}\inftya_n(t+2)n\), centered at t=-2
Solution & Explanation:Substitute x=2+t. Then x-2=t, so q(t)=∑ a_n tn and the t-series is centered at 0.

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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.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55 (Select the center, coefficient pattern, or term form for a given power series. Standards tags: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55).

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