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

CAL2.140 Algebraic Transformations of Power 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 CAL2.140 Algebraic Transformations of Power Series. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.140 Algebraic Transformations of Power Series - Choose the transformed power series for a shifted, scaled, multiplied, or divided function. Standards: 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 CAL2.140 Algebraic Transformations of Power Series skill assessments:

Problem 1Difficulty: Mastery
If \(f(x)=\sum_{n=0}\inftya_nxn\), which series represents \(\frac{f(2x)-f(0)}{x}\)?
A\(\sum_{n=0}\inftya_n2nxn-1\)
B\(\sum_{n=0}\inftya_{n+1}2nxn\)
C\(\sum_{n=1}\inftya_n2nxn\)
D\(\sum_{n=0}\inftya_{n+1}2n+1xn\)
Solution & Explanation:The substitution gives \(f(2x)=\sum a_n2nxn\). Subtracting \(f(0)=a_0\) removes the constant term, and dividing by \(x\) shifts the old index \(n+1\) to the new index \(n\).
Problem 2Difficulty: Mastery
Suppose \(f(t)=\sum_{n=0}\inftya_n(t-1)n\) converges for \(-2
A\(\sum_{n=0}\inftya_n(3x-2)n\), valid for \(-2
B\(\sum_{n=0}\inftya_n[3(x-1)]n\), valid for \(-\frac23
C\(\sum_{n=0}\inftya_n[3(x-1)]n\), valid for \(0
D\(\sum_{n=0}\inftya_n[3(x-1)]n\), valid for \(-2
Solution & Explanation:The centered input is \((3x-2)-1=3(x-1)\). The original interval condition \(-2<3x-2<4\) simplifies to \(0
Problem 3Difficulty: Mastery
Using the Maclaurin series for cosine, choose the series for \(\frac{\cos x-1}{x2}\).
A\(\sum_{n=0}\infty(-1)n\frac{x2n}{(2n)!}\)
B\(\sum_{n=0}\infty(-1)n+1\frac{x2n}{(2n+2)!}\)
C\(\sum_{n=0}\infty(-1)n\frac{x2n}{(2n+2)!}\)
D\(\sum_{n=1}\infty(-1)n\frac{x2n}{(2n)!}\)
Solution & Explanation:Subtracting 1 removes the constant cosine term. The first remaining term is \(-x2/2!\), so after division by \(x2\) the constant term is negative.

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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 (Choose the transformed power series for a shifted, scaled, multiplied, or divided function. Standards: 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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