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

CAL2.114 Series and Partial Sums Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.114 Series and Partial Sums. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.114 Series and Partial Sums - Choose the correct partial sum, sigma notation, or definition connecting a series to partial sums. 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 CAL2.114 Series and Partial Sums skill assessments:

Problem 1Difficulty: Mastery
For \(r\ne1\), suppose \(S_n=A\frac{1-rn}{1-r}\). Which term formula is consistent with these partial sums and \(S_0=0\)?
A\(a_k=\frac{A}{1-r}\)
B\(a_k=A(1-rk)\)
C\(a_k=Ark-1\)
D\(a_k=Ark\)
Solution & Explanation:The formula is the n-term geometric partial sum with first term A and ratio r. Therefore the kth term is \(A rk-1\).
Problem 2Difficulty: Mastery
A planned partial-sum plot shows points \((n,S_n)\) approaching a horizontal line y = L. Which statement correctly connects the plot to the series?
AThe graph of partial sums cannot be used to describe a series.
BIf the points approach L, then every term equals L.
CThe series must equal the largest plotted partial sum.
DIf the approach continues so \(S_n\to L\), then \(\sum a_n=L\).
Solution & Explanation:A series value is the limit of the partial sums. The graph supports convergence to L only when the partial sums continue approaching that line.
Problem 3Difficulty: Mastery
Let \(T_N=\sum_{k=1}Na_{2k}\). What does \(T_N\) represent?
AThe term \(a_{2N}\) only
BThe Nth partial sum of \(\sum_{k=1}\inftya_k\)
CThe full infinite series \(\sum_{k=1}\inftya_k\)
DThe Nth partial sum of the even-indexed subseries \(a_2+a_4+a_6+\cdots\)
Solution & Explanation:\(T_N=a_2+a_4+\cdots+a_{2N}\), so it is a partial sum of the even-indexed subseries. It skips odd-indexed terms, so it is not generally \(S_N\) for the original series.

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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 correct partial sum, sigma notation, or definition connecting a series to partial sums. 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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