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

CAL2.132 Remainder and Approximation of Series 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 CAL2.132 Remainder and Approximation of Series Sums. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.132 Remainder and Approximation of Series Sums - Select the number of terms or error estimate needed to meet a specified accuracy. Standards tags: 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 CAL2.132 Remainder and Approximation of Series Sums skill assessments:

Problem 1Difficulty: Mastery
For a positive decreasing f, suppose integral_50infty f(x) dx = 0.012 and integral_51infty f(x) dx = 0.0115. If R_50=sum_{n=51}infty f(n), which conclusion is guaranteed?
AR_50 = 0.012
B0.012 <= R_50 <= 0.0115
CR_50 <= 0.0115 only
D0.0115 <= R_50 <= 0.012
Solution & Explanation:For a positive decreasing function, integral_{N+1}infty f <= R_N <= integral_Ninfty f. With N=50, this gives 0.0115 <= R_50 <= 0.012.
Problem 2Difficulty: Mastery
For sum_{n=0}infty (3/4)n, what is the least N so that the partial sum through n=N has relative error at most 1% compared with the exact sum?
A15
B17
C16
D14
Solution & Explanation:The exact sum is 4 and the tail is 4(3/4)^(N+1). The relative error is (3/4)^(N+1). This first falls at or below 0.01 when N=16.
Problem 3Difficulty: Mastery
For sum_{n=1}infty 6/(4n+1)2, what is the least N so the integral-test upper bound for R_N is at most 0.001?
A374
B375
C376
D1500
Solution & Explanation:The upper bound is integral_Ninfty 6/(4x+1)2 dx = (3/2)/(4N+1). Solving (3/2)/(4N+1) <= 0.001 gives N >= 374.75, so N=375.

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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 (Select the number of terms or error estimate needed to meet a specified accuracy. Standards tags: 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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