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

CAL2.143 Maclaurin Series for Common Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.143 Maclaurin Series for Common Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.143 Maclaurin Series for Common Functions - Select the Maclaurin series for e^x, sin x, cos x, 1/(1-x), or ln(1+x). 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

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.143 Maclaurin Series for Common Functions skill assessments:

Problem 1Difficulty: Mastery
Which single check best rules out cos x as the series for ln(1+x)?
Aln(1+x) has f(0)=0, while cos x has constant term 1.
BBoth series alternate signs.
CBoth series converge for all real x.
Dln(1+x) has only even powers.
Solution & Explanation:The Maclaurin constant term equals f(0). Since ln(1+0)=0 but cos(0)=1, the constant term immediately distinguishes the two series. Alternation alone is not enough.
Problem 2Difficulty: Mastery
Which choice gives the Maclaurin series for ln(1+x/2) through the x5 term?
Ax/2 - x2/8 + x3/24 - x4/64 + x5/160
Bx/2 + x2/8 + x3/48 + x4/384 + x5/3840
Cx/2 - x3/48 + x5/3840
D1 + x/2 + x2/4 + x3/8 + x4/16 + x5/32
Solution & Explanation:Use ln(1+u)=u-u2/2+u3/3-u4/4+u5/5+... with u=x/2. The x5 term is (x/2)5/5 = x5/160.
Problem 3Difficulty: Mastery
Which choice gives the Maclaurin series for cos(-2x2)?
Asum_{n=0}^∞ (-1)n(2x2)2n/(2n)!
Bsum_{n=0}^∞ (-1)n+1(2x2)2n+1/(2n+1)!
Csum_{n=0}^∞ (-2x2)n/n!
Dsum_{n=0}^∞ (-2x2)n
Solution & Explanation:Cosine is even, so cos(-2x2)=cos(2x2). Substitute 2x2 into the cosine series to get sum (-1)n(2x2)2n/(2n)!.

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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 Maclaurin series for e^x, sin x, cos x, 1/(1-x), or ln(1+x). 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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