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

CAL2.146 Taylor Polynomial Approximation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.146 Taylor Polynomial Approximation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.146 Taylor Polynomial Approximation - Choose the Taylor polynomial estimate for a function value near the center. 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 CAL2.146 Taylor Polynomial Approximation skill assessments:

Problem 1Difficulty: Mastery
Use the degree-4 Maclaurin polynomial T_4(x)=1-3x+6x2-10x3+15x4 for (1+x)^(-3) to estimate (1.1)^(-3). Round to four decimal places.
A0.7515
B0.7500
C1.3715
D0.9091
Solution & Explanation:Evaluate at x=0.1: 1-0.3+0.06-0.01+0.0015=0.7515. The coefficients come from the binomial expansion for exponent -3, not from a simple alternating geometric series.
Problem 2Difficulty: Mastery
For a function with f(0)=2, f'(0)=-1, f''(0)=3, and f'''(0)=-6, a theorem gives ∣R_3(0.2)∣ <0.0005. What is the degree-3 Taylor estimate for f(0.2)? Round to four decimal places.
A1.8600
B1.8605
C2.2680
D1.8520
Solution & Explanation:T_3(0.2)=2-0.2+3(0.2)2/2-6(0.2)3/6=1.8520. The remainder bound tells how close the true value is; it is not added to the estimate.
Problem 3Difficulty: Mastery
An alternating Taylor polynomial for a function at x=0.4 is T_5(0.4)=0.4-0.43/6+0.45/120. Which is the polynomial estimate, rounded to four decimal places?
A0.3893
B0.4108
C0.3894
D0.3807
Solution & Explanation:Compute the finite polynomial value: 0.4-0.43/6+0.45/120=0.3894. The estimate is the truncated polynomial value; the next term would be for an error analysis, not part of T_5.

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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 Taylor polynomial estimate for a function value near the center. 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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