Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Mathematical Practices; CCSS.HSM; CCSS.MP1-MP8; ISTE 2,3,5,6; AASL Inquire/Curate/Engage; California Mathematics Framework 2023; Integrated CAL2-MTD, CAL2-RPI

CAL2.155 Error, Accuracy, and 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 CAL2.155 Error, Accuracy, and Approximation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.155 Error, Accuracy, and Approximation - Select the best statement about numerical, measurement, modeling, or truncation error. Standards: AP Calculus BC Mathematical Practices; CCSS.HSM; CCSS.MP1-MP8; ISTE 2,3,5,6; AASL Inquire/Curate/Engage; California Mathematics Framework 2023; Integrated CAL2-MTD, CAL2-RPI

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 CAL2.155 Error, Accuracy, and Approximation skill assessments:

Problem 1Difficulty: Mastery

An approximation is 2.71820 and a proof shows the absolute error is at most 0.00007. Which statement is guaranteed?

AThe exact value lies in [2.71813, 2.71827], so the value is guaranteed to round to 2.718 to three decimal places.

BThe exact value must be 2.71820 exactly.

CThe value is guaranteed to four decimal places because the bound has five decimal places.

DThe relative error is 0.00007.

Solution & Explanation:The error bound gives the interval 2.71820 ± 0.00007, or [2.71813, 2.71827]. Every number in this interval rounds to 2.718 to three decimals, but not to a single four-decimal value.

Problem 2Difficulty: Mastery

A table of sampled values is used to approximate an integral by joining adjacent points with line segments. Which statement best describes the method's error sources?

AThe trapezoidal estimate is exact for the piecewise-linear interpolant, but the interpolant may differ from the true function and the data may have measurement error.

BThe trapezoidal estimate is exact for the true function regardless of curvature.

CMeasurement error disappears after interpolation.

DPiecewise-linear interpolation creates no approximation error unless x-values are unequal.

Solution & Explanation:The trapezoidal rule exactly integrates the line segments connecting the data points. Error remains if the true curve is not that interpolant or if the sampled values are inaccurate.

Problem 3Difficulty: Mastery

Euler's method is used for y' = y, y(0)=1 with h = 0.1 for one step. The Euler value is 1.1, while the exact value is e⁰.1 ≈ 1.10517. Which statement best identifies the local error?

AThe local error is about 0.00517 and comes from truncating the exponential Taylor expansion after the linear term.

BThe local error is exactly 0 because Euler's method uses the derivative.

CThe local error is about 0.10517 because the initial value is 1.

DThe local error is a measurement error in h.

Solution & Explanation:Euler's one-step value is 1 + 0.1 = 1.1. The exact solution gives e⁰.1 ≈ 1.10517, so the local error is about 0.00517, reflecting omitted higher-order Taylor terms.

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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 Mathematical Practices; CCSS.HSM; CCSS.MP1-MP8; ISTE 2,3,5,6; AASL Inquire/Curate/Engage; California Mathematics Framework 2023; Integrated CAL2-MTD, CAL2-RPI (Select the best statement about numerical, measurement, modeling, or truncation error. Standards: AP Calculus BC Mathematical Practices; CCSS.HSM; CCSS.MP1-MP8; ISTE 2,3,5,6; AASL Inquire/Curate/Engage; California Mathematics Framework 2023; Integrated CAL2-MTD, CAL2-RPI).