Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.72 Work by a Variable Force Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.72 Work by a Variable Force. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.72 Work by a Variable Force - Select the correct work integral and units for a force that varies with position. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; 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 CAL2.72 Work by a Variable Force skill assessments:

Problem 1Difficulty: Mastery
A force component is F(x) = 25 - x2 newtons. An object moves from x = 1 m to x = 6 m. Which setup gives the signed work done by the force?
AW = ∫_16 ∣25 - x2∣ dx, joules
BW = ∫_61 (25 - x2) dx, joules
CW = ∫_16 (25 - x2) dx, newtons
DW = ∫_16 (25 - x2) dx, joules
Solution & Explanation:The force becomes negative after x = 5, but signed work still integrates F(x) as given. Absolute value would change the interpretation.
Problem 2Difficulty: Mastery
A spring force in pounds is F(x) = 9x when x is measured in feet. Which setup gives the additional work to stretch it from 6 inches to 18 inches beyond natural length?
AW = ∫_618 9x dx, foot-pounds
BW = (1/12)∫_0.51.5 9x dx, foot-pounds
CW = ∫_0.51.5 9x dx, foot-pounds
DW = ∫_01.5 9x dx, foot-pounds
Solution & Explanation:The force law uses feet, so convert 6 in and 18 in to 0.5 ft and 1.5 ft. No extra 1/12 factor is needed after converting the limits to feet.
Problem 3Difficulty: Mastery
A force law F(x) = 0.2x3 + 5 newtons uses x in meters. Which setup gives the work from x = -2 to x = 2?
AW = ∫_-22 0.6x2 dx, joules
BW = ∫_-22 (0.2x3 + 5) dx, joules
CW = ∫_2^-2 (0.2x3 + 5) dx, joules
DW = F(2) - F(-2), joules
Solution & Explanation:The signed work integral follows the interval from -2 to 2 and integrates the force law itself. Endpoint force difference is not work.

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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 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Select the correct work integral and units for a force that varies with position. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55).

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