Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; TEKS 19 TAC section 111.55

CAL2.5 Units and Dimensional Analysis Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.5 Units and Dimensional Analysis. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.5 Units and Dimensional Analysis - Choose the units and interpretation that match a rate, accumulated quantity, work integral, or model parameter. Standards: AP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; CAL2-FOUND; TEKS 19 TAC section 111.55. (AP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; 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 CAL2.5 Units and Dimensional Analysis skill assessments:

Problem 1Difficulty: Mastery

A proposed model for distance is s(t)=a ln(t/t0)+b, where s is measured in kilometers and t and t0 are measured in hours. Which units are consistent?

Aa: 1/hour; b: kilometers; t/t0 has hours

Ba: kilometers per hour; b: dimensionless; t/t0 is kilometers

Ca: hours; b: kilometers per hour; t/t0 is dimensionless

Da: kilometers; b: kilometers; t/t0 is dimensionless

Solution & Explanation:The logarithm is valid because t/t0 is dimensionless. Since ln(t/t0) is dimensionless, a must have kilometers, and b must also have kilometers to match s.

Problem 2Difficulty: Mastery

For a waiting-time density f(t) in 1/minute, what are the units and interpretation of ∫_0^∞ t f(t) dt when t is in minutes?

Adimensionless; total probability

B1/minute; density height

Cminutes; expected waiting time

Dminute squared; time-weighted area

Solution & Explanation:The units are (min)(1/min)(min)=min. The extra factor t makes this an expected value, not the total probability.

Problem 3Difficulty: Mastery

A periodic force model is F(t)=A cos(2πt/T+φ), where F is measured in newtons and t in hours. Which units are consistent?

AA: hours; T: newtons; φ: newtons per hour

BA: newtons; T: hours; φ: dimensionless radians

CA: newtons per hour; T: dimensionless; φ: hours

DA: dimensionless; T: 1/hour; φ: newtons

Solution & Explanation:The cosine input must be dimensionless, so t/T must be a pure number and T has hours. The amplitude A carries the newton units of F, while φ is a dimensionless phase.

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Frequently Asked Questions

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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 prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; TEKS 19 TAC section 111.55 (Choose the units and interpretation that match a rate, accumulated quantity, work integral, or model parameter. Standards: AP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; CAL2-FOUND; TEKS 19 TAC section 111.55.).