Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55

CAL2.91 Differential Equations from Context Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.91 Differential Equations from Context. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.91 Differential Equations from Context - Choose the differential equation that models a verbal description of change. Standards: AP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; 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 CAL2.91 Differential Equations from Context skill assessments:

Problem 1Difficulty: Mastery
A service queue has Q(t) tasks. Arrivals occur at rate lambda(t). Service completion saturates at rate mu(t)Q/(K + Q), and tasks abandon the queue at rate aQ. Which equation models Q?
AdQ/dt = lambda(t) + mu(t)Q/(K + Q) - aQ
BdQ/dt = mu(t)Q/(K + Q) - lambda(t) - aQ
CdQ/dt = lambda(t) - mu(t)(K + Q)/Q - aQ
DdQ/dt = lambda(t) - mu(t)Q/(K + Q) - aQ
Solution & Explanation:Arrivals add lambda(t). Service completions and abandonment both remove tasks, so dQ/dt = lambda(t) - mu(t)Q/(K + Q) - aQ.
Problem 2Difficulty: Mastery
A cylindrical candle has fixed height H and volume V(t) = pi r2H. It melts from the side so the volume loss rate is proportional to lateral surface area 2pi rH. Which equation models V?
AdV/dt = -kV
BdV/dt = -2k pi H V
CdV/dt = -2k sqrt(pi H V)
DdV/dt = -k/(2sqrt(pi H V))
Solution & Explanation:Since r = sqrt(V/(pi H)), the lateral area is 2pi H r = 2sqrt(pi H V). Volume decreases at k times that area, so dV/dt = -2k sqrt(pi H V).
Problem 3Difficulty: Mastery
In an RC circuit, capacitor voltage V(t) satisfies C dV/dt = I, where current I = (E(t) - V)/R. Which differential equation models V?
AdV/dt = RC(E(t) - V)
BdV/dt = (E(t) - V)/(RC)
CdV/dt = (V - E(t))/(RC)
DdV/dt = C(E(t) - V)/R
Solution & Explanation:Substitute I = (E(t) - V)/R into C V' = I to get C V' = (E(t) - V)/R. Dividing by C gives V' = (E(t) - V)/(RC).

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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 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55 (Choose the differential equation that models a verbal description of change. Standards: AP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55.).

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