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

CAL2.86 Logistic Differential Equation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.86 Logistic Differential Equation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.86 Logistic Differential Equation - Select the correct logistic differential equation, carrying capacity, equilibrium values, or solution behavior. 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

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 CAL2.86 Logistic Differential Equation skill assessments:

Problem 1Difficulty: Mastery
In a logistic model P' = rP(1 - P/K), which population level has the same growth rate as P = K/5?
AP = K/10
BP = K/4
CP = 4K/5
DP = K
Solution & Explanation:The growth-rate factor is P(1 - P/K). With x = P/K, x(1 - x) is symmetric around x = 1/2, so x = 1/5 and x = 4/5 give the same rate.
Problem 2Difficulty: Mastery
In dF/dt = aF - bF2, F is measured in hundreds of fish. If a = 0.12 per year and the positive equilibrium is F = 18, what are b and the carrying capacity in fish?
Ab = 1/150 and carrying capacity = 1800 fish
Bb = 150 and carrying capacity = 18 fish
Cb = 0.12 and carrying capacity = 1800 fish
Db = 18 and carrying capacity = 150 fish
Solution & Explanation:The positive equilibrium is K = a/b, so b = a/K = 0.12/18 = 1/150. Since F is measured in hundreds of fish, F = 18 means 1800 fish.
Problem 3Difficulty: Mastery
If x = P/500 satisfies x' = 0.7x(1 - x), what differential equation does P satisfy?
AP' = 0.7P(1 - P/500)
BP' = 500P(1 - P/0.7)
CP' = 0.7(P/500)(1 - P/500)
DP' = 350P(1 - P)
Solution & Explanation:Since P = 500x, P' = 500x' = 500(0.7x(1 - x)) = 0.7P(1 - P/500).

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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 (Select the correct logistic differential equation, carrying capacity, equilibrium values, or solution behavior. 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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