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

CAL2.80 Separable Differential Equation Setup Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.80 Separable Differential Equation Setup. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.80 Separable Differential Equation Setup - Select the correct separation step for a differential equation of the form dy/dx = g(x)h(y). 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 CAL2.80 Separable Differential Equation Setup skill assessments:

Problem 1Difficulty: Mastery

For y not equal to -2 or 2, simplify and separate dy/dx = ((1 - x)/(1 + x²))((4 - y²)/(2 - y)). Which step is valid?

A(y + 2) dy = ((1 - x)/(1 + x²)) dx

Bdy/(y + 2) = ((1 - x)/(1 + x²)) dx

Cdy = ((1 - x)/(1 + x²))(y + 2) dx

D((1 - x)/(1 + x²)) dy = (y + 2) dx

Solution & Explanation:Since 4 - y² = (2 - y)(2 + y), the dependent factor simplifies to y + 2 on the stated interval. The independent-variable factor is (1 - x)/(1 + x²), and the dependent-variable factor is y + 2. On intervals where the displayed division is valid, a separation step moves dx to the right and divides by the dependent-variable factor, giving dy/(y + 2) = ((1 - x)/(1 + x²)) dx. The tempting form dy = ((1 - x)/(1 + x²))(y + 2) dx is not fully separated because it still leaves a dependent-variable factor on the dx side.

Problem 2Difficulty: Mastery

For x not equal to 0, y + sin y nonzero, and cos y nonzero, which step separates dy/dx = ((x² + 1)/x)(cos y/(y + sin y))?

A(cos y/(y + sin y)) dy = ((x² + 1)/x) dx

Bdy = ((x² + 1)/x)(cos y/(y + sin y)) dx

C((y + sin y)/cos y) dy = ((x² + 1)/x) dx

D((x² + 1)/x) dy = (cos y/(y + sin y)) dx

Solution & Explanation:The independent-variable factor is (x² + 1)/x, and the dependent-variable factor is cos y/(y + sin y). On intervals where the displayed division is valid, a separation step moves dx to the right and divides by the dependent-variable factor, giving ((y + sin y)/cos y) dy = ((x² + 1)/x) dx. The tempting form dy = ((x² + 1)/x)(cos y/(y + sin y)) dx is not fully separated because it still leaves a dependent-variable factor on the dx side.

Problem 3Difficulty: Mastery

A quantity Q satisfies dQ/dt = (t/(t² + 4))(1/(Q² + 1)). Which setup separates Q and t?

A(1/(Q² + 1)) dQ = (t/(t² + 4)) dt

BdQ = (t/(t² + 4))(1/(Q² + 1)) dt

C(t/(t² + 4)) dQ = (1/(Q² + 1)) dt

D(Q² + 1) dQ = (t/(t² + 4)) dt

Solution & Explanation:The independent-variable factor is t/(t² + 4), and the dependent-variable factor is 1/(Q² + 1). On intervals where the displayed division is valid, a separation step moves dt to the right and divides by the dependent-variable factor, giving (Q² + 1) dQ = (t/(t² + 4)) dt. The tempting form dQ = (t/(t² + 4))(1/(Q² + 1)) dt is not fully separated because it still leaves a dependent-variable factor on the dt side.

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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 separation step for a differential equation of the form dy/dx = g(x)h(y). 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).