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

CAL2.78 Slope Fields from Differential Equations Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.78 Slope Fields from Differential Equations. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.78 Slope Fields from Differential Equations - Choose the slope field that matches a differential equation or the equation that matches a slope field. 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 CAL2.78 Slope Fields from Differential Equations skill assessments:

Problem 1Difficulty: Mastery
A slope field has horizontal segments on y = 0 and y = 4, positive slopes for 0 < y < 4, negative slopes for y < 0 and y > 4, and the largest upward slopes near y = 2. Which equation matches?
Ady/dx = y(4 - y)
Bdy/dx = y(y - 4)
Cdy/dx = (y - 2)2
Ddy/dx = 4 - y
Solution & Explanation:The product y(4 - y) is zero at y = 0 and y = 4, positive between those values, and negative outside. The positive product is greatest halfway between the zeros, at y = 2.
Problem 2Difficulty: Mastery
In a slope field, the isocline for slope -1 is y = x + 1, the isocline for slope 0 is y = x, and the isocline for slope 2 is y = x - 2. Which equation matches?
Ady/dx = y - x
Bdy/dx = x - y
Cdy/dx = x + y
Ddy/dx = (x - y)2
Solution & Explanation:For dy/dx = x - y, setting the slope to k gives x - y = k, or y = x - k. The listed isoclines correspond to k = -1, 0, and 2 exactly.
Problem 3Difficulty: Mastery
In a slope field, the isocline for slope 0 is y = 2x, the isocline for slope 3 is y = 2x - 3, and the isocline for slope -1 is y = 2x + 1. Which equation matches?
Ady/dx = 2x - y
Bdy/dx = y - 2x
Cdy/dx = 2x + y
Ddy/dx = x - 2y
Solution & Explanation:For dy/dx = 2x - y, setting the slope equal to k gives 2x - y = k, so y = 2x - k. That gives y = 2x for k = 0, y = 2x - 3 for k = 3, and y = 2x + 1 for k = -1.

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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 slope field that matches a differential equation or the equation that matches a slope field. 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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