Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.63 Accumulation with Inflow and Outflow Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.63 Accumulation with Inflow and Outflow. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.63 Accumulation with Inflow and Outflow - Choose the correct net amount, total amount, or final quantity from rates entering and leaving a system. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; 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 CAL2.63 Accumulation with Inflow and Outflow skill assessments:

Problem 1Difficulty: Mastery
A reservoir contains 150 gallons at t=0. For 0<=t<=5, R_in(t)=20-2t and R_out(t)=5+t, in gallons/hr. What is the amount at t=5?
A375/2 gallons
B75/2 gallons
C225/2 gallons
D150 gallons
Solution & Explanation:The net rate is 15-3t. The net change is integral_05(15-3t)dt=75/2 gallons. Add the initial 150 gallons to get 375/2 gallons.
Problem 2Difficulty: Mastery
For 0<=t<=pi, R_in(t)=5 and R_out(t)=a(1+sin t). What value of a makes the final amount equal the initial amount?
A5
Bpi/(pi+2)
C5pi/(pi+2)
D(pi+2)/(5pi)
Solution & Explanation:Final equals initial when total inflow equals total outflow. Total inflow is 5pi, and total outflow is a integral_0pi(1+sin t)dt=a(pi+2). Thus a=5pi/(pi+2).
Problem 3Difficulty: Mastery
A container starts with 10 units. For t>=0, R_in(t)=6/(t+1)2 and R_out(t)=2/(t+1)3. What limiting amount does the model predict?
A14 units
B15 units
C16 units
D9 units
Solution & Explanation:Total inflow is 6 and total outflow is integral_0infinity 2/(t+1)3 dt=1. Net change is 5 units, so the limiting amount is 10+5=15 units.

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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 Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Choose the correct net amount, total amount, or final quantity from rates entering and leaving a system. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55).

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