Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; TEKS 19 TAC section 111.55

CAL2.7 Derivative and Antiderivative Connections Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.7 Derivative and Antiderivative Connections. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.7 Derivative and Antiderivative Connections - Choose the statement that correctly connects a derivative, an antiderivative, and a definite integral. Standards tags: AP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; 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 CAL2.7 Derivative and Antiderivative Connections skill assessments:

Problem 1Difficulty: Mastery
Let F'(u)=f(u) and let u(x) be differentiable. Which statement correctly connects derivative, antiderivative, and definite integral?
ABecause d/dx[F(u(x))]=f(u(x)), ∫_ab f(u(x))u'(x)dx=F(b)-F(a).
BBecause d/dx[f(u(x))]=F(u(x))u'(x), ∫_ab f(u(x))u'(x)dx=f(u(b))-f(u(a)).
CBecause u is a new variable, ∫_ab f(u(x))u'(x)dx=F(u(a))-F(u(b)).
DBecause d/dx[F(u(x))]=f(u(x))u'(x), ∫_ab f(u(x))u'(x)dx=F(u(b))-F(u(a)).
Solution & Explanation:The chain rule identifies F(u(x)) as an antiderivative of f(u(x))u'(x). Evaluating that antiderivative at x=b and x=a gives F(u(b))-F(u(a)).
Problem 2Difficulty: Mastery
Let A(x)=∫_1x f(t)dt and F'(x)=f(x). Which statement correctly reconstructs F from A and F(1)?
AF(x)=F(1)-A(x).
BF(x)=A(x)-F(1).
CF(x)=F(1)+A(x).
DF(x)=f(1)+A(x).
Solution & Explanation:Since A(x)=F(x)-F(1), rearranging gives F(x)=F(1)+A(x). The accumulation function records change from x=1.
Problem 3Difficulty: Mastery
Let F'(x)=f(x) and suppose F(1)=4 and F(3)=9. Which statement correctly evaluates ∫_31 f(x)dx?
A∫_31 f(x)dx=F(3)-F(1)=5.
B∫_31 f(x)dx=F(1)-F(3)=-5.
C∫_31 f(x)dx=F(1)+F(3)=13.
D∫_31 f(x)dx=f(1)-f(3).
Solution & Explanation:The order of the limits matters. From 3 to 1, the upper endpoint is 1, so the value is F(1)-F(3)=4-9=-5.

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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 prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; TEKS 19 TAC section 111.55 (Choose the statement that correctly connects a derivative, an antiderivative, and a definite integral. Standards tags: AP Calculus BC prerequisite skills and Unit 6; CCSS.HSF.IF, HSF.TF, HSA.SSE; CCSS.MP1, MP2, MP5, MP6, MP7; Integrated Calculus II Standards CAL2-FOUND; TEKS 19 TAC section 111.55).

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