Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55

CAL2.28 Power Reduction Formulas Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.28 Power Reduction Formulas. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.28 Power-Reduction Formulas - Select the correct power-reduction formula and resulting simplified integral. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; 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 CAL2.28 Power Reduction Formulas skill assessments:

Problem 1Difficulty: Mastery
Which antiderivative is correct for ∫ 64sin4(x)cos4(x) dx after full power reduction?
AF(x)=3x/2+sin(4x)/2+sin(8x)/16+C
BF(x)=3x/4-sin(4x)/4+sin(8x)/32+C
CF(x)=8x-sin(4x)+sin(8x)/8+C
DF(x)=3x/2-sin(4x)/2+sin(8x)/16+C
Solution & Explanation:From sin4(x)cos4(x)=(3-4 cos(4x)+cos(8x))/128, multiplying by 64 gives 3/2-2 cos(4x)+cos(8x)/2. Integrating yields 3x/2-sin(4x)/2+sin(8x)/16+C.
Problem 2Difficulty: Mastery
Which exact value is correct for ∫_0^(π/2) sin4(x)cos4(x) dx after full power reduction?
A3π/128
Bπ/64
C3π/256
D5π/256
Solution & Explanation:Use sin4(x)cos4(x)=(3-4 cos(4x)+cos(8x))/128. The sine terms in the antiderivative vanish at the endpoints, leaving 3(π/2)/128=3π/256.
Problem 3Difficulty: Mastery
Which exact value is correct for ∫_0^(π/2) (sin4(x)+cos4(x)) dx after power reduction?
A3π/16
B3π/8
Cπ/2
D5π/16
Solution & Explanation:The sum reduces to (3+cos(4x))/4. Its antiderivative is 3x/4+sin(4x)/16, which gives 3π/8 on [0,π/2].

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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 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55 (Select the correct power-reduction formula and resulting simplified integral. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55).

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