Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.152

Pre CAL.152 Binomial Theorem and Combinatorial Coefficients Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.152 Binomial Theorem and Combinatorial Coefficients. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.152 Binomial Theorem and Combinatorial Coefficients - Binomial Theorem and Combinatorial Coefficients

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

Pre-Calculus

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 Pre CAL.152 Binomial Theorem and Combinatorial Coefficients skill assessments:

Problem 1Difficulty: Mastery
Find the coefficient of x⁸ in the expansion of (x − 2/x)¹⁴.
Solution & Explanation:Term is C(14,k)x¹⁴⁻²ᵏ(−2)ᵏ. For x⁸, solve 14−2k=8 ⇒ k=3. Coefficient = C(14,3)(−2)³ = 364·(−8) = −2912.
Problem 2Difficulty: Mastery
What is the constant term in the expansion of (x + 1/x)¹⁴?
A3003
B3430
C1716
D3432
Solution & Explanation:Constant term needs 14−2k=0 ⇒ k=7. The constant term is the binomial coefficient C(14,7)=3432.
Problem 3Difficulty: Mastery
Find the coefficient of x¹⁹ in (x + 1)²⁰ + (x − 1)²⁰.
Solution & Explanation:The x¹⁹ term is C(20,19)x¹⁹·1 in (x+1)²⁰, but it is C(20,19)x¹⁹·(−1)¹ in (x−1)²⁰. Adding gives 20 + (−20) = 0.

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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 Pre-Calculus Math students. It aligns with educational standard Pre-CAL.152 (Binomial Theorem and Combinatorial Coefficients).

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