Pre-Calculus - Polynomials
Authored by Denise Williams
Mathematics
10th Grade - University
CCSS covered
Used 284+ times
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This Pre-Calculus quiz focuses on polynomial functions and their properties, making it appropriate for advanced high school students in grades 11-12 or early college courses. The questions comprehensively assess students' understanding of polynomial operations, factoring techniques, and graphical analysis. Students must demonstrate mastery of factoring by grouping, polynomial division, the Rational Root Theorem, finding zeros of polynomial functions, and determining end behavior based on leading coefficients and degrees. The quiz also requires students to work with complex numbers when solving cubic equations, apply Descartes' Rule of Signs to determine the number of negative roots, and solve polynomial inequalities using sign analysis. To succeed on this assessment, students need strong algebraic manipulation skills, conceptual understanding of how polynomial structure relates to graphical behavior, and the ability to connect multiple representations of polynomial functions. Created by Denise Williams, a Mathematics teacher in US who teaches grade 10-University. This comprehensive assessment serves multiple instructional purposes, from formative assessment during a polynomial unit to summative evaluation of student mastery before advancing to more complex Pre-Calculus topics. Teachers can use individual questions as warm-up problems to review specific concepts like the Factor Theorem or polynomial division, while the complete quiz works well as homework practice or in-class review before major assessments. The variety of question types—from computational problems requiring algebraic manipulation to conceptual questions about graph interpretation—makes this quiz particularly valuable for identifying specific areas where students need additional support. This assessment aligns with Common Core standards A-APR.2, A-APR.3, and F-IF.7c, which address polynomial operations, polynomial identities, and graphing polynomial functions respectively.
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17 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Factor by grouping:
3x3-x2+6x-2
Tags
CCSS.HSA.APR.A.1
CCSS.HSA.SSE.A.2
2.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Solve
8x³+125=0
Tags
CCSS.8.EE.A.2
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
(2x3 - 5x2 + 3x + 7) ÷ (x - 2)
Tags
CCSS.HSA.APR.D.6
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
List all possible rational zeros
f(x) = 3x5-5x2+x+6
Tags
CCSS.HSA.APR.B.3
CCSS.HSA.APR.B.2
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Give the equation of the 4th degree polynomial with zeros: 1 with multiplicity 2 and i.
Tags
CCSS.HSA.APR.B.3
6.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
What is the predicted end behavior of: y=-2x4+3x-1
Tags
CCSS.HSF.IF.B.4
CCSS.HSF.IF.C.7
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Decide if (x-3) is a factor of 3x3+10x2-x-12
Tags
CCSS.HSA.APR.B.2
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