Operations with polynomials Dividing polynomials Polynomial functions Analyzing graphs of polynomial functions Focus Standards Addressed in this Unit: CC.2.2.HS.D.3 – Extend the knowledge of arithmetic operations and apply to polynomials CC.2.2.HS.D.4 – Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs Important Standards Addressed in this Unit: N/A Misconceptions: Misinterpretations of the properties of exponents Difficulties using the various factoring methods Confusion when interpreting domain and of polynomial functions Concepts/Content: Simplify Degree Long division Synthetic division Polynomial Leading coefficient End behavior Relative maximum and minimum Extrema Turning points Competencies/Skills: Multiply, divide, and simplify monomial expressions involving powers Add, subtract, and multiply polynomials Divide polynomials using long division Divide polynomials using synthetic division Evaluate polynomial functions Identify general shapes of graphs of polynomial functions Graph polynomial functions and locate their zeros Find the relative maxima and minima of polynomial functions Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework
Solving radical equations Focus Standards Addressed in this Unit: CC.2.2.HS.D.2 – Write expressions in equivalent forms to solve problems CC.2.1.HS.F.1 – and extend the properties of exponents to solve problems with rational exponents Important Standards Addressed in this Unit: N/A Misconceptions: Difficulty simplifying basic radical expressions Problems involving rationalizing the denominator tend to be troublesome at times Basic arithmetic errors when solving equations and simplifying expressions Concepts/Content: nth root Radical sign Index Rationalizing the denominator Conjugate Radical equation Extraneous solution Competencies/Skills: Simplify radicals Use a calculator to approximate radicals Simplify radical expressions Add, subtract, multiply, and divide radical expressions Write expressions with radical exponents in radical form and vice versa Solve equations containing radicals Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test Interdisciplinary Connections: N/A Additional Resources: Glencoe Algebra 2 textbook USA TestPrep
CC.2.1.HS.F.7 – Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems Important Standards Addressed in this Unit: N/A Misconceptions: Difficulties with graphing quadratic equations Confusion with choosing the correct factoring method when solving quadratic equations Basic arithmetic errors when using completing the square or the quadratic formula Concepts/Content: Quadratic Parabola Axis of symmetry Vertex Standard form Root Zero Factored form FOIL Imaginary unit Complex number Complex conjugates Completing the square Quadratic formula Discriminant Competencies/Skills: Graph quadratic functions Find and interpret the maximum and minimum values of a quadratic function Solve quadratic equations by graphing Estimate solutions of quadratic equations by graphing quadratic equations by factoring Perform operations with pure imaginary numbers Perform operations with complex numbers Solve quadratic equations by using the square root property quadratic equations by completing the square quadratic equations by using the quadratic formula Use the discriminant to determine the number and type of roots of a quadratic equation Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework
Independence Fundamental counting principle Permutation Combination Probability Success Failure Random Odds Probability distribution Relative-frequency histogram problems involving dependent events Solve problems involving permutations Solve problems involving combinations Find the probability and odds of events Create and use graphs of probability distributions Small group collaboration Online remedial/enrichment videos Assessments: informal questioning in-class formative assessments review of homework periodic quizzes unit test Interdisciplinary Connections: N/A Additional Resources: Glencoe Algebra 2 textbook USA TestPrep