Honors Algebra 2

Honors Algebra 2 Piscataway High School

Teacher: Mr. Ross Email: [email protected] Textbook: Algebra 2 (2015), HMH (Kanold, Burger, et al.)

Course Overview Full year course: 5.0 credits (Honors Algebra 2 has a 5 point weight added to your grade) Prerequisite: Honors Geometry, Geometry 9 Description: Algebra 2 is a college prep course that builds on Algebra 1 topics but extends the study of algebra beyond linear and quadratic functions. Topics include analysis and modeling with a variety of complex functions such as quadratic, exponential, polynomial, logarithmic, square root, cube root, and rational. Students will also learn techniques to solve many types of equations using the basic skills acquired in Algebra 1 and will complete an introductory study of trigonometry. Additional topics may include graphing in three dimensions, probability, and combinatorics, if time permits.

The Algebra 2 course is structured as follows: Unit Topic Length Unit 1 Number Sets 5 Days

Unit 2 Introductory Graph Analysis 9 Days

Unit 3 Quadratic Functions 12 Days

Unit 4 Graphing Higher Order Polynomials 12 Days Rational Functions: Graph Analysis 10 Days Unit 5 Rational Functions: Applications 10 Days Unit 6 Powers, Roots, and Radicals 15 Days

Unit 7 Exponential and Logarithmic Relations 15 Days

Unit 8 Trigonometry 12 Days

Unit 9 Systems 6 Days Scope and Sequence – First Semester

Unit Topic Concepts and Skills Timing (1 day = 1 hour) Assessment for Units 1 and 2 administered by the end of Cycle 3 Unit 1 Number Sets  Review solving absolute value equations, inequalities, special cases (i.e, 5 days x<2 and x<3, x<2 or x<3)  Graph on a number line verses a coordinate plane (IE: x < 2 )  Review compound inequalities: conjunctions and disjunctions  Use Venn diagrams to analyze set relationships  Set-builder notation vs. interval notation Unit 2 Introductory Graph  Write equations of lines given 2 points 9 days Analysis  Parallel versus perpendicular lines  Point slope form versus slope intercept form  Graph analysis of linear, absolute value, piecewise, linear inequalities, and quadratic functions  Emphasize domain and range of all functions covered so far  Practice using function notation  f(x)+k, kf(x), f(kx), f(x+k) Assessment for Unit 3 administered by the end of Cycle 6 Unit 3 Quadratic Functions  Factor to find roots of quadratic functions 12 days  Define i  Complex solutions of quadratic equations vs. imaginary zeroes of quadratic functions (through quadratic formula and completing the square)  Three forms of a quadratic function  Find a vertex using –b/2a and by finding the midpoints of the roots  Write equations of quadratics given a vertex and a point on the curve  f(x)+k, kf(x), f(kx), f(x+k) Assessment for Unit 4 administered by the end of Cycle 9 Unit 4 Graphing Higher Order  Perform operations with polynomials 12 days Polynomials  End behaviors (odd and even degree) and multiplicity of roots  Factoring to find zeroes  Factoring by grouping and U substitution  Synthetic vs. long division  Descartes rule of signs  Rational zero theorem  Connecting x-intercepts (zeros) of functions to factors of equations (roots)  f(x)+k, kf(x), f(kx), f(x+k) Assessment for Unit 5 administered by the beginning of Cycle 12 Unit 5a Rational Functions:  Vertical asymptotes connected to restrictions to domain 10 days Graph Analysis  Horizontal asymptotes through degrees of numerator/denominator  Introduction to limits, connecting to end behavior  Continuity vs. point of discontinuity vs. discontinuous functions  Domain and range  Emphasize translations from the parent graph and restrictions on domain  f(x)+k, kf(x), f(kx), f(x+k) Unit 5b Rational Functions:  Simplifying rational expressions 10 days Applications  Performing operations on rational expressions  Solving rational equations Unit Topic Concepts and Skills Timing (1 day = 1 hour)  Solving direct, inverse, joint variations  Distance, work and mixture problems  Simplify complex fractions Scope and Sequence – Second Semester

Unit Approximate time frame Concepts and Skills Timing (1 day = 1 hour) Assessment for Unit 6 administered by the end of Cycle 17 Unit 6 Powers, Roots, and  Composition of functions 15 days Radicals  Definition of inverses  Laws of exponents  Radical notation vs. Exponent notation  Solve Radical equations  Graph analysis of radical equations  domain and range  f(x)+k, kf(x), f(kx), f(x+k) Assessment for Unit 7 administered by the end of Cycle 21 Unit 7 Exponential and  Exponentials vs. Logarithms 15 days Logarithmic Relations  Graph analysis (asymptotes, domain and range)  f(x)+k, kf(x), f(kx), f(x+k)  change of base formula  Modeling  Growth (doubling) , decay (half-life), logarithms, interest  Arithmetic/Geometric Series (time permitting)  Connect to linear and exponential relationships Assessment for Unit 8 administered by the end of Cycle 24 Unit 8 Trigonometry  Introduction to unit circle 12 days  Ordered pairs  Proof of Pythagorean identities  Six trig functions  Radians vs. Degrees  Graph analysis  Amplitude, period, phase shift, vertical shift  f(x)+k, kf(x), f(kx), f(x+k) No standardized assessment is planned for Unit 9 Unit 9 Systems  Three variable systems 6 days  Use graphing calculator to solve systems using reduced row echelon form  Linear Programming  Classes of functions o Non-linear system of equations o Line intersecting a circle o System of quadratic equations