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Algebra II at a Glance

Unit 1: Complex • Define the imaginary unit • Perform operations involving complex numbers, rationalizing numerators and denominators and determining the modulus of a complex , plot complex numbers on a . • Solve quadratic equations with complex solutions - connect the discriminant with the number and type of zeros and number of x-intercepts. • Transform any in x from standard, vertex, or factored form to any of the other forms. • Graphing quadratic equations in all forms: standard, vertex and factored (review) • Solve quadratic inequalities in two variables

Unit 2: Functions • Use interval notation. • Define, use and interpret function notation; evaluate functions. • Define and use vocabulary of relations and functions (relation, domain, range, input, output, function, independent/dependent variable, zero). • Interpret multiple representations (algebraic, graphical, table of values, list of ordered pairs, mapping diagram, and verbal description) of functions; identify, use, and create different representations of the same function. • Perform operations on functions including composition using multiple representations. • Perform transformations of graphs of functions (to include linear, quadratic, and cosine, piecewise-defined including , and the step function) with multiple representations. • Identify and apply characteristics and behaviors of functions including domain, range, intercepts, zeros, intervals of increasing/decreasing/constant behavior, relative and absolute extrema, end behavior (Function presented graphically.)

Unit 3: • Simplify expressions - using , subtraction, and long division of polynomials. • Define a polynomial function; identify the degree, leading coefficient and constant term of a polynomial function. • Known and apply the Remainder Theorem. • Graph polynomial functions presented in factored form or that are factorable using the leading coefficient test, the multiplicity and type of zeros, the Fundamental Theorem of Algebra and the maximum possible number of extrema. • Write an algebraic representation for a polynomial function when given sufficient information (including a graph). • Solve polynomial equations.

Unit 4: Rational Expressions and Equations • Identify rational expressions, equations, and functions. • Determine the greatest common factor of polynomial expressions and use it to simplify rational expressions. • Multiply and divide rational expressions (including long division). • Add and subtract rational expressions. • Determine the least common denominator of given rational expressions. • Simplify rational expressions including those involving complex fractions. • Solve rational equations by multiplying both sides of the equation by the least common multiple of the denominators. • Attend to domain restrictions and extraneous solutions. • Identify and apply characteristics and behaviors of rational functions including domain, range, intercepts, zeros, end behavior, asymptotes, removable discontinuities. • Graph rational functions. • Find equations of rational functions given sufficient information.

Unit 5: Exponents and • Define rational exponents. • Convert between rational exponent notation and radical notation. • Simplify expressions involving rational exponents and radicals. (This includes review of properties of exponents) • Define . • Convert between exponential and logarithmic forms of equations. • Use properties of logarithms to expand and condense expressions (omit change of base). • Solve simple exponential and logarithmic equations using the one-to-one property and rewriting (includes applications). • Define exponential functions. • Identify and apply characteristics and behaviors of exponential functions including domain, range, intercepts, zeros, end behavior and asymptotes. • Graph basic logarithmic functions of the form y=log base b of x and simple transformations.

Unit 6: • Vocabulary of trigonometry (Sine, Cosine, Tangent, Secant, Cosecant, Cotangent, coterminal angles, radians, degrees, standard position, terminal side, initial side) • Pythagorean Identities, quotient Identities, reciprocal Identities • Evaluate using the unit circle. • Graph y = sin x and y = cos x. Define amplitude, midline, period.