## Algebra II  Semester I

Domain:  The Complex Number System (NCN)
 Learning Standard: Perform arithmetic operations with complex numbers. Test Questions NCN09-12.01   Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. 24, 25, 26 NCN09-12.02   Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 4, 5 Learning Standard:  Use complex numbers in polynomial identities and equations. Test Questions NCN09-12.07   Solve quadratic equations with real coefficients that have complex solutions. 6, 7, 23

Domain:  Seeing Structure in Expressions (ASSE)
 Learning Standard:  Interpret the structure of expressions. Test Questions ASSE09-12.02 02   Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). 1, 2, 3

Domain:  Arithmetic with Polynomials and Rational Expressions (AAPR)
 Learning Standards:  Perform arithmetic operations on polynomials. Test Questions AAPR09-12.01   Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication: add, subtract, and multiply polynomials. 45, 46, 47, 48 Learning Standards: Understand the relationship between zeros and factors of polynomials. Test Questions AAPR09-12.02   Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). 53, 55 AAPR09-12.03   Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. 8, 9, 10, 18, 19, 54, 56, 57, 58 Learning Standards: Rewrite rational expressions. Test Questions AAPR09-12.06   Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. 49, 50, 51, 52

Domain:  Creating Equations (ACED)
 Learning Standards:  Create equations that describe numbers or relationships. Test Questions ACED09-12.01   Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. 21, 36, 37, 44 ACED09-12.02   Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 15, 39 ACED09-12.03   Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 38, 40, 41, 42, 43

Domain:  Interpeting Functions (FIF)
 Learning Standards:  Interpret functions that arise in applications in terms of the context. Test Questions FIF09-12.04   For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 13, 17 FIF09-12.05   Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 11, 12, 20, 27 Learning Standard:  Analyze functions using different representations. Test Questions FIF09-12.08   Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 22, 28, 29 FIF09-12.09   Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 14, 16

Domain:  Building Functions (FBF)
 Learning Standards:  Build a function that models a relationship between two quantities. Test Questions FBF09-12.01    Write a function that describes a relationship between two quantities.★ Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. 33, 34, 35 Learning Standards:  Build new functions from existing functions. Test Questions FBF09-12.03   Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 30, 31, 32

Multiple Choice = 58 questions               Free Response:  14 points                Overall:  72 points