Common Core Standards for Mathematics
Algebra II (V09) - Semester One
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. 28, 29, 30
NCN 09-12.02 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 6, 7
Learning Standard: Use complex numbers in polynomial identities and equations Test Questions
NCN 09-12.07 Solve quadratic equations with real coefficients that have complex solutions. 31, 32, 33
Domain: Seeing Structure in Expressions (ASSE)
Learning Standard: Interpret the structure of expressions Test Questions
ASSE09-12.02 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). 3, 4, 5, 10
Domain: Arithmetic with Polynomials and Rational Expressions (AAPR)
Learning Standard: Understand the relationship between zeros and factors of polynomials Test Questions
AAPR 09-12.02 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). 40, 44
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, 18, 21, 45, 46, 48
Learning Standard: 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. 39, 41, 42, 43
Domain: Creating Equations (ACED)
Learning Standard: 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. 25, 34
ACED09-12.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 22, 38
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context Test Questions
FIF09-12.02 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 14, 47
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. 16 19, 49, 50, 51
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. 12, 20, 24, 27, 37
FIF09-12.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
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. 26, 36
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. 17, 23
Domain: Building Functions (FBF)
Learning Standard: 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. 1, 2, 11, 13, 35
Domain: Interpreting Categorical & Quantitative Data (SID)
Learning Standard: Summarize, represent, and interpret data on a single count or measurement variable Test Questions
SID09-12.04 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. 52, 53, 54, 55
Domain: Making Inferences & Justifying Conclusions (SIC)
Learning Standard: Understand and evaluate random processes underlying statistical experiments Test Questions
SIC09-12.01 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.  56, 57
SIC09-12.02 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?  58, 60
Learning Standard: Make inferences and justify conclusions from sample surveys, experiments, and observational studies Test Questions
SIC09-12.03 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 59, 61
SIC09-12.06 Evaluate reports based on data. 62, 63


Multiple Choice: 63 points
Free Response:
12 points
75 points