Common Core State Standards for Mathematics
Accelerated Algebra II (V09) - Semester Two
Domain: Arithmetic with Polynomials and Rational Expressions (AAPR)
Learning Standard: Rewrite rational expressions Test Questions
AAPR09-12.07 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. 35, 36, 37, 38
Domain: Creating Equations (ACED)
Learning Standard: Create equations that describe numbers or relationships Test Questions
ACED09-12.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 19, 21, 22, 24
Domain: Reasoning with Equations and Inequalities (AREI)
Learning Standard: Understand solving equations as a process of reasoning and explain the reasoning Test Questions
AREI09-12.02 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. 6, 7, 8, 39
Learning Standard: Represent and solve equations and inequalities graphically Test Questions
AREI 09-12.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 10, 11, 12, 13
Domain: Seeing Structure in Expressions (ASSE)
Learning Standard: Write Expressions in equivalent forms to solve problems Test Questions
ASSE 09-12.04 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. 25, 26, 27, 28
Domain: Building Functions (FBF)
Learning Standard: 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.
17, 18, 20
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context Test Questions
FIF 09-12.05 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. 40, 41, 42
Learning Standard: Analyze functions using different representations Test Questions
FIF 09-12.07 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.
  • Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
14, 15, 55, 57
FIF 09-12.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 23
FIF 09-12.09 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. 16
Domain: Linear, Quadratic, & Exponential Models (FLE)
Learning Standard: Construct and compare linear, quadratic, and exponential models and solve problems Test Questions
FLE09-12.04 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 1, 2, 3, 4, 5
Domain: Trigonometric Functions (FTF)
Learning Standard: Extend the domain of trigonometric functions using the unit circle Test Questions
FTF09-12.01 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 9, 49, 50, 51
FTF09-12.02 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. 52, 53
Learning Standard: Model periodic phenomena with trigonometric functions Test Questions
FTF 09-12.05 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. 54, 56, 60, 61
Learning Standard: Prove and apply trigonometric identities Test Questions
FTF 09-12.08 Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and use it to find sin(?), cos(?), or tan(?) given sin(?), cos(?), or tan(?) and the quadrant of the angle. 58, 59, 62, 63
Domain: Making Inferences & Justifying Conclusions (SIC)
Learning Standard: Understand and evaluate random processes underlying statistical experiments Test Questions
SIC 09-12.01 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 47, 48
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? 29
Learning Standard: Make inferences and justify conclusions from sample surveys, experiments, and observational studies Test Questions
SIC 09-12.03 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 30, 31
SIC09-12.04 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. 32, 33
SIC09-12.06 Evaluate reports based on data. 34
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. 43, 44, 45, 46

Total: 63 points
Free Response: 12 points
Overall:
75 points

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