District Assessment Connection for South Dakota Core Standards
Algebra II (V09) - Semester Two
Domain: Arithmetic with Polynomials and Rational Expressions (AAPR)
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. 56, 57, 58
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, divide rational expressions. 59, 60
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. 51
ACED09-12.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 50
ACED09-12.04 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. 31, 49
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. 2, 3, 5, 7, 19, 20, 61, 62
Domain: Seeing Structure in Expressions (ASSE)
Learning Standard: Interpret the structure of expression 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). 10, 38, 39, 40
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.
23, 24, 26, 29
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. 4, 6, 13, 15, 48

FBF09-12.04 Find inverse functions.

• Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
21, 25
FBF09-12.05 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. 36, 37
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context Test Questions
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. 14, 16, 41, 43, 71
Learning Standard: Analyze functions using different representations Test Questions
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.
• 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.
42, 44, 45, 46, 52, 53, 54, 55
FIF09-12.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 17, 33, 34, 35
Domain: Linear, Quadratic, and 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. 11, 12, 30, 32, 47
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. 64, 66
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. 63, 67, 68, 69
Learning Standard: Prove and apply trigonometric identities Test Questions
FTF09-12.05 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. 70, 72, 73, 74
FTF09-12.08 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. 65
Domain: The Real Number System (NRN)
Learning Standard: Extend the properties of exponents to rational exponents Test Questions
NRN09-12.01 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. 1, 8, 9
NRN09-12.02 Rewrite expressions involving radicals and rational exponents using the properties of exponents. 18, 22, 27, 28

Total Questions: 74 points
Free Response: 15 points
Overall: 89 points

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