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 Last Updated: 09 July 2018 09 July 2018
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 
AAPR0912.06 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 
AAPR0912.07(+) 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 
ACED0912.01 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 
ACED0912.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  50 
ACED0912.04 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 
AREI0912.02 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 
ASSE0912.02 Use the structure of an expression to identify ways to rewrite it. For example, see x^{4} – y^{4} as (x^{2})^{2} – (y^{2})^{2}, thus recognizing it as a difference of squares that can be factored as (x^{2} – y^{2})(x^{2} + y^{2}).  10, 38, 39, 40 
Domain: Building Functions (FBF)  
Learning Standard: Build a function that models a relationship between two quantities  Test Questions 
FBF0912.01 Write a function that describes a relationship between two quantities.

23, 24, 26, 29 
Learning Standard: Build new functions from existing functions  Test Questions 
FBF0912.03 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 
FBF0912.04 Find inverse functions.

21, 25 
FBF0912.05 (+) 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 
FIF0912.05 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 personhours 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 
FIF0912.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

42, 44, 45, 46, 52, 53, 54, 55 
FIF0912.08 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 
FLE0912.04 For exponential models, express as a logarithm the solution to ab^{ct} = 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 
FTF0912.01 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.  64, 66 
FTF0912.02 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 
FTF0912.05 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.  70, 72, 73, 74 
FTF0912.08 Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(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 
NRN0912.01 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 5^{1/3} to be the cube root of 5 because we want (5^{1/3})^{3} = 5^{(1/3)3} to hold, so (5^{1/3})^{3} must equal 5.  1, 8, 9 
NRN0912.02 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