# Algebra 1 S2 (V07) Common Core State Standards for Mathematics

Domain: The Real Number System
 Cluster: Extend the properties of exponents to rational exponents Test Questions N.RN.1  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. 10, 11, 12, 13 N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. 7, 8, 9, 14, 15, 16, 17, 18, 19, 20

Domain: Seeing Structure in Expressions
 Cluster: Write expressions in equivalent forms to solve problems. Test Questions A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 35, 36, Free Response 4a, Free Response 4b

Domain:  Arithmetic with Polynomial and Rational Expressions
 Cluster:  Perform arithmetic operations on polynomials. Test Questions A.APR.1 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. 28, 29, 30, 31, 32, 33, 34

Domain:  Reasoning with Equations and Inequalities
 Cluster:  Solve equations and inequalities in one variable. Test Questions A.REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 37, 38, 39, 40, 41, 42

Domain:  Interpreting Functions
 Cluster: Interpret functions that arise in applications in terms of a context. Test Questions F.IF.4 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.★ 50, 51, 52, 56, 57, 58 F.IF.5 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.★ 23, 59, 64, Free Response 4c
 Cluster: Analyze functions using different representations. Test Questions F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined (Algebra II) functions, including step (Algebra II) functions and absolute value functions. e. Graph exponential and logarithmic (Algebra II) functions, showing intercepts and end behavior, and trigonometric (Algebra II) functions, showing period, midline, and amplitude. 43, 44, 45, 47 F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t,    y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. 21, 46, 48, 49

Domain:  Building Functions
 Cluster:  Build new functions from existing functions. Test Questions F.BF.3 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. (Algebra II)) 53, 54, 55, Free Response 1

Domain:  Linear, Quadratic, and Exponential Models
 Cluster:  Construct and compare linear, quadratic, and exponential models and solve problems. Test Questions F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. 62, 65, 66, Free Response 2a, Free Response 2b F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 22, 26, 27, 63 F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Free Response 2c, Free Response 2d, Free Response 3

Domain:  Interpreting Categorical and Quantitative Data
 Cluster:  S.ID.0 Summarize, represent, and interpret data on a single count or measurement variable. Test Questions S.ID.0   Summarize, represent, and interpret data on a single count or measurement variable. 1, 2, 3, 4, 5, 6
 Cluster:  Summarize, represent, and interpret data on two categorical and quantitative variables. Test Questions S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.  Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. 24, 25, 60, 61

TOTAL QUESTIONS = 66 questions
FREE RESPONSE = 18 points
OVERALL = 84 points