Common Core State Standards for Mathematics
Accelerated Algebra II (V09) - Semester One
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. 14, 15
NRN09-12.02 Rewrite expressions involving radicals and rational exponents using the properties of exponents. 10, 11, 12, 13, 16
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. 17, 18
NCN09-12.02 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. 1, 2, 3, 4
Learning Standard: Use complex numbers in polynomial identities and equations Test Questions
NCN09-12.07 Solve quadratic equations with real coefficients that have complex solutions. 5, 19, 20
NCN09-12.08 Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). 21, 22
NCN09-12.09 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. 23, 53
Domain: Seeing Structure in Expressions (ASSE)
Learning Standard: Interpret the structure of expressions Test Questions
ASSE09-12.01 Interpret expressions that represent a quantity in terms of its context.
  • Interpret parts of an expression, such as terms, factors, and coefficients.
  • Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
25, 26
ASS09-12.02 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). 24, 27
Domain: Arithmetic with Polynomials and Rational Expressions (AAPR)
Learning Standard: Understand the relationship between zeros and factors of polynomials Test Questions
AAPR09-12.02 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). 29, 30
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. 6, 31
Learning Standard: Use polynomial identities to solve problems Test Questions
AAPR09-12.04 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples. 28, 32, 33, 34
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. 35
ACED09-12.02 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 36, 37
ACED09-12.03 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 38
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. 39
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. 7, 8, 9, 40
Learning Standard: Solve systems of equations Test Questions
AREI09-12.07 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. 41, 42
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context Test Questions
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. 43, 44, 49, 50
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. 45, 46
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.
47, 48, 52
FIF09-12.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 51, 54
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. 55, 56
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.
57, 58

 

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