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Common Core Algebra 1 Topics Crosswalk Writing and Solving Equations and Inequalities – Explain and prove methods of solution, more robust applications Solving Systems of Linear Equations – Explain and prove methods of solution Polynomial Expressions, Functions, and Equations – Solve by factoring, including factoring by grouping and factoring trinomials with leading coefficients – Solve quadratics by completing the square; use and prove the quadratic formula – Add, Subtract, and Multiply Polynomials of any degree Statistics – Measures of Central Tendency: Mean, Median, Mode – Measures of Spread: Range, Interquartile Range, Standard deviation – Conditional Relative Frequencies and Association – Linear Modeling: Correlation Coefficient, Residual Analysis Functions and Modeling – Domain and Range of a Function, in a modeling context – Arithmetic and Geometric Sequences – Behavior of a Function (Increasing, Decreasing, Positive, Negative, Roots) – Solving Equations Using the Graphs of Functions, Including Absolute Value Equations – Graphing Linear, Exponential, Absolute Value, Quadratic, Cubic, Square Root, Cube Root, and Piecewise Functions, and Modeling with all types of functions – Transformations of Graphs of Functions Red Topics are traditionally taught in Algebra 2/Trig Blue Topics are traditionally taught in Precalculus Green topics are traditionally taught in AP Statistics Purple Topics are topics presented in much greater depth in the Common Core

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Comparison of Standards Example: Factoring and Quadratic Equations 2005 Standards A.A.19 Identify and factor the difference of two perfect squares A.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF) A.A.27 Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots Common Core Standards A-SSE.A.2 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 ). A-REI.B.4 Solve quadratic equations in one variable. – 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. – Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

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