• The New SAT:  Passport to Advanced Math Domain
Details

 Application 1. Create quadratic or exponential functions. The student will create a quadratic or exponential function or equation that models a context. The equation will have rational coefficients and may require multiple steps to simplify or solve the equation. 2. Choose and produce equivalent forms of expressions to reveal and explain properties of a quantity. The student will, given a context, determine the most suitable form of an expression or equation to reveal a particular trait. Procedural Skill and Fluency 3. Create equivalent expressions involving radicals and rational exponents. The student will create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms. 4. Create equivalent forms of expressions using structure. The student will create an equivalent form of an algebraic expression by using structure and fluency with operations. 5. Solve quadratic equations. The student will solve a quadratic equation having rational coefficients. The equation can be presented in a wide range of forms to reward attending to algebraic structure and can require manipulation in order to solve. 6. Perform arithmetic operations on polynomials. The student will add, subtract, and multiply polynomial expressions and simplify the result. The expressions will have rational coefficients. 7. Solve radical and rational equations in one variable, including examples where there are extraneous solutions. The student will solve an equation in one variable that contains radicals or contains the variable in the denominator of a fraction. The equation will have rational coefficients, and the student may be required to identify when a resulting solution is extraneous. 8. Solve a system of equations consisting of one linear and one quadratic equation in two variables. The student will solve a system of one linear equation and one quadratic equation. The equations will have rational coefficients. 9. Rewrite simple rational expressions. The student will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result. The expressions will have rational coefficients. Conceptual Understanding 10. Interpret parts of nonlinear expressions in terms of their context. The student will make connections between a context and the nonlinear equation that models the context to identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation. 11. Understand the relationship between zeros and factors of polynomials; use it to sketch graphs. The student will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of a polynomial based on other information provided. 12. Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation, interpret graphs in the context of solving systems of equations, select a nonlinear equation corresponding to a given graph, determine the equation of a curve given a verbal description of a graph, determine key features of the graph of a linear function from its equation, or determine the impact to a graph of a change in the defining equation. 13. Use function notation, and interpret statements using  function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions. 14. Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.