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Passport to Advanced Math

Passport to Advanced Math questions include topics that are especially important for students to master before studying advanced math. Chief among these topics is the understanding of the structure of expressions and the ability to analyze, manipulate, and rewrite these expressions. This domain also includes reasoning with more complex equations, and interpreting and building functions.

Passport to Advanced Math is one of the three SAT Suite of Assessment Math subscores, reported on a scale of 1 to 15. The Passport to Advanced Math subscore is reported for all SAT Suite Math Tests except for PSAT 8/9.

This domain will feature multiple-choice and student-produced response question types. Calculator use is sometimes permitted, but not always needed or recommended.

Passport to Advanced Math questions ask students to:

  1. 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. Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.
  3. Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms.
  4. Create an equivalent form of an algebraic expression by using structure and fluency with operations.
  5. 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. Add, subtract, and multiply polynomial expressions and simplify the result. The expressions will have rational coefficients.
  7. 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 one linear equation and one quadratic equation. The equations will have rational coefficients.
  9. Rewrite simple rational expressions. Students will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result. The expressions will have rational coefficients.
  10. Interpret parts of nonlinear expressions in terms of their context. Students 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, and use that knowledge to sketch graphs. Students 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 on 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.