PAM - Passport to Advanced Math Module Overview

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Passport to Advanced Math

Word cloud with advanced math terms As a test that provides an entry point to postsecondary education and careers, the redesigned SAT's Math Test will include topics that are central to the ability of students to progress to later, more advanced mathematics. Problems in Passport to Advanced Math will cover topics that have great relevance and utility for college and career work.

Chief among these topics is the understanding of the structure of expressions and the ability to analyze, manipulate, and rewrite these expressions. This includes an understanding of the key parts of expressions, such as terms, factors, and coefficients, and the ability to interpret complicated expressions made up of these components. Students will be able to show their skill in rewriting expressions, identifying equivalent forms of expressions, and understanding the purpose of different forms.

This category also includes reasoning with more complex equations, including solving quadratic and higher-order equations in one variable and understanding the graphs of quadratic and higher-order functions. Finally, this category includes the ability to interpret and build functions, another skill crucial for success in later mathematics and scientific fields.

Essential Questions

  • What types of situations are modeled with quadratic functions, and how do you write and solve these equations?
  • What types of situations are modeled with exponential functions, and how do you write and solve these equations?
  • How do we turn a rational exponent into a radical expression and how do we simplify these expressions?
  • How would you solve a system of equations consisting of a linear and a quadratic function?
  • How can we rewrite an expression to obtain equivalent forms?  
  • What is the significance of the different parts of an equation and can you identify these in context?
  • What is the relationship between zeros, factors, and graphs of polynomials?

Key Terms

1. Polynomial  - An algebraic expression with one or more, unlike terms.

2. Rational Exponent  - An exponent that is written as a fraction, with the numerator representing the power and the denominator representing the root.

3. Radical  - A square root.

4. Extraneous Solution  - A solution of the simplified form of an equation that does not satisfy the original equation.

5. Zero of a Function  - Where the x-intercept would be in a graph of the function or what value of x makes the entire function equal zero.

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