What Types of Questions Are in the Passport to Advanced Math – SAT® Math Test?

A scale, pencil and calculator lying on a paper with advanced math numericals

Passport to Advanced Math questions assess your skills with quadratic functions, quadratic equations, polynomials, rational equations, systems of equations, exponential functions, exponential equations, connections between graphs and functions, functional notation, and complex equations.

As you prepare for the SAT® Math test, you should know that you need to understand Heart of Algebra questions and skills before moving on to the Passport to Advanced Math skills. Your algebraic skills are crucial for the Advanced Math questions.

Passport to Advanced Math questions occur in the calculator and no-calculator sections of the SAT Math exam. You will find multiple-choice questions and student-produced responses (grid-ins) while working through these question types.

Question Types

Passport for Advanced Math questions can be broken into four categories.

  1. Structures of expressions
  2. Evaluate, manipulate, and edit expressions 
  3. Understand complex equations 
  4. Translate and create functions

Here is a breakdown of what you need to know for each of these question types:

Structure of Expressions

  • Some Passport to Advanced Math questions will ask you to manipulate the structure of an expression to isolate variables. You may also be asked to display your understanding of structure by writing equivalents for expressions or finding solutions.


  1. 3x 2 + y 2 = 46
    y = 2x
    If ( x,y ) is a solution to the system of equations, what is the value of x 2?

Evaluate, Manipulate, and Edit Expressions

  • For other Passport to Advanced Math questions, you must evaluate connections between graphs and expressions. These questions require that you understand nonlinear relationships between two variables.
  • You will also find questions that ask you to use equations to make inferences about a graph, write an equation that represents the curve of a graph, or use a given equation to describe the characteristics of a graph. Sometimes, these questions ask about the changes in a graph that result from changes in the equation.
  • These questions target your understanding of real-life connections to the variable or expression, and you will be asked to evaluate the context of an expression.

    You can practice building connections between the real-world context and the graphs, variables, or equations in question. Start by establishing how the context is represented in the equation or variable.

    For some questions, you will have to establish how the context is represented in a component of the graph.
  • Expect to find questions that ask you to simplify or rewrite expressions. Hone in your ability to apply basic skills (like addition, subtraction, division, and multiplication) to two expressions. You can also expect to simplify polynomial expressions through addition, subtraction, division, and multiplication.
  • Some of these questions will ask you to manipulate an expression to produce an equivalent.
  • Some questions will also ask you to emphasize a specific context by manipulating an expression. You can do this by isolating a variable or reworking the form of the expression.


  1. A research project has been tracking the population of Monarch butterflies in Southern California. The population of butterflies has increased by 3% in the last two years. The population (P) was at 30,000 at the start of the study. Using n to represent the change over time, which equation best represents the population’s growth.
  2. Which graph accurately represents this equation?
  3. Which equation accurately represents the graph above?
  4. If the expression x 24x-2 is written in the equivalent form of 44x-2 + A, then what is Ain terms of x ?

Understand Complex Equations

  • These questions will assess your understanding of the relationship at play between factors of polynomials and zeros. To display your understanding, you may need to produce a graph. 
  • Be prepared to recognize if the given expression functions as a factor of a polynomial.
  • Practice questions that ask you to solve systems of equations that include both linear equations and quadratic equations. 
  • Practice questions that ask you to solve for a variable in an equation where the variable is placed in the denominator. You should also practice solving for variables in equations that include radicals. 
  • You should know how to recognize extraneous solutions.
  • Know how to convert the form of an equation to solve it in the form of a quadratic equation.


  1. If r 2 – 28c = 60 and r > 0, then what is the value of r – 3?
  2. How many solutions are possible for the following system of equations: y = x 2 + 4x – 2, y = x + 3
  3. The given system of equations has three solutions. One of these solutions is extraneous. Solve for the extraneous solution.

Translate and Create Functions

  • You should know how to read and translate expressions in function notation. To be more specific, you will use function notation to solve problems that focus on conceptual understandings. This means that you will need to produce or solve for a function that describes changes. Be familiar with the structure of a function. 
  • Be prepared to write, simplify, or solve functions to represent a given context.


  1. The function ƒ is defined by ƒ(x) = x 3 + 3x 2 + cx + 4 where c is a constant. If the graph of ƒ shows intersections on the x-axis at (4,0),(-1,0), and (p,0), then what is the value of c ?
  2. A function ƒ(x) = x 3 + 3.6x is represented by the graph above. Using ras a constant, the equation ƒ(x) = r has three solutions. What is a possible value of r ?

You should dedicate time to practicing each of these question types. It is important to know which questions frequently confuse you and which questions require skills you need to study. Remember, 16 of the 58 questions in the SAT Math exam will fall into these categories. You can use UWorld’s SAT Prep Course to prepare!

The course comes with resources like performance tracking tools, detailed explanations for questions, and thousands of challenging practice questions. The performance tracking tools will effectively pinpoint your weak points, and you can use the data from your scores to create an effective study plan.

Try it out to improve your scores and gain realistic experience with the style and level of difficulty in Passport to Advanced Math questions.

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