Passport to Advanced Math is the SAT's bridge to the kind of algebraic manipulation you will see in a college precalculus or calculus course. The questions are not about memorizing identities — they are about fluency with structure. Can you factor a quadratic by inspection? Can you read the vertex of a parabola off its standard form? Can you simplify a rational expression without losing a domain restriction? Can you translate between f(x), a graph, and a table of values without panicking? Most students who plateau between 650 and 720 plateau here, because the section rewards algebraic intuition that takes deliberate practice to build. ScoreReady's Passport drills hammer the specific manipulations that show up most often on released exams: completing the square, recognizing the discriminant, applying exponent rules, polynomial long division shortcuts, and interpreting transformations. The worked solutions narrate the mental moves an expert makes — what to factor first, what to substitute, what to graph mentally — so that with enough reps these moves become automatic.
Content domain
Passport to Advanced Math
Quadratics, polynomials, exponentials, rational expressions, and function notation.
Topics in Passport to Advanced Math
Quadratic Equations
Factor, complete the square, and apply the quadratic formula.
Polynomial Operations
Add, multiply, and factor polynomial expressions.
Exponential Functions and Exponent Rules
Apply exponent rules and interpret exponential growth.
Rational Expressions
Simplify, add, and divide rational expressions.
Function Notation and Composition
Evaluate, compose, and interpret functions in multiple representations.
Study tips for Passport to Advanced Math
- Memorize the quadratic discriminant b^2 - 4ac and what each sign means: positive gives two real roots, zero gives one, negative gives none. The SAT loves to ask "for what value of k does this have no real solutions."
- Vertex form y = a(x - h)^2 + k tells you the vertex (h, k) by inspection. If a question asks for a maximum or minimum, convert to vertex form rather than using calculus or a calculator.
- When simplifying rational expressions, factor numerator and denominator completely first. Cancel only common factors, never common terms.
- Exponent rules: when bases match, multiply by adding exponents and divide by subtracting. When exponents match, multiply or divide the bases. Mixing these up accounts for most exponential errors.
- For function composition f(g(x)), evaluate inside-out. Substitute the entire expression for g(x) into f, then simplify. Going outside-in produces wrong answers that the test specifically lists as choices.