SAT Math · 28% of the test
Passport to Advanced Math
Passport to Advanced Math focuses on the algebra that bridges into precalculus: quadratic functions and equations, polynomial expressions and their factored forms, rational expressions, exponential functions, and radical expressions.
What's actually tested
Passport to Advanced Math is where the SAT separates the 600-band student from the 700-band student. Quadratic items appear on every form and may ask you to solve, factor, complete the square, identify the vertex, or interpret the parabola in a real-world model. Polynomial items typically test factoring, the relationship between zeros and factors, and end behavior. Exponential items test growth-versus-decay setup and require recognizing the y = a·b^t form. Rational items test simplification, restricted values, and (less often) solving rational equations.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Quadratic functions and equations
Solving, factoring, vertex form, and parabolic models.
Polynomial expressions and factoring
Multiplying, factoring, and the zeros of polynomials.
Rational expressions and equations
Simplifying ratios of polynomials and solving rational equations.
Exponential expressions and radicals
Exponent rules, scientific notation, and exponential growth/decay.
Sample practice questions in this topic
- Easy Quadratic functions and equations What is the sum of the solutions to the equation x² + 11x + 30 = 0?
- Easy Quadratic functions and equations What is the sum of the solutions to the equation x² + 2x = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² − 49 = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² − 11x + 30 = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² + 2x − 3 = 0?
- Hard Quadratic functions and equations What is the sum of the solutions to the equation x² − 1 = 0?
- Easy Quadratic functions and equations What is the sum of the solutions to the equation x² − 16 = 0?
- Easy Quadratic functions and equations What is the sum of the solutions to the equation x² − 16 = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² − 7x + 12 = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² + 3x − 4 = 0?
- Medium Quadratic functions and equations What is the sum of the solutions to the equation x² + 3x + 2 = 0?
- Hard Quadratic functions and equations What is the sum of the solutions to the equation x² + 1x − 12 = 0?
See all 56 questions in Passport to Advanced Math →
How students lose points here
Forgetting to check both roots of a quadratic when the question asks for "the value of x," dropping a negative when completing the square, and applying the linear sum-and-product rules to a polynomial that isn't monic without first dividing through. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
For quadratics, drill until each surface form (factored, standard, vertex) is recognizable in under five seconds. For exponentials, build a small bank of memorized growth-vs-decay templates (compound interest, half-life, population growth) and pattern-match every new word problem to one of them. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.