Quizzes, exams, and flashcards about Advanced Math: Advanced Math 1 — quadratics, exponents and growth.
← SAT
Equivalent expressions, nonlinear equations and nonlinear functions — ≈35% of the Math section, 13 to 15 questions, and the domain that separates a good Math score from a very good one.
Three skill points, and "advanced" means nonlinear rather than difficult:
A quadratic written in a particular form is telling you something particular, and the SAT chooses the form on purpose.
A very large share of this domain is one question in disguise: you are given a quadratic in one form and asked for something that another form states outright. Learn which form answers which question and these stop being calculations.
The discriminant, b² − 4ac, is the companion fact: positive means two real solutions, zero means exactly one, negative means none. Questions that ask for the value of a coefficient that gives "exactly one solution" are asking for the discriminant to be zero, and solving the quadratic instead is the slow road.
In y = a·b^x, a is the starting value and b is the growth factor — not the growth rate. A 7% annual increase is b = 1.07, and a 7% decrease is b = 0.93. A question that gives you a percentage in words and four expressions among the choices is testing exactly that conversion, and one of the wrong choices will always be the one that uses 0.07.
The built-in graphing calculator can find the intersection of a line and a parabola, the zeros of a polynomial and the vertex of a quadratic directly, and on this domain that is often the fastest correct route. But equivalent-expression questions are algebra with no numbers in them, and there is nothing to graph — factoring is the only method. Know which kind of question you are looking at before you reach for anything.
