SAT Advanced Math: what your AP classes already cover

Equivalent expressions, nonlinear equations and systems, and nonlinear functions: quadratics, polynomials, rationals, exponentials. This is where AP Precalculus pays off most directly.

Each row is one SAT Advanced Math skill and the AP units on this site where you already practice it. Revisit those notes, then work through the two examples below before opening the answers.

Advanced Math skills, matched to AP units

SAT skill	Where it comes up in AP	Why it carries over
Equivalent expressions	AP Precalculus, Unit 1 AP Precalculus, Unit 2	Factoring, expanding and rewriting expressions are the working tools of Precalculus Units 1 and 2.
Nonlinear equations in one variable and systems of equations in two variables	AP Precalculus, Unit 1 AP Precalculus, Unit 2	Polynomial and exponential equations, and where two graphs meet.
Nonlinear functions	AP Precalculus, Unit 1 AP Precalculus, Unit 2 AP Calculus AB, Unit 1	Zeros, asymptotes, end behavior and transformations of nonlinear functions; limits make the end-behavior ideas exact.

Worked example 1: Equivalent expressions

Which expression is equivalent to \((2x+5)^2-(2x-5)^2\)?

Show the answer and working

Answer: \(40x\)

A difference of squares: \((a+b)(a-b)\) with \(a=2x+5\) and \(b=2x-5\) gives \((4x)(10)=40x\). Expanding both squares also works, but takes longer under SAT timing.

Worked example 2: Nonlinear functions

A savings balance is modeled by \(B(t)=500(1.04)^t\) dollars after \(t\) years. By what percent does the balance grow each year?

Show the answer and working

Answer: 4%

Each year multiplies the balance by the growth factor \(1.04\), an increase of \(4\%\). AP Precalculus Unit 2 reads growth factors the same way.