SAT Topics: Advanced Math

(Nonlinear Algebra)

Advanced math could mean many things, but in this case it just means fancy algebra. This is where you find problems involving square roots, quadratics, and exponential functions. The official breakdown of sub-categories or skills is as follows:

Equivalent Expressions— This category might be called messy algebra. There are powers (including fractional or negative exponents), radicals, parentheses, and/or multiple variables, and you need to simplify the mess. You need to factor, apply the distributive principle, simplify using exponent rules, and so on. If you don't know what else to do, one thing you might be able to try is to graph everything in Desmos and see which answer choice looks like the given expression. Beware especially of subtracting parentheses. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Nonlinear Equations— The full titile is "Nonlinear equations in one variable and systems in two variables" This is where you might have to solve a quadratic equation. (About half of the problems in this category have to do with solutions to quadratic equations.) If they give you a system or any other kind of weird equation, you will probably need to form it into a quadratic equation and then solve the quadratic equation. (For example, they might give you a system involving a linear equation and a quadratic equation, and you can substitute the first into the second to form a single quadratic equation.) Occasionally you might need to solve an equation involving a radical or a rational function, which you can do by turning it into a quadratic equation (square both sides, or multiply both sides by the denominator). Often you can just use Desmos to graph it and find the zeros. You might also need to solve an absolute value equation. If you've forgotten how, or even if you haven't, a quick method will probably be to graph it using Desmos. The hard difficulty level is huge, and it includes many of the painful, obnoxious math problems on the SAT. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Nonlinear functions— As with linear algebra, there is a lot of overlap between the category of functions and the category of equations, and it can be hard to tell them apart sometimes. This is where you might meet graphs of quadratic functions or exponential functions. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.