Summary
◦ Don’t “solve for x” or “solve for y” unless you absolutely have to. (Don’t worry; your math teacher
won’t find out.) Instead, look for direct solutions to SAT problems. ETS rarely uses problems that
necessarily require time-consuming computations or endless fiddling with big numbers. There’s
almost always a trick—if you can spot it.
◦ If a problem contains an expression that can be factored, factor it. If it contains an expression that
already has been factored, unfactor it.
◦ To solve simultaneous equations, simply add or subtract the equations. If you don’t have the answer,
look for multiples of your solutions. When the simultaneous equation question asks for a single
variable and addition and subtraction don’t work, try to make something disappear. Multiply the
equations to make the coefficient(s) of the variable(s) you don’t want go to zero when the equations
are added or subtracted.
◦ Some SAT problems require algebraic manipulation. Use tricks when you can, but if you have to
manipulate the equation, take your time and work carefully to avoid unnecessary mistakes. You
don’t get partial credit on the SAT for getting the problem mostly correct.
◦ When working with inequalities don’t forget to flip the sign when you multiply and divide by
negative numbers.
◦ When working with inequalities over a range of values, treat each side of the inequality as a
separate problem. Then combine the problems in a logical order, making sure the “arrows” are
pointing to the correct numbers.
◦ When writing a system of equations, start with the most straightforward piece of information. You
can also use the equations in the answer choices to help you narrow down the possibilities for your
equations. Eliminate any answers in which an equation doesn’t match your equation.
◦ When a question asks for an extraneous solution, first solve your equation, and then plug the
answers back into the equation. If the equation is not true when solved with the solution, then that
solution is extraneous.
◦ When solving quadratic equations, you may need to FOIL or factor to get the equation into the
easiest form for the question task. Don’t forget about the common equations that ETS uses when
writing questions about quadratics.
◦ To solve for the roots of a quadratic equation, set it equal to zero by moving all the terms to the left
side of the equation, or use the quadratic formula:
x =
