SAT Math: Nonlinear Equations (Drill 3)

About This Drill

SAT Math: Nonlinear Equations (Drill 3) is a Math practice drill covering Nonlinear Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT nonlinear equation questions involve quadratic-linear systems, radical equations that require checking for extraneous solutions, rational equations, and using the discriminant to analyze the number of real solutions to a quadratic.

Questions in This Drill

1. How many real solutions does the system y = x² and y = −4 have?
2. What is the solution to √2x + 3 = x?
3. If 3/(x − 1) = 6, what is the value of x?
4. The equation x⁴ − 5x² + 4 = 0 can be factored as (x² − 1)(x² − 4) = 0. How many real solutions does it have?
5. For what value of k does the equation x² + 6x + k = 0 have exactly one real solution?