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In Algebra 1, students are normally expected to become proficient in a wide range of methods for resolving linear and quadratic equations. In order to solve equations, Algebra 1 emphasizes "applying the same thing to both sides of the equation." Algebra 1 challenges students to find roots (solutions) using a variety of strategies, including the quadratic formula, graph function connections on the coordinate plane, and converting between different types of quadratics via the lens of linear and quadratic functions.

The concepts from Algebra 1 are expanded upon in more detail in Algebra 2. A considerably wider set of functions, such as logarithms, radicals, and rational functions, are presented to students in Algebra 2. As students start to investigate the unit circle in Algebra 2, trigonometric functions frequently become a crucial new emphasis. Algebra 2 often includes conic sections like hyperbolas, parabolas, and ellipses as well as solutions with real and complex numbers, including arithmetic with imaginary values. Algebra 2 reveals that two "imaginary" solutions exist for fundamental parabolas that students believed had no solutions during Algebra 1.