Patterns, Algebra, and Functions
This domain covers algebraic structure and function reasoning. You should understand variables and expressions, simplifying and factoring polynomials, solving linear equations and inequalities, systems of equations, and quadratic equations. Know slope as rate of change, the slope-intercept and point-slope forms, and how to interpret intercepts in context. For functions, be able to identify domain and range, evaluate f(x), recognize linear vs. nonlinear growth, and connect tables, graphs, and equations. Sequences (arithmetic and geometric) and their rules also appear.
Common traps: reversing the inequality sign when multiplying or dividing by a negative; forgetting that dividing by a variable can lose solutions; misreading slope as a y-value; and confusing the direction of a horizontal shift in a function (f(x−h) shifts right, not left). On systems, a question may ask how many solutions exist-parallel lines give none, identical lines give infinitely many. In quadratics, remember the discriminant b²−4ac tells you the number of real roots.
Worked example: Solve 3(x − 2) + 4 = 2x + 5. Distribute: 3x − 6 + 4 = 2x + 5, so 3x − 2 = 2x + 5. Subtract 2x: x − 2 = 5, so x = 7. Check: 3(5) + 4 = 19 and 2(7) + 5 = 19. Always substitute back to verify.
Practice translating word problems into equations and interpreting graphs in real-world contexts, since these blend process and algebra.