الرياضيات المتقدمة

المواضيع الفرعية

Equivalent expressions

Factoring polynomials, expanding, combining like terms, and working with rational expressions.

Nonlinear equations in one variable

Solving quadratic, polynomial, and rational equations. Using the discriminant to classify solutions.

Systems with a linear and nonlinear equation

Solving systems where one equation is linear and one is quadratic or another curve.

Nonlinear functions

Interpreting quadratic, exponential, and radical functions from equations, tables, and graphs.

Function notation and transformations

Evaluating f(x), g(f(x)), and identifying the effect of a, h, k on f(x) = a·f(x−h)+k.

x = (−b ± √(b² − 4ac)) / 2a (quadratic formula)

y = a(x − h)² + k (vertex form)

D = b² − 4ac (discriminant)

a² − b² = (a+b)(a−b) (difference of squares)

(a ± b)² = a² ± 2ab + b² (perfect square)

f(t) = a · bᵗ (exponential growth/decay)

Factor first — most quadratics on the SAT factor cleanly without needing the formula.
The discriminant tells you how many real solutions exist before you solve.
Vertex form is fastest for finding the maximum or minimum value.
For exponential functions, b > 1 means growth; 0 < b < 1 means decay.