Advanced Math

Quadratics, exponentials, equivalent expressions and the function notation that ties them together.

• Equivalent expressions (nonlinear) An expression has many faces and all of them are true at once: x^2 - 9, (x+3)(x-3) and (x-1)^2 + 2x - 10 are the same object wearing different clothes. 12 questions · 3 worked examples
• Exponential functions A linear model asks how much is added each period; an exponential model asks what is it multiplied by. 12 questions · 3 worked examples · 3 figures
• Function notation and evaluation Nothing on this skill is hard arithmetic. 12 questions · 3 worked examples · 3 figures
• Interpreting nonlinear graphs and models Most nonlinear items on the Digital SAT never ask you to complete the square or write a growth factor. 12 questions · 3 worked examples · 6 figures
• Nonlinear equations Once the variable is squared, rooted or sitting in a denominator, "do the same thing to both sides" stops being a plan. 12 questions · 3 worked examples · 1 figure
• Nonlinear systems A line and a parabola share zero, one, or two points — and after one substitution that count is just the discriminant of a quadratic you already know how to read. 12 questions · 3 worked examples · 2 figures
• Polynomial operations and structure Most polynomial products on the Digital SAT do not ask for the whole expansion. 12 questions · 3 worked examples
• Quadratic functions and graphs A quadratic function can be written three ways, and the three ways are not stylistic preferences — each one puts a different fact about the parabola in plain sight and hides the other two. 12 questions · 3 worked examples · 3 figures
• Radicals and rational exponents One conversion rule does everything on this skill: x^{a/b} = \sqrt[b]{x^a}. 12 questions · 3 worked examples
• Rational equations and expressions A rational equation is an ordinary equation wearing a trap. 12 questions · 3 worked examples