A ball leaves your hand and traces a curve — it climbs, slows, stops, and drops. It never travels in a straight line. Advanced Math is the part of the Digital SAT that leaves straight lines behind: quadratics, exponentials, and polynomials, the equations built to bend.
The skill the test rewards is reading the form an equation is written in. Each form is a container that displays a different fact on the outside.
Let the form talk
- Factored form hands you the roots. y = (x − 3)(x + 5) crosses zero at 3 and −5 with no work.
- Vertex form hands you the peak or valley. y = (x − 2)² + 4 turns at the point (2, 4).
- Exponential form hands you a rate. y = 500(1.08)ᵗ grows 8% each step; 500(0.5)ᵗ halves each step.
Read what the question wants — a root, a maximum, a starting amount, a growth rate — then reach for the form that already shows it, converting only if you must.
What turns them hard
Hard items live in the link between a graph and an equation. They give you a feature — the curve doubles every 5 units, or it touches the x-axis once at −3 instead of crossing it — and ask which parameter in the equation produced it, or the reverse. A parabola that touches the axis without crossing has a repeated root, which means a perfect-square factor. Knowing which feature maps to which piece of the equation is the whole game at the top of this domain.
Before solving, ask what shape the equation is in and what that shape reveals for free. Half of Advanced Math is refusing to do work the form has already done for you.
Common questions
What is on the Digital SAT Advanced Math section?
Quadratic, exponential, and polynomial equations and expressions, function notation, and the connections between an equation and its graph.
What does it mean when a parabola touches the x-axis once?
It has a repeated (double) root, so the quadratic is a perfect square such as (x − 3)². The curve meets the axis at that point without crossing it.