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Test Advanced Math
DOMAIN 02 · 13–15 QUESTIONS (~35% OF EXAM)

Master SAT Advanced Math.
Nonlinear power unlocked.

Advanced Math determines whether your score breaks 700+. Master quadratic vertices, discriminant analysis, polynomial root theorems, and exponential decay models with proven Desmos visual tactics.

Core Advanced Math Subtopics

Deep-dive into each subtopic with concept breakdowns, formula sheets, and hard module practice.

01

Quadratic Functions & Vertex Form

Finding minimum/maximum values, completing the square, converting standard to vertex form, and axis of symmetry $x = -b/(2a)$.

y = a(x - h)² + k
Study Quadratics →
02

The Discriminant & Solution Types

Evaluating $b^2 - 4ac > 0$ (2 real roots), $= 0$ (1 root/tangent), and $< 0$ (no real solutions) for parameterized constants.

D = b² - 4ac
Study Discriminant →
03

Polynomial Division & Roots

Factoring higher-degree polynomials, polynomial long division, synthetic division, and remainder theorem $f(c) = r$.

P(x) = D(x)·Q(x) + R
Study Polynomials →
04

Exponential Growth & Decay

Modeling population growth, radioactive decay, compound interest rates, and interpreting time scaling factors $t/k$.

y = a(1 ± r)^(t/k)
Study Exponential Models →
05

Radical & Rational Equations

Solving equations with square roots and fractions, eliminating common denominators, and checking for extraneous solutions.

√(ax + b) = cx + d
Study Radicals →
06

Non-linear & Line-Parabola Systems

Finding intersection points between a line and a parabola, circles and lines, and setting equal for single-point tangency.

y = ax² + bx + c ∩ y = mx + d
Study Nonlinear Systems →
DESMOS ADVANCED HACK

Instant Min/Max & Vertex Reading with Sliders

When an SAT question asks for the maximum height of a quadratic projectile, type the equation into Desmos. Tap the vertex point directly to view $(h, k)$ coordinates without expanding or factoring.

Explore Full Desmos Guide →
// Desmos Vertex Form
f(x) = -16(x - 2.5)² + 144
// Click Peak Point
Vertex: (2.5, 144) → Max = 144