Advanced Math — one screen
≈35% of Math · 13–15 questions · the same size as Algebra and one step harder. With Algebra it is 70% of the section.
The three skills
| Skill | What it asks |
|---|---|
| Equivalent expressions | Rewrite without changing value: factor, expand, simplify, complete the square |
| Nonlinear equations and systems | Solve quadratics, radicals, rationals; find where a line meets a curve |
| Nonlinear functions | Read and interpret parabolas and exponentials |
Factoring, the four patterns
| Pattern | Form | Example |
|---|---|---|
| Common factor | ab + ac = a(b + c) | 6x² + 9x = 3x(2x + 3) |
| Difference of squares | a² − b² = (a + b)(a − b) | x² − 49 = (x + 7)(x − 7) |
| Trinomial | x² + (p+q)x + pq = (x + p)(x + q) | x² + 7x + 12 = (x + 3)(x + 4) |
| Perfect square | a² ± 2ab + b² = (a ± b)² | x² − 10x + 25 = (x − 5)² |
Quadratics: three forms, three facts
| Form | Written | Hands you |
|---|---|---|
| Standard | y = ax² + bx + c | y-intercept c; vertex at x = −b/2a |
| Factored | y = a(x − r)(x − s) | The zeros r and s; vertex at their midpoint |
| Vertex | y = a(x − h)² + k | The vertex (h, k) directly |
x = [−b ± √(b2 − 4ac)] / 2athe quadratic formula
b2 − 4ac > 0 → two real solutions
b2 − 4ac = 0 → exactly one
b2 − 4ac < 0 → none
Exponentials
y = a × bxa is the start, b the multiplier
b > 1 → growth
0 < b < 1 → decay
increases 8% a year → b = 1.08
halves every 6 hours → y = a(0.5)^(t/6)
Linear changes by the same amount each step; exponential changes by the same factor.
Exponent and radical rules
xa × xb = x^(a+b)
xa / xb = x^(a−b)
(xa)b = x^(ab)
x^(−a) = 1 / xa
x^(1/n) = the nth root of x
x^(m/n) = the nth root of xm
Where points go
- Squaring both sides of a radical equation and not checking for extraneous solutions.
- Reading the vertex of a(x − h)² + k as (−h, k) — the sign flips.
- Treating b in a·bˣ as a rate rather than a multiplier: 8% growth is 1.08, not 0.08.
- Forgetting the ± in the quadratic formula.
- Cancelling a term rather than a factor in a rational expression.
The calculator does the heavy lifting
Graph it. Zeros, vertices, intersections and the number of solutions are all visible, and a question asking "how many real solutions" is answered by counting crossings.
Educerie · written from the published College Board Assessment Framework for the Digital SAT Suite (Math, Advanced Math). Original text. Last reviewed 12 September 2026.