Curriculum fit: Digital SAT Math, Advanced Math domain. Practice questions here are original, not official SAT questions. US: Algebra I and Algebra II.
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What Is It?
Advanced Math covers nonlinear relationships: quadratic equations and functions, exponential growth and decay, polynomials, and rewriting expressions in equivalent forms. It builds on Algebra I and II.
Typical tasks include solving a quadratic, finding the vertex of a parabola, deciding how many real solutions an equation has, and building an exponential model from a description.
Key Formulas and Ideas
- Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a.
- Discriminant b² − 4ac: positive means 2 real solutions, zero means 1, negative means none.
- Vertex form: f(x) = a(x − h)² + k has its vertex at (h, k).
- Exponential model: y = a × bˣ, where b > 1 is growth and 0 < b < 1 is decay.
Worked Examples
Solve a Quadratic
Solve x² − 5x + 6 = 0.
- Factorise: find two numbers that multiply to 6 and add to −5, which are −2 and −3.
- (x − 2)(x − 3) = 0.
- x = 2 or x = 3.
✓ Answer x = 2 or x = 3
Exponential Model
A population of 200 doubles every 3 years. How many are there after 9 years?
- 9 years is 3 doubling periods.
- 200 × 2³ = 200 × 8.
✓ Answer 1600
Vertex
What is the minimum value of f(x) = (x − 2)² + 5?
- A squared term is never negative, so its smallest value is 0.
- That happens at x = 2, giving f(2) = 5.
✓ Answer 5
Common Mistakes to Avoid
- Forgetting the ± when solving by square roots.
- Mixing up the sign in vertex form: (x − 2) means h = 2.
- Treating exponential growth as linear.
- Not checking whether an answer makes sense in context, such as a negative length.
Practice Questions
Frequently Asked Questions
When should I use the quadratic formula?
When factorising is not obvious. It works for any quadratic.
What are equivalent expressions?
Expressions that look different but have the same value for every x, such as (x + 1)² and x² + 2x + 1.
Keep Going With These Guides
Solving Quadratic Equations: Factorising and the Formula
Solve quadratics by factorising and with the quadratic formula, using worked examples. Covers GCSE quadratic equations and Algebra 1 and 2 methods.
GCSEA-LevelHigh SchoolExponential Growth and Decay: Formulas and Worked Examples
Model repeated percentage change with y = a × bˣ, including compound growth, depreciation and doubling, with step-by-step examples.
GCSEA-LevelHigh SchoolSAT Math Algebra: Linear Equations and Systems Practice
Practise the Digital SAT Algebra skills: linear equations, inequalities, systems of equations and linear models, with worked examples.
High SchoolAdmissions testsSources and Review
- College Board: The SAT Math section
- College Board: How the SAT is structured
- Common Core State Standards: Mathematics (high school)
Reviewed by StudyMorrow editorial review on 5 Nov 2026.