Advanced Level
Algebra
Tackle the most challenging algebra problems on the SAT with confidence.
What You'll Learn
Complex Systems
Solve challenging systems with non-linear elements and constraints.
Function Composition
Work with composite functions and inverse functions.
Algebraic Manipulation
Perform complex manipulations to solve sophisticated problems.
Advanced Applications
Apply algebra to solve multi-step real-world problems.
Key Concepts
- •Non-linear Systems: Solve systems with quadratic or other non-linear equations
- •Function Inverses: Find and work with inverse functions
- •Parametric Equations: Work with equations involving parameters
- •Complex Word Problems: Multi-step problems requiring strategic thinking
- •Algebraic Proofs: Justify solutions using algebraic reasoning
Example Problem
If f(x) = 2x + 3 and g(x) = x² - 1, what is f(g(2))?
Solution:
First, find g(2):
g(2) = 2² - 1 = 4 - 1 = 3
Then, find f(3):
f(3) = 2(3) + 3 = 6 + 3 = 9
Answer: f(g(2)) = 9
Study Tips
- ✓For function composition, always work from the inside out
- ✓Break complex problems into smaller, manageable steps
- ✓Check if there are multiple solutions and verify each one
- ✓Look for patterns and relationships that can simplify the problem
Start Practicing
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