SAT Math Advanced Flashcards
SAT Math — Advanced Flashcard Deck
20 flashcards with spaced repetition. Press Space to flip, then rate your recall (1—4).
Additional Flashcard Topics
Quadratic Formula: x = (-b ± √(b²-4ac)) / 2a. The discriminant b²-4ac determines the number of real roots. Factor first if possible; use the formula when factoring is difficult.
Trigonometric Ratios: SOH CAH TOA, sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. The unit circle extends these to all angles.
Exponential Growth/ Decay: y = a(1±r)^t. Growth uses +; decay uses -. The base (1±r) determines the rate. Doubling time and half-life are common applications.
Logarithm Properties: log_b(xy) = log_b(x) + log_b(y), log_b(x/y) = log_b(x) - log_b(y), log_b(x^n) = n·log_b(x). Change of base: log_b(x) = ln(x)/ln(b).
Complex Numbers: i = √(-1). Operations follow algebraic rules with i² = -1. Complex conjugates: (a+bi)(a-bi) = a²+b².
Intuition
Advanced SAT math covers the most challenging topics that distinguish top scorers, quadratics, trigonometry, coordinate geometry, exponentials, logarithms, and complex numbers. Quadratics model parabolic relationships and can be solved by factoring, completing the square, or the quadratic formula. Trigonometry connects angles to side lengths in right triangles and extends to the unit circle. Logarithms are the inverse of exponentiation, useful for solving equations where the unknown is in the exponent. These topics appear in the hardest SAT math questions and require fluency with multiple solution strategies.
Common Pitfalls
- Discriminant misinterpretation: b² - 4ac > 0 means two real roots, = 0 means one repeated root, < 0 means no real roots, confusing these leads to wrong conclusions about solutions.
- Unit circle sign errors: In the unit circle, cosine is the x-coordinate and sine is the y-coordinate, mixing these up produces wrong values in quadrants II, III, and IV.
- Logarithm change of base: Forgetting that log_b(x) = ln(x)/ln(b), the change of base formula is essential when your calculator only has natural log.
- Exponential vs polynomial growth: Exponential functions eventually grow faster than any polynomial. Don’t assume 2^x < x^10 for large x, check the crossover point.
- Completing the square errors: When completing the square for x² + bx, add (b/2)², not b². The constant term is always (half the linear coefficient) squared.
Cross-References
- Site Home: Main landing page for sat notes.
- Practice: Practice problems for revision.
- Algebra: Algebraic foundations for advanced topics.
- Geometry: Coordinate geometry connects algebra and shapes.
Detailed Content
Core Concepts
Worked Examples
Common Mistakes
- Rushing through foundational material
- Not practising problems after reading
- Failing to connect concepts across topics