Overview
This lecture provides a concise summary of key math formulas frequently needed for the SAT, including algebraic, quadratic, exponential, and trigonometric relationships.
Percent Change and Linear Equations
- Percent change is calculated as (new-old)/old × 100.
- The distance formula is d = rt, where d is distance, r is rate, and t is time.
Quadratics: Forms and Solutions
- Vertex form of a parabola: y = a(x-h)^2 + k, where (h, k) is the vertex.
- The vertex x-value of a parabola: x = -b/(2a).
- A quadratic equation ax^2 + bx + c = 0 has:
- 2 real solutions if b^2 - 4ac > 0.
- 1 real solution if b^2 - 4ac = 0.
- 0 real solutions if b^2 - 4ac < 0.
Roots of Quadratic Equations
- Sum of roots of ax^2 + bx + c = 0 is -b/a.
- Product of roots is c/a.
Exponential and Trigonometric Relationships
- Exponential growth is y = a(r)^t, where a is the starting value, r is the growth rate, and t is time.
- The relationship between sine and cosine: sin(x) = cos(90-x).
- Key values on the unit circle:
- 30°: (√3/2, 1/2)
- 45°: (√2/2, √2/2)
- 60°: (1/2, √3/2)
Absolute Value Equations
- Solving absolute value equations results in two cases (one positive, one negative).
Key Terms & Definitions
- Percent Change — The amount of change divided by the original value, multiplied by 100.
- Vertex Form — Alternate quadratic equation form to easily identify the vertex.
- Discriminant — b^2 - 4ac; indicates the number of real solutions for a quadratic.
- Sum/Product of Roots — Shortcut formulas for the sum and product of quadratic roots.
- Exponential Growth — Growth modeled by repeatedly multiplying by a fixed rate.
- Unit Circle — A circle of radius one, used for trigonometric values.
- Absolute Value Equations — Equations involving the distance from zero; always yield two cases.
Action Items / Next Steps
- Memorize these formulas for use on SAT math problems.
- Practice applying each formula with sample SAT questions.