SAT Math Flashcards (Algebra 2)

Algebra 2 Key Concepts

• Binomial: An expression with two distinct terms, such as x + y.

• Roots of a Parabola: Also known as zeros, these are the x-values where the quadratic function intersects the x-axis.

• Quadratic Equation: Represented as y = ax² + bx + c, where a, b, and c are constants.

• Discriminant: Calculated as b² - 4ac, it indicates the number of roots a quadratic function has.

  • If negative, the function has no real roots (imaginary roots).

• Vertex Form of Quadratic: Expressed as y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

• Vertex Minimum/Maximum: The y-value of the vertex represents the minimum (if a > 0) or maximum (if a < 0) of the parabola.

• Parabola Orientation: When a > 0, the parabola opens upwards, resulting in a minimum point; when a < 0, it opens downwards, yielding a maximum point.

Permutations and Combinations

• Permutation: Refers to arrangements of objects where order matters, calculable by the factorial of the number of objects involved.

• Combination: Arrangements of objects where order doesn’t matter, calculated using combinations formula.

Logarithms

• Logarithm: The inverse operation of exponentiation.

  • Example: log₂64 = x translates to 2ˣ = 64, solving for x gives x = 6.

• Log Rules: Includes various properties for manipulating logarithmic expressions.

Matrices and Complements

• Matrices: Foundational for organizing data in rows and columns, requiring practice for understanding complex operations.

• Completing the Square: A method used to transform a quadratic equation into vertex form; involves practice for mastery.

Problem-Solving Examples

• Seating Arrangement with Adjacency Constraint: To calculate seating arrangements for 4 boys where 2 must sit next to each other, treat the 2 as a single unit. Results in 12 combinations by accounting for internal arrangements.

• Arranging Books: Selecting and arranging 4 books from 9 different titles can yield 3024 different arrangements using factorial calculations.

Formulas

• Permutation Formula: P(n, r) = n! / (n - r)! describes ways to arrange r objects from n total.

• Combination Formula: C(n, r) = n! / [r!(n - r)!] calculates ways to choose r objects from n without regard to order.

Multiplication of Radicals

• Example Calculation: For 2√7 x 2√7,
  • Step 1: Collect like terms: 2 x 2 x √7 x √7
  • Step 2: Simplify to 4 x √49 = 4 x 7 = 28.