Mathematics Lecture Notes on Exponents, Products, and Sequences

These flashcards cover key mathematical concepts related to exponents, radicals, equations of lines, and sequences.

Laws of Exponents

Rules that describe how to handle mathematical operations involving exponents.

Product Rule

When multiplying two powers with the same base, add the exponents: bx * by = bx+y.

Quotient Rule

When dividing two powers with the same base, subtract the exponents: bx / by = bx−y.

Negative Exponent

A negative exponent represents the reciprocal of the base raised to the opposite positive exponent: b−x = 1 / bx.

Distributive Property

A property that allows you to multiply a sum by multiplying each addend separately and then adding the results.

FOIL Method

A technique for multiplying two binomials: First, Outer, Inner, Last.

Square of a Binomial

(x ± y)² = x² ± 2xy + y².

Special Products

Formulas used to simplify the multiplication of binomials and polynomials.

Rationalizing the Denominator

The process of eliminating a radical from the denominator of a fraction.

Slope-Intercept Form

A linear equation in the form y = mx + b where m is the slope and b is the y-intercept.

Point-Slope Form

A linear equation in the form y - y₀ = m(x - x₀) where (x₀, y₀) is a point on the line and m is the slope.

Arithmetic Sequence

A sequence of numbers in which the difference between consecutive terms is constant.

Common Difference (d)

The fixed amount that is added to each term of an arithmetic sequence.

Geometric Sequence

A sequence in which each term is found by multiplying the previous term by a constant called the common ratio.

Quadratic Equation

An equation of the form ax² + bx + c = 0 where a, b, and c are real numbers, and a ≠ 0.

Discriminant

The value of b² - 4ac which determines the nature of the roots of a quadratic equation.

Sum of Roots

In a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a.

Product of Roots

In a quadratic equation ax² + bx + c = 0, the product of the roots is c/a.