MATE0008 - Desarollo de destrezas básicas en matemáticas (Repaso Examen Parcial 1) - Universidad de Puerto Rico en Arecibo

Vocabulary flashcards covering properties of operations, number sets, and basic polynomial concepts from the notes.

Identity property of addition

The identity element is 0; a + 0 = a for any number a.

Identity property of multiplication

The identity element is 1; a × 1 = a for any number a.

Associative property of addition

Grouping of addends does not change the sum: (a + b) + c = a + (b + c).

Associative property of multiplication

Grouping of factors does not change the product: (ab)c = a(bc).

Commutative property of addition

Changing the order of addends does not change the sum: a + b = b + a.

Commutative property of multiplication

Changing the order of factors does not change the product: ab = ba.

Distributive property

Multiplication distributes over addition: a(b + c) = ab + ac.

Multiplicative inverse

For a ≠ 0, the multiplicative inverse is 1/a, since a·(1/a) = 1.

Additive inverse

The additive inverse of a is -a; a + (-a) = 0.

Irrational numbers

Numbers that cannot be expressed as a ratio of integers; non-terminating, non-repeating decimals (e.g., √7, π).

Rational numbers

Numbers expressible as p/q with integers p and q ≠ 0.

Integers

Whole numbers including negatives, zero, and positives; symbolized by Z.

Natural numbers

Nonnegative integers ( convention varies on including 0 ); symbolized by N.

Real numbers

All numbers on the number line; consists of rational and irrational numbers; symbolized by R.

Polynomial

An expression formed by a sum of monomials with nonnegative integer exponents.

Monomial

A polynomial with a single term (e.g., 3x^2, 5).

Binomial

A polynomial with exactly two terms (e.g., x + 1).

Leading coefficient

The coefficient of the term with the highest degree in a polynomial.

Degree of a polynomial

The greatest exponent of the variable in the polynomial.

Coefficient

The numerical factor multiplying a variable term; for 3y^6, the coefficient is 3.

Like terms

Terms that have the same variable part (same variables with same exponents) and can be combined.

Term

A summand in a polynomial; may be a constant or a monomial.

Variable

A symbol representing a quantity that can change (e.g., x, y).

Constant term

A term with no variables; just a number.