Pre Calculus Study Notes

What are natural numbers?

Natural numbers are the set of positive integers starting from 1: 1, 2, 3…

What is an example of a whole number?

Whole numbers include all natural numbers and zero: 0, 1, 2, 3…

What are integers?

Integers are whole numbers that can be positive, negative, or zero: …−2, −1, 0, 1, 2…

What defines a rational number?

Rational numbers can be expressed as fractions, such as ⅔, −4, and 0.75.

What are irrational numbers?

Irrational numbers cannot be expressed as simple fractions and are non-repeating and non-terminating, like √2 and π.

What is the commutative property of addition?

The commutative property states that a + b = b + a.

What does the associative property state?

The associative property states that (a + b) + c = a + (b + c).

What is the distributive property?

The distributive property states that a(b + c) = ab + ac.

What does the identity property for addition state?

The identity property states that a + 0 = a.

What is the zero exponent rule?

The zero exponent rule states that a^0 = 1, where a ≠ 0.

What is the product rule of exponents?

The product rule states that a^m × a^n = a^(m+n).

What is the power rule of exponents?

The power rule states that (a^m)^n = a^(mn).

What is the definition of a polynomial?

A polynomial is an expression made of terms with variables raised to whole number powers.

What is the degree of a polynomial?

The degree of a polynomial is the highest exponent in the expression.

What is the general form of a polynomial?

The general form of a polynomial is P(x) = an x^n + a{n-1} x^{n-1} + … + a1 x + a0.

What is factoring in relation to polynomials?

Factoring involves writing a polynomial as a product of simpler factors.

What is the quadratic formula?

The quadratic formula is x = (−b ± √(b² − 4ac)) / (2a).

What is a rational expression?

A rational expression is a fraction with polynomials in both the numerator and the denominator.

What is the distance formula?

The distance formula is d = √((x₂ − x₁)² + (y₂ − y₁)²).

What is the slope formula?

The slope formula is m = (y₂ − y₁) / (x₂ − x₁).

What is an absolute value equation?

An absolute value equation has the form |x| = a, which leads to two cases: x = a and x = -a.

What is a complex number?

A complex number includes a real part and an imaginary part, expressed as a + bi.