Intensified Algebra 2/Trigonometry Summer Review Flashcards

Vocabulary flashcards covering core algebraic properties, exponent rules, order of operations, radical simplified rules, line properties, and number set classifications from the summer assignment notes.

Commutative Property

Algebraic property stating that changing the order of terms in addition or multiplication does not change the result, as shown by $a+b+c=a+c+b$.

Reflexive Property

Algebraic property stating that a value or expression is equal to itself, represented as $a+b=a+b$ or $\cos(3x+5)=\cos(3x+5)$.

Associative Property

Algebraic property stating that changing the grouping of numbers in addition or multiplication does not change their sum or product, represented as $a+(b+c)=(a+b)+c$.

Identity Property

Algebraic property stating that adding $0$ to a value or multiplying it by $1$ leaves the value unchanged ($a+0=a$ or $a \cdot 1=a$).

Inverse Property

Algebraic property stating that adding a number's opposite yields $0$ ($a+(-a)=0$) or multiplying by its reciprocal yields $1$ ($a \cdot \frac{1}{a}=1$).

Symmetric Property

Algebraic property stating that if $a=b+c$, then $b+c=a$.

Transitive Property

Algebraic property stating that if $a=b$ and $b=c$, then $a=c$.

Distributive Property

Algebraic property stating that multiplying a sum by a number gives the same result as multiplying each addend individually, represented as $a(b+c)=ab+ac$.

Product of Powers

Exponent rule stating that when multiplying expressions with the same base, you add the exponents: $a^m \cdot a^n = a^{m+n}$.

Power of a Power

Exponent rule stating that to raise a power to another power, you multiply the exponents: $(a^m)^n = a^{m \cdot n}$.

Power of a Product

Exponent rule stating that raising a product to a power is equal to multiplying each factor raised to that power: $(ab)^m = a^m b^m$.

Negative Power

Exponent rule stating that a base raised to a negative exponent equals its reciprocal with a positive exponent: $a^{-n} = \frac{1}{a^n}$.

Zero Power

Exponent rule stating that any non-zero base raised to the power of zero equals one: $a^0 = 1$.

Quotient of Powers

Exponent rule stating that when dividing expressions with the same base, you subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Power of Quotient

Exponent rule stating that raising a quotient to a power is equivalent to raising both the numerator and denominator to that power: $\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$.

Order of Operations (PEMDAS)

The sequence of operations used to simplify expressions: 1) Parentheses and grouping symbols, 2) Exponents, 3) Multiplication & Division (Left to Right), 4) Addition & Subtraction (Left to Right).

Simplest Radical Form

An expression under a radical sign where: 1) no integer under the radical has a perfect square factor, 2) no fractions are under the radical, and 3) no radicals remain in the denominator.

Slope Formula

The ratio describing the steepness of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Parallel Lines

Lines in the same plane that never intersect and have equal slopes.

Perpendicular Lines

Lines that intersect at right angles and have negative reciprocal slopes.

x-intercept

The point where a line crosses the x-axis, calculated by substituting $0$ for $y$ in the equation.

y-intercept

The point where a line crosses the y-axis, calculated by substituting $0$ for $x$ in the equation.

Real Numbers

The comprehensive set of numbers that includes all rational and irrational numbers.

Rational Numbers

Numbers that can be expressed as a quotient or ratio of two integers.

Irrational Numbers

Real numbers that cannot be expressed as a fraction of two integers, such as $\sqrt{7}$ or $\pi$.

Integers

The set of whole numbers and their negative opposites, including $\dots, -3, -2, -1, 0, 1, 2, 3, \dots$.

Whole Numbers

The set of non-negative integers starting from zero ($0, 1, 2, 3, \dots$).

Natural Numbers

The set of positive counting numbers starting from one ($1, 2, 3, 4, \dots$).